Decoding Developmental Blueprints: A Guide to Single-Cell Multi-Omics GRN Inference for Evolutionary Insights and Disease

Grayson Bailey Dec 02, 2025 378

The integration of single-cell multi-omics technologies is revolutionizing our ability to infer gene regulatory networks (GRNs) with unprecedented resolution.

Decoding Developmental Blueprints: A Guide to Single-Cell Multi-Omics GRN Inference for Evolutionary Insights and Disease

Abstract

The integration of single-cell multi-omics technologies is revolutionizing our ability to infer gene regulatory networks (GRNs) with unprecedented resolution. This article provides a comprehensive guide for researchers and drug development professionals, exploring the foundational principles of GRNs in evolutionary developmental biology. It details state-of-the-art computational methods—from foundational models like scGPT to innovative tools like LINGER and cRegulon—for inferring regulatory interactions from paired transcriptomic and epigenomic data. The content further addresses critical troubleshooting strategies for data sparsity and model interpretability, outlines rigorous validation frameworks against resources like ChIP-seq and eQTLs, and synthesizes how these advances are illuminating the regulatory underpinnings of cell fate decisions, disease mechanisms, and therapeutic target discovery.

The Landscape of Gene Regulation: From Cellular Heterogeneity to Foundational Models

A Gene Regulatory Network (GRN) is a collection of molecular regulators that interact with each other and with other substances in the cell to govern the gene expression levels of mRNA and proteins [1]. These networks represent the complex regulatory relationships that control cellular functions, development, and responses to environmental stimuli. GRNs provide a systems-level explanation of biological processes, enabling researchers to understand how genetic information flows through biological systems to determine cell identity, function, and behavior [1] [2]. In the context of single-cell multi-omics research, GRN inference has become crucial for understanding cellular heterogeneity and the mechanisms underlying development and disease [3] [4].

GRNs are mathematically represented as bipartite networks where nodes represent biological entities (genes and their regulators), and edges represent the regulatory interactions between them [1]. Molecular regulators include transcription factors (TFs), RNA-binding proteins, and non-coding RNAs that participate in the control of gene expression. The directionality of these networks is fundamental, as TFs regulate target genes and typically not vice versa [2]. The study of GRNs has been revolutionized by single-cell technologies, which enable the analysis of regulatory relationships at unprecedented resolution across diverse cell types and states [3] [5].

Core Components of GRNs

Nodes: The Biological Entities

Nodes in GRNs represent distinct biological entities involved in gene regulation. The primary node types include:

  • Protein-coding genes: Genes that encode transcription factors and other regulatory proteins
  • Transcription Factors (TFs): Proteins that bind to specific DNA sequences to activate or repress transcription
  • Regulatory Elements (REs): Non-coding DNA sequences such as promoters, enhancers, and silencers that regulate gene expression
  • RNA species: Including messenger RNA (mRNA), non-coding RNAs (e.g., microRNAs, lncRNAs) that participate in post-transcriptional regulation [1]

Each node possesses specific properties, including expression levels, activation states, and spatial-temporal localization patterns that influence its regulatory potential.

Edges: The Regulatory Interactions

Edges represent functional relationships between nodes and are characterized by:

  • Direction: From regulator to target, indicating the flow of regulatory information
  • Type: Activation (positive regulation) or repression (negative regulation)
  • Strength: The magnitude of regulatory influence, often quantified using statistical scores
  • Evidence: Experimental validation from various data sources [1]

GRN edges can represent different interaction types:

  • TF-TG (Transcription Factor-Target Gene): Trans-regulatory relationships
  • RE-TG (Regulatory Element-Target Gene): Cis-regulatory relationships
  • TF-RE (Transcription Factor-Regulatory Element): Binding relationships [3]

Regulatory Units: Regulons and cRegulons

A regulon is a group of genes regulated as a unit, generally controlled by the same regulatory gene that expresses a protein acting as a repressor or activator [6]. In eukaryotes, this term refers to any group of non-contiguous genes controlled by the same regulatory gene [6]. The concept of core and extended regulons has emerged through comparative genomics, where core regulons contain functions directly related to the primary regulatory signal, while extended regulons reflect specific adaptations to environmental niches [7].

cRegulons (cellular regulons) represent the set of regulatory relationships active in specific cellular contexts, often inferred through computational approaches like SCENIC (Single-Cell Regulatory Network Inference and Clustering) [8]. These context-specific regulatory units enable the identification of transcription factors driving particular cell states in development and disease.

Table 1: Key Regulatory Units in Gene Regulatory Networks

Regulatory Unit Definition Characteristics Biological Significance
Regulon Group of genes regulated by a common transcription factor Genes may be non-contiguous; coordinated expression response Enables coordinated cellular responses to stimuli [6]
Core Regulon Subset of regulon conserved across species Functions directly related to TF-inducing signal Maintains essential, evolutionarily conserved functions [7]
Extended Regulon Condition-specific portion of regulon Contains adaptive functions for specific niches Facilitates rapid adaptation to environmental changes [7]
cRegulon Context-specific regulon activity Inferred from single-cell data using tools like SCENIC Identifies drivers of cell identity and state transitions [8]
Modulon Set of regulons collectively regulated Responds to overall conditions or stresses Coordinates broader cellular programs beyond single TF control [6]

Computational Methods for GRN Inference

Traditional and Modern Approaches

GRN inference methods have evolved from correlation-based approaches to sophisticated machine learning models that integrate multiple data types:

Co-expression-based methods such as WGCNA, ARACNe, and GENIE3 infer TF-TG relationships from gene expression data by capturing covariation patterns [1] [3]. While useful, these methods typically produce undirected edges and cannot distinguish causal relationships from correlations [1] [3].

Integrated methods combine multiple data types to improve inference accuracy. For example, PANDA integrates protein-protein interactions, gene expression, and transcription factor binding motifs to reconstruct condition-specific regulatory networks [1]. MONSTER estimates phenotypic-specific regulatory networks using gene expression and TF binding motif data, then computes TF involvement in state transitions [1].

Single-cell multi-omics methods represent the cutting edge in GRN inference. LINGER uses lifelong neural networks to infer GRNs from single-cell multiome data, incorporating atlas-scale external bulk data and TF motif knowledge as manifold regularization [3]. PRISM-GRN employs a Bayesian model that incorporates known GRNs along with scRNA-seq and scATAC-seq data in a probabilistic framework [4]. GAEDGRN utilizes gravity-inspired graph autoencoders to capture directed network topology in GRN inference [9].

Table 2: Comparison of GRN Inference Methods and Their Applications

Method Approach Data Requirements Key Features Reported Performance
LINGER [3] Lifelong neural network scMultiome data + external bulk atlas Manifold regularization using TF motifs 4-7x relative increase in accuracy over existing methods
PRISM-GRN [4] Bayesian model scRNA-seq + scATAC-seq ± prior GRN Biologically interpretable architecture; works with unpaired data Superior precision in sparse regulatory scenarios
GAEDGRN [9] Graph autoencoder scRNA-seq + prior GRN Captures directed network topology; gene importance scoring High accuracy and reduced training time on 7 cell types
MONSTER [1] Regression-based Gene expression + TF motifs Identifies TF drivers of cell state transitions at network level Reveals regulatory changes in phenotype transitions
SCENIC [8] Regulatory inference scRNA-seq Identifies regulons and cellular activity states Enables cell clustering based on regulatory states

Validation Frameworks

Validating inferred GRNs requires comparison with experimentally determined ground truth data. Common validation approaches include:

  • ChIP-seq data: Chromatin immunoprecipitation followed by sequencing provides direct evidence of TF binding to genomic regions [3]
  • eQTL studies: Expression quantitative trait loci link genetic variants to gene expression changes, validating cis-regulatory relationships [3]
  • Perturbation studies: CRISPR-based TF knockout followed by expression profiling tests causal relationships [10]

Performance metrics such as Area Under the Receiver Operating Characteristic Curve (AUC) and Area Under the Precision-Recall Curve (AUPR) ratio provide quantitative assessment of inference accuracy [3].

Experimental Protocols for GRN Analysis

Protocol 1: GRN Inference with LINGER from Single-Cell Multiome Data

Principle: LINGER leverages lifelong learning to incorporate knowledge from external bulk data while refining predictions on single-cell multiome data, using neural networks with manifold regularization [3].

Workflow:

  • Input Data Preparation

    • Obtain single-cell multiome data (paired gene expression and chromatin accessibility)
    • Perform quality control: Filter cells based on mitochondrial percentage, unique molecular counts, and doublet detection
    • Normalize expression and accessibility counts using standard pipelines
    • Annotate cell types using marker genes and reference datasets

  • External Data Integration

    • Download bulk RNA-seq and ATAC-seq data from reference databases (ENCODE)
    • Preprocess external data using consistent genomic coordinates and gene annotations
    • Align feature spaces between single-cell and bulk datasets

  • Model Pre-training

    • Initialize neural network with three layers: Input (TFs + REs), hidden (regulatory modules), output (target gene expression)
    • Pre-train model on external bulk data to learn general regulatory principles
    • Apply manifold regularization to enrich TF motifs binding to REs in the same regulatory module

  • Model Refinement

    • Apply Elastic Weight Consolidation (EWC) loss to retain knowledge from bulk data while adapting to single-cell data
    • Use Fisher information to determine parameter deviation magnitude
    • Train until convergence on validation set

  • GRN Extraction

    • Calculate Shapley values to estimate regulatory strength of TF-TG and RE-TG interactions
    • Compute TF-RE binding strength through correlation of parameters in the hidden layer
    • Construct cell population, cell type-specific, and cell-level GRNs

linger ExternalData External Bulk Data (ENCODE) PreTraining Model Pre-training on Bulk Data ExternalData->PreTraining ModelRefinement Model Refinement with EWC Regularization PreTraining->ModelRefinement SingleCellData Single-cell Multiome Data SingleCellData->ModelRefinement GRNExtraction GRN Extraction via Shapley Values ModelRefinement->GRNExtraction Output Cell Type-Specific GRNs GRNExtraction->Output

Protocol 2: cRegulon Analysis with SCENIC

Principle: SCENIC (Single-Cell Regulatory Network Inference and Clustering) identifies regulons and their activity in single-cell RNA-seq data by combining gene co-expression with transcription factor binding motif analysis [8].

Workflow:

  • Data Preprocessing

    • Load single-cell RNA-seq count matrix
    • Normalize and scale data using standard methods (e.g., Seurat or Scanpy)
    • Identify highly variable genes for downstream analysis

  • Co-expression Module Identification

    • Run GENIE3 or GRNBoost2 to identify potential TF-target associations
    • Create gene co-expression modules for each transcription factor

  • Regulon Formation

    • Perform cis-regulatory motif analysis using RcisTarget
    • Retain direct targets with enriched motif occurrence in regulatory regions
    • Define regulons as TF plus its confident direct targets

  • Cellular Regulon Activity Scoring

    • Calculate regulon activity per cell using AUCell
    • Binarize activity to identify cells with active regulons
    • Cluster cells based on regulon activity rather than gene expression

  • Differential Regulon Analysis

    • Identify regulons with differential activity between conditions
    • Perform pathway enrichment analysis on target genes of differential regulons
    • Visualize results using t-SNE or UMAP projections colored by regulon activity

scenic ScRNA scRNA-seq Data Coexpression Co-expression Analysis ScRNA->Coexpression MotifAnalysis Motif Enrichment (RcisTarget) Coexpression->MotifAnalysis RegulonDef Regulon Definition (TF + Targets) MotifAnalysis->RegulonDef AUCell Activity Scoring (AUCell) RegulonDef->AUCell Results cRegulon Activity Matrix AUCell->Results

Table 3: Key Research Reagent Solutions for GRN Analysis

Category Specific Items Function/Application Example Uses
Sequencing Technologies 10x Genomics Single-Cell Multiome Simultaneous measurement of gene expression and chromatin accessibility LINGER input data generation [3]
Bulk Reference Data ENCODE RNA-seq/ATAC-seq Provides external regulatory context across diverse cellular contexts Training data for LINGER pre-training [3]
Motif Databases JASPAR, CIS-BP Transcription factor binding specificity profiles Regulon definition in SCENIC and PRISM-GRN [3] [8]
Validation Resources ChIP-seq datasets Ground truth for TF-binding events Validation of trans-regulatory predictions [3]
Validation Resources eQTL datasets (GTEx, eQTLGen) Links genomic variants to expression changes Cis-regulatory relationship validation [3]
Software Tools LINGER, PRISM-GRN, SCENIC GRN inference from single-cell data Cell type-specific regulatory network reconstruction [3] [4] [8]
Perturbation Tools CRISPR-based editors Functional validation of regulatory relationships Causal testing of TF-target relationships [10]

Analysis and Interpretation of GRN Data

Network Topology and Architecture

GRN analysis extends beyond edge identification to network topology characterization. Key topological features include:

  • Node degree: The number of relationships in which a node engages, with in-degree (number of TFs regulating a gene) and out-degree (number of genes regulated by a TF) providing distinct biological insights [2]
  • Hub identification: TF hubs regulate many target genes, while gene hubs are regulated by many TFs, indicating central positions in regulatory hierarchies [2]
  • Betweenness centrality: Identifies nodes that connect different network modules and may control information flow [2]
  • Flux capacity: The product of in-degree and out-degree for regulator nodes, indicating their potential influence on information propagation [2]

Network motifs—recurring regulatory patterns—provide insights into functional circuit design. Common motifs include feed-forward loops, feedback loops, and single-input modules that generate specific dynamic behaviors.

Evolutionary and Developmental Perspectives

GRNs evolve through changes in network architecture, with important implications for evolutionary developmental biology (Evo-Devo) [10]. Core regulons—containing functions directly related to the TF-inducing signal—tend to be conserved across species, while extended regulons evolve rapidly to reflect species-specific adaptations [7]. Heterochrony (changes in timing) and homeosis (changes in identity) at the single-cell level can drive the emergence of novel cell types through alterations in GRN architecture [10].

In mammalian hematopoietic stem cells, sequence heterochrony—changing the order in which transcription factors C/EBPα and GATA become active—switches daughter cell identity from eosinophils to basophils [10]. This demonstrates how temporal rewiring of GRNs can generate cellular diversity without changes in gene content.

Disease Applications

GRN analysis provides insights into disease mechanisms by identifying dysregulated regulatory programs. In glioblastoma, SCENIC analysis identified IRF and STAT family transcription factors as specific regulators of a unique tumor cell subset that creates an immunomodulatory microenvironment [8]. In chlorine-induced acute lung injury, regulatory network analysis revealed Ets1, Elf1, and Elk3 as key upregulated transcription factors in T cells following exposure [8].

Hypertension research using GRN approaches has demonstrated that genes with differential expression have interactive effects, highlighting the importance of network-level understanding beyond single gene analyses [8]. These applications underscore the translational potential of GRN research in identifying therapeutic targets and biomarkers.

The emergence of single-cell multi-omics technologies represents a paradigm shift in our ability to decipher the complex regulatory logic governing evolutionary developmental biology (evo-devo). These technologies enable the simultaneous measurement of multiple molecular layers—transcriptomics, epigenomics, and spatial context—within individual cells, providing unprecedented resolution for deconstructing cellular heterogeneity and lineage relationships [11]. For the first time, researchers can systematically infer Gene Regulatory Networks (GRNs) that underlie cell fate decisions, tissue patterning, and phylogenetic constraints across species.

In evo-devo research, GRNs serve as the fundamental computational framework encoding the developmental program of an organism. Traditional bulk sequencing methods obscured cell-to-cell variation, masking rare transitional states and regulatory dynamics critical for understanding evolutionary processes. The integration of single-cell transcriptomics with epigenomic profiling and spatial information now permits the reconstruction of combinatorial regulatory modules that drive cellular differentiation and evolutionary adaptation [12] [11]. This technological revolution is powered by concurrent advances in both experimental methods and computational frameworks, particularly foundation models pretrained on millions of cells that enable zero-shot transfer learning across biological contexts and species [11].

Technological Foundations and Current Methodologies

Multi-Omic Profiling Platforms

Single-cell multi-omics technologies have evolved from single-modality measurements to integrated platforms that capture complementary molecular features from the same cell. The current landscape encompasses diverse methodological approaches targeting different combinations of omics layers.

Table 1: Single-Cell Multi-Omics Technologies and Applications

Technology Type Measured Modalities Key Applications in Evo-Devo References
scEpi2-seq DNA methylation + Histone modifications (H3K9me3, H3K27me3, H3K36me3) Epigenetic memory during cell type specification; Dynamics of heterochromatin formation [13]
scGPT (Foundation Model) Cross-modal integration (transcriptomics + epigenomics) Zero-shot cell annotation; In silico perturbation modeling; Cross-species comparison [11]
cRegulon Framework TF combinatorics + chromatin accessibility + gene expression Identification of conserved regulatory modules across species; Cell type attractor states [12]
Spatial Molecular Imaging (CosMx SMI) Whole transcriptome + protein markers + spatial context Tissue organization principles; Stem cell niche characterization; Morphogenetic gradients [14]

The scEpi2-seq method exemplifies cutting-edge innovation in epigenetic profiling, achieving simultaneous detection of histone modifications and DNA methylation at single-cell resolution. This technique leverages TET-assisted pyridine borane sequencing (TAPS) instead of bisulfite conversion, preserving adapter sequences for more efficient library preparation. Application of scEpi2-seq to mouse intestinal development revealed how H3K27me3 and DNA methylation interact during cell type specification, demonstrating that differentially methylated regions can exhibit independent regulation alongside histone modification control [13].

Computational Frameworks for GRN Inference

The complexity of single-cell multi-omics data has driven the development of sophisticated machine learning approaches for GRN inference. These methods have evolved from classical statistical models to deep learning architectures capable of capturing nonlinear regulatory relationships.

Table 2: Machine Learning Methods for GRN Inference from Single-Cell Data

Algorithm Learning Type Key Technology Compatible Data Types
cRegulon Unsupervised Matrix factorization + mixture modeling scRNA-seq + scATAC-seq
GRNFormer Supervised Graph Transformer Single-cell transcriptomics
DeepMAPS Unsupervised Heterogeneous graph transformer scATAC-seq + Multi-omic
GCLink Contrastive learning Graph contrastive link prediction Single-cell multi-omics
scGPT Foundation model Transformer + masked gene modeling Cross-modal integration

The cRegulon algorithm represents a significant conceptual advance by modeling combinatorial regulation of transcription factors based on diverse GRNs derived from single-cell multi-omics data [12]. Unlike earlier methods that considered single TFs (Regulons) or TF-enhancer units (eRegulons), cRegulon identifies modules of cooperating TFs that collectively regulate common target genes. This approach more accurately reflects the biological reality of developmental regulation, where master transcription factors often act in complexes to determine cell fate. Through benchmarking and applications to real datasets, cRegulon has demonstrated superior performance in identifying TF combinatorial modules as fundamental regulatory units underlying Waddington's epigenetic landscape [12].

Experimental Protocols and Workflows

Protocol: scEpi2-seq for Simultaneous Histone Modification and DNA Methylation Profiling

Principle: scEpi2-seq enables joint profiling of histone modifications and DNA methylation in single cells by combining antibody-directed chromatin tagging with TET-assisted pyridine borane sequencing [13].

Reagents and Equipment:

  • Protein A-micrococcal nuclease (pA-MNase) fusion protein
  • validated antibodies for specific histone modifications (e.g., H3K9me3, H3K27me3, H3K36me3)
  • TAPS conversion reagents
  • Single-cell barcoded adapters with UMI, T7 promoter, and Illumina handles
  • Fluorescence-activated cell sorting (FACS) system
  • 384-well plates

Step-by-Step Workflow:

  • Cell Preparation and Permeabilization: Isolate single cells and permeabilize to enable antibody access while maintaining viability.
  • Antibody Incubation: Incubate with histone modification-specific antibodies in appropriate buffer conditions.
  • pA-MNase Tethering: Add pA-MNase fusion protein to bind antibody-targeted nucleosomes.
  • Single-Cell Sorting: Sort individual cells into 384-well plates containing reaction buffer using FACS.
  • MNase Digestion: Initiate targeted chromatin cleavage by adding Ca2+ to activate MNase.
  • Fragment Processing: Repair DNA ends and add poly-A tails to MNase-generated fragments.
  • Adapter Ligation: Ligate barcoded adapters containing cell-specific barcodes, UMIs, and promoter sequences.
  • TAPS Conversion: Pool material and perform TET-assisted pyridine borane conversion to detect methylated cytosines.
  • Library Preparation: Conduct in vitro transcription, reverse transcription, and PCR amplification.
  • Sequencing: Perform paired-end sequencing on Illumina platforms.

Quality Control Metrics:

  • Minimum of 50,000 CpGs detected per cell
  • Fraction of reads in peaks (FRiP) >0.7
  • C-to-T conversion efficiency >95%
  • Correlation with ENCODE reference data >0.8

Protocol: cRegulon Analysis for Combinatorial TF Module Identification

Principle: cRegulon infers regulatory modules by modeling combinatorial regulation of transcription factors across multiple cell types/states using single-cell multi-omics data [12].

Input Data Requirements:

  • Paired or unpaired scRNA-seq and scATAC-seq data
  • Cell type annotations or clustering results
  • Transcription factor binding motif database

Computational Steps:

  • Data Preprocessing: Quality control, normalization, and batch correction for both modalities.
  • GRN Construction: Infer cluster-specific gene regulatory networks using established methods.
  • Combinatorial Effect Calculation: For each cluster-specific GRN, compute pairwise TF combinatorial effects considering co-regulation and activity specificity.
  • Matrix Factorization: Model the combinatorial effect matrix as a mixture of rank-1 matrices corresponding to regulatory modules.
  • Module Extraction: Identify TF modules, associated regulatory elements, and target genes through optimization.
  • Cell Type Annotation: Annotate cell types based on cRegulon activities and validate with known markers.

Implementation Considerations:

  • The method accommodates both paired and unpaired multi-omics data
  • Key parameters include the number of modules and sparsity constraints
  • Output includes TF modules, REs, TGs, and their associations across cell types

G cRegulon Analysis Workflow (Combinatorial TF Module Identification) DataInput scRNA-seq + scATAC-seq Data QC Quality Control & Normalization DataInput->QC Cluster Cell Clustering & Annotation QC->Cluster GRN Cluster-Specific GRN Construction Cluster->GRN Matrix Combinatorial Effect Matrix GRN->Matrix Factorize Matrix Factorization (Mixture of Rank-1 Matrices) Matrix->Factorize Modules TF Combinatorial Modules (cRegulons) Factorize->Modules Validate Biological Validation & Interpretation Modules->Validate Output Regulatory Units Underlying Cell Type Landscape Validate->Output

Successful implementation of single-cell multi-omics approaches requires both wet-lab reagents and computational resources optimized for evo-devo GRN inference.

Table 3: Essential Research Reagent Solutions for Single-Cell Multi-Omics

Resource Category Specific Product/Platform Function in Workflow
Spatial Profiling CosMx Spatial Molecular Imager (Bruker) High-plex single-cell imaging of RNA and protein in tissue context
Epigenetic Profiling scEpi2-seq Reagent System Simultaneous detection of histone modifications and DNA methylation
Single-Cell Partitioning 10x Genomics Chromium System High-throughput single-cell partitioning and barcoding
Multi-omic Assay NEBNext Single-Cell Multi-Omics Kit Simultaneous profiling of transcriptome and epigenome from same cell
Foundation Models scGPT, scPlantFormer, Nicheformer Pretrained models for cross-species annotation and perturbation modeling
GRN Inference cRegulon Software Package Identification of TF combinatorial modules from multi-omics data
Data Integration BioLLM Framework Standardized benchmarking and integration of single-cell foundation models

Bruker's CosMx Spatial Molecular Imager enables whole transcriptome imaging at single-cell resolution within intact tissue sections, providing critical spatial context for GRN inference in developing organisms [14]. For computational analysis, foundation models like scGPT—pretrained on over 33 million cells—demonstrate exceptional performance in zero-shot cell type annotation and in silico perturbation modeling, significantly accelerating comparative analyses across species [11].

Integrated Analysis and Visualization Framework

The interpretation of single-cell multi-omics data requires specialized visualization strategies that represent the interconnected nature of transcriptional and epigenetic regulation across spatial contexts.

G Multi-Omic Data Integration Framework For Evo-Devo GRN Inference Transcriptome Single-Cell Transcriptomics Integration Multimodal Data Integration (PathOmCLIP, StabMap, TMO-Net) Transcriptome->Integration Epigenome Single-Cell Epigenomics Epigenome->Integration Spatial Spatial Context Spatial->Integration Foundation Foundation Model Processing (scGPT, Nicheformer) Integration->Foundation Combinatorial Combinatorial Module Detection (cRegulon Algorithm) Foundation->Combinatorial GRNOutput Evo-Devo GRN Model With Spatial Constraints Combinatorial->GRNOutput

This integrated framework highlights how different data modalities converge to reconstruct evolutionarily informed GRNs. The modularity of GRNs enables reduction of complexity while preserving biological meaning, with regulatory modules serving as fundamental units that can be compared across species to infer evolutionary trajectories [12] [11]. Tools like cRegulon specifically exploit this modularity to identify conserved and divergent regulatory programs underlying homologous developmental processes.

The single-cell multi-omics revolution has fundamentally transformed our approach to GRN inference in evolutionary developmental biology. By simultaneously profiling transcriptomic, epigenomic, and spatial information from individual cells, researchers can now reconstruct regulatory networks with unprecedented resolution and context specificity. The development of specialized technologies like scEpi2-seq for epigenetic profiling and computational frameworks like cRegulon for identifying combinatorial TF modules represents significant milestones in this rapidly advancing field.

Looking forward, several emerging trends promise to further accelerate discovery. Foundation models pretrained on massive single-cell datasets will enable increasingly accurate cross-species predictions and in silico perturbation studies [11]. The integration of spatial context with multi-omic measurements will illuminate how tissue microenvironment influences regulatory dynamics [14] [15]. Finally, the development of standardized benchmarking platforms like BioLLM will promote reproducibility and collaborative model development across the scientific community [11]. As these technologies mature, they will continue to provide deeper insights into the evolutionary principles that shape developmental gene regulatory networks across the tree of life.

The integration of single-cell multi-omics into evolutionary developmental biology (Evo-Devo) has revolutionized our capacity to decipher the gene regulatory networks (GRNs) that orchestrate cell fate, shape developmental trajectories, and underlie disease mechanisms. GRNs are mathematical representations of the complex interactions between transcription factors (TFs), cis-regulatory elements (CREs), and their target genes that collectively control cellular identity and function [16] [17]. The emerging field of ecological evolutionary developmental biology (Eco-Evo-Devo) emphasizes that these developmental processes are not isolated but are shaped by environmental cues and evolutionary pressures [18]. Rather than being a loose aggregation of research topics, Eco-Evo-Devo provides a coherent conceptual framework for exploring the causal relationships among developmental, ecological, and evolutionary levels, positioning GRN analysis as a central tool for understanding phenotypic diversification [18].

The advent of single-cell technologies has been pivotal, enabling researchers to move beyond bulk tissue analysis and capture the cellular heterogeneity that underpins developmental and evolutionary processes. While bulk sequencing averages signals across thousands of cells, single-cell sequencing (SCS) reveals cell-to-cell variability, identifies rare populations, and allows for the reconstruction of evolutionary relationships [19]. This is particularly powerful in Evo-Devo research, where understanding the emergence of novel cell types and the divergence of developmental pathways across species is paramount. Modern single-cell multi-omics platforms can now simultaneously profile multiple molecular layers—such as the transcriptome and epigenome—from the same cell, providing an unprecedented, matched view of the regulatory state [3] [16]. This technological leap addresses the central biological question of how genomic sequence and environmental interaction give rise to organismal form and function through the mechanism of GRN activity.

Application Note: Inferring GRNs from Single-Cell Multiome Data

Inferring GRNs from single-cell multiome data (e.g., simultaneously measured scRNA-seq and scATAC-seq) requires computational methods that can integrate these disparate data types to predict regulatory interactions. The underlying methodological foundations are diverse, each with distinct strengths and limitations for specific biological questions [16].

Table: Methodological Foundations for GRN Inference

Approach Underlying Principle Key Advantages Common Limitations
Correlation-based Measures co-expression or association (e.g., Pearson's correlation, mutual information) between TFs and potential target genes [16]. Simple, intuitive, and computationally efficient. Cannot distinguish direct from indirect regulation; infers undirected networks [16].
Regression models Models a target gene's expression as a function of multiple predictor TFs and CREs, using techniques like linear or penalized regression (LASSO) [16]. Provides interpretable coefficients indicating regulatory strength and direction. Can be unstable with highly correlated predictors; may overfit without regularization [16].
Probabilistic models Uses graphical models to represent the probabilistic dependence between variables like TFs and their targets [16]. Allows for filtering and prioritization of interactions based on probability. Often relies on distributional assumptions that may not fit all gene expression data [16].
Deep learning models Employs neural networks (e.g., multi-layer perceptrons, autoencoders) to learn complex, non-linear regulatory relationships from the data [16]. Highly versatile and can model complex, non-linear mechanisms. Requires large amounts of data; less interpretable ("black box"); computationally intensive [16].

Protocol: GRN Inference with LINGER and scTFBridge

This protocol details the use of two state-of-the-art deep learning methods, LINGER and scTFBridge, which are designed to leverage single-cell multiome data and external knowledge for robust GRN inference.

I. Experimental Design and Data Preparation

  • Single-Cell Multiome Sequencing: Perform single-cell multiome sequencing (e.g., using the 10x Genomics Multiome platform) on your sample of interest to obtain paired gene expression and chromatin accessibility data from the same cells [3] [19].
  • Data Preprocessing:
    • Gene Expression Matrix: Process raw sequencing data through a standard scRNA-seq pipeline (e.g., Cell Ranger). Output a cell-by-gene count matrix. Perform quality control to remove low-quality cells and doublets, followed by normalization and log-transformation [3] [17].
    • Chromatin Accessibility Matrix: Process scATAC-seq data to identify accessible peaks. Output a cell-by-peak count matrix. Quality control is essential to remove low-quality cells [3] [17].
    • Cell Type Annotation: Annotate cell types by integrating the data with existing references or by performing unsupervised clustering and marker gene identification [3].
  • External Data and Prior Knowledge Curation:
    • For LINGER, download a large-scale external bulk dataset, such as the ENCODE project data, which contains hundreds of samples across diverse cellular contexts [3].
    • For scTFBridge, and to enhance LINGER, compile a database of TF-motif binding information from resources like JASPAR or Cistrome [20] [21].

II. Computational GRN Inference Procedure

Workflow Title: GRN Inference with Lifelong Learning & Disentanglement

ExternalData External Bulk Data (e.g., ENCODE) PreTraining Pre-training on Bulk Data ExternalData->PreTraining PriorKnowledge TF-Motif Prior Knowledge DisentangledModel Disentangled Deep Generative Model (Shared & Omic-Specific Latent Spaces) PriorKnowledge->DisentangledModel SCMultiome Single-Cell Multiome Data LifelongLearning Lifelong Learning Refinement (Elastic Weight Consolidation) SCMultiome->LifelongLearning SCMultiome->DisentangledModel PreTraining->LifelongLearning NetworkInference GRN Inference via Shapley Values & Explainable AI LifelongLearning->NetworkInference DisentangledModel->NetworkInference Output Cell-type-specific GRNs (TF-TG, RE-TG, TF-RE) NetworkInference->Output

LINGER Workflow (Lifelong neural network for gene regulation) [3]:

  • Pre-training on External Bulk Data: Initialize a neural network model (BulkNN) designed to predict target gene (TG) expression using TF expression and regulatory element (RE) accessibility as input. Pre-train this model on the large-scale external bulk data (e.g., from ENCODE) to learn a general regulatory profile.
  • Lifelong Learning Refinement: Refine the pre-trained model on the single-cell multiome data using elastic weight consolidation (EWC). This regularization technique uses the Fisher information to control how much model parameters can deviate from the bulk-data prior, preventing catastrophic forgetting and ensuring stable adaptation to the new data.
  • Regulatory Strength Calculation: After training, compute the regulatory strength of TF-TG and RE-TG interactions using Shapley values from cooperative game theory. Shapley values provide a unified measure of each feature's (TF or RE) contribution to the prediction of each target gene's expression, offering an interpretable measure of regulatory influence.
  • TF-RE Binding Inference: Generate TF-RE binding strength by calculating the correlation between TF and RE parameters learned in the model's second layer, which is guided by the incorporated motif information.

scTFBridge Workflow [20]:

  • Model Training: Train a disentangled deep generative model (scTFBridge) on the single-cell multiome data. The model is designed to separate (disentangle) the latent data representation into components that are shared across the transcriptomic and epigenomic layers and components that are specific to each layer.
  • Integration of Motif Binding: Inform the model's shared latent space with known TF-motif binding information. This step aligns the shared embeddings with specific TF regulatory activities, enhancing the biological interpretability of the model.
  • Explainable GRN Inference: Use explainability methods to compute regulatory scores for REs and TFs. These scores enable robust inference of the GRN, identifying key regulators and their target genes.

III. Downstream Analysis and Validation

  • GRN Analysis: Analyze the inferred cell-type-specific GRNs to identify key driver TFs, autoregulatory loops, and core regulatory modules.
  • Trajectory Inference: Project the GRN dynamics onto developmental trajectories to understand how regulatory programs shift during cell state transitions [17].
  • Functional Enrichment: Perform gene ontology (GO) or pathway enrichment analysis on modules of co-regulated genes to understand the biological processes controlled by specific TFs.
  • Experimental Validation: Prioritize key inferred regulatory interactions for experimental validation using techniques such as CRISPR perturbation [3] or ChIP-seq [16] to confirm the causal role of identified TFs.

The Scientist's Toolkit: Research Reagent Solutions

Table: Essential Research Reagents and Platforms for Single-Cell Multi-omics GRN Studies

Reagent / Platform Function / Application Key Characteristics
10x Genomics Multiome ATAC + Gene Expression Simultaneous profiling of chromatin accessibility (ATAC-seq) and gene expression (RNA-seq) in the same single cell [3] [19]. Provides a paired view of the epigenomic and transcriptomic state; high-throughput; commercial standard.
Fluidigm C1 System Plate-based microfluidics platform for single-cell isolation and library preparation [19]. Suitable for processing hundreds of cells with high sensitivity; ideal for full-length transcriptome protocols like Smart-seq3.
Mission Bio Tapestri Targeted scDNA-seq platform for high-throughput genotyping of thousands of cells [19]. Enables linking of clonal genetic architecture to transcriptional phenotypes; focuses on pre-defined genomic regions.
Bioskryb ResolveDNA Whole-genome amplification platform for single-cell whole-genome or whole-exome sequencing [19]. Provides broader genomic coverage for analyzing single-nucleotide variants and copy number alterations at lower throughput.
JASPAR / Cistrome Databases Curated databases of transcription factor binding motifs and chromatin profiles [20] [21]. Provides essential prior knowledge for linking accessible chromatin regions to potential TF binding.
ChIP-seq / CUT&Tag Genome-wide profiling of protein-DNA interactions for specific transcription factors [17]. Gold-standard experimental method for validating TF binding sites inferred from GRN models.
CM-579CM-579, CAS:1846570-40-8, MF:C29H40N4O3, MW:492.7 g/molChemical Reagent
COH000COH000, MF:C25H25NO5, MW:419.5 g/molChemical Reagent

Application in Evolutionary and Developmental Biology

Case Study: Deciphering the Neural Crest GRN

The neural crest is a vertebrate-specific cell population that gives rise to diverse structures, including parts of the craniofacial skeleton, peripheral nervous system, and pigment cells. Its evolution is considered a key event in vertebrate diversification. A core objective in Evo-Devo is to reconstruct the GRN underlying neural crest development and to understand how it evolved.

Experimental Diagram Title: Reconstructing the Neural Crest GRN Across Species

Sample Sample Collection: Vertebrate Embryos (e.g., chick, mouse) & Non-Vertebrate Relatives (e.g., ascidian) Sequencing Single-Cell Multiome Sequencing (Neural Crest Cell Lineages) Sample->Sequencing Inference Cross-Species GRN Inference using LINGER/scTFBridge Sequencing->Inference Comparison Comparative GRN Analysis Inference->Comparison Insight1 Identification of Core Conserved Kernel Comparison->Insight1 Insight2 Identification of Species-Specific Regulatory Innovations Comparison->Insight2

Protocol [22] [18] [23]:

  • Sample Collection: Collect embryos from a model vertebrate (e.g., chick or mouse) at key developmental time points encompassing neural crest specification, migration, and differentiation. For evolutionary contrast, include embryos from a non-vertebrate deuterostome relative, such as the ascidian Ciona intestinalis, where a cell population with properties similar to neural crest has been identified [22].
  • Single-Cell Multiome Sequencing: Dissect tissue containing neural crest precursors and their derivatives. Use the 10x Genomics Multiome platform to generate paired scRNA-seq and scATAC-seq libraries for thousands of cells from each species.
  • Cross-Species GRN Inference: Process the data for each species separately through the LINGER or scTFBridge pipeline. The prior knowledge of TF motifs should be derived from databases like JASPAR to facilitate cross-species comparison.
  • Comparative GRN Analysis: Compare the inferred GRNs to identify:
    • The Conserved Kernel: A set of TFs (e.g., SoxE, FoxD, Tfap2) and their regulatory interactions that are present in both the vertebrate and non-vertebrate GRNs, representing an ancient, core regulatory module [22] [18].
    • Vertebrate-Specific Innovations: New TFs incorporated into the network, novel regulatory interactions, or the co-option of existing modules, which likely contributed to the evolutionary elaboration of the neural crest.

This integrated approach moves beyond simple gene expression comparisons to reveal the precise architectural changes in the underlying GRN that facilitated the evolution of this key developmental cell type.

Application Note: Eco-Evo-Devo of Skeletal Morphology

A central tenet of Eco-Evo-Devo is that environmental factors can influence development to generate phenotypic variation that is subject to evolutionary selection. This protocol outlines how to use single-cell multi-omics to study the interaction between environment and GRNs in shaping skeletal morphology, a classic Evo-Devo model [18] [24].

Protocol:

  • Environmental Perturbation: Subject model organisms (e.g., stickleback fish or mice from different ecological niches) to controlled environmental variables, such as diet, temperature, or mechanical stress, known to affect skeletal development [18].
  • Time-Course Sampling: Collect developing skeletal tissue (e.g., limb bud) from experimental and control groups across multiple developmental stages.
  • Multiomic Profiling: Perform single-cell multiome sequencing on all samples. Use sample multiplexing techniques (e.g., cell hashing) to pool samples for sequencing, reducing batch effects [19].
  • GRN Inference and Integration: Infer GRNs for each condition and time point. Use a tool like scMKL [21] to classify cells based on environmental treatment and identify the key transcriptomic and epigenomic features (pathways, TF activities) that are responsive to the environmental cue.
  • Linking Mechanism to Phenotype: Correlate changes in GRN architecture (e.g., rewiring of a specific TF module) with quantitative morphological measurements of the resulting skeletal phenotype. This directly links an environmental input, through a developmental GRN, to an evolved adaptive output.

The emergence of foundation models represents a paradigm shift in single-cell multi-omics analysis, enabling the learning of universal cellular representations that transform our ability to decipher gene regulatory networks (GRNs). These models, pre-trained on massive datasets comprising millions of cells, capture fundamental biological principles that transfer across diverse downstream tasks. This application note examines two pioneering frameworks—scGPT and scPlantFormer—detailing their architectural innovations, training methodologies, and experimental protocols for GRN inference in evolutionary developmental biology research. We provide comprehensive benchmarking data, implementation workflows, and reagent solutions to equip researchers with practical tools for leveraging these transformative technologies in drug development and basic research.

Foundation models are large-scale neural networks pre-trained on extensive datasets that learn generalizable representations transferable to various downstream tasks [11]. In single-cell biology, these models have emerged as powerful tools for deciphering cellular heterogeneity, gene regulation, and developmental processes. The conceptual parallel between natural language and cellular biology—where genes correspond to words and cells to documents—has enabled the successful adaptation of transformer architectures to biological data [25] [26].

Universal representation learning in single-cell biology involves capturing fundamental principles of gene expression, regulation, and cellular identity that remain consistent across tissues, species, and experimental conditions. scGPT and scPlantFormer exemplify this approach, demonstrating exceptional capability in cross-species annotation, perturbation modeling, and gene regulatory network inference [11] [26]. Their performance stems from pre-training on datasets of unprecedented scale—33 million cells for scGPT and 1 million plant cell profiles for scPlantFormer—allowing them to distill critical biological insights concerning genes and cells [25] [26].

For evolutionary developmental biology (evo-devo), these models offer particular promise in uncovering conserved regulatory principles across species and tracing the evolutionary trajectories of cell types. By learning universal representations, foundation models can bridge the gap between model organisms and humans, accelerating the translation of basic research findings into therapeutic insights.

Model Architectures and Technical Specifications

Core Architectural Components

Both scGPT and scPlantFormer build upon the transformer architecture but incorporate distinct modifications tailored to biological data.

scGPT employs a standard transformer decoder architecture similar to GPT models in natural language processing. The model uses gene expressions as input tokens, embedding them into a continuous representation space before processing through multiple transformer blocks with masked self-attention [25] [27]. This design enables scGPT to learn contextual relationships between genes and predict expression values in a self-supervised manner through masked gene modeling.

scPlantFormer implements a transformer encoder architecture with CellMAE (Cell Masked Autoencoding) pretraining, specifically optimized for plant single-cell omics [26]. The model incorporates phylogenetic constraints into its attention mechanism, allowing it to capture evolutionary relationships between species [11]. This design excels at cross-species data integration and resolving batch effects common in plant single-cell datasets.

Key Technical Innovations

Table 1: Technical Specifications of Foundation Models

Feature scGPT scPlantFormer
Architecture Type Transformer Decoder Transformer Encoder with CellMAE
Pre-training Data 33+ million cells [25] 1 million Arabidopsis thaliana cells [26]
Pre-training Objectives Masked gene modeling, contrastive learning [11] Mean square error loss, plant-specific optimization [26]
Key Innovation Generative pre-training across diverse cell types Phylogenetic constraints in attention mechanism
Handling Multi-omics Native support for multi-omic integration [25] Specialized for plant transcriptomics with cross-species capabilities

G Input Single-Cell Expression Matrix Tokenization Gene Tokenization & Embedding Input->Tokenization Transformer Transformer Layers (Self-Attention Mechanism) Tokenization->Transformer Pretraining Pre-training Objectives (Masked Gene Modeling) Transformer->Pretraining Representation Universal Cell & Gene Representations Pretraining->Representation Output Transfer to Downstream Tasks Representation->Output

Figure 1: Foundation Model Training Workflow. Both scGPT and scPlantFormer follow this general pipeline, transforming single-cell data into universal representations through self-supervised pre-training.

Experimental Protocols and Implementation

Data Preprocessing and Quality Control

Protocol 1: Single-Cell Data Preprocessing for Foundation Models

  • Quality Control Metrics

    • Calculate mitochondrial percentage, excluding cells with >20% mitochondrial reads
    • Filter cells with unusually high or low total counts (outside 3 median absolute deviations)
    • Remove cells with detected genes <200 or >6000 to eliminate doublets and low-quality cells
    • Apply Scrublet to identify and remove potential doublets [28]

  • Normalization Procedure

    • Normalize counts per cell to 10,000 counts (TPM/CPM)
    • Apply log1p transformation: X_norm = log(1 + X)
    • Identify highly variable genes using Seurat's vst method (2000-5000 genes)
    • Scale data to zero mean and unit variance [28] [27]

  • Batch Effect Considerations

    • Identify batch covariates (donor, technology, laboratory)
    • For integration tasks, use Harmony or Combat for preliminary batch correction
    • Note: Foundation models can address batch effects during fine-tuning [29]

Model Training and Fine-tuning

Protocol 2: Transfer Learning for Downstream Tasks

  • Task Formulation

    • Cell type annotation: Frame as classification problem using reference atlases
    • GRN inference: Formulate as edge prediction between TFs and target genes
    • Perturbation response: Model as regression from treatment to expression changes

  • Fine-tuning Procedure for scGPT

    [27]

  • Fine-tuning Procedure for scPlantFormer

    • Utilize species-specific tokenization for cross-species applications
    • Leverage phylogenetic tree information during attention calculation
    • Apply label transfer from reference species to query species
    • Use data augmentation with random masking for improved generalization [26]

GRN Inference Methodology

Protocol 3: Gene Regulatory Network Inference

  • Data Requirements

    • Single-cell multiome data (paired RNA-seq + ATAC-seq) preferred
    • Minimum of 5,000 cells for robust inference
    • Cell type annotations at appropriate resolution
    • External bulk data for validation (ENCODE, GTEx) [3]

  • Implementation with LINGER Framework

    • Pre-train on external bulk data from ENCODE (400+ samples)
    • Refine on single-cell data using elastic weight consolidation
    • Extract regulatory strengths using Shapley values
    • Construct cell type-specific GRNs from general GRN [3]

  • Validation Procedures

    • Compare with ChIP-seq ground truth for trans-regulatory edges
    • Validate cis-regulatory predictions with eQTL data from GTEx
    • Perform enrichment analysis for known regulatory pathways
    • Assess network topology properties (scale-free, modularity) [3] [30]

Performance Benchmarks and Comparative Analysis

Quantitative Performance Metrics

Table 2: Benchmarking Results Across Downstream Tasks

Task Model Performance Metrics Comparative Advantage
Cell Type Annotation scGPT 92% accuracy on PBMC datasets [25] Zero-shot capability to novel cell types
scPlantFormer 92% cross-species accuracy [11] Effective across plant species
GRN Inference LINGER 4-7x relative increase in accuracy vs. baselines [3] Incorporates atlas-scale external data
scGPT Superior AUPRC in perturbation prediction [25] Generative modeling of network dynamics
Multi-omic Integration GLUE Lowest FOSCTTM error in benchmark [29] Graph-linked embedding for distinct feature spaces
scGPT Effective integration of transcriptomics and epigenomics [25] Unified representation space
Cross-species Analysis scPlantFormer Accurate annotation between Arabidopsis and rice [26] Phylogenetic attention mechanism

Application to Evolutionary Developmental Biology

Foundation models demonstrate particular utility in evo-devo research through their ability to:

  • Identify Conserved Regulatory Programs

    • Detect homologous cell types across divergent species
    • Trace evolutionary trajectories of regulatory elements
    • Identify lineage-specific regulatory innovations [26]

  • Model Developmental Processes

    • Reconstruct differentiation trajectories from universal representations
    • Predict the effects of regulatory perturbations on cell fate decisions
    • Infer ancestral cell states from comparative analysis [28] [30]

  • Accelerate Translational Applications

    • Bridge model organisms to human biology for drug target identification
    • Predict conserved toxicity pathways across species
    • Identify cell type-specific expression of drug targets [11]

G cluster_0 External Data Integration Multiome Single-Cell Multiome Data Pretrain Foundation Model Pre-training Multiome->Pretrain Representations Universal Representations Pretrain->Representations GRN Gene Regulatory Network Inference Representations->GRN EvoDevo Evo-Devo Applications GRN->EvoDevo External Bulk Data (ENCODE, GTEx) External->Pretrain Prior Prior Knowledge (Motifs, Interactions) Prior->GRN

Figure 2: GRN Inference Workflow for Evo-Devo Research. Foundation models integrate multi-omic data with external resources to infer regulatory networks applicable to evolutionary studies.

Research Reagent Solutions

Essential Computational Tools

Table 3: Key Research Reagents and Computational Tools

Resource Type Function Access
scGPT Model Zoo Pre-trained Models Task-specific fine-tuning starting points GitHub: bowang-lab/scGPT [27]
scPlantFormer Plant Foundation Model Cross-species analysis in plants GitHub Repository [26]
LINGER GRN Inference Lifelong learning for regulatory networks Nature Biotechnology [3]
GLUE Multi-omic Integration Graph-linked unified embedding Nature Biotechnology [29]
CellXGene Data Repository 33+ million cells for reference mapping CZ CELLxGENE Discover [11]
BioLLM Benchmarking Framework Standardized evaluation of foundation models [11]

The integration of foundation models into single-cell multi-omics analysis represents a transformative advancement with profound implications for evolutionary developmental biology and drug development. scGPT and scPlantFormer exemplify how universal representation learning can uncover fundamental principles of gene regulation that transcend species boundaries.

Future developments will likely focus on multimodal integration—combining transcriptomic, epigenomic, proteomic, and spatial data within unified foundation models [11]. Additionally, interpretability enhancements will be crucial for translating model predictions into mechanistic biological insights, particularly for identifying key regulatory drivers of development and disease [11] [31].

For drug development professionals, these models offer accelerating pathways from target identification to validation by predicting cell type-specific responses to perturbations and identifying conserved regulatory mechanisms across species. The ability to conduct in silico experiments on universal representations provides an efficient alternative to costly screening approaches while offering insights into fundamental biological processes.

As foundation models continue to evolve, they will increasingly serve as the computational scaffold for understanding the regulatory logic of development, evolution, and disease—ultimately bridging the gap between cellular omics and actionable biological understanding.

The Waddington epigenetic landscape serves as a powerful metaphor for understanding cellular differentiation and fate decisions during development. Originally proposed by Conrad H. Waddington, this conceptual framework depicts a developing cell as a ball rolling down a sloping hillside characterized by valleys and ridges [32]. The path taken by the ball represents a specific developmental trajectory, with branching points corresponding to fate decisions, and the end points of the valleys (the basins) representing the terminally differentiated cell types [33] [32]. In modern systems biology, this metaphorical landscape has been formalized mathematically, where the various cell states are conceptualized as attractors within a high-dimensional state space defined by the activity levels of genes in a gene regulatory network (GRN) [32] [34]. The stability of a cell type is then understood in terms of the depth and size of these attractor basins, with the barriers between basins correlating with the difficulty of transitioning from one cell state to another [32].

This framework has gained renewed importance with the advent of single-cell multi-omics technologies, which enable the simultaneous measurement of gene expression and chromatin accessibility in individual cells [3] [35]. These rich datasets provide an unprecedented opportunity to infer the architecture of GRNs and computationally reconstruct the Waddington landscape for specific biological systems, from embryonic development to disease processes like cancer [33]. The ability to quantify this landscape offers profound insights into the mechanisms underlying cellular heterogeneity, phenotypic plasticity, and the reprogramming of cell identity [32]. This Application Note provides detailed protocols for applying this framework through GRN inference from single-cell multiome data, with specific examples from developmental biology and cancer research.

Theoretical Foundations: From Metaphor to Quantitative Model

The Modern Interpretation of Attractor States

In contemporary quantitative biology, Waddington's metaphorical landscape is formalized through dynamical systems theory. The state of a cell is represented by a vector ( S(t) = (x1, x2, ..., xN) ), where each ( xi ) represents the expression value or cellular concentration of the product of gene ( i ) in an N-gene regulatory network [32]. The probability landscape ( P ) is defined over this N-dimensional state space, where states with locally highest probability (lowest potential, where ( U = -\ln P )) represent the attractor states of the underlying GRN [32]. These attractors correspond to distinct cell phenotypes—including stable differentiated states, progenitor states, and pathological states like cancer subtypes [33] [32].

The stability of these cellular states is quantitatively related to the barrier heights between attractor basins in the landscape. Higher barriers correspond to longer escape times, making transitions between cell types less likely and thus representing more stable cellular states [32]. This quantitative relationship provides crucial insights for understanding differentiation processes and designing cellular reprogramming strategies. The developmental progression from a pluripotent stem cell to differentiated lineages can be visualized as a ball moving from the broad, elevated basin of the undifferentiated state down to deeper, more confined basins representing terminally differentiated cells [32].

Mathematical Formalisms for Landscape Construction

Several mathematical approaches exist for quantifying the Waddington landscape, with Hopfield networks providing one particularly powerful framework [34]. These auto-associative artificial neural networks store patterns as attractors of the network and can recall these patterns from noisy or incomplete inputs, effectively modeling the recall of stable gene expression patterns during differentiation [34]. For a network of N genes, the state of the system is defined by the expression levels of these genes, and the attractors represent the stable expression configurations corresponding to different cell types.

An alternative approach utilizes ordinary differential equations (ODEs) based on known regulatory interactions [33]. For a GRN model, the system can be described by equations of the form ( dx/dt = F(x) ), where ( x ) is a vector of gene expression levels and ( F ) represents the regulatory logic [33] [32]. The epigenetic landscape can then be constructed by performing numerous stochastic simulations from different initial conditions and calculating the probability distribution of the states [33]. For instance, in a study of breast cancer subtypes, 10,000 stochastic simulations were used to map the attractor landscape containing HER2+ and triple-negative breast cancer (TNBC) basins [33].

G cluster_landscape Waddington Landscape Stem Cell (Pluripotent) Stem Cell (Pluripotent) Progenitor Cell (Multipotent) Progenitor Cell (Multipotent) Stem Cell (Pluripotent)->Progenitor Cell (Multipotent) Differentiated State A Differentiated State A Progenitor Cell (Multipotent)->Differentiated State A Differentiated State B Differentiated State B Progenitor Cell (Multipotent)->Differentiated State B Differentiated State C Differentiated State C Progenitor Cell (Multipotent)->Differentiated State C Valley 2 Valley 3 Valley 4 Valley 1 Valley 1->Valley 2 Valley 1->Valley 3 Valley 1->Valley 4

Figure 1: The Waddington Landscape Metaphor for Cell Fate Decisions. This diagram visualizes the progressive restriction of cell fate during development, from pluripotent stem cells to various differentiated states through branching valleys on an epigenetic landscape.

Protocol 1: Inferring GRNs from Single-Cell Multiome Data Using LINGER

Background and Principles

The LINGER (Lifelong neural network for gene regulation) framework represents a significant advance in GRN inference from single-cell multiome data, achieving a fourfold to sevenfold relative increase in accuracy over existing methods [3]. Unlike approaches that rely on gene expression data alone, LINGER integrates single-cell paired gene expression and chromatin accessibility data while incorporating atlas-scale external bulk data across diverse cellular contexts [3]. This approach addresses a fundamental challenge in GRN inference: learning complex regulatory mechanisms from limited independent data points. The method incorporates prior knowledge of transcription factor (TF) motifs as a manifold regularization, significantly enhancing prediction accuracy for both cis-regulatory and trans-regulatory interactions [3].

LINGER employs a lifelong learning strategy (also called continuous learning), where knowledge learned from past data (external bulk datasets) helps learn new tasks (single-cell data) with limited data more effectively [3]. The framework constructs GRNs containing three types of interactions: trans-regulation (TF-TG), cis-regulation (RE-TG), and TF-binding (TF-RE), providing a comprehensive view of gene regulatory mechanisms [3]. After initial GRN inference from reference single-cell multiome data, LINGER enables estimation of transcription factor activity solely from bulk or single-cell gene expression data, leveraging abundant gene expression datasets to identify driver regulators in case-control studies [3].

Step-by-Step Protocol

Input Data Requirements and Preprocessing
  • Single-cell multiome data: Input data should include count matrices of gene expression and chromatin accessibility along with cell type annotations [3]. The data should be preprocessed using standard single-cell analysis pipelines, including quality control, normalization, and feature selection [35].
  • External bulk data: Collect large-scale external bulk data from sources like the ENCODE project, which contains hundreds of samples covering diverse cellular contexts [3]. This data will be used for pre-training.
  • Prior knowledge bases: Compile TF motif information from databases such as JASPAR or CIS-BP to inform TF-RE connections [3].
  • Validation data: For performance assessment, collect independent validation datasets such as ChIP-seq data for trans-regulatory validation and eQTL data (from GTEx or eQTLGen) for cis-regulatory validation [3].
Model Architecture and Training

Table 1: LINGER Model Components and Their Functions

Component Architecture Function Key Parameters
BulkNN Three-layer neural network Pre-training using external bulk data Layer weights and biases
scNN Three-layer neural network Single-cell data refinement Regulatory module parameters
Manifold Regularization Motif-based constraint Enrichment of TF motifs binding to REs in same regulatory module Regularization strength
EWC Loss Elastic Weight Consolidation Preservation of knowledge from bulk data during single-cell training Fisher information matrix

  • Pre-training on bulk data: Initialize the neural network model (BulkNN) to predict target gene (TG) expression using TF expression and regulatory element (RE) accessibility as input. Train this model on the external bulk data to learn initial regulatory relationships [3].

  • Refinement on single-cell data: Apply elastic weight consolidation (EWC) loss to refine the model on single-cell data while preserving knowledge gained from bulk data [3]. The EWC regularization uses the Fisher information to determine the magnitude of parameter deviation, encouraging the posterior distribution to remain close to the prior distribution derived from bulk data [3].

  • Regulatory strength inference: After training, infer the regulatory strength of TF-TG and RE-TG interactions using Shapley values, which estimate the contribution of each feature for each gene [3]. Calculate TF-RE binding strength from the correlation of TF and RE parameters learned in the second layer of the neural network [3].

Network Construction and Validation

  • GRN assembly: Construct cell population GRNs, cell type-specific GRNs, and cell-level GRNs based on the general GRN and cell type-specific profiles derived from the model [3].

  • Performance validation: Validate trans-regulatory inferences against ChIP-seq data by calculating the area under the receiver operating characteristic curve (AUC) and area under the precision-recall curve (AUPR) ratio [3]. For cis-regulatory inferences, assess consistency with eQTL studies by grouping RE-TG pairs by distance and comparing AUC and AUPR ratios across different distance groups [3].

  • Downstream analysis applications:

    • Identify disease or trait-related cell types, TFs, and GRNs by integrating genome-wide association studies (GWAS) data [3].
    • Construct regulon activity on external expression data to identify driver regulators as differentially active TFs [3].

G External Bulk Data\n(ENCODE) External Bulk Data (ENCODE) Pre-training\n(BulkNN) Pre-training (BulkNN) External Bulk Data\n(ENCODE)->Pre-training\n(BulkNN) TF Motif Databases TF Motif Databases TF Motif Databases->Pre-training\n(BulkNN) scRNA-seq Data scRNA-seq Data Refinement\n(EWC Loss) Refinement (EWC Loss) scRNA-seq Data->Refinement\n(EWC Loss) scATAC-seq Data scATAC-seq Data scATAC-seq Data->Refinement\n(EWC Loss) Pre-training\n(BulkNN)->Refinement\n(EWC Loss) Inference\n(Shapley Values) Inference (Shapley Values) Refinement\n(EWC Loss)->Inference\n(Shapley Values) Population GRN Population GRN Inference\n(Shapley Values)->Population GRN Cell Type GRN Cell Type GRN Inference\n(Shapley Values)->Cell Type GRN Single Cell GRN Single Cell GRN Inference\n(Shapley Values)->Single Cell GRN

Figure 2: LINGER Workflow for GRN Inference. This diagram illustrates the lifelong learning approach that integrates external bulk data and TF motif information with single-cell multiome data to infer gene regulatory networks at multiple resolutions.

Research Reagent Solutions

Table 2: Essential Research Reagents for Single-Cell Multiome GRN Inference

Reagent/Resource Function Example Sources
10x Genomics Multiome Simultaneous profiling of gene expression and chromatin accessibility from the same single cell 10x Genomics
ENCODE Consortium Data Atlas-scale external bulk data for pre-training ENCODE Project
ChIP-seq Validation Data Ground truth for trans-regulatory interactions Cistrome Data Browser
eQTL Data (GTEx/eQTLGen) Validation of cis-regulatory predictions GTEx Portal, eQTLGen
TF Motif Databases Prior knowledge for TF-RE connections JASPAR, CIS-BP

Protocol 2: Constructing and Analyzing Attractor Landscapes in Breast Cancer

Background and Biological System

The attractor landscape framework provides particular insight into cancer heterogeneity, where multiple cell states coexist within tumors and contribute to therapy resistance and cancer recurrence [33]. In a recent study of breast cancer subtypes, researchers investigated how NF-κB epigenetic variability contributes to progression of the HER2+ BC subtype toward a more aggressive triple-negative breast cancer (TNBC) phenotype [33]. The study focused on a GRN involving NF-κB and key epithelial-mesenchymal transition (EMT) transcription factors TWIST1, SIP1, and SLUG, which constitute a broader regulatory network active across diverse tumor contexts [33].

This GRN exhibits an epigenetic landscape with two attractor basins corresponding to the observed expression profiles of HER2+ and TNBC subtypes, separated by an unstable stationary state [33]. The research demonstrated that stochastic fluctuations in NF-κB levels induce spontaneous irreversible transitions from HER2+ to TNBC attractor basins at different times, contributing to subtype heterogeneity [33]. This system provides an excellent model for studying attractor dynamics in a pathological context and illustrates how the Waddington landscape framework can explain cellular plasticity and fate transitions in cancer.

Step-by-Step Protocol for Landscape Construction

GRN Model Specification

  • Network definition: Construct a GRN model that includes NF-κB (p65:p50 heterodimer) as a key regulator that activates expression of TWIST1, SNAIL, and SLUG, as well as its own subunits p50 and p65 through positive feedback [33].

  • Ordinary Differential Equations: Implement ODEs based on the regulatory interactions. For a general GRN with genes ( x1, x2, ..., xn ), the system can be described by: [ \frac{dxi}{dt} = Fi(x1, x2, ..., xn) - \gammai xi ] where ( Fi ) represents the regulatory logic governing production and ( \gammai ) represents degradation [33].

  • Parameter calibration: Calibrate model parameters using experimentally measured RNA levels of all network components across the cell types of interest (e.g., HER2+ and TNBC subtypes) simultaneously [33]. Fine-tune parameters to reproduce temporal dynamics, such as recovery times after perturbation with NF-κB inhibitor DHMEQ [33].

Landscape Mapping and Analysis

  • Stationary state identification: Solve the algebraic equations derived from the ODE system (set ( dx/dt = 0 )) to find all stationary states [33]. Characterize the stability of each state by analyzing the eigenvalues of the Jacobian matrix.

  • Stochastic simulations: Perform numerous stochastic simulations (e.g., 10,000 simulations) starting from different uniformly distributed initial conditions in the phase space [33]. Use methods like the Gillespie algorithm or Langevin dynamics to incorporate intrinsic noise.

  • Landscape visualization: Construct the epigenetic landscape by calculating the probability distribution of states from the stochastic simulations [33]. Visualize the landscape in 2D or 3D projections using key genes or factors as axes (e.g., p50 vs p65) [33].

  • Transition analysis: Simulate long-term single-cell trajectories to observe spontaneous transitions between attractor basins [33]. Analyze the directionality and timing of these transitions, noting that irreversible transitions indicate asymmetry in the landscape topography.

Experimental Validation

  • Perturbation experiments: Treat cells with pathway-specific inhibitors (e.g., DHMEQ for NF-κB inhibition) and measure recovery dynamics of network components [33]. Compare experimental recovery times with model predictions.

  • Single-cell analysis: Use single-cell RNAseq to characterize heterogeneity in patient samples and cell lines [33]. Analyze correlation patterns between network components (e.g., p65 and p50) across different subtypes, as more symmetric attractor basins may exhibit lower correlation [33].

  • Attractor stability assessment: Evaluate how mutations or drugs alter attractor basin sizes and transition probabilities by measuring their effects on gene expression patterns and subtype proportions [33].

G NF-κB\n(p65:p50) NF-κB (p65:p50) TWIST1 TWIST1 NF-κB\n(p65:p50)->TWIST1 SLUG SLUG NF-κB\n(p65:p50)->SLUG SIP1 SIP1 NF-κB\n(p65:p50)->SIP1 p50 p50 NF-κB\n(p65:p50)->p50 p65 p65 NF-κB\n(p65:p50)->p65 HER2+ Attractor HER2+ Attractor TNBC Attractor TNBC Attractor HER2+ Attractor->TNBC Attractor Stochastic Transition

Figure 3: GRN Model for Breast Cancer Subtypes. This network diagram shows the key regulatory interactions in the NF-κB-centered GRN that generates two attractor states corresponding to HER2+ and TNBC breast cancer subtypes.

Research Reagent Solutions

Table 3: Essential Reagents for Breast Cancer Attractor Landscape Study

Reagent/Resource Function Example Sources
Breast Cancer Cell Lines Model systems for different subtypes (HCC-1954 for HER2+, MDA-MB-231 for TNBC) ATCC
NF-κB Inhibitor (DHMEQ) Perturbation agent to test network dynamics and recovery Commercial suppliers
qPCR Reagents Quantification of NF-κB, TWIST1, SNAIL, and SLUG expression Various manufacturers
Single-cell RNAseq Kits Characterization of heterogeneity in cell populations 10x Genomics, Parse Biosciences

Protocol 3: Quantum Algorithms for Attractor Identification in Boolean GRN Models

Background and Principles

Boolean networks (BNs) provide a powerful, coarse-grained approach to modeling GRNs, where genes are represented as binary agents (ON/OFF) and their interactions are captured through Boolean functions [36]. In this framework, attractors—stable states or cycles of states of the system—are associated with biological phenotypes, making their identification crucial for understanding cellular differentiation and fate decisions [36]. However, traditional computing approaches struggle with the exponential growth of the state space in such models (with ( 2^n ) possible states for n genes), limiting exhaustive simulations to relatively small networks (typically ( n \leq 29 )) [36].

A novel quantum search algorithm has been developed for identifying attractors in synchronous Boolean networks, offering potential advantages for analyzing larger GRNs [36]. This algorithm uses iterative quantum amplitude suppression to systematically identify all attractors of a Boolean network, with each run guaranteed to discover a new attractor [36]. The approach demonstrates strong resilience to noise on current NISQ (noisy intermediate-scale quantum) devices, making it a promising advance toward practical quantum-enhanced biological modeling [36].

Step-by-Step Protocol

Boolean Network Formulation

  • Gene binarization: Convert gene expression data to binary values (ON/OFF) using appropriate thresholding methods. For single-cell data, this can be based on expression levels relative to cell population distributions.

  • Boolean function definition: For each gene, define a Boolean function that determines its state based on the states of its regulators. These functions can be derived from known regulatory interactions or inferred from data.

  • Update scheme specification: Implement a synchronous update scheme where all genes are updated simultaneously at each time step based on the current state of the system [36].

Quantum Algorithm Implementation

  • Qubit initialization: Initialize the qubit system to a superposition of all possible states using Hadamard gates applied to each qubit [36]. For n genes, this creates a superposition of all ( 2^n ) possible states.

  • Boolean function application: Implement the Boolean functions as quantum gates that evolve the superposition state [36]. Each possible network state evolves into its corresponding time-evolved state according to the synchronous update rules.

  • Iterative amplitude suppression:

    • Run the algorithm and measure to identify the first attractor.
    • Apply quantum amplitude suppression to iteratively suppress known attractor basins, increasing the probability of detecting new ones in subsequent runs [36].
    • Repeat until all attractors are identified, with each run guaranteed to find a new attractor [36].

  • Noise mitigation: Implement error mitigation strategies tailored to the specific quantum hardware being used, as the algorithm has shown robustness to noise on current NISQ devices like the ibm_brisbane processor [36].

Validation and Analysis

  • Classical verification: For small networks, verify quantum algorithm results using classical methods such as the BoolNet package in R [36].

  • Biological interpretation: Map identified attractors to known or potential cellular phenotypes based on their gene expression patterns.

  • Basin analysis: Analyze the size and structure of attractor basins to assess the relative stability of different cellular states.

Research Reagent Solutions

Table 4: Computational Resources for Quantum-Enhanced GRN Analysis

Resource Function Access Method
Quantum Computing Simulators Algorithm development and testing without quantum hardware Qiskit, Cirq, Forest
IBM Quantum Processors Implementation and execution of quantum algorithms IBM Quantum Experience
BoolNet R Package Classical verification of attractor identification CRAN Repository
Quantum Algorithm Libraries Pre-built functions for quantum amplitude suppression Open-source quantum computing libraries

The Waddington landscape framework provides a powerful conceptual and quantitative approach for understanding cellular differentiation and fate decisions in the context of gene regulatory networks. The protocols outlined here—ranging from GRN inference using cutting-edge machine learning methods like LINGER to attractor landscape construction in specific biological systems and the emerging application of quantum algorithms for attractor identification—provide researchers with practical tools for applying this framework to their specific research questions.

The integration of single-cell multi-omics data with increasingly sophisticated computational methods is transforming the Waddington landscape from a qualitative metaphor to a quantitative, predictive framework [3] [35]. This enables not only deeper understanding of developmental processes and disease mechanisms but also practical applications in drug development and cellular reprogramming. As these methods continue to evolve, particularly with advances in quantum computing and AI-driven modeling, we anticipate increasingly accurate and comprehensive reconstructions of epigenetic landscapes that will further illuminate the fundamental principles governing cellular identity and fate decisions.

A Toolkit for Discovery: Methodological Approaches for GRN Inference from Multi-Omics Data

In evolutionary developmental biology (evo-devo), understanding the gene regulatory networks (GRNs) that control cellular identity and morphological diversity is a fundamental pursuit. The advent of single-cell multi-omics technologies, which allow for the simultaneous measurement of a cell's transcriptome and epigenome (e.g., via paired scRNA-seq and scATAC-seq), has provided the data necessary to reconstruct these networks with unprecedented resolution [3] [37]. The computational challenge lies in accurately inferring the causal regulatory relationships between transcription factors (TFs), cis-regulatory elements (CREs), and their target genes from these sparse and noisy data. This has led to the development of diverse computational approaches, each with distinct foundations and assumptions, which are critically assessed in this application note.

Methodological Foundations and Comparative Analysis

Computational methods for GRN inference from single-cell multi-omics data can be broadly categorized into several paradigms. The table below summarizes the core principles, key tools, and specific applications of these foundational approaches.

Table 1: Foundational Computational Approaches for GRN Inference from Single-Cell Multi-omics Data

Methodological Foundation Core Principle Representative Tools Application in GRN Inference
Correlation & Association Identifies co-variation or spatial association between TF expression/activity and target gene expression, or between chromatin accessibility and gene expression. scSAGRN [37], PCC [3] Infers TF-gene and peak-gene linkages based on statistical dependencies, often using neighborhood information from integrated data.
Regression Models Models the expression of a target gene as a linear or non-linear function of the expression levels of TFs and the accessibility of CREs. Elastic Net, LINGER (initial layer) [3] Directly predicts gene expression from regulator activities, with coefficients interpreted as regulatory strengths.
Probabilistic Models Uses a Bayesian framework to integrate multi-omics data and prior knowledge (e.g., known GRNs, motifs) to infer a posterior probability of regulatory interactions. PRISM-GRN [4], BREM-SC [38] Provides robust, interpretable GRN inference with inherent uncertainty quantification, valuable for sparse single-cell data.
Deep Learning Models Employs multi-layer neural networks (e.g., VAEs, GANs) to learn complex, non-linear relationships between input modalities and infer latent regulatory structures. LINGER [3], scMODAL [39], BABEL [38] Captures high-order interactions; can be enhanced with lifelong learning from external atlas-scale data.
Collismycin ACollismycin ABench Chemicals
ConteltinibConteltinib, CAS:1384860-29-0, MF:C32H45N9O3S, MW:635.8 g/molChemical ReagentBench Chemicals

Performance Benchmarking of Computational Methods

The performance of GRN inference methods is typically benchmarked using ground truth data from independent experimental sources, such as ChIP-seq for TF-target gene interactions and eQTL studies for cis-regulatory linkages [3] [37]. Key evaluation metrics include the Area Under the Receiver Operating Characteristic Curve (AUC) and the Area Under the Precision-Recall Curve (AUPR), with the latter being particularly informative for imbalanced datasets where true edges are sparse.

Table 2: Performance Benchmarking of Selected GRN Inference Methods

Method Foundation Reported Performance Key Advantage
LINGER [3] Deep Learning (Lifelong) 4x to 7x relative increase in AUC over existing methods; superior AUPR ratio across blood cell ChIP-seq ground truths. Leverages atlas-scale external bulk data for highly accurate inference from limited single-cell data.
scSAGRN [37] Spatial Association Outperforms FigR, GLUE, SEASTAR, and SCENIC+ in TF recovery, peak-gene, and TF-gene linkage prediction on human bone marrow and cell line data. Effectively identifies key activating and repressive TFs by incorporating spatial correlation.
PRISM-GRN [4] Probabilistic (Bayesian) Superior precision in GRN reconstruction, especially for sparse true interactions; performs well with unpaired data and limited prior information. Biologically interpretable architecture; robust and flexible across various biological contexts.
Elastic Net [3] Regression Lower prediction accuracy for gene expression compared to non-linear neural network models, particularly for genes with negative correlations. Provides a simple, linear baseline model.

Experimental Protocols for GRN Inference and Validation

This section outlines a generalized workflow for inferring and validating GRNs from single-cell multiome data, synthesizing protocols from the cited methodologies.

Protocol 1: Data Preprocessing and Feature Selection

Goal: Prepare scRNA-seq and scATAC-seq count matrices for GRN inference. Reagents & Materials:

  • Cell Ranger ARC (10x Genomics): For initial alignment, barcode assignment, and feature counting of multiome data.
  • Scanpy / Seurat: Software suites for single-cell data analysis in Python/R.
  • Motif Database (e.g., JASPAR, CIS-BP): A collection of TF binding motifs for identifying TF-binding sites in accessible chromatin regions.

Procedure:

  • Quality Control: Filter cells based on metrics like the number of detected genes, total UMI counts for RNA, the number of fragments for ATAC, and mitochondrial gene percentage. Filter features (genes/peaks) detected in only a minimal number of cells.
  • Normalization & Scaling: Normalize scRNA-seq data by total UMI count per cell and log-transform. Normalize scATAC-seq data using TF-IDF transformation.
  • Feature Selection: For scRNA-seq, identify highly variable genes (HVGs). For scATAC-seq, identify highly accessible peaks. Optionally, derive gene activity scores from peak data by summing accessibility in a gene's promoter and distal regulatory elements.
  • TF-RE Matching: Scan accessible peak sequences for known TF motifs to create a prior binding potential matrix.

Protocol 2: GRN Inference Using the LINGER Framework

Goal: Infer a high-confidence GRN by leveraging a deep learning model pre-trained on external bulk data. Reagents & Materials:

  • Pre-trained BulkNN model [3]: A neural network model pre-trained on diverse bulk RNA-seq and ATAC-seq data from sources like ENCODE.
  • LINGER Software: Available computational implementation of the LINGER method.
  • Elastic Weight Consolidation (EWC) Loss Function: A regularization technique to retain knowledge from previous tasks (bulk data) when learning new ones (single-cell data).

Procedure:

  • Model Pre-training: Train a three-layer neural network (BulkNN) on the external bulk atlas data to learn a general model of gene regulation across diverse contexts. The model takes TF expression and RE accessibility as input to predict target gene expression.
  • Lifelong Learning Fine-tuning: Refine the pre-trained BulkNN model on the target single-cell multiome data using EWC. This prevents catastrophic forgetting of bulk data knowledge while adapting to the single-cell context.
  • Regulatory Strength Calculation: Pass the single-cell data through the fine-tuned neural network. Use Shapley values, a technique from interpretable AI, to quantify the contribution of each TF and RE to the prediction of each target gene's expression. These values represent the directed regulatory strengths for the TF-TG and RE-TG edges in the GRN.
  • TF-RE Edge Inference: Calculate the correlation between the parameters learned for TFs and REs in the second layer of the neural network to infer TF-RE binding strength.

The following diagram illustrates the core LINGER workflow:

linger_workflow cluster_pretrain Pre-training Phase cluster_finetune Fine-tuning & Inference Phase BulkData External Bulk Data (ENCODE) BulkNN BulkNN Model Training BulkData->BulkNN PretrainedModel Pre-trained Model (Prior Knowledge) BulkNN->PretrainedModel EWC Fine-tuning with Elastic Weight Consolidation PretrainedModel->EWC Knowledge Prior SingleCellData Single-cell Multiome Data SingleCellData->EWC FineTunedModel Fine-tuned LINGER Model EWC->FineTunedModel Shapley Shapley Value Analysis FineTunedModel->Shapley GRN Inferred GRN (TF-RE, RE-TG, TF-TG) Shapley->GRN

Protocol 3: Validation and Downstream Analysis

Goal: Assess the biological accuracy of the inferred GRN and perform evolutionary or developmental analysis. Reagents & Materials:

  • ChIP-seq Datasets: Ground truth data for specific TF-binding events from public repositories (e.g., GEO).
  • eQTL Datasets: Ground truth for variant-gene links from consortia like GTEx or eQTLGen [3].
  • GWAS Catalog: A repository of trait- and disease-associated genetic variants.
  • Motif Enrichment Tools (e.g., HOMER): To validate the enrichment of specific TF motifs in the CREs linked to their target genes.

Procedure:

  • Validation against Ground Truth: Calculate the AUC and AUPR for the inferred TF-TG edges using ChIP-seq data as a positive set. Similarly, validate RE-TG links using cis-eQTL data, stratifying by genomic distance [3].
  • Integration with GWAS: Overlap non-coding GWAS hits for traits of interest (e.g., skeletal morphology in evo-devo contexts) with the inferred CREs in the GRN. This links evolutionary traits to specific regulatory elements and their target genes [3] [24].
  • Driver Regulator Identification: Using the inferred GRN, estimate TF activity from external scRNA-seq or bulk RNA-seq datasets (e.g., from case-control studies or different species). Identify driver TFs as those with differentially active regulons [3].
  • Cross-Species Comparison (for Evo-Devo): Apply the GRN inference pipeline to homologous cell types or tissues from different species. Compare network topologies to identify conserved and divergent regulatory modules underlying phenotypic evolution [22].

The Scientist's Toolkit: Research Reagent Solutions

The following table details key computational and data resources essential for conducting GRN inference studies.

Table 3: Essential Research Reagents and Resources for GRN Inference

Resource Name Type Function in GRN Research
10x Genomics Multiome Kit Wet-lab Reagent Generates paired scRNA-seq and scATAC-seq libraries from the same single cell, providing the foundational data for GRN inference.
ENCODE Consortium Data Reference Data Provides a large-scale atlas of bulk RNA-seq, ChIP-seq, and ATAC-seq across cell types, used for pre-training models like LINGER's BulkNN [3].
JASPAR/CIS-BP Database Curated databases of TF binding motifs, used to connect accessible chromatin regions to potential binding TFs [3].
GTEx/eQTLGen Validation Data Provide genotype-gene expression association data, serving as ground truth for validating predicted cis-regulatory interactions (RE-TG links) [3].
LINGER Software Computational Tool A deep learning framework that uses lifelong learning to achieve high-accuracy GRN inference from single-cell multiome data [3].
PRISM-GRN Software Computational Tool A Bayesian model that incorporates prior knowledge and multi-omics data for precise, robust, and interpretable GRN reconstruction [4].
scMODAL Software Computational Tool A deep learning framework for integrating diverse single-cell omics data, which can support downstream GRN analysis [39].
TRRUST Database A curated database of human and mouse transcriptional regulatory networks, useful as prior knowledge or for validation [37].
CPI-4203CPI-4203, MF:C16H14N4O, MW:278.31 g/molChemical Reagent
CPI-455

Visualizing a Generalized GRN Inference Workflow

The following diagram summarizes the logical flow of information and analysis steps in a standard GRN inference pipeline, from raw data to biological insight.

grn_general_workflow RawData Paired scRNA-seq & scATAC-seq Data Preprocess Data Preprocessing & Integration RawData->Preprocess Features Feature Matrices: TF Expr, RE Access, TG Expr Preprocess->Features MethodCorr Correlation (e.g., scSAGRN) Features->MethodCorr MethodDL Deep Learning (e.g., LINGER) Features->MethodDL MethodProb Probabilistic (e.g., PRISM-GRN) Features->MethodProb InferredGRN Inferred GRN MethodCorr->InferredGRN MethodDL->InferredGRN MethodProb->InferredGRN Validation Validation & Downstream Analysis InferredGRN->Validation BiologicalInsight Biological Insight: Evo-Devo Mechanisms, Disease Drivers Validation->BiologicalInsight

Inference of Gene Regulatory Networks (GRNs) is a central problem in computational biology, essential for understanding how cells alter gene expression in response to different environments and how noncoding genetic variants cause disease [3]. GRNs are composed of transcription factors (TFs) that bind DNA regulatory elements to activate or repress the expression of target genes [3]. Despite extensive efforts, GRN inference accuracy has remained disappointingly low, marginally exceeding random predictions [3]. The LINGER (Lifelong neural network for gene regulation) framework represents a paradigm shift in this field, achieving a fourfold to sevenfold relative increase in accuracy over existing methods by incorporating atlas-scale external bulk data across diverse cellular contexts and prior knowledge of transcription factor motifs as a manifold regularization [3].

Principles of the LINGER Methodology

Core Architecture and Lifelong Learning

LINGER is a computational framework designed to infer GRNs from single-cell multiome data using count matrices of gene expression and chromatin accessibility along with cell type annotation as input [3]. It outputs a cell population GRN, cell type-specific GRNs, and cell-level GRNs, each containing three types of interactions: trans-regulation (TF–TG), cis-regulation (RE–TG), and TF-binding (TF–RE) [3]. The framework integrates comprehensive gene regulatory profiles from external bulk data through lifelong machine learning (also called continuous learning), where knowledge learned in the past helps learn new tasks with little data or effort [3].

The LINGER framework implements a three-layer neural network model to fit the expression of target genes (TGs), taking as input TF expression and the accessibility of regulatory elements (REs) [3]. The second layer consists of weighted sums of TFs and REs, forming regulatory modules guided by TF–RE motif matching through manifold regularization [3]. This leads to the enrichment of TF motifs binding to REs that belong to the same regulatory module [3].

Key Technical Innovations

LINGER's approach addresses three major challenges in GRN inference:

  • Mitigating Limited Data: Learning complex regulatory mechanisms from limited independent data points is a daunting challenge, even with single-cell data offering large numbers of cells, as most are not independent [3]. LINGER overcomes this through lifelong learning incorporating large-scale external bulk data [3].
  • Incorporating Prior Knowledge: Integrating prior knowledge such as motif matching into non-linear models is challenging [3]. LINGER addresses this through manifold regularization that enables prior knowledge incorporation into the model [3].
  • Enhancing Accuracy: Previously inferred GRN accuracy assessed by experimental data was only marginally better than random prediction [3]. LINGER achieves a substantial improvement through its novel architecture and training methodology [3].

Experimental Protocol for LINGER Implementation

Data Preprocessing and Input Requirements

Input Data Requirements:

  • Single-cell multiome data (paired gene expression and chromatin accessibility)
  • Count matrices for both gene expression and chromatin accessibility
  • Cell type annotations
  • External bulk data from atlas-scale resources (e.g., ENCODE project)
  • Prior knowledge databases of transcription factor motifs

Preprocessing Steps:

  • Quality Control: Filter cells based on standard QC metrics (mitochondrial content, number of features, doublet detection)
  • Normalization: Normalize gene expression and chromatin accessibility counts using standard methods (e.g., SCTransform for scRNA-seq, term frequency-inverse document frequency for scATAC-seq)
  • Integration: Align paired measurements across modalities using cell barcodes
  • Feature Selection: Identify highly variable genes and accessible chromatin regions for downstream analysis
  • External Data Alignment: Map external bulk data to the same feature space as single-cell data

Model Training Protocol

Phase 1: Pre-training on External Bulk Data

  • Initialize neural network architecture with three layers
  • Train model (BulkNN) using external bulk data from ENCODE project containing hundreds of samples covering diverse cellular contexts [3]
  • Optimize parameters to predict TG expression from TF expression and RE accessibility
  • Apply manifold regularization incorporating TF–RE motif matching knowledge

Phase 2: Refinement on Single-cell Data

  • Initialize model with pre-trained parameters from BulkNN
  • Apply Elastic Weight Consolidation (EWC) loss, using bulk data parameters as a prior [3]
  • Determine magnitude of parameter deviation using Fisher information, which reflects the sensitivity of the loss function to parameter changes [3]
  • Train model on single-cell multiome data with EWC regularization encouraging the posterior to remain close to the prior, retaining knowledge while adapting to new data [3]

Phase 3: Regulatory Network Extraction

  • Infer regulatory strength of TF–TG and RE–TG interactions using Shapley value, which estimates the contribution of each feature for each gene [3]
  • Generate TF–RE binding strength by correlation of TF and RE parameters learned in the second layer [3]
  • Construct cell type-specific and cell-level GRNs based on the general GRN and cell type-specific profiles [3]

Validation and Benchmarking Protocol

Performance Assessment:

  • Ground Truth Collection: Collect putative targets of TFs from ChIP–seq data using systematic standards (e.g., 20 datasets in blood cells as ground truth) [3]
  • Evaluation Metrics: Calculate area under the receiver operating characteristic curve (AUC) and area under the precision–recall curve (AUPR) ratio by sliding trans-regulatory predictions [3]
  • Cis-regulatory Validation: Calculate consistency of cis-regulatory coefficients with expression quantitative trait loci (eQTL) studies from GTEx and eQTLGen that link genotype variants to their target genes [3]
  • Comparative Analysis: Compare against baseline methods including PCC, elastic net, and single-cell neural network (scNN) without external data integration

Table 1: Quantitative Performance Comparison of LINGER Against Baseline Methods

Method AUC (Trans-regulation) AUPR Ratio (Trans-regulation) AUC (Cis-regulation, eQTLGen) AUPR Ratio (Cis-regulation, eQTLGen)
LINGER Significantly higher Significantly higher Higher across all distance groups Higher across all distance groups
scNN Moderate Moderate Moderate Moderate
BulkNN Low Low Low Low
PCC Lowest Lowest Lowest Lowest

LINGER Workflow and Signaling Pathways

The following diagram illustrates the complete LINGER workflow, from data input through network inference and downstream applications:

linger_workflow cluster_inputs Input Data cluster_training Model Training cluster_outputs Output Networks cluster_apps Downstream Applications SC_Multiome Single-cell Multiome Data Pretrain Pre-training on External Bulk Data SC_Multiome->Pretrain External_Bulk External Bulk Data (ENCODE) External_Bulk->Pretrain TF_Motifs TF Motif Prior Knowledge TF_Motifs->Pretrain Cell_Annotations Cell Type Annotations Cell_Annotations->Pretrain Refine Refinement on Single-cell Data (EWC Regularization) Pretrain->Refine Extract Regulatory Network Extraction (Shapley) Refine->Extract Population_GRN Cell Population GRN Extract->Population_GRN CellType_GRN Cell Type-Specific GRNs Extract->CellType_GRN CellLevel_GRN Cell-Level GRNs Extract->CellLevel_GRN GWAS_Integration GWAS Integration & Disease Interpretation Population_GRN->GWAS_Integration TF_Activity TF Activity Estimation from Expression Data CellType_GRN->TF_Activity Driver_Regulators Driver Regulator Identification CellLevel_GRN->Driver_Regulators

Research Reagent Solutions for GRN Inference

Table 2: Essential Research Reagents and Computational Tools for GRN Inference

Resource Type Specific Examples Function in GRN Inference
Single-cell Multiome Platforms 10x Genomics Multiome ATAC-seq + Gene Expression Provides paired measurements of chromatin accessibility and gene expression from the same single cell [3]
External Reference Data ENCODE project bulk data [3], GTEx eQTLs [3], eQTLGen [3] Provides atlas-scale regulatory information across diverse cellular contexts for training and validation
Prior Knowledge Databases Transcription factor motif databases (JASPAR, CIS-BP) Informs TF-RE binding predictions through motif matching and manifold regularization [3]
Validation Data Sources ChIP-seq datasets [3], eQTL studies [3] Serves as ground truth for benchmarking trans-regulatory and cis-regulatory predictions
Computational Frameworks LINGER implementation [3], BEAST2 for phylogenetic inference [40] Provides algorithms for network inference and evolutionary analysis
Experimental Model Systems PBMCs from 10x Genomics [3], CAMA-1 breast cancer cell line [40], Pristionchus pacificus [41] Offer biologically relevant systems for method development and validation

Applications in Evolutionary Developmental Biology

Integrating GRN Inference with Evolutionary Analysis

The integration of GRN inference with evolutionary developmental biology (evo-devo) provides powerful insights into the regulatory mechanisms underlying phenotypic diversity. LINGER enables the reconstruction of evolutionary relationships among cells by linking genotypic and phenotypic variation, which is particularly valuable for understanding developmental decisions in evolutionary model systems [40] [41]. For example, in the nematode Pristionchus pacificus, which exhibits developmental plasticity of mouth form and feeding behavior, GRN inference can reveal the regulatory network underlying evolutionary novelties [41]. The mouth-dimorphism (predator vs. bacterivore) in P. pacificus is determined by a complex regulatory network involving key regulators eud-1, sult-1, and nhr-40, where subtle changes in regulatory structure can influence evolutionary trajectories [41].

Addressing Structural Uncertainty in Evolutionary Contexts

A significant challenge in evolutionary GRN inference is structural uncertainty—multiple competing model structures that could explain the same biological data [41]. This is particularly relevant in evolutionary contexts where regulatory networks may have diverged between species or populations. Comprehensive model comparison approaches, such as fitting thousands of distinct regulatory network models to gene expression data across experimental conditions, can identify conserved regulatory features supported by data across multiple contexts [41]. LINGER's ability to integrate diverse data sources and prior knowledge provides a robust framework for addressing this structural uncertainty in evolutionary studies.

Table 3: LINGER Performance in Evolutionary Developmental Biology Contexts

Application Domain Key Regulatory Components Identified Biological Insight Gained
Mouth-form Evolution in Nematodes eud-1, sult-1, nhr-40 regulatory network [41] High degree of positive regulation and interconnectivity between key developmental regulators [41]
Cancer Evolution and Drug Resistance K-Ras, β-catenin pathways in breast cancer [40] Multiple genetic lineages independently acquired resistance mechanisms, suggesting need for multi-lineage targeting strategies [40]
Developmental Plasticity Environmental influence on phenotypic ratios [41] Regulatory networks that enable flexible responses to environmental cues while maintaining developmental robustness

Advanced Technical Considerations

Addressing Practical Indistinguishability in GRN Inference

A critical challenge in GRN inference is practical indistinguishability—the inability to uniquely infer network structure given typical experimental data constraints [41]. This arises from several factors characteristic of biological data: intrinsic and extrinsic noise, limited temporal sampling, and the impossibility of measuring all relevant system states [41]. LINGER addresses these challenges through several mechanisms:

  • Lifelong Learning: Incorporation of external bulk data mitigates limitations of sparse single-cell data [3]
  • Manifold Regularization: Integration of prior knowledge constraints the solution space [3]
  • Bayesian Framework: EWC regularization provides a principled approach to balancing prior knowledge with new evidence [3]

Comparative Analysis of Modeling Approaches

The maximalist approach of comparing thousands of potential network structures, as demonstrated in evolutionary studies of P. pacificus, represents a powerful strategy for robust GRN inference [41]. However, this approach is computationally intensive and may not be feasible for all research questions. LINGER provides a more efficient alternative through its neural network architecture and regularization strategies, while still accommodating structural uncertainty through its flexible framework.

Downstream Applications and Translational Potential

Disease Association and Therapeutic Targeting

LINGER enables enhanced interpretation of disease-associated variants and genes through several mechanisms:

  • GWAS Integration: Reveals complex regulatory landscapes of genome-wide association studies [3]
  • TF Activity Estimation: Enables estimation of transcription factor activity solely from bulk or single-cell gene expression data, leveraging abundant gene expression data to identify driver regulators from case-control studies [3]
  • Therapeutic Target Identification: Identifies key regulatory nodes that could be targeted for therapeutic intervention, particularly in complex diseases like cancer where multiple lineages may independently acquire resistance mechanisms [40]

Drug Development Applications

For drug development professionals, LINGER offers several valuable capabilities:

  • Mechanism of Action Elucidation: Identifies regulatory pathways affected by drug treatments
  • Resistance Mechanism Prediction: Reveals multiple evolutionary pathways to drug resistance, informing combination therapy strategies [40]
  • Biomarker Discovery: Identifies regulatory drivers that could serve as predictive biomarkers for treatment response
  • Target Prioritization: Ranks regulatory factors by their network influence and disease relevance

The framework's ability to reconstruct cancer cell phylogenetic relationships and link them to phenotypic outcomes, such as drug resistance in breast cancer and multiple myeloma tumors, demonstrates its utility across biological contexts and disease stages [40]. By revealing evidence of genetic evolution across disease progression and convergent evolution where multiple lineages evolve toward a common mechanism of resistance, LINGER provides insights essential for developing durable therapeutic strategies [40].

Gene regulatory networks (GRNs) represent the complex collections of molecular regulators that interact to govern cellular gene expression, ultimately determining cell function, fate, and phenotypic outcomes [42]. In evolutionary developmental biology (evo-devo), understanding how these networks evolve to produce diverse body plans and structures represents a central challenge [43] [44]. While traditional GRN analysis has focused on linear regulator-target relationships, emerging evidence indicates that combinatorial regulation - where multiple transcription factors (TFs) collaborate to control common target genes - plays a pivotal role in developmental processes and evolutionary innovation [12].

Current regulatory units like Regulons (target genes controlled by a single TF) or eRegulons (incorporating regulatory elements) fail to capture the cooperative nature of TF interactions observed in key developmental processes [12]. For instance, in mammalian embryonic stem cells, Sox2, Nanog, and Pou5f1 cooperatively govern pluripotency, while MYOD, MYOG, MEF2A, and MYF6 collectively dictate skeletal muscle specification [12]. Similarly, studies of deuterostome body axis formation have revealed conserved GRNs orchestrated by Nodal, Gdf1/3, and Lefty that exhibit evolutionary rewiring through enhancer hijacking events [44].

The cRegulon framework addresses this gap by modeling combinatorial regulation from single-cell multi-omics data, providing regulatory units that underpin the cell type landscape and offering new insights into the modular architecture of GRNs across evolutionary timescales [12] [45].

What is cRegulon? Definition and Conceptual Framework

cRegulon represents a computational framework for identifying combinatorial regulatory modules from single-cell multi-omics data. Specifically, a cRegulon comprises:

  • A set of TF pairs (TF module) that cooperatively regulate gene expression
  • A corresponding set of binding regulatory elements (REs)
  • A set of target genes (TGs) whose expressions are co-regulated by these TFs and REs [12]

This framework extends beyond existing methods by simultaneously modeling TF combinatorial interactions while accounting for cell-type specificity in regulation. The GRN of a cell type may be composed of several distinct cRegulons that regulate gene expression in distinct pathways or processes, while a single cRegulon may be shared by GRNs of multiple cell types, reflecting evolutionary conservation of regulatory modules [12].

Table 1: Core Components of a cRegulon

Component Description Biological Significance
TF Module Set of transcription factor pairs that cooperatively regulate targets Determines specificity of regulatory control; often evolutionarily conserved
Regulatory Elements DNA regions (enhancers, promoters) where TFs bind Provides context-specific accessibility and modulation
Target Genes Genes whose expression is controlled by the TF module Executes functional programs defining cell identity

Computational Methodology and Workflow

Data Input and Preprocessing

The cRegulon pipeline begins with single-cell multi-omics data, typically paired scRNA-seq and scATAC-seq data, which can be aligned at either the cell level or context level [12]. The initial processing stages include:

  • Data preprocessing and normalization to account for technical variability
  • Cell clustering to identify putative cell types or states
  • GRN construction for each cell cluster using established inference methods

This foundation enables subsequent identification of combinatorial regulation patterns across different cellular contexts.

Identifying TF Combinatorial Modules

The core innovation of cRegulon lies in its approach to detecting TF combinatorial interactions:

For each cluster-specific GRN, cRegulon combines co-regulation effects and activity specificities to define a combinatorial effect for each TF pair. This generates a matrix (C) containing pairwise combinatorial effects across all cell clusters [12].

To model the modularity of GRNs, the method assumes (C) can be approximated by a mixture of rank-1 matrices, each corresponding to a module of co-regulating TFs. The optimization model is designed to identify these TF modules across all cell clusters simultaneously with cell type annotation [12].

The mathematical formulation involves solving:

[ \min \|C - \sum{k=1}^{K} \lambdak uk uk^\top\|_F^2 ]

where (uk) represents the k-th TF module, (\lambdak) represents its contribution, and (K) is the number of modules [12].

Workflow Visualization

cluster_1 Input Data cluster_2 Preprocessing cluster_3 cRegulon Core cluster_4 Output RNA scRNA-seq Data Preprocess Normalization & Clustering RNA->Preprocess ATAC scATAC-seq Data ATAC->Preprocess GRN Per-cluster GRN Inference Preprocess->GRN Matrix Combinatorial Effect Matrix C GRN->Matrix Decompose Rank-1 Matrix Decomposition Matrix->Decompose Modules TF Modules Identification Decompose->Modules cRegulons cRegulons (TF Modules + REs + TGs) Modules->cRegulons Annotation Cell Type Annotation Modules->Annotation

Experimental Protocol: Implementing cRegulon Analysis

Data Requirements and Preparation

For successful cRegulon analysis, researchers should prepare:

  • Single-cell multiome data: Paired scRNA-seq and scATAC-seq from the same cells
  • Cell type annotations: Pre-defined or computationally derived cell cluster labels
  • Quality controls: Minimum of 500 cells per cell type for robust inference
  • Reference data: Species-appropriate TF motif databases for RE-TF linking

Step-by-Step Computational Protocol

  • Data Integration and Normalization

    • Process scRNA-seq data using standard normalization (SCTransform recommended)
    • Process scATAC-seq data using peak calling and chromatin accessibility quantification
    • Integrate datasets using mutual nearest neighbors or label transfer methods

  • GRN Inference for Cell Clusters

    • Split data by cell type/cluster annotations
    • For each cluster, run GRN inference using methods like SCENIC+ or LINGER [3]
    • Extract TF-RE-TG connections for each cluster-specific network

  • cRegulon Identification

    • Compute pairwise TF combinatorial effects using cRegulon's matrix construction
    • Run optimization algorithm to decompose matrix into rank-1 components
    • Extract TF modules, associated REs, and target genes for each cRegulon
    • Annotate cell types by cRegulon activities

  • Validation and Biological Interpretation

    • Compare with known TF complexes from literature and databases
    • Perform functional enrichment analysis on target gene sets
    • Validate using orthogonal data (e.g., ChIP-seq, perturbation studies)

Benchmarking and Performance Assessment

cRegulon has demonstrated superior performance in identifying TF combinatorial modules compared to existing approaches. Validation using simulated datasets and real biological systems shows enhanced accuracy in both module identification and cell type annotation [12] [45]. When applied to a mixture of four cell lines, cRegulon successfully captured biologically relevant regulatory units specific to each cellular context.

Biological Applications and Insights

Case Study: Human Fetal Atlas cRegulons

Application of cRegulon to human fetal development data identified 25 distinct cRegulons associated with major developmental pathways [46]. These modules capture the coordinated action of TFs driving cell fate decisions during embryogenesis.

Table 2: Representative cRegulons from Human Fetal Atlas Analysis

cRegulon Top Transcription Factors Biological Functions
M1 FOXG1, RFX4, NEUROD2, NEUROG2, ASCL1, ESRRB Neural progenitor state maintenance
M9 HNF4A, HES1, PROX1, HNF1A, ONECUT1, GATA6, PDX1 Pancreatic exocrine development
M12 STAT5B, TAL1, GATA2, GATA1 Hemopoietic lineage commitment
M15 MYOG, TBX1, MYOD1, MYF6, MYF5 Muscle structure development
M18 CEBPA, XBP1, ONECUT2, HNF4A, ONECUT1, HNF1A Lipid-glucose homeostasis

Evolutionary Developmental Biology Insights

The cRegulon framework provides unique insights into evo-devo by enabling comparative analysis of regulatory modules across species. For example, studies of Nodal signaling in amphioxus revealed how GRN rewiring through enhancer hijacking events led to the co-option of Gdf1/3-like for body axis patterning, replacing the ancestral Gdf1/3 function [44]. This evolutionary innovation was facilitated by the translocation of Gdf1/3-like to the Lefty genomic region, enabling shared regulatory control.

cRegulon analysis can detect such conserved combinatorial modules despite genomic rearrangements, revealing the evolutionary constraints on TF cooperation. The framework supports the hypothesis that developmental system drift often occurs through reorganization of regulatory connections while preserving core functional modules [44].

Research Reagent Solutions

Table 3: Essential Research Reagents for cRegulon-based Studies

Reagent/Method Function in Analysis Considerations
10x Genomics Multiome Provides paired scRNA-seq + scATAC-seq data Enables direct correlation of chromatin accessibility and gene expression
SCENIC+ Infers enhancer-driven gene regulatory networks Provides input GRNs for cRegulon analysis [12]
LINGER Lifelong learning approach for GRN inference Incorporates atlas-scale external data as regularization [3]
cisTarget Databases Species-specific motif collections Essential for linking TFs to regulatory elements
CRISPR Perturbation Functional validation of predicted TF modules Establishes causal relationships in regulatory networks [47]

Integration with Evolutionary Developmental Biology Research

For evolutionary developmental biologists, cRegulon offers a powerful approach to investigate how changes in combinatorial regulation drive phenotypic evolution. The methodology enables:

  • Comparative cRegulon analysis across species to identify conserved versus derived TF cooperativity
  • Tracking regulatory module evolution through developmental time and across phylogenetic distances
  • Identifying network motifs that may be targets of evolutionary constraint or innovation
  • Linking regulatory changes to morphological diversification through module rewiring

The framework is particularly valuable for studying developmental system drift, where similar developmental outcomes are achieved through different genetic pathways [44]. By decomposing GRNs into reusable cRegulon modules, researchers can trace how evolution tinkers with combinatorial partnerships to generate diversity while preserving essential functions.

Visualizing Combinatorial Regulation Logic

cluster_cRegulon cRegulon Module TF1 TF A RE1 Enhancer 1 TF1->RE1 TG1 Target Gene 1 TF1->TG1 TF2 TF B TF2->RE1 RE2 Enhancer 2 TF2->RE2 TF3 TF C TF3->RE2 TG3 Target Gene 3 TF3->TG3 RE1->TG1 TG2 Target Gene 2 RE1->TG2 RE2->TG2 RE2->TG3 Legend1 TF-TF Cooperation Legend2 TF-RE Binding Legend3 RE-TG Regulation

cRegulon represents a significant advancement in GRN inference by explicitly modeling the combinatorial nature of transcriptional regulation. By identifying reusable regulatory modules that underpin cell type landscapes, the framework provides evolutionary developmental biologists with a powerful tool to decipher how changes in regulatory architecture drive phenotypic evolution.

The methodology's ability to integrate single-cell multi-omics data while accounting for cellular context makes it particularly valuable for studying the evolvability of developmental programs. As single-cell technologies continue to advance and atlas-scale projects expand, cRegulon analysis promises to reveal fundamental principles of how cooperative TF interactions constraint and facilitate evolutionary innovation.

Future developments may extend cRegulon to incorporate spatial transcriptomics data, enable cross-species module alignment, and integrate non-TF regulators such as signaling molecules and chromatin modifiers, further enhancing its utility for evolutionary developmental biology research.

The integration of spatial context with multimodal single-cell data is revolutionizing our understanding of Gene Regulatory Networks (GRNs) in evolutionary developmental biology. Frameworks such as PathOmCLIP and Nicheformer represent a paradigm shift in computational biology, enabling researchers to decipher the complex spatiotemporal regulatory logic that governs cell fate decisions, tissue patterning, and evolutionary adaptations. These approaches move beyond traditional single-modality analysis by harmonizing diverse data types—including transcriptomics, epigenomics, proteomics, and high-resolution histology—within their native spatial context. This integration is particularly crucial for GRN inference, as gene regulation is inherently spatial, with regulatory outcomes depending on precise cellular microenvironments and tissue organization.

PathOmCLIP introduces a novel approach to bridging histological imaging with spatial gene expression data through contrastive learning, allowing for the prediction of gene expression patterns directly from tissue morphology. Meanwhile, Nicheformer functions as a transformer-based foundation model trained on an unprecedented scale of spatially resolved cells, enabling the prediction of spatial context for dissociated cells and revealing spatial determinants of gene regulation. Together, these frameworks provide powerful new avenues for constructing more accurate, context-aware GRNs that reflect the true complexity of developmental processes and evolutionary trajectories across species.

Table 1: Core Framework Overview

Framework Primary Architecture Key Innovation Primary Data Modalities Scale of Pretraining
PathOmCLIP Contrastive learning model Aligns histology images with spatial gene expression Histology, spatial transcriptomics Validation across 5 tumor types [11]
Nicheformer Transformer-based foundation model Predicts spatial context for dissociated cells scRNA-seq, spatial transcriptomics 57M dissociated + 53M spatially resolved cells [11] [48]

PathOmCLIP: Methodology and Applications

Experimental Protocol and Workflow

PathOmCLIP (Pathology Omics Contrastive Language-Image Pretraining) employs a sophisticated multimodal learning approach to align histopathology images with spatial transcriptomic profiles. The methodology can be broken down into several key stages:

  • Data Acquisition and Preprocessing: Collect paired whole-slide histology images (typically H&E stained) and spatial transcriptomics data from the same tissue section. The spatial transcriptomics data provides gene expression measurements for specific locations (spots) on the tissue, each associated with spatial coordinates.

  • Image Patch Processing: Extract image patches centered on the spatial transcriptomics spots using the registered coordinates. Process these patches using a convolutional neural network (CNN) encoder to generate compact image feature embeddings.

  • Gene Expression Processing: The spatial gene expression vector for each spot is processed through a dedicated encoder (e.g., a multilayer perceptron or transformer) to generate gene expression embeddings.

  • Contrastive Learning Alignment: The core innovation of PathOmCLIP lies in its contrastive learning objective, which brings the image and gene expression embeddings of corresponding spots closer together in a shared latent space while pushing apart non-corresponding pairs.

  • Model Validation and Application: Validate the model by testing its ability to predict gene expression from histology images alone on held-out datasets. PathOmCLIP has been validated across five different tumor types, demonstrating robust cross-tissue performance [11].

PathOmCLIP HST Histology & Spatial Transcriptomics Data IP Image Patch Extraction HST->IP GEE Gene Expression Encoder (MLP) HST->GEE IE Image Encoder (CNN) IP->IE CL Contrastive Learning Alignment IE->CL GEE->CL OM Output: Multimodal Embedding CL->OM

PathOmCLIP Workflow: Illustrates the multimodal alignment of histology images and spatial gene expression.

Application in GRN Inference and Spatial Biology

PathOmCLIP enables several advanced applications critical for GRN inference in developmental biology:

  • Histology-to-Expression Prediction: Once trained, PathOmCLIP can predict spatial gene expression patterns for new histology images alone, dramatically expanding the potential to extract molecular information from vast histological archives.
  • Identification of Morphological Regulators: By identifying genes whose expression is most predictable from histology, researchers can pinpoint key regulators that directly link tissue morphology to transcriptional programs, offering crucial candidates for GRN hubs.
  • Cross-Modal Data Imputation: The model can impute missing spatial gene expression data based on histological context, enhancing data completeness for downstream GRN inference algorithms.

Nicheformer: Methodology and Applications

Experimental Protocol and Workflow

Nicheformer is a transformer-based foundation model specifically designed for single-cell and spatial omics integration. Its protocol involves large-scale pretraining followed by task-specific fine-tuning:

  • Data Curation and Integration: Assemble a massive, diverse collection of single-cell RNA sequencing (scRNA-seq) and spatial transcriptomics datasets. Nicheformer was pretrained on the largest collection to date—over 57 million dissociated cells and 53 million spatially resolved cells across 73 human and mouse tissues [11] [48].

  • Foundation Model Pretraining: The model is pretrained on this colossal corpus using self-supervised learning objectives. This step allows the model to learn universal representations of cellular states and their potential spatial contexts.

  • Spatial Task Fine-Tuning: The pretrained model is subsequently fine-tuned on specific spatial tasks, such as spatial density prediction or niche and region label prediction. This adapts the general cellular representation to spatially explicit applications.

  • Spatial Context Prediction: A key application involves predicting the spatial context of dissociated cells. By inputting scRNA-seq data from dissociated cells, Nicheformer can infer their original spatial microenvironment, effectively transferring rich spatial information to vast scRNA-seq datasets.

  • Downstream Analysis: The model supports various downstream tasks, including spatial clustering, identification of spatially variable genes, and inference of cell-cell communication patterns within niches.

Nicheformer PTD Large-Scale Pretraining Data (57M dissociated + 53M spatial cells) PT Self-Supervised Pretraining PTD->PT FM Foundation Model PT->FM FT Task-Specific Fine-Tuning FM->FT SCP Spatial Context Prediction FT->SCP SA Spatial Analysis: Clustering, GRN Inference SCP->SA

Nicheformer Workflow: Shows the process from large-scale pretraining to spatial context prediction.

Application in GRN Inference and Spatial Biology

Nicheformer provides several unique capabilities for enhancing GRN inference:

  • Spatial Context for Dissociated Cells: By predicting spatial context for scRNA-seq data, Nicheformer enables researchers to incorporate spatial information into GRN inference from the vast repository of existing single-cell datasets, which lacked native spatial resolution.
  • Niche-Aware GRN Construction: The model allows for the construction of GRNs that are specific to particular spatial niches or microenvironments, revealing how the same cell type might exhibit different regulatory programs based on its precise tissue location.
  • Cross-Species Spatial Analysis: The inclusion of both human and mouse data in its training corpus enables Nicheformer to facilitate comparative analysis of spatial gene regulation across species, a powerful approach for evolutionary developmental biology.

Integrated Analysis: Comparative Performance and Applications

Benchmarking and Performance Metrics

When evaluated on their respective tasks, both PathOmCLIP and Nicheformer demonstrate significant advancements over previous methods. PathOmCLIP shows high accuracy in connecting tumor histology with spatial gene expression across multiple cancer types [11]. Nicheformer consistently achieves top performance on novel spatial prediction problems, demonstrating the advantage of its transformer-based architecture and massive training scale [48].

Large-scale benchmarking efforts like HESCAPE (H&E + Spatial ContrAstive PrEtraining) are crucial for evaluating multimodal learning methods that leverage both histology images and gene expression data. Such benchmarks have revealed that effective integration requires carefully addressing technical challenges like batch effects, and that gene expression encoders pretrained on spatial transcriptomics data outperform those trained without spatial context [49].

Table 2: Functional Comparison and Applications

Feature PathOmCLIP Nicheformer Significance for GRN Inference
Primary Strength Histology-gene expression alignment Spatial context prediction for single cells Links morphology to regulation; provides spatial priors
Key Innovation Cross-modal contrastive learning Massive-scale pretraining + fine-tuning Enables novel data integration paradigms
Spatial Resolution Spot-level (spatial transcriptomics) Single-cell & spot-level Enables fine-grained spatial regulatory analysis
Validation Scope 5 tumor types [11] 73 tissues across human & mouse [11] [48] Demonstrates broad applicability across biological contexts
GRN Relevance Identifies morphology-associated regulators Reveals spatial determinants of regulation Connects tissue patterning with transcriptional programs

Successful implementation of spatial and multimodal integration methods requires specific computational tools and data resources. The following table outlines key components of the research toolkit for working with frameworks like PathOmCLIP and Nicheformer.

Table 3: Research Reagent Solutions for Spatial Multimodal Analysis

Resource Category Specific Examples Function and Application
Spatial Transcriptomics Platforms 10x Genomics Visium/Xenium, MERFISH, ISS Generate paired histology and spatial gene expression data [50] [49]
Foundation Models scGPT, scPlantFormer, Geneformer Provide pretrained gene expression encoders for transfer learning [11] [49]
Histology Encoders CTransPath, UNI, Phikon Extract features from histology images for multimodal alignment [49]
Benchmarking Frameworks HESCAPE, BioLLM Standardized evaluation of multimodal integration methods [11] [49]
Data Repositories DISCO, CZ CELLxGENE Discover Provide access to millions of single-cell and spatial datasets for pretraining and analysis [11]
Multimodal Integration Tools StabMap, TMO-Net, GIST Enable integration of diverse omics modalities beyond transcriptomics [11]

Integrated Experimental Protocol for Spatial GRN Inference

This protocol combines elements from PathOmCLIP and Nicheformer approaches to create a comprehensive workflow for spatial GRN inference in evolutionary developmental biology research.

Sample Preparation and Data Generation

  • Tissue Collection and Preservation: Collect developmental tissue samples at specific stages of interest. Immediately snap-freeze in liquid nitrogen or use appropriate fixation methods that preserve RNA quality while maintaining tissue architecture.

  • Spatial Multimodal Data Generation: Process tissue sections using compatible spatial transcriptomics platforms (e.g., 10x Genomics Xenium or Visium). For technologies requiring separate processing:

    • Perform spatial transcriptomics according to manufacturer protocols
    • Acquire high-resolution histology images (H&E or other stains) from consecutive sections or the same section if compatible
    • Ensure proper spatial registration between modalities using landmark alignment or automated registration tools [51]

  • Single-Cell RNA Sequencing: For complementary dissociated single-cell analysis, prepare single-cell suspensions from adjacent tissue regions and perform scRNA-seq using standard protocols (10x Chromium, SMART-seq, etc.).

Data Processing and Multimodal Integration

  • Initial Data Processing:

    • Spatial transcriptomics: Process raw sequencing data through space Ranger or equivalent pipelines to generate count matrices with spatial coordinates
    • Histology images: Apply preprocessing including normalization, stain deconvolution, and tissue segmentation
    • scRNA-seq: Process through standard pipelines (Cell Ranger, Scanpy, Seurat) for quality control, normalization, and clustering

  • Multimodal Alignment with PathOmCLIP Framework:

    • Extract image patches centered on spatial transcriptomics spots
    • Train or apply pretrained PathOmCLIP model to learn joint embeddings of histology and gene expression
    • Use the model to identify genes with strong morphology-expression associations

  • Spatial Context Transfer with Nicheformer:

    • Map dissociated scRNA-seq data to spatial reference using Nicheformer's spatial prediction capabilities
    • Impute spatial coordinates for single cells based on their transcriptional profiles
    • Annotate spatial niches and microenvironments across the tissue landscape

GRN Inference and Validation

  • Spatially-Resolved GRN Construction:

    • Integrate spatially aligned data with GRN inference tools (e.g., LINGER, which incorporates atlas-scale external data [3], or cRegulon for combinatorial regulation [12])
    • Generate niche-specific GRNs by subsetting data based on spatial annotations
    • Identify regulatory differences across tissue regions and microenvironments

  • Experimental Validation:

    • Perform spatial validation of key regulatory predictions using multiplexed error-robust fluorescence in situ hybridization (MERFISH) or sequential FISH (seqFISH) for candidate genes
    • Validate regulatory interactions through CRISPR-based perturbations followed by spatial transcriptomics
    • Compare GRN architectures across species or developmental timepoints to identify evolutionary conserved versus divergent regulatory modules

  • Downstream Analysis and Interpretation:

    • Map spatially variable GRN components onto tissue structures
    • Correlate regulatory dynamics with morphological features
    • Construct spatial trajectory analyses to understand regulatory progression during development

The integration of single-cell multi-omics data has revolutionized evolutionary developmental biology (Evo-Devo), enabling researchers to decipher the gene regulatory networks (GRNs) that underlie the emergence of novel traits and morphological diversity. Evo-Devo investigates how changes in embryonic development during single generations relate to evolutionary changes that occur between generations [52]. The field has uncovered that distantly related organisms share conserved genetic toolkits, such as Hox genes, which pattern the anterior-posterior axis in both fruit flies and mice, despite their divergent morphologies [53]. The completion of this workflow enables the identification of cell type-specific regulatory programs and the molecular mechanisms driving evolutionary innovations, such as the loss of eyes in cavefish or the diversification of cichlid jaw structures [54] [52].

This application note provides a detailed protocol for constructing GRNs from single-cell multiome data (paired gene expression and chromatin accessibility), framing the process within the context of Evo-Devo research. The workflow progresses from raw data preprocessing and dimensionality reduction to the final inference of regulatory networks, empowering researchers to explore the evolutionary forces that shape developmental programs.

The following workflow diagram outlines the end-to-end process for inferring gene regulatory networks from single-cell multi-omics data, highlighting the key computational stages.

Materials and Reagents

Research Reagent Solutions

Table 1: Essential reagents and computational tools for single-cell multi-omics GRN inference.

Item Name Function/Application Specifications
10x Genomics Multiome Kit Simultaneous profiling of gene expression and chromatin accessibility in single cells Enables paired scRNA-seq and scATAC-seq from the same cell
SHARE-Seq Protocol Alternative method for co-profiling transcriptome and epigenome Captures histone modifications or open chromatin with RNA
ENCODE Consortium Data Atlas-scale external bulk data for regulatory element annotation Provides diverse cellular contexts for prior knowledge integration
TF Motif Databases Prior knowledge of transcription factor binding specificities Enables linking accessible regions to potential regulators (e.g., JASPAR, CIS-BP)
ChIP-seq Validation Data Ground truth data for benchmarking GRN predictions Curated TF-target interactions for specific cell types
eQTL Datasets (GTEx/eQTLGen) Independent validation of cis-regulatory relationships Links genetic variants to gene expression changes

Methods

Data Preprocessing and Quality Control

Objective: To process raw sequencing data into high-quality count matrices for downstream analysis.

Protocol:

  • Data Demultiplexing and Alignment: Process BAM files from the sequencing facility. Use cellranger-arc (10x Genomics) or a similar pipeline to demultiplex cellular barcodes and align reads to the reference genome.
  • Quality Control and Doublet Detection:
    • Calculate standard QC metrics: total counts per cell, percentage of mitochondrial reads (for scRNA-seq), fraction of fragments in peaks (for scATAC-seq), and nucleosome signal.
    • Employ doublet detection tools (e.g., scDblFinder). Visually inspect QC metrics in a preliminary UMAP to identify and remove low-quality cells or doublets, which often cluster separately [55].
  • Feature Selection: For scRNA-seq data, identify highly variable genes. For scATAC-seq data, select high-confidence peaks or regulatory elements, often focusing on those with high variability or deviation [56].

Dimensionality Reduction and Cell Clustering

Objective: To project high-dimensional data into a low-dimensional space, enabling the identification of cell populations and states.

Protocol:

  • Dimensionality Reduction:
    • Principal Component Analysis (PCA): Perform linear dimensionality reduction on the highly variable features. This is computationally efficient and is often used as an input for downstream nonlinear methods [55] [57].
    • Nonlinear Embedding (UMAP/t-SNE): Construct a neighborhood graph of cells and project it into 2D for visualization. The choice between UMAP and t-SNE involves a trade-off: UMAP better preserves global data structure and is faster, while t-SNE can reveal finer local structures [55]. Tools like SnapATAC2 provide a highly efficient, matrix-free algorithm for nonlinear dimensionality reduction that scales linearly with the number of cells [56].
  • Cell Clustering and Annotation: Cluster cells using algorithms like Leiden or Louvain on the neighborhood graph. Manually annotate cell types based on the expression of known marker genes and the accessibility of cell type-specific regulatory elements.

Gene Regulatory Network Inference

Objective: To infer directional regulatory interactions between transcription factors (TFs), regulatory elements (REs), and target genes (TGs).

Protocol:

  • Select a GRN Inference Method: Choose a method based on the experimental design and biological question. The table below benchmarks state-of-the-art tools.
  • Run GRN Inference: Follow the method-specific protocol. As an example, the protocol for LINGER is detailed here [3]:
    • Input: A count matrix of gene expression, a count matrix of chromatin accessibility, and cell type annotations.
    • External Knowledge Integration: Pre-train a neural network model on atlas-scale external bulk data (e.g., from ENCODE) to learn a general regulatory profile.
    • Model Refinement: Refine the pre-trained model on the single-cell multiome data using Elastic Weight Consolidation (EWC). This applies the knowledge from the bulk data as a Bayesian prior, preventing overfitting to the smaller single-cell dataset.
    • Regulatory Strength Calculation: Use Shapley values from the trained model to infer the strength of TF-TG (trans) and RE-TG (cis) interactions. Infer TF-RE binding strength from the correlation of parameters in the model's hidden layer.

Table 2: Benchmarking of GRN Inference Methods for Single-Cell Multi-omics Data. AUC = Area Under the Receiver Operating Characteristic Curve; AUPR = Area Under the Precision-Recall Curve.

Method Underlying Approach Key Features Reported Performance
LINGER [3] Lifelong Neural Network Incorporates external bulk data via lifelong learning; uses motif matching as manifold regularization 4-7x relative increase in AUC vs. baselines; superior cis-regulatory AUC/AUPR across distance groups
PRISM-GRN [4] Bayesian Model Integrates prior known GRNs with multi-omics data in a probabilistic, biologically interpretable framework Higher precision in sparse, imbalanced true networks; captures causality well
SCENIC+ [3] Machine Learning Infers cis-regulatory interactions and TF activations from multiome data Baseline method for comparison
PCC [58] Correlation (Pearson) Simple, linear co-expression measure Lower performance compared to nonlinear/multi-omic methods

Troubleshooting

The following diagram illustrates the logical flow for diagnosing and resolving common issues in GRN inference.

Application in Evolutionary Developmental Biology

The integration of GRN inference with Evo-Devo questions allows for a mechanistic understanding of evolutionary processes. The workflow below shows how to apply GRN inference to a classic Evo-Devo model.

Blind Cavefish vs Surface Fish Blind Cavefish vs Surface Fish Generate scMulti-omics Data\n(Eye Field Cells) Generate scMulti-omics Data (Eye Field Cells) Blind Cavefish vs Surface Fish->Generate scMulti-omics Data\n(Eye Field Cells) Infer Cell-Type Specific GRNs Infer Cell-Type Specific GRNs Generate scMulti-omics Data\n(Eye Field Cells)->Infer Cell-Type Specific GRNs Compare GRN Architectures Compare GRN Architectures Infer Cell-Type Specific GRNs->Compare GRN Architectures Identify Key TF Drivers of Eye Loss Identify Key TF Drivers of Eye Loss Compare GRN Architectures->Identify Key TF Drivers of Eye Loss Validate with CRISPR Validate with CRISPR Identify Key TF Drivers of Eye Loss->Validate with CRISPR

Case Study: Unveiling the Regulatory Logic of Evolutionary Novelties

  • Identify Drivers of Novel Traits: Apply the GRN workflow to related species with divergent morphological traits. For example, to understand eye loss in the blind cavefish (Astyanax mexicanus), generate multiome data from the developing eye field in both cavefish and surface fish embryos [54]. Inferring and comparing GRNs can reveal which TFs and REs are dysregulated, pinpointing the core regulatory logic behind this evolutionary loss.
  • Trace Regulatory Element Evolution: GRN inference can predict changes in cis-regulation. A predicted change in a RE's activity, even if the TF itself is unchanged, suggests evolutionary tinkering in the regulatory sequence, a common mechanism in Evo-Devo [53]. This can reveal how old genes are co-opted for new functions.
  • Explore Co-option and Novelty: The evolution of snake venom provides a prime example of gene co-option, where genes for ancient physiological functions were recruited into a novel toxic role [54]. GRN inference can help identify the TFs responsible for activating this novel expression program in the venom gland, illustrating how new traits evolve without new genes.

Navigating Computational Challenges: Strategies for Robust and Interpretable GRNs

Overcoming Data Sparsity and the Curse of Dimensionality

In single-cell multi-omics research, particularly in the context of Gene Regulatory Network (GRN) inference for evolutionary developmental biology (EvoDevo), two fundamental computational barriers persistently challenge researchers: data sparsity and the curse of dimensionality (COD). Data sparsity in single-cell RNA sequencing (scRNA-seq) arises from technical limitations where only a fraction (∼1–60%, averaging <10%) of the transcriptome is detected in individual cells, creating numerous "dropout" events where transcripts are missed entirely [59]. Simultaneously, the curse of dimensionality manifests when analyzing high-dimensional data (typically >10,000 genes across thousands of cells), where accumulating technical noise causes detrimental effects including impaired distance metrics, inconsistent statistical results, and broken principal component structures [59] [60]. These challenges collectively obscure true biological signals, complicate the identification of cell types and states, and fundamentally limit our ability to reconstruct accurate GRNs—the very blueprints that explain how inherited developmental programs generate phenotypic diversity across species [43].

For evolutionary developmental biologists, these technical challenges directly impede investigations into how developmental programs evolve through changes in gene expression and regulatory interactions [43]. Overcoming data sparsity and COD is therefore not merely a computational exercise but a prerequisite for understanding the molecular basis of phenotypic diversity.

Quantitative Comparison of Computational Solutions

The following table summarizes key computational methods designed to address data sparsity and the curse of dimensionality in single-cell multi-omics data, with particular relevance to GRN inference in evolutionary developmental biology.

Table 1: Computational Methods for Addressing Data Sparsity and Dimensionality Challenges

Method Primary Function Key Innovation Performance Advantages Applicability to GRN Inference
RECODE [59] [60] Noise reduction for high-dimensional data Resolves COD without dimension reduction; parameter-free Recovers expression of lowly expressed genes; enables precise cell fate transition delineation Improves input data quality for any downstream GRN method
LINGER [3] GRN inference from single-cell multiome data Lifelong learning incorporating atlas-scale external bulk data 4-7x relative increase in accuracy over existing methods; reveals complex GWAS regulatory landscapes Directly infers trans-regulation (TF-TG), cis-regulation (RE-TG), and TF-binding (TF-RE)
GLUE [29] Multi-omics data integration Graph-linked unified embedding with explicit regulatory interactions Superior performance in heterogeneous data; enables triple-omics integration; corrects previous atlas annotations Provides integrated data for GRN inference; directly infers regulatory interactions
PRISM-GRN [4] GRN recovery from multi-omics data Bayesian model incorporating prior knowledge with biologically interpretable architecture Higher precision in sparse regulatory interactions; captures causality; works with unpaired omics data Specifically designed for cell type-specific GRN reconstruction
VIA [61] Trajectory inference in single-cell omics Lazy-teleporting random walks with MCMC refinement Captures complex trajectories (cyclic, disconnected); scalable to >1 million cells; preserves global connectivity Reveals developmental trajectories informing GRN dynamics

Detailed Methodological Protocols

Protocol: RECODE for Resolving the Curse of Dimensionality

Principle: RECODE (Resolution of the Curse of Dimensionality) employs high-dimensional statistical theory to separate technical noise from biological signal without dimension reduction, specifically tailored for scRNA-seq data with Unique Molecular Identifiers (UMIs) [59] [60].

Step-by-Step Procedure:

  • Input Data Preparation: Format UMI count matrix with genes as features and cells as observations. No pre-filtering of lowly expressed genes is required.
  • Noise Modeling: Model technical noise as the difference between observed UMI counts and true RNA counts divided by their total counts, accounting for random sampling noise inherent in scRNA-seq protocols.
  • Variance Normalization: Apply data-driven variance normalization to assess applicability of RECODE to the dataset. Successful normalization predicts method applicability.
  • COD Resolution: Implement RECODE's deterministic algorithm to resolve the three manifestations of COD:
    • COD1 (Loss of Closeness): Corrects impaired distance metrics among neighboring cells/clusters
    • COD2 (Inconsistency of Statistics): Fixes inconsistent contribution rates in PCA and other statistics
    • COD3 (Inconsistency of Principal Components): Recovers true PCA structures obscured by technical noise
  • Output Generation: Generate noise-reduced expression values for all genes, including lowly expressed genes that are typically removed in conventional preprocessing.

Validation Metrics:

  • Assess clustering improvement via Silhouette scores
  • Evaluate preservation of rare cell populations
  • Measure accuracy in recovering known gene expression patterns in developmental time courses

Applications in EvoDevo: RECODE enables precise delineation of closely related cell types in developing tissues, identification of rare transitional cell states during organogenesis, and improved detection of subtle expression differences driving evolutionary innovations [59].

Protocol: LINGER for GRN Inference with External Data Integration

Principle: LINGER (Lifelong Neural Network for Gene Regulation) uses lifelong machine learning to incorporate atlas-scale external bulk data and TF motif knowledge as manifold regularization when inferring GRNs from single-cell multiome data [3].

Step-by-Step Procedure:

  • Data Inputs:
    • Single-cell multiome data (paired gene expression and chromatin accessibility)
    • Cell type annotations
    • External bulk data from diverse cellular contexts (e.g., ENCODE project)
    • Prior knowledge of TF motifs

  • Model Architecture:

    • Implement three-layer neural network to predict target gene expression from TF expression and regulatory element (RE) accessibility
    • Design second layer as weighted sums of TFs and REs, forming regulatory modules guided by TF-RE motif matching

  • Training Protocol:

    • Pre-training: Train neural network model (BulkNN) on external bulk data covering diverse cellular contexts
    • Refinement: Apply Elastic Weight Consolidation (EWC) loss using bulk data parameters as prior, with Fisher information determining parameter deviation magnitude
    • Regularization: Incorporate manifold regularization using TF-RE motif knowledge

  • Regulatory Inference:

    • Calculate regulatory strength of TF-TG and RE-TG interactions using Shapley values to estimate feature contributions
    • Generate TF-RE binding strength from correlation of TF and RE parameters learned in the second layer
    • Construct cell type-specific and cell-level GRNs based on general GRN and cell type-specific profiles

  • Validation:

    • Validate trans-regulatory inferences against ChIP-seq data (ground truth)
    • Assess cis-regulatory inferences using eQTL studies from GTEx and eQTLGen
    • Perform downstream analyses including GWAS enrichment and driver regulator identification

Applications in EvoDevo: LINGER reveals evolutionary changes in GRN architecture underlying phenotypic differences between species, identifies key regulatory drivers in developmental pathways, and elucidates how noncoding variants associated with evolutionary innovations alter gene regulation [3].

Visualization of Computational Workflows

LINGER Workflow for GRN Inference

linger_workflow external_data External Bulk Data (ENCODE) pretrain Pre-training on Bulk Data external_data->pretrain motif_knowledge TF Motif Prior Knowledge motif_knowledge->pretrain multiome_data Single-cell Multiome Data refine Refinement with EWC Regularization multiome_data->refine pretrain->refine inference Regulatory Inference with Shapley Values refine->inference grn_output Cell Type-Specific GRNs inference->grn_output

Integrated Multi-omics Analysis Pipeline

multiomics_pipeline scrna_seq scRNA-seq Data recode RECODE Noise Reduction scrna_seq->recode scatac_seq scATAC-seq Data glue GLUE Multi-omics Integration scatac_seq->glue recode->glue linger LINGER GRN Inference glue->linger prism PRISM-GRN Network Recovery glue->prism via VIA Trajectory Inference glue->via biological_insight Evolutionary Developmental Insights linger->biological_insight prism->biological_insight via->biological_insight

Essential Research Reagent Solutions

Table 2: Key Research Reagents and Computational Resources for Single-Cell Multi-omics GRN Inference

Resource Type Specific Examples Function in Research Application in EvoDevo
Single-cell Multiome Kits 10X Genomics Multiome ATAC + Gene Expression Simultaneous measurement of chromatin accessibility and gene expression in same cell Captures coordinated regulatory changes during evolution of developmental programs
Reference Datasets ENCODE project bulk data [3]; GTEx eQTL data [3] Provides external context for regulatory inference; validation of cis-regulatory predictions Enables comparative analysis of regulatory elements across species
Prior Knowledge Bases TF motif databases; curated ChIP-seq datasets [3] Informs manifold regularization in GRN inference; provides ground truth for validation Identifies conserved and diverged regulatory interactions in evolution
Benchmarking Resources Gold-standard simultaneous omics datasets (SNARE-seq, SHARE-seq) [29] Enables rigorous method validation and performance assessment Establishes confidence in evolutionary inferences from computational predictions
Software Tools LINGER, GLUE, RECODE, PRISM-GRN, VIA [3] [61] [59] Provides specialized algorithms for each step in analytical pipeline Enables comprehensive reconstruction of evolutionary changes in developmental GRNs

Experimental Validation Framework

Protocol: Validating Inferred GRNs in Evolutionary Contexts

Principle: Establish functional validation pipelines to test computational predictions of GRN changes underlying evolutionary innovations in developmental programs [43].

Step-by-Step Procedure:

  • Comparative GRN Mapping:
    • Apply LINGER or PRISM-GRN to single-cell multiome data from related species with divergent phenotypes
    • Identify differentially wired network modules using graph comparison algorithms
    • Prioritize candidate regulatory changes based on network topology and association with phenotypic differences

  • Functional Testing:

    • Design CRISPR-based perturbations of candidate cis-regulatory elements in model systems
    • Assess phenotypic consequences using morphological and molecular readouts
    • Measure expression changes of putative target genes via single-cell RNA sequencing

  • Conservation Analysis:

    • Trace evolutionary trajectories of GRN modules by analyzing intermediate species where available
    • Correlate timing of regulatory changes with fossil evidence of phenotypic evolution
    • Identify conserved network kernels versus evolutionarily flexible peripheral connections

Validation Metrics:

  • Precision and recall against known regulatory interactions from literature
  • Enrichment of GWAS signals in predicted regulatory paths [3]
  • Concordance between predicted and experimentally validated phenotypic effects

The integration of advanced computational methods like LINGER, RECODE, and GLUE represents a transformative approach to overcoming the fundamental challenges of data sparsity and dimensionality in single-cell multi-omics. By leveraging lifelong learning to incorporate external data, resolving COD without discarding biological information, and explicitly modeling regulatory interactions across omics layers, these methods enable unprecedented reconstruction of accurate, cell type-specific GRNs. For evolutionary developmental biology, these capabilities open new avenues for investigating how changes in developmental programs produce phenotypic diversity across species—addressing questions that were previously intractable with conventional approaches. As single-cell technologies continue to advance, generating ever-larger and more complex datasets, the computational frameworks described here will play an increasingly central role in unlocking the regulatory logic of evolutionary innovation.

Mitigating Technical Noise and Batch Effects in Cross-Study Integration

In the field of evolutionary developmental biology, the inference of Gene Regulatory Networks (GRNs) from single-cell multi-omics data represents a pivotal challenge for understanding the molecular mechanisms driving cellular differentiation and lineage specification. Single-cell sequencing technologies enable genome- and epigenome-wide profiling of thousands of individual cells, offering unprecedented biological insights into cellular heterogeneity [62] [31]. However, technical noise and batch effects obscure high-resolution structures, hindering rare-cell-type detection and cross-dataset comparisons essential for robust GRN inference [62]. These artifacts mask subtle biological signals, impair reproducibility, and limit the scope of downstream analyses, particularly when integrating data across multiple experiments or sequencing runs [63]. As the number of single-cell RNA sequencing (scRNA-seq) experiments grows, researchers increasingly combine results across experiments or process cells from the same experiment assayed in separate sequencing runs, gaining cellular throughput at the cost of introducing batch effects [63]. This application note provides a comprehensive framework for mitigating these technical challenges, enabling more accurate GRN inference in single-cell multi-omics studies of evolutionary developmental processes.

Technical Noise and Batch Effects: Characterization and Impact on GRN Inference

Technical noise in single-cell multi-omics data arises from multiple sources, including amplification bias, molecular dropout events, library preparation artifacts, and sequencing depth variations. Batch effects represent systematic technical variations between different experimental batches, sequencing runs, or platforms that are unrelated to biological signals. In the context of GRN inference, these artifacts profoundly impact the accurate reconstruction of regulatory relationships between transcription factors (TFs), cis-regulatory elements (CREs), and their target genes.

Single-cell data are particularly susceptible to these issues due to the inherent sparsity of measurements and the complex nature of multi-omics integration [64]. Technical noise can obscure the covariation patterns between TFs and their target genes that methods like correlation analysis, regression models, and deep learning approaches rely upon for GRN inference [31]. For instance, dropout events in scRNA-seq data can create false negatives in TF-target gene relationships, while batch effects can introduce spurious correlations that lead to incorrect regulatory edge predictions.

Recent benchmarking studies demonstrate that the process of batch correction itself can create measurable artifacts in the data if poorly calibrated [63]. Many published methods alter the data considerably during correction, potentially distorting legitimate biological signals along with technical noise. This highlights the critical need for carefully calibrated noise reduction and batch integration strategies that preserve biologically relevant information while removing technical artifacts.

Comparative Analysis of Noise Reduction and Batch Correction Methods

Performance Evaluation of Batch Correction Methods

A comprehensive evaluation of eight widely used batch correction methods for scRNA-seq data revealed significant variations in their performance and tendency to introduce artifacts [63]. The study employed a novel approach to measure the degree to which methods alter data during batch correction, examining both fine-scale distances between cells and cluster-level effects.

Table 1: Performance Comparison of scRNA-seq Batch Correction Methods

Method Performance Rating Artifact Introduction Recommended for GRN Studies
Harmony Consistently performs well Minimal artifacts Yes
Combat Performs poorly Detectable artifacts No
ComBat-seq Performs poorly Detectable artifacts No
BBKNN Performs poorly Detectable artifacts No
Seurat Performs poorly Detectable artifacts No
MNN Performs poorly Considerable alteration No
SCVI Performs poorly Considerable alteration No
LIGER Performs poorly Considerable alteration No

Among the evaluated methods, Harmony was the only approach that consistently performed well across all testing methodologies without introducing detectable artifacts [63]. Methods including MNN, SCVI, and LIGER performed poorly, often altering the data considerably during the correction process. Combat, ComBat-seq, BBKNN, and Seurat introduced artifacts that could be detected in the testing setup, making them suboptimal choices for preparing data for GRN inference [63].

Advanced Platforms for Comprehensive Noise Reduction

The RECODE platform represents a significant advancement in noise reduction for single-cell data, simultaneously addressing technical noise and batch effects while preserving full-dimensional data [62]. Unlike methods that rely on dimensionality reduction, RECODE maintains the complete feature space, enabling more accurate downstream analyses including GRN inference.

RECODE employs high-dimensional statistics and noise variance stabilizing normalization to comprehensively address technical noise across diverse single-cell modalities [62]. The platform's recent upgrade includes iRECODE, which specifically addresses batch effects while retaining the method's effectiveness for technical noise reduction. This dual capability makes it particularly valuable for cross-study integration in evolutionary developmental biology research, where datasets often originate from multiple laboratories and experimental conditions.

The algorithm underlying RECODE has undergone recent improvements that substantially enhance both accuracy and computational efficiency [62]. The platform has demonstrated effectiveness across multiple single-cell modalities, including single-cell high-throughput chromosome conformation capture (scHi-C) and spatial transcriptomics, making it suitable for comprehensive multi-omics GRN inference studies.

Experimental Protocols for Effective Noise Mitigation

Protocol 1: Batch Effect Correction Using Harmony

Principle: Harmony performs batch correction by iteratively clustering cells and correcting dataset-specific effects within each cluster, effectively integrating datasets while preserving biological heterogeneity.

Materials:

  • scRNA-seq count matrix (cells × genes)
  • Batch annotation metadata
  • Computational environment: R/Python with Harmony installed

Procedure:

  • Data Preprocessing:
    • Normalize raw counts using standard scRNA-seq preprocessing (e.g., SCTransform or log-normalization)
    • Select highly variable genes (2000-5000 genes) for dimensionality reduction
    • Perform PCA on the normalized and scaled data (50 dimensions recommended)

  • Harmony Integration:

    • Input: PCA matrix and batch metadata
    • Set parameters: theta = 2.0 (diversity clustering penalty), lambda = 1.0 (ridge regression penalty)
    • Run Harmony integration with default settings for 10-20 iterations
    • Obtain corrected PCA embeddings

  • Downstream Analysis:

    • Use corrected embeddings for clustering and visualization
    • Project corrected embeddings to gene expression space for GRN inference
    • Validate integration using known biological controls and batch mixing metrics

Validation Metrics:

  • Batch mixing scores (local structure preservation)
  • Biological conservation metrics (cluster purity)
  • Visualization assessment (UMAP/t-SNE)
Protocol 2: Comprehensive Noise Reduction Using RECODE

Principle: RECODE employs high-dimensional statistics to simultaneously reduce technical and batch noise while preserving full-dimensional data structure, enabling more accurate GRN inference from single-cell multi-omics data.

Materials:

  • Single-cell multi-omics data (scRNA-seq, scATAC-seq, or paired multiome data)
  • Batch annotation metadata (for iRECODE)
  • RECODE computational platform

Procedure:

  • Data Preparation:
    • Format input data as count matrices for each modality
    • Annotate batches and experimental conditions
    • Pre-filter low-quality cells and genes

  • RECODE Application:

    • For technical noise reduction: Apply RECODE with default parameters
    • For combined technical and batch noise: Apply iRECODE function
    • Set noise characterization parameters based on data quality metrics
    • Run stabilization algorithm until convergence

  • Output Processing:

    • Obtain denoised count matrices for each modality
    • Preserve full feature dimensions for downstream GRN inference
    • Validate noise reduction using spike-in controls or biological replicates

Integration with GRN Inference:

  • Use denoised expression and accessibility matrices as input to GRN methods
  • Apply LINGER or similar multi-omics GRN inference frameworks
  • Validate network predictions using orthogonal data (e.g., ChIP-seq, motif databases)
Protocol 3: External Data Integration with LINGER for Enhanced GRN Inference

Principle: LINGER (Lifelong neural network for gene regulation) incorporates atlas-scale external bulk data across diverse cellular contexts and prior knowledge of transcription factor motifs as manifold regularization, significantly improving GRN inference accuracy from single-cell multiome data.

Materials:

  • Single-cell multiome data (paired gene expression and chromatin accessibility)
  • Atlas-scale external bulk data (e.g., ENCODE project resources)
  • TF motif databases and prior knowledge bases
  • LINGER computational framework

Procedure:

  • Data Preparation:
    • Process single-cell multiome data to generate count matrices for RNA and ATAC
    • Perform cell-type annotation and quality control
    • Curate external bulk data covering diverse cellular contexts

  • Model Pre-training:

    • Pre-train neural network model (BulkNN) using external bulk data
    • Incorporate TF-RE motif matching as manifold regularization
    • Establish initial parameter priors based on bulk data knowledge

  • Model Refinement:

    • Apply elastic weight consolidation (EWC) loss using bulk data parameters as prior
    • Refine model on single-cell data with Fisher information-guided parameter deviation
    • Update posterior distribution combining prior knowledge with single-cell data likelihood

  • GRN Inference:

    • Extract regulatory strengths using Shapley value analysis
    • Construct cell population GRN, cell-type-specific GRNs, and cell-level GRNs
    • Infer TF-TG trans-regulation, RE-TG cis-regulation, and TF-RE binding interactions

Validation:

  • Compare predictions to ChIP-seq ground truth data
  • Assess cis-regulatory consistency with eQTL studies
  • Evaluate biological relevance in developmental contexts

Visualization of Noise Mitigation Workflows

Workflow for Cross-Study GRN Inference

G cluster_0 Noise Mitigation & Batch Correction RawData Raw Single-cell Multi-omics Data QC Quality Control & Filtering RawData->QC BatchInfo Batch Metadata BatchInfo->QC Norm Data Normalization QC->Norm Harmony Harmony Batch Correction Norm->Harmony RECODE RECODE/iRECODE Noise Reduction Harmony->RECODE Harmony->RECODE LINGER LINGER GRN Inference with Lifelong Learning RECODE->LINGER ExternalData External Bulk Data (ENCODE, etc.) ExternalData->LINGER GRN Cell Type-Specific GRNs LINGER->GRN Validation Experimental Validation GRN->Validation

The Scientist's Toolkit: Essential Research Reagents and Computational Solutions

Table 2: Key Research Reagent Solutions for Noise-Robust GRN Inference

Item Function/Application Implementation Notes
Harmony Algorithm Batch effect correction for scRNA-seq data Only method consistently performing without artifacts in benchmarks [63]
RECODE/iRECODE Platform Simultaneous technical and batch noise reduction Preserves full-dimensional data; applicable to diverse single-cell modalities [62]
LINGER Framework GRN inference with external data integration Achieves 4-7x relative accuracy increase over existing methods [3]
ENCODE Bulk Data Resources External reference for lifelong learning Provides diverse cellular contexts for regularization [3]
TF Motif Databases Prior knowledge for manifold regularization Enriches TF-RE connections in regulatory modules [3]
ChIP-seq Validation Sets Ground truth for trans-regulatory assessment Essential for benchmarking GRN inference accuracy [3]
eQTL Resources (GTEx, eQTLGen) Cis-regulatory validation Enables assessment of RE-TG linkage accuracy [3]
CPI-637CPI-637, MF:C22H22N6O, MW:386.4 g/molChemical Reagent
CPUY201112CPUY201112: Potent HSP90 Inhibitor for Research

Effective mitigation of technical noise and batch effects is paramount for accurate GRN inference from single-cell multi-omics data in evolutionary developmental biology research. The integration of robust computational approaches—specifically Harmony for batch correction, RECODE for comprehensive noise reduction, and LINGER for leveraging external data resources—enables researchers to overcome the significant challenges posed by technical variability. The protocols outlined in this application note provide a structured framework for implementing these advanced methods, facilitating more reliable identification of regulatory mechanisms driving developmental processes across diverse cellular contexts and experimental conditions. As single-cell technologies continue to evolve, these noise mitigation strategies will become increasingly essential for unlocking the full potential of multi-omics data in deciphering the complex regulatory networks that underlie evolutionary developmental processes.

Gene regulatory networks (GRNs) represent the complex web of interactions between transcription factors, cis-regulatory elements, and their target genes that control developmental processes and evolutionary changes [43] [65]. The emergence of single-cell multi-omics technologies has revolutionized evolutionary developmental biology (EvoDevo) by enabling simultaneous profiling of chromatin accessibility, gene expression, and epigenetic modifications in individual cells [66] [58]. However, the computational frameworks developed to reconstruct GRNs from these data—particularly deep learning models—increasingly resemble "black boxes" that offer limited biological insight into their decision-making processes [67] [68] [69].

This model interpretability gap presents a significant challenge for researchers seeking to understand the molecular mechanisms underlying phenotypic evolution. As GRN inference methods grow in complexity, including transformer-based architectures and foundation models trained on millions of single-cell datasets [68], the need for Explainable AI (XAI) techniques becomes increasingly critical. This Application Note provides detailed protocols for applying SHAP and other XAI methods to enhance the biological interpretability of GRN models in evolutionary developmental studies, enabling researchers to bridge the gap between predictive accuracy and mechanistic understanding.

Foundations of GRN Inference in Evolutionary Developmental Biology

The GRN Concept in Evolutionary Trajectories

Gene regulatory networks represent the molecular infrastructure that transforms genotypic variations into phenotypic diversity through development. The GRN concept posits that developmental programs exhibit a fundamentally network-like structure, with genetically encoded components linked by recursive regulatory interactions [43]. From an evolutionary perspective, changes to GRN architecture—including gene duplications, cis-regulatory modifications, and network co-option—drive the emergence of novel traits across evolutionary timescales [44] [70].

In insects, for example, GRN evolution underpins diverse morphological adaptations. Studies in Drosophila species have demonstrated that changes in cis-regulatory regions can lead to new trait acquisition by altering network connectivity, while butterfly wing patterns emerge through co-option processes that reshape color pattern GRNs [70]. The Nodal signaling pathway governing body axis formation in deuterostomes represents another well-characterized example, where GRN rewiring through enhancer hijacking events has altered developmental programs in cephalochordate amphioxus while maintaining functional output [44].

Methodological Foundations for GRN Inference

Modern GRN inference leverages diverse mathematical frameworks to reconstruct regulatory relationships from single-cell multi-omic data [58]. The table below summarizes the primary computational approaches:

Table 1: Methodological Foundations for GRN Inference

Approach Underlying Principle Strengths Limitations
Correlation-based Guilt-by-association through co-expression Simple implementation; captures linear and non-linear associations Cannot distinguish direct vs. indirect regulation; directionality challenges
Regression models Predicts gene expression from TF expression/accessibility Interpretable coefficients; handles multiple predictors Overfitting with many predictors; correlated predictors cause instability
Probabilistic models Graphical models capturing dependence between variables Uncertainty quantification; handles noise effectively Distributional assumptions may not hold for all genes
Dynamical systems Models system behavior evolving over time Captures temporal dynamics; interpretable parameters Computationally intensive; requires time-series data
Deep learning Artificial neural networks learning complex patterns Captures non-linear interactions; high predictive power "Black box" nature; extensive data requirements

Single-cell multi-omics technologies have been particularly transformative for GRN inference, with methods like SHARE-seq and 10x Multiome enabling simultaneous profiling of chromatin accessibility and gene expression in individual cells [58]. These advances have spurred development of sophisticated GRN inference tools including SCENIC+ [65], HALO [66], and Pando [65] that integrate multiple data modalities to reconstruct enhancer-driven regulatory networks.

Explainable AI Techniques for GRN Interpretation

SHAP (SHapley Additive exPlanations) for Feature Importance

SHAP values originate from cooperative game theory and provide a unified approach to feature importance attribution by measuring the marginal contribution of each feature to the model's prediction across all possible feature combinations.

Protocol 3.1.1: SHAP Analysis for Transcription Factor Importance

  • Purpose: To quantify the contribution of individual transcription factors to gene expression predictions in GRN models.
  • Input Requirements:
    • Trained GRN model (e.g., neural network, gradient boosting machine)
    • Preprocessed single-cell multi-omics data (scRNA-seq + scATAC-seq)
    • TF-binding predictions from motif databases (e.g., CIS-BP, JASPAR)
  • Procedure:
    • Model Preparation: Extract gene expression predictions for key developmental marker genes (e.g., Alx3 for stripe patterning) from your GRN model.
    • Background Distribution: Select a representative subset of cells (typically 100-500) to establish baseline prediction values.
    • SHAP Value Calculation: For each cell and target gene, compute SHAP values using either:
      • KernelSHAP (model-agnostic)
      • TreeSHAP (for tree-based models)
      • DeepSHAP (for deep learning models)
    • Result Interpretation:
      • Generate summary plots showing global feature importance across all cells
      • Create force plots for specific cell states to visualize local explanations
      • Plot SHAP dependence plots to reveal interaction effects between TFs
  • Technical Notes:
    • Computational demands scale exponentially with feature count; pre-filter TFs using prior biological knowledge
    • For single-cell data, consider aggregating SHAP values by cell type or developmental stage
    • Combine with motif enrichment analysis to validate biological relevance

Model-Specific Interpretability Techniques

Different GRN inference architectures require specialized XAI approaches:

Protocol 3.2.1: Attention Mechanism Analysis in Transformer Models

  • Purpose: To interpret regulatory relationships learned by transformer-based single-cell foundation models [68].
  • Procedure:
    • Extract attention weights from all layers and heads of the transformer architecture
    • Compute average attention from the [CLS] token to gene tokens across cell types
    • Identify consistently high-attention gene pairs across developmental trajectories
    • Validate high-attention regulatory relationships using orthogonal data (e.g., ChIP-seq, STARR-seq)
  • Output: Attention maps visualizing gene-gene regulatory priorities across cell states.

Protocol 3.2.2: Integrated Gradients for Deep Neural Networks

  • Purpose: To attribute predictions of deep learning GRN models to input features.
  • Procedure:
    • Select baseline input (e.g., zero expression or population mean)
    • Interpolate between baseline and actual input along straight path
    • Compute gradients of model predictions with respect to inputs
    • Accumulate gradients along interpolation path
  • Application: Particularly effective for interpreting VAE-based architectures like MIDAA [71].

Benchmarking XAI Performance in Biological Context

Evaluating XAI method effectiveness requires biological ground truth data:

Table 2: XAI Validation Framework for GRN Inference

Validation Method Application Interpretation
Recovery of known regulatory interactions Compare top explanations against literature-curated gold standards (e.g., TRRUST, RegNetwork) Higher precision indicates better biological relevance
Enrichment of ChIP-seq supported interactions Test if high-attribution TF-gene pairs show experimental binding support Validates mechanistic plausibility of explanations
Stability across cell types Assess consistency of explanations across related cell states Robust explanations should show gradual changes along differentiation trajectories
Conservation across species Compare explanatory features in orthologous GRNs Evolutionarily conserved explanations suggest functional importance

Integrated Workflow: XAI for Evolutionary GRN Analysis

The following diagram illustrates the comprehensive workflow for applying XAI techniques to GRN inference in evolutionary developmental biology:

G clusterXAI XAI Techniques clusterValidation Validation Approaches Start Input: Single-cell Multi-omics Data DataProcessing Data Preprocessing & Feature Selection Start->DataProcessing GRNInference GRN Model Inference (SCENIC+, HALO, Pando) DataProcessing->GRNInference XAIAnalysis XAI Application (SHAP, Attention, IG) GRNInference->XAIAnalysis SHAP SHAP Analysis (Feature Importance) XAIAnalysis->SHAP Attention Attention Mechanisms (Transformer Models) XAIAnalysis->Attention IG Integrated Gradients (Deep Networks) XAIAnalysis->IG LRP Layer-wise Relevance Propagation XAIAnalysis->LRP BioValidation Biological Validation & Interpretation ChipSeq ChIP-seq/STARR-seq Validation BioValidation->ChipSeq Perturbation Genetic Perturbation Analysis BioValidation->Perturbation CrossSpecies Cross-species Conservation BioValidation->CrossSpecies FunctionalAssay Functional Enhancer Assays BioValidation->FunctionalAssay EvoDevoInsights Evolutionary Hypotheses & Mechanistic Insights SHAP->BioValidation Attention->BioValidation IG->BioValidation LRP->BioValidation ChipSeq->EvoDevoInsights Perturbation->EvoDevoInsights CrossSpecies->EvoDevoInsights FunctionalAssay->EvoDevoInsights

Diagram 1: Integrated XAI-GRN Workflow for EvoDevo Research

Research Reagent Solutions for XAI-GRN Studies

Table 3: Essential Research Reagents and Computational Tools

Category Specific Tools/Databases Application in XAI-GRN Studies
GRN Inference Methods SCENIC+ [65], HALO [66], Pando [65], CellOracle [65] Base models for regulatory network reconstruction from single-cell multi-omics data
XAI Libraries SHAP, Captum, LRP, Transformers Interpret Model interpretation and feature importance attribution
Motif & Annotation Databases CIS-BP, JASPAR, UniBind [65], pycisTarget [65] TF-binding site information for validating regulatory predictions
Single-cell Multi-omics Platforms 10x Genomics Multiome, SHARE-seq [58] Experimental data generation for model training and validation
Validation Datasets ENCODE ChIP-seq, SCREEN enhancer annotations [65] Ground truth data for benchmarking XAI explanations
Specialized Architectures MIDAA [71], Pathway-Guided Interpretable DL [69] Knowledge-guided models with inherent interpretability features

Case Study: Applying SHAP to Analyze GRN Rewiring in Amphioxus Axis Formation

Biological Context

The Nodal signaling pathway governing body axis formation exhibits substantial GRN rewiring in cephalochordate amphioxus compared to other deuterostomes [44]. While the core function in dorsal-ventral and left-right patterning is conserved, the network architecture has undergone significant modification, including:

  • Translocation and neofunctionalization of Gdf1/3-like gene
  • Altered maternal versus zygotic expression patterns
  • Enhancer hijacking events between Gdf1/3-like and Lefty

Protocol: XAI-Enhanced GRN Comparison

Protocol 6.2.1: Comparative GRN Analysis with SHAP

  • Purpose: To identify the most influential regulatory differences driving GRN evolution in amphioxus axis formation.
  • Procedure:
    • Model Training:
      • Construct GRN models for amphioxus and vertebrate Nodal signaling using SCENIC+
      • Train separate models on single-cell multi-omics data from comparable developmental stages
    • SHAP Analysis:
      • Compute SHAP values for all TFs in both networks
      • Identify TFs with largest differential importance between species
      • Focus on Gdf1/3-like, Nodal, and Lefty regulatory connections
    • Validation:
      • Compare high-SHAP-value regulatory connections with experimental mutant phenotypes [44]
      • Test predicted enhancer elements using transgenic reporter assays
  • Expected Output: Quantitative assessment of regulatory rewiring events, prioritizing key TFs for functional validation.

The following diagram illustrates the specific GRN rewiring in amphioxus and how XAI techniques pinpoint key evolutionary changes:

G AncestralGRN Ancestral Deuterostome GRN MaternalGdf Maternal Gdf1/3 AncestralGRN->MaternalGdf ZygoticNodal Zygotic Nodal AncestralGRN->ZygoticNodal LeftyAncestral Lefty AncestralGRN->LeftyAncestral XAIAnalysis XAI Analysis (SHAP, Attention) AncestralGRN->XAIAnalysis Comparative Analysis AxisFormation Body Axis Formation MaternalGdf->AxisFormation Synergistic activation ZygoticNodal->AxisFormation LeftyAncestral->AxisFormation Feedback inhibition AmphioxusGRN Amphioxus GRN (Rewired) MaternalNodal Maternal Nodal* AmphioxusGRN->MaternalNodal GdfLike Gdf1/3-like* AmphioxusGRN->GdfLike LeftyAmphioxus Lefty AmphioxusGRN->LeftyAmphioxus AmphioxusGRN->XAIAnalysis MaternalNodal->AxisFormation Compensatory function GdfLike->AxisFormation Novel role SharedEnhancer Shared Enhancer Region GdfLike->SharedEnhancer LeftyAmphioxus->SharedEnhancer SharedEnhancer->AxisFormation Co-regulation KeyInsights Key Evolutionary Changes: - Maternal Nodal compensation - Gdf1/3-like enhancer hijacking - Network redundancy reduction XAIAnalysis->KeyInsights

Diagram 2: XAI-Powered Analysis of GRN Rewiring in Amphioxus

Implementation Considerations and Best Practices

The application of XAI techniques to single-cell multi-omics data presents significant computational challenges. For large-scale atlas studies encompassing millions of cells, we recommend:

  • Strategic Subsampling: Apply XAI methods to representative subsets followed by full-dataset validation
  • GPU Acceleration: Leverage GPU-compatible implementations (e.g., PyTorch-based SHAP) [71]
  • Hierarchical Interpretation: Implement multi-resolution analysis from individual cells to cell-type aggregates

Biological Validation Framework

Interpretable AI outputs must undergo rigorous biological validation:

Protocol 7.2.1: Functional Validation of XAI-Generated Hypotheses

  • CRISPR-based Enhancer Validation:
    • Design sgRNAs targeting high-SHAP-value regulatory regions
    • Perform CRISPRi/F in relevant cell models
    • Measure expression changes in putative target genes
  • Cross-species Conservation Analysis:
    • Compare explanatory features across orthologous GRNs
    • Test if evolutionarily conserved regulatory connections receive higher importance scores
    • Assess whether species-specific innovations are correctly identified
  • Integration with Experimental Perturbation Data:
    • Compare XAI outputs with genetic perturbation effects (CRISPR screens)
    • Validate predicted master regulators through knockout experiments

Avoiding Common Pitfalls

  • Technical Artifacts: Normalize for technical confounders (batch effects, sequencing depth) before interpretation
  • Context Specificity: Remember that explanations are model-specific; validate across multiple GRN inference methods
  • Biological Plausibility: Ground interpretations in established biological knowledge while remaining open to novel discoveries

The integration of Explainable AI techniques with single-cell multi-omic GRN inference represents a powerful approach for advancing evolutionary developmental biology. By applying the protocols and frameworks outlined in this Application Note, researchers can transform black-box predictions into testable biological hypotheses about the regulatory mechanisms underlying phenotypic diversity. As single-cell technologies continue to evolve and foundation models grow in sophistication [68], the principles of interpretability and biological validation will remain essential for extracting meaningful insights from complex computational models.

Best Practices for Feature Selection and Handling Non-Linear Relationships

In evolutionary developmental biology (EvoDevo), the core objective is to unravel the molecular basis of phenotypic diversity by understanding the gene regulatory networks (GRNs) that control embryonic development [43]. A GRN is a network-like structure where genes (nodes) interact through their expressed products (edges) to control developmental programs [43]. The evolution of developmental programs occurs largely through changes in the connectivity and composition of these GRNs [43].

The advent of single-cell multi-omics technologies presents both an unprecedented opportunity and a significant challenge for GRN inference. Researchers can now simultaneously measure multiple molecular modalities—such as gene expression (scRNA-seq), chromatin accessibility (scATAC-seq), and DNA methylation—from individual cells [29]. This multi-dimensional view is essential because regulatory processes are too complex to reliably model with transcriptomic data alone [17]. However, this richness introduces the critical challenge of feature selection: identifying which molecular features among thousands are most biologically relevant for reconstructing accurate GRNs, particularly when these features interact through complex, non-linear relationships.

Effective feature selection is not merely a technical preprocessing step; it is foundational to generating biologically meaningful GRN models that can reveal how developmental programs evolve. This Application Note provides structured protocols and best practices to navigate this complex analytical landscape.

Feature selection techniques are broadly categorized into three groups, each with distinct advantages, limitations, and suitability for single-cell multi-omics data [72].

Table 1: Categories of Feature Selection Techniques

Method Category Core Principle Key Advantages Common Techniques Suitability for Multi-omics GRN Inference
Filter Methods Selects features based on statistical measures (e.g., correlation) independent of the model [72]. • Computationally fast and efficient• Model-agnostic• Easy to implement [72] Correlation criteria, Chi-square tests [72] Pre-filtering: Useful for initial, rapid reduction of feature space dimensionality before more sophisticated analysis.
Wrapper Methods Uses a predictive model to evaluate different feature subsets based on their performance [72]. • Model-specific optimization• Can capture feature interactions [72] Recursive Feature Elimination (RFE), Forward/Backward Selection [72] Limited use: Often computationally prohibitive for the vast number of features in single-cell data.
Embedded Methods Performs feature selection as an integral part of the model training process [72]. • Balances efficiency and effectiveness• Model-specific learning [72] LASSO (ℓ1-norm), Elastic Net, tree-based importance [72] [73] High: Efficiently handles high-dimensionality and can be tailored to specific GRN inference algorithms.

For single-cell multi-omics, embedded methods are often most practical due to their ability to handle high dimensionality without the computational burden of wrapper methods. Furthermore, specialized non-linear feature selection networks have been developed that use â„“2,p-norm regularization within neural networks to select discriminative feature subsets while capturing non-linear structure, which is crucial for complex biological data [73].

The following protocols outline a streamlined workflow for feature selection and GRN inference in a single-cell multi-omics context.

Protocol 1: Feature Selection for Transcriptomics-Based GRN Inference

This protocol uses SCENIC++, a widely adopted tool for inferring GRNs from single-cell transcriptomics data [17].

1. Input Data Preparation:

  • Input: A filtered single-cell RNA-seq count matrix (cells x genes).
  • Preparation: Normalize and log-transform the count matrix. Create a loom file object for use with SCENIC.

2. Co-expression Module Inference:

  • Gene Filtering: Filter out lowly expressed genes to reduce noise.
  • Co-expression Network: Run a correlation analysis and GENIE3 to infer potential regulatory relationships between Transcription Factors (TFs) and target genes based on co-expression [17].

3. Regulon Construction & Scoring:

  • Regulon Formation: Refine the co-expression modules using cis-regulatory motif analysis to identify direct targets of TFs, forming "regulons."
  • Cellular Activity: Score the activity of each regulon in each individual cell using AUCell [17].

4. Output & Analysis:

  • Output: A binary activity matrix for regulons across cells and a list of regulated target genes for each TF.
  • Downstream Analysis: Identify cell-type specific regulators using Regulatory Specificity Score (RSS) and visualize results.

G Start Input: scRNA-seq Count Matrix Norm Normalize & Log-Transform Start->Norm Filter Filter Lowly Expressed Genes Norm->Filter CoExp Infer Co-expression Modules (GENIE3) Filter->CoExp Regulon Refine with Motif Analysis (cisTarget) CoExp->Regulon Score Score Regulon Activity (AUCell) Regulon->Score End Output: GRN & Cell Regulon Activity Score->End

Diagram 1: SCENIC workflow for GRN inference from scRNA-seq.

Protocol 2: Multi-Omics Integration and Feature Selection with GLUE

For a more robust GRN inference that incorporates multiple data modalities, the GLUE (Graph-Linked Unified Embedding) framework is recommended [29].

1. Data & Guidance Graph Preparation:

  • Inputs: Unpaired data from multiple omics layers (e.g., scRNA-seq, scATAC-seq).
  • Guidance Graph: Construct a prior knowledge graph linking features across modalities (e.g., connect an ATAC-seq peak to a gene if it overlaps the gene's promoter or body). This graph explicitly models regulatory interactions [29].

2. Model Initialization & Training:

  • Modality-Specific Autoencoders: Initialize a separate variational autoencoder for each omics layer, tailored to its specific feature distribution.
  • Adversarial Alignment: Train the model using an iterative procedure that aligns the cell embeddings from different modalities in a shared latent space, guided by the feature embeddings from the guidance graph [29].

3. Iterative Optimization & Inference:

  • Alignment: The process converges when cell states are accurately aligned across modalities.
  • Regulatory Inference: The model outputs integrated cell embeddings and a refined, data-oriented graph of regulatory interactions, providing a multi-omics GRN [29].

4. Batch Effect Correction (Optional):

  • Application: If batch effects are present, enable the batch correction covariate in the GLUE decoders to prevent over-correction and ensure valid integration [29].

G SubGraph1 Input Data scRNA-seq Genes scATAC-seq Peaks Autoencoder Modality-Specific Autoencoders SubGraph1->Autoencoder SubGraph2 Guidance Graph (Prior Knowledge) Links features across modalities Alignment Adversarial Multimodal Alignment SubGraph2->Alignment Autoencoder->Alignment Output Integrated Cell Embeddings & Refined Regulatory Graph Alignment->Output

Diagram 2: Multi-omics GRN inference with GLUE framework.

The Scientist's Toolkit: Essential Reagents & Computational Tools

Table 2: Key Research Reagent Solutions for Single-Cell Multi-Omics

Item / Tool Name Function / Application Relevant Assay
10X Multiome Kit Enables simultaneous measurement of gene expression and chromatin accessibility from the same single cell. scRNA-seq + scATAC-seq [29]
SHARE-Seq A high-throughput method for jointly profiling gene expression and chromatin accessibility. scRNA-seq + scATAC-seq [29]
snmC-seq Measures DNA methylation at single-cell resolution. scMethyl-seq [29]
CisTarget Databases Databases of evolutionarily conserved transcription factor binding motifs used for regulon refinement. SCENIC/SCENIC+ [17]
GLUE Framework A modular computational framework for integrating unpaired multi-omics data and inferring regulatory interactions. Multi-omics Integration & GRN Inference [29]
CrenigacestatCrenigacestat, CAS:1421438-81-4, MF:C22H23F3N4O4, MW:464.4 g/molChemical Reagent

Table 3: Computational Tools for GRN Inference and Feature Selection

Tool Name Primary Input Data Feature Selection & Modelling Approach Key Feature
SCENIC+ scRNA-seq (and integrated scATAC-seq) Linear modeling; signed, weighted interactions [17] Infers enhancer-driven gene regulatory networks.
GLUE Unpaired multi-omics (e.g., RNA, ATAC) Non-linear; weighted interactions; uses a guidance graph [29] [17] Explicitly models interactions across omics layers.
CellOracle scRNA-seq (and unpaired scATAC-seq) Linear; signed, weighted interactions [17] Models the effect of in-silico perturbations on cell identity.
Pando Paired or integrated multi-omics Linear or non-linear; signed, weighted interactions [17] Utilizes a flexible generalized linear model framework.
NFSN General feature selection Non-linear neural network with â„“2,p-norm regularization [73] Jointly performs non-linear feature selection and regression.

Concluding Remarks

In the context of EvoDevo, where the goal is to trace the evolutionary history and rewiring of GRNs—as exemplified by the shift in the Nodal signaling network in amphioxus [44]—rigorous feature selection is not optional. It is the critical step that determines whether inferred networks reflect biological reality or technical artifact.

The protocols and tools outlined here provide a pathway to robust GRN inference. Starting with a well-defined biological question, researchers should:

  • Choose a feature selection strategy commensurate with their data type and computational resources, prioritizing embedded or non-linear methods for complex multi-omics data.
  • Select a GRN inference tool that aligns with their available omics data, leveraging multi-omics integration frameworks like GLUE for a more complete and accurate picture.
  • Validate predictions through experimental follow-up, such as CRISPR mutagenesis, to test the functional role of predicted regulatory nodes and edges, thereby closing the loop between computation and biological insight [43] [44]. By adhering to these best practices, researchers can reliably decode the regulatory logic of development and its evolution.

Inference of Gene Regulatory Networks (GRNs) from single-cell multi-omics data represents a cornerstone of modern evolutionary developmental biology (evo-devo) research, enabling the dissection of molecular circuits that orchestrate cell fate decisions, differentiation trajectories, and evolutionary adaptations. However, this field grapples with significant methodological limitations that compromise biological validity. High rates of false positives and negatives obscure true regulatory interactions, while scalability issues hinder application to the massive datasets now generated. Furthermore, a critical gap exists in dynamic network inference across pseudo-temporal trajectories, which is essential for understanding developmental processes. This Application Note synthesizes recent computational advances that directly address these bottlenecks, providing validated protocols and reagent solutions to empower researchers in constructing more accurate, scalable, and dynamic GRN models from complex single-cell data.

Quantitative Benchmarking of Contemporary GRN Inference Methods

The performance of GRN inference methods is typically evaluated using Area Under the Receiver Operating Characteristic Curve (AUROC) and Area Under the Precision-Recall Curve (AUPRC). The following table summarizes the reported performance of several recently developed methods on benchmark datasets.

Table 1: Performance Metrics of Recent GRN Inference Methods

Method Core Innovation Reported Performance (AUROC/AUPRC) Key Application Context
inferCSN [74] Cell state-specific networks via pseudo-temporal windowing Outperformed GENIE3, SINCERITIES, PPCOR, and LEAP on simulated datasets (BF, CY, LI, LL) Robust to dataset type and scale; ideal for analyzing T-cell states and tumor subclones
DAZZLE [75] Dropout Augmentation for model regularization Shows improved performance and increased stability over baseline models (e.g., DeepSEM) Handles zero-inflation in large datasets (>15,000 genes) with minimal gene filtration
MultiGNN [76] Supervised GNN using multi-omics features Consistently outperformed other methods across seven different datasets Effectively integrates scRNA-seq and scATAC-seq to reduce false positives
scMKL [21] Multiple Kernel Learning for interpretable integration Statistically significant (p<0.001) superior AUROC vs. MLP, XGBoost, SVM on multiple cancer datasets Identifies key pathways and TF binding sites in breast, prostate, and lung cancer

Experimental Protocols for Advanced GRN Inference

Protocol: Constructing State-Specific GRNs with inferCSN

This protocol details the procedure for inferring gene regulatory networks that are specific to cell type and state using single-cell RNA-seq data, based on the inferCSN method [74].

Primary Application in Evo-Devo: Uncovering dynamic rewiring of regulatory networks across developmental pseudo-time.

Input Requirements:

  • A pre-processed scRNA-seq count matrix (cells x genes).
  • Cell type annotations (optional but recommended).

Procedure:

  • Data Preprocessing: Filter cells and genes based on quality control metrics (e.g., mitochondrial counts, number of features). Normalize and log-transform the count matrix.
  • Pseudo-time Inference: Calculate pseudo-temporal ordering of cells using a tool like Monocle or RNA velocity. This orders cells along a continuum representing a biological process like differentiation.
  • Cell State Windowing:
    • Analyze the density distribution of cells along the inferred pseudo-time.
    • Identify natural transition points (troughs in density) between cell states.
    • Partition all cells into multiple consecutive windows based on these transition points to mitigate density bias.
  • Network Construction per Window: For each window, apply a sparse regression model with L0 and L2 regularization. This model predicts the expression of each target gene based on the expression of potential regulators, inferring the network topology.
  • Network Calibration: Use a reference network (e.g., from a public database of known interactions) to calibrate the inferred, state-specific GRN for each window, improving accuracy.

Troubleshooting Tip: If the pseudo-time trajectory is inaccurate, the resulting state-specific networks will be confounded. Validate the trajectory using known marker genes.

Protocol: Multi-Omic GRN Inference with MultiGNN

This protocol describes a supervised learning framework, MultiGNN, that integrates scRNA-seq and scATAC-seq data to infer GRNs with improved distinction between direct and indirect regulations [76].

Primary Application in Evo-Devo: Identifying conserved, direct transcriptional regulation across species by integrating chromatin accessibility.

Input Requirements:

  • A scRNA-seq count matrix (cells x genes).
  • A scATAC-seq peak matrix (cells x peaks).
  • A prior, potentially incomplete GRN (e.g., from a database like STRING) for supervised learning.

Procedure:

  • Data Preprocessing:
    • Perform standard quality control on both scRNA-seq and scATAC-seq matrices independently using a tool like Seurat.
    • Select highly variable genes from the RNA matrix.
  • Regulatory Potential Calculation: Transform the scATAC-seq peak matrix into a gene-level "regulatory potential" matrix. This is done by summing the accessibility of all peaks near a gene's transcriptional start site, weighted by their genomic distance.
  • Feature Integration with Graph Neural Networks:
    • Construct an initial graph where nodes are genes/TFs and edges are from the prior network.
    • Use two separate Graph Convolutional Network (GCN) encoders: one processes the gene expression matrix, and the other processes the gene regulatory potential matrix.
    • The outputs of both GCNs are fused to create a unified node representation matrix that captures both transcriptional and epigenomic information.
  • Link Prediction: Feed the unified node representations into a Multi-Layer Perceptron (MLP) to predict the probability of a regulatory link (edge) between every TF-target gene pair.

Troubleshooting Tip: The performance of MultiGNN is dependent on the quality of the prior network. Use the most context-specific prior available for your biological system.

Protocol: Mitigating Dropout Effects with DAZZLE

This protocol utilizes DAZZLE, a method that enhances GRN inference robustness against the high dropout (zero-inflation) noise characteristic of scRNA-seq data [75].

Primary Application in Evo-Devo: Achieving reliable network inference from datasets with challenging signal-to-noise ratios, such as those from early embryonic stages or rare cell types.

Input Requirements:

  • A scRNA-seq count matrix (cells x genes).

Procedure:

  • Data Transformation: Transform the raw count matrix using ( log(x+1) ) to stabilize variance.
  • Dropout Augmentation (DA): During each training iteration, randomly select a small proportion of non-zero expression values and artificially set them to zero. This simulates additional dropout events, teaching the model to be resilient to such noise.
  • Model Training with an Autoencoder:
    • Employ a Variational Autoencoder (VAE) framework where the adjacency matrix of the GRN is a trainable parameter.
    • The model is trained to reconstruct its input, and the trained adjacency matrix is the inferred GRN.
    • Include a noise classifier within the model to identify which zeros are likely technical dropouts, further improving reconstruction.
  • Stabilized Sparsity Control: Introduce a sparsity-inducing loss term only after the initial phases of model training to prevent premature over-regularization and improve the stability of the final network.

Troubleshooting Tip: The proportion of values to augment with zeros is a key parameter. Start with a low value (e.g., 1-5%) and adjust based on the observed dropout rate in your data.

D DAZZLE Workflow Input scRNA-seq Count Matrix LogXform log(x+1) Transformation Input->LogXform DA Dropout Augmentation (Artificially zero values) LogXform->DA VAE VAE Training with Sparsity Control DA->VAE Output Inferred GRN (Adjacency Matrix) VAE->Output

The Scientist's Toolkit: Research Reagent Solutions

Table 2: Essential Computational Tools and Resources for Single-Cell Multi-omics GRN Inference

Resource Name Type Primary Function in GRN Inference Relevant Citation
inferCSN Software Package Infers cell type and state-specific GRNs from scRNA-seq using pseudo-temporal windowing. [74]
DAZZLE Software Package Infers GRNs with improved robustness to scRNA-seq dropout noise via Dropout Augmentation. [75]
MultiGNN Software Framework A supervised Graph Neural Network that integrates scRNA-seq and scATAC-seq for GRN inference. [76]
scMKL Software Package Provides interpretable integration of multi-omics data for classification and feature analysis. [21]
CZ CELLxGENE / DISCO Data Repository Provides curated, massive-scale single-cell datasets for model training and validation. [11]
BEELINE Benchmarking Framework Provides standardized datasets and evaluation protocols for benchmarking GRN inference algorithms. [75] [76]
JASPAR / Cistrome Prior Knowledge Database Curated transcription factor binding motifs and chromatin profiles for network calibration. [21]

Visualizing Signaling Pathways from Inferred GRNs

A critical application of state-specific GRNs is the identification of active signaling pathways driving developmental transitions. The diagram below illustrates a generalized workflow for processing a multi-omic dataset to reveal a key pathway, such as Wnt signaling, active in a specific cell state.

C From Data to Pathway Insight Multiome Multi-omics Input (scRNA-seq + scATAC-seq) StateGRN State-Specific GRN (e.g., inferCSN) Multiome->StateGRN Subnet Extract Pathway Sub-network StateGRN->Subnet Model Validate & Model Perturbation Subnet->Model Insight Mechanistic Insight (e.g., Wnt drives state transition) Model->Insight ATAC scATAC-seq ATAC->Multiome RNA scRNA-seq RNA->Multiome

Workflow Description: Starting with multi-omics data (scRNA-seq and scATAC-seq), a state-specific GRN is inferred for a window of cells along a pseudo-time trajectory (e.g., a progenitor state). Comparative analysis of GRNs across different states (e.g., progenitor vs. differentiated) reveals a sub-network of TFs and target genes that are dynamically rewired. This sub-network, when mapped to prior knowledge (e.g., KEGG, WikiPathways), can be annotated as a specific signaling pathway, such as Wnt. The activity of this pathway, supported by both expression and chromatin accessibility of key genes, provides a testable mechanistic hypothesis for its role in driving the state transition, which can be validated experimentally or through in silico perturbation modeling [11].

Benchmarking and Biological Validation: Ensuring Accuracy and Functional Relevance

Gene Regulatory Network (GRN) inference is a central problem in evolutionary developmental biology and single-cell multi-omics research. The accuracy of inferred regulatory interactions depends critically on robust validation datasets that provide experimental evidence of true molecular relationships. Gold-standard datasets derived from Chromatin Immunoprecipitation followed by sequencing (ChIP-seq), expression Quantitative Trait Loci (eQTL) studies, and genetic perturbation experiments provide essential ground truth for benchmarking computational methods. These resources enable researchers to validate predicted transcription factor (TF)-target gene relationships, enhancer-promoter connections, and causal regulatory interactions, thereby ensuring biological relevance in network models. The integration of these validation frameworks is particularly crucial for studying the evolution of developmental programs, where rewiring of GRNs underlies phenotypic diversity.

Comprehensive Catalog of Gold-Standard Datasets

The table below summarizes the primary categories of gold-standard datasets used for validating GRN inferences, their specific applications, and key benchmarks for performance evaluation.

Table 1: Gold-Standard Dataset Categories for GRN Validation

Dataset Type Biological Question Addressed Validation Metrics Reported Performance Benchmarks
ChIP-seq TF Binding Direct physical TF-DNA interaction Precision, Recall, F1 score, Area Under ROC Curve (AUC) Significantly enriched for binding sites (p < 0.05) [77]
eQTL Mapping Genotype-driven expression variation Area Under Precision-Recall Curve (AUPR) ratio, AUC Higher AUC/AUPR across different RE-TG distance groups [3]
Perturbation Data Causal regulatory relationships Concordance with known biological processes Fourfold to sevenfold relative increase in inference accuracy [3]
Chromatin Interaction Enhancer-target gene assignments Gene Set Enrichment (GSE) testing concordance Top EnTDefs significantly outperform nearest-gene approach [78]

ChIP-seq Datasets for Direct TF Binding Validation

Experimental Protocol: ChIP-seq in Maize Leaf Protoplasts

Large-scale ChIP-seq provides the most direct evidence of transcription factor binding and serves as a critical benchmark for evaluating predicted cis-regulatory elements. The following protocol outlines the methodology used to generate a comprehensive ChIP-seq resource in maize:

  • Protoplast Isolation and Transformation: Peel the lower epidermis of 9-day-old seedling leaves to allow gentle penetration of cell wall digestion enzymes, releasing approximately 10^7 intact mesophyll protoplasts. Achieve over 90% transformation efficiency by fusing TF coding sequences to an Avi epitope tag for biotinylation by co-expressed biotin ligase [79].
  • Chromatin Immunoprecipitation: Utilize the strong biotin-streptavidin interaction with magnetic beads to obtain high signal-to-noise ratios. Perform over 200 ChIP-seq experiments for 104 TFs expressed in the developing maize leaf section [79].
  • Library Preparation and Sequencing: Generate tagmentation ChIP-seq libraries using a hyper-stable Tn5 transposase fused to the C-terminal of E. coli elongation factor Ts. Sequence libraries following standard protocols [79].
  • Quality Control and Peak Calling: Process data using the ENCODE2 uniform pipeline. Apply normalized strand cross-correlation (≥1.05) and relative strand cross-correlation (≥0.8) thresholds. Call reproducible peaks with an irreproducible discovery rate ≤0.01 after confirming biological replicate reproducibility (Pearson correlation ≥0.8) [79].

This protocol generated 2,147,366 reproducible TF-binding peaks, with a median of 16,000 binding sites per TF, which were used to validate the completeness and precision of integrated cis-regulatory elements (iCREs) [77]. Performance benchmarking demonstrated that predictions from all tested CRE identification methods were significantly enriched (p < 0.05) for the binding sites in the ChIP-seq dataset, whereas repeats and transposable elements were depleted [77].

chipseq_workflow ProtoplastIsolation Protoplast Isolation TFTransformation TF Transformation & Biotinylation ProtoplastIsolation->TFTransformation ChromatinPrep Chromatin Fragmentation & Immunoprecipitation TFTransformation->ChromatinPrep LibraryPrep Library Preparation (Tn5 Tagmentation) ChromatinPrep->LibraryPrep Sequencing Sequencing LibraryPrep->Sequencing QualityControl Quality Control Sequencing->QualityControl PeakCalling Peak Calling QualityControl->PeakCalling Validation GRN Validation PeakCalling->Validation

Figure 1: ChIP-seq Experimental Workflow for GRN Validation

Research Reagent Solutions for ChIP-seq

Table 2: Essential Research Reagents for ChIP-seq Experiments

Reagent/Resource Function Specific Example
Avi Epitope Tag Enables biotinylation for highly specific pull-down Maize TFs fused to Avi tag [79]
Biotin Ligase Enzymatically biotinylates Avi-tagged TFs Co-expressed with TF-Avi fusion [79]
Streptavidin Magnetic Beads Capture biotinylated TF-DNA complexes High signal-to-noise ratio ChIP [79]
Hyper-stable Tn5 Transposase Efficient tagmentation for library prep Fused to E. coli elongation factor Ts [79]
ChIP-seq Gold Standard Benchmarking CRE predictions 104 TF ChIP-seq dataset from maize leaf [77] [79]

eQTL Datasets for Genotype-Regulation Relationships

Protocol for eQTL-Based Validation of cis-Regulatory Interactions

Expression Quantitative Trait Loci (eQTL) mapping provides evidence for genetic variants that influence gene expression, serving as a valuable validation resource for predicted enhancer-target gene relationships. The following methodology outlines the application of eQTL data for benchmarking GRN inferences:

  • Data Collection: Obtain variant-gene links defined by eQTL studies from resources such as GTEx (Genotype-Tissue Expression) for various human tissues and eQTLGen for blood-based cohorts [3].
  • Stratification by Distance: Divide regulatory element-target gene (RE-TG) pairs into different genomic distance groups to account for varying functional ranges of regulatory interactions [3].
  • Performance Assessment: Calculate the Area Under the Receiver Operating Characteristic Curve (AUC) and Area Under the Precision-Recall Curve (AUPR) ratio by sliding the trans-regulatory predictions against the eQTL ground truth. Methods like LINGER have demonstrated higher AUC and AUPR ratios across all distance groups compared to baseline approaches [3].

This validation approach is particularly valuable for assessing cis-regulatory predictions in single-cell multi-omics GRN inference methods, where linking distal regulatory elements to their target genes remains challenging. The method provides evidence that regulatory predictions align with natural genetic variation that affects gene expression, strengthening their biological relevance.

Perturbation Datasets for Causal Inference Validation

CRISPR-Based Perturbation Screening for GRN Validation

Genetic perturbation experiments provide causal evidence for regulatory relationships, serving as the highest standard for validating predicted GRN interactions. The following approaches are used to generate and utilize perturbation data:

  • Perturb-seq Methodology: Combine CRISPR-based gene editing with single-cell RNA-seq to systematically investigate gene function. Introduce targeted genetic perturbations and measure their effects on the transcriptome to map gene regulatory networks and identify key drivers of cellular behavior [80].
  • Mutant Analysis: Generate and characterize mutant lines for specific regulatory genes. For example, in amphioxus, Gdf1/3-like mutants showed defects in axial development, while Gdf1/3 mutants did not, revealing evolutionary rewiring of the body axis GRN [44].
  • Validation of Predictions: Use perturbation results to test computational predictions of regulatory interactions. Methods that incorporate these causal relationships during development show improved performance in identifying driver regulators [3].

Perturbation data is especially valuable in evolutionary developmental biology studies, where it can reveal how GRNs have been rewired during evolution. For example, functional genetic evidence in amphioxus demonstrated that a pivotal enhancer hijacking event allowed the emergence of a new GRN for body axis formation, highlighting the mechanistic basis of developmental system drift [44].

perturbation_validation GRNPrediction GRN Prediction from Multi-omics Data ExperimentalDesign Perturbation Design (CRISPR, Mutagenesis) GRNPrediction->ExperimentalDesign DataGeneration Phenotypic Data Collection (Imaging, Sequencing) ExperimentalDesign->DataGeneration CausalValidation Causal Relationship Validation DataGeneration->CausalValidation CausalValidation->GRNPrediction Feedback ModelRefinement GRN Model Refinement CausalValidation->ModelRefinement

Figure 2: Perturbation Data for Causal GRN Validation

Integrated Validation Frameworks for Single-Cell Multi-omics

Benchmarking Protocol for GRN Inference Methods

Comprehensive validation of GRN inferences requires integrated frameworks that combine multiple gold-standard datasets. The following protocol outlines a systematic approach for benchmarking method performance:

  • Ground Truth Compilation: Collect putative targets of TFs from ChIP-seq data across multiple biological contexts (e.g., 20 datasets in blood cells) and variant-gene links from eQTL studies (e.g., GTEx, eQTLGen) [3].
  • Multi-modal Assessment: Evaluate trans-regulatory strength (TF-TG relationships) against ChIP-seq ground truth using AUC and AUPR ratio. Assess cis-regulatory inference (RE-TG relationships) against eQTL data across different genomic distance groups [3].
  • Cell-Type Specific Validation: Apply cell-type-specific gold standards where available, acknowledging that general benchmarks may perform favorably in many contexts [78].
  • Functional Concordance Testing: Use Gene Set Enrichment (GSE) testing to assess concordance of results with known TF Gene Ontology annotations and other functional benchmarks [78].

This integrated approach enables rigorous evaluation of GRN inference methods. For example, the LINGER method demonstrated a fourfold to sevenfold relative increase in accuracy over existing approaches when validated against such comprehensive benchmarks [3].

Research Reagent Solutions for Multi-omics Validation

Table 3: Essential Resources for Multi-omics GRN Validation

Resource Category Specific Examples Application in Validation
Reference Datasets ENCODE ChIP-seq, GTEx eQTL, FANTOM5 Benchmarking enhancer-target predictions [3] [78]
Software Tools Seurat, MOFA+, Harmony Data integration and batch correction [81] [80]
GRN Inference Methods LINGER, PRISM-GRN, scSAGRN Comparative performance benchmarking [3] [4] [37]
Experimental Validation Platforms Perturb-seq, CROP-seq Functional confirmation of predictions [80]

Gold-standard validation datasets from ChIP-seq, eQTL studies, and perturbation experiments provide essential foundations for benchmarking GRN inferences in evolutionary developmental biology research. The integration of these complementary data types enables comprehensive evaluation of both physical binding associations and functional regulatory relationships. As single-cell multi-omics technologies continue to advance, these validation frameworks will become increasingly important for distinguishing true biological signals from computational artifacts, ultimately leading to more accurate models of gene regulatory network evolution and function. Researchers should prioritize methods that demonstrate robust performance across multiple validation datasets rather than optimizing for any single metric, thereby ensuring biological relevance and translational potential in both basic research and drug development applications.

In the field of single-cell multi-omics research, accurately inferring gene regulatory networks (GRNs) is fundamental to understanding the molecular mechanisms governing evolutionary developmental biology. GRNs are collections of molecular regulators, particularly transcription factors (TFs), regulatory elements (REs), and target genes (TGs), that interact to determine gene activation and silencing in specific cellular contexts [3] [31]. The evaluation of computational methods that reconstruct these networks presents significant challenges due to the complexity of biological systems and limitations in establishing complete ground truth data. Performance metrics such as the Area Under the Receiver Operating Characteristic Curve (AUC) and the Area Under the Precision-Recall Curve (AUPR) have emerged as standard quantitative measures for benchmarking GRN inference accuracy against experimentally validated regulatory interactions [3] [82]. These metrics provide researchers, scientists, and drug development professionals with crucial tools for assessing method reliability before applying them to investigate developmental processes or identify therapeutic targets.

Core Performance Metrics in GRN Evaluation

Theoretical Foundations of AUC and AUPR

The Area Under the Receiver Operating Characteristic Curve (AUC) and Area Under the Precision-Recall Curve (AUPR) are ranking-based metrics that evaluate the ability of GRN inference methods to distinguish true regulatory interactions from non-interactions. AUC measures the overall performance across all possible classification thresholds, plotting the True Positive Rate (sensitivity) against the False Positive Rate (1-specificity). A perfect classifier achieves an AUC of 1, while random guessing yields 0.5 [3] [82]. AUPR focuses specifically on the precision-recall relationship, making it particularly valuable for evaluating performance on imbalanced datasets where true positives are rare compared to the vast number of potential false positives in GRN inference [82]. The AUPR ratio, which compares the AUPR of a method to that of a random predictor, provides a standardized measure of improvement over chance [3].

Practical Application in Benchmarking Studies

In practical applications, these metrics are calculated by comparing inferred regulatory strengths against known ground truth networks. For example, LINGER demonstrated a fourfold to sevenfold relative increase in accuracy over existing methods when evaluated using these metrics [3]. The regulatory strength of transcription factor-target gene (TF-TG) pairs is typically ranked, and the resulting ordered list is assessed against confirmed interactions. AUC values quantify how well the method separates true regulators from non-regulators across all thresholds, while AUPR emphasizes the method's performance in identifying true positives despite the overwhelming number of potential false positives inherent in GRN inference tasks [3] [82].

Table 1: Key Characteristics of AUC and AUPR Metrics

Metric Interpretation Strength Limitation Ideal Use Case
AUC Probability that a random true positive is ranked higher than a random true negative Robust summary of overall performance across thresholds Less informative for highly imbalanced data Initial method comparison when false positive rate matters
AUPR Relationship between precision and recall at different thresholds More informative for imbalanced datasets where positives are rare More difficult to interpret in isolation Focused evaluation of positive prediction accuracy
AUPR Ratio Ratio of method AUPR to random predictor AUPR Standardized measure of improvement over chance Depends on the specific dataset composition Normalized comparison across different datasets

Ground Truth Data for Validation

Classification of Ground Truth Evidence

Establishing reliable ground truth data represents a fundamental challenge in GRN inference benchmarking. A comprehensive evaluation requires multiple forms of experimental evidence, each with distinct strengths and limitations for validation purposes [82].

Table 2: Categories of Ground Truth Data for GRN Validation

Ground Truth Category Description Examples Strengths Limitations
Direct TF-TG Binding Evidence of physical binding between TF and DNA ChIP-seq, ChIP-ATLAS [3] [83] Direct evidence of regulatory potential Does not confirm functional regulation; cell-type specificity challenges
Cis-regulatory Validation Links between regulatory elements and target genes eQTL studies (GTEx, eQTLGen) [3] Provides functional evidence of regulation Limited by statistical power and tissue/cell type availability
Model Organism Databases Curated regulatory interactions from well-studied organisms RegulonDB [82] High-quality, curated data Limited transferability to human and other complex eukaryotes
Genetic Perturbation Evidence from targeted genetic manipulations Knockout, knockdown, overexpression [82] Establishes causal relationships Technically challenging and low-throughput

Practical Implementation of Ground Truth Comparisons

In practice, benchmarking studies typically collect multiple ground truth datasets relevant to the biological context. For example, a study of blood cells might collect 20 ChIP-seq datasets from relevant cell types as ground truth for trans-regulatory interactions [3]. Similarly, eQTL data from GTEx and eQTLGen can validate cis-regulatory predictions, with performance assessed across different genomic distance groups between REs and TGs [3]. The selection of appropriate ground truth data requires careful consideration of cellular context, technical quality, and relevance to the biological questions being investigated.

Experimental Protocols for Benchmarking GRN Methods

Protocol 1: Performance Assessment Using ChIP-seq Ground Truth

This protocol details the evaluation of trans-regulatory predictions (TF-TG interactions) against transcription factor binding data from ChIP-seq experiments.

Materials and Reagents:

  • Computational Environment: High-performance computing cluster with sufficient memory (≥64 GB RAM recommended)
  • Software Tools: Programming environment (R/Python) for metric calculation
  • Ground Truth Data: Curated ChIP-seq targets from databases like ChIP-Atlas or hTFtarget [3] [83]

Procedure:

  • Data Preparation:
    • Obtain predicted regulatory strengths for all TF-TG pairs from the GRN inference method
    • Download and process ChIP-seq ground truth data, applying consistent gene identifiers
    • For each TF with ChIP-seq data, compile all potential target genes in the genome as the negative set

  • Metric Calculation:

    • Rank all potential target genes for each TF by the predicted regulatory strength
    • Generate the ROC curve by calculating true positive rate (TPR) and false positive rate (FPR) at successive rank thresholds
    • Compute AUC by integrating the area under the ROC curve
    • Generate the precision-recall curve by calculating precision and recall at successive thresholds
    • Compute AUPR by integrating the area under the precision-recall curve

  • Statistical Validation:

    • Repeat the analysis for all available ChIP-seq ground truth datasets
    • Perform statistical testing (e.g., Wilcoxon signed-rank test) to compare AUC/AUPR values across methods
    • Report both aggregate performance and method performance for individual TFs

Troubleshooting Tip: Ensure consistent gene annotation between predicted networks and ground truth data, as identifier mismatches can artificially deflate performance metrics.

Protocol 2: Validation of Cis-Regulatory Predictions Using eQTL Data

This protocol describes the evaluation of cis-regulatory interactions (RE-TG) using expression quantitative trait loci (eQTL) data as ground truth.

Materials and Reagents:

  • eQTL Data Sources: Public repositories such as GTEx or eQTLGen [3]
  • Genomic Coordinates: Reference genome and gene annotation file

Procedure:

  • Data Preprocessing:
    • Download and process eQTL summary statistics, retaining significant variant-gene pairs
    • Map eQTL variants to regulatory elements (REs) based on genomic position
    • Categorize RE-TG pairs by genomic distance (e.g., <1kb, 1-10kb, 10-100kb, 100kb-1Mb)

  • Performance Assessment:

    • For each distance category, rank RE-TG pairs by predicted regulatory strength
    • Calculate AUC and AUPR using eQTL-supported pairs as positives and all other RE-TG pairs in the same distance category as negatives
    • Compare performance across distance categories to assess the method's sensitivity to genomic distance

  • Result Interpretation:

    • Note that performance typically decreases with increasing RE-TG distance
    • Methods with strong distance-based performance maintain reasonable AUC even at larger distances [3]
    • Report performance stratified by distance to provide comprehensive evaluation

G start Start GRN Benchmarking gt_select Select Appropriate Ground Truth Data start->gt_select method_run Run GRN Inference Methods gt_select->method_run metric_calc Calculate Performance Metrics (AUC/AUPR) method_run->metric_calc result_compare Compare Results Across Methods metric_calc->result_compare conclusion Draw Conclusions on Method Performance result_compare->conclusion

Figure 1: Workflow for comprehensive benchmarking of GRN inference methods, highlighting the sequential process from data selection to final conclusion.

Case Study: Benchmarking the LINGER Framework

The LINGER (Lifelong neural network for gene regulation) framework provides an illustrative case study for comprehensive GRN evaluation. When benchmarked on peripheral blood mononuclear cell (PBMC) data, LINGER demonstrated a fourfold to sevenfold relative increase in accuracy compared to existing methods including standard neural networks (scNN), bulk data-trained models (BulkNN), and correlation-based approaches (PCC) [3].

For trans-regulatory validation, researchers collected 20 ChIP-seq datasets from blood cells as ground truth. LINGER achieved significantly higher AUC and AUPR ratio values compared to other methods, indicating superior performance in identifying true TF-target relationships [3]. For cis-regulatory validation, the method was evaluated using eQTL data from GTEx and eQTLGen, with performance assessed across different genomic distance groups. LINGER maintained higher AUC and AUPR ratios than scNN across all distance categories, demonstrating robust identification of functional RE-TG connections [3].

This benchmarking approach exemplifies rigorous methodology: multiple ground truth sources, comparison against relevant baseline methods, and stratified analysis to understand performance characteristics across different regulatory contexts.

The Scientist's Toolkit: Essential Research Reagents

Table 3: Key Research Reagent Solutions for GRN Benchmarking Studies

Reagent/Resource Function in GRN Evaluation Example Sources Application Notes
ChIP-seq Datasets Ground truth for direct TF-DNA binding ChIP-Atlas, ENCODE [3] [83] Select cell-type relevant datasets; requires careful processing
eQTL Resources Validation of cis-regulatory relationships GTEx, eQTLGen [3] Use significant variant-gene pairs at appropriate FDR thresholds
Reference Networks Curated regulatory interactions from model organisms RegulonDB, DREAM challenges [82] Useful for initial method development but limited transferability
Single-cell Multiome Data Paired scRNA-seq + scATAC-seq for inference 10x Multiome, SHARE-seq [3] [84] Enables simultaneous profiling of gene expression and chromatin accessibility
Benchmarking Platforms Standardized evaluation frameworks BEELINE [83] Provides synthetic and real networks for controlled comparisons

Advanced Considerations in GRN Evaluation

Addressing Technical Challenges in Single-cell Data

Single-cell sequencing data presents unique challenges for GRN inference evaluation, including technical noise, sparsity (dropouts), and limited independent data points despite large cell numbers [3] [82]. These characteristics can significantly impact benchmarking results by introducing false negatives and reducing statistical power. Evaluation frameworks must account for these data-specific properties when interpreting performance metrics [82]. Methods that incorporate external data sources, such as LINGER's use of atlas-scale bulk data, can help mitigate these limitations [3].

Emerging Methods and Future Directions

Recent advances in GRN inference include deep learning approaches that leverage graph-based structures to capture global regulatory information [83], disentangled generative models that separate shared and private features across omics layers [84], and methods that explicitly model combinatorial regulation through cRegulons [12]. As these sophisticated approaches emerge, evaluation frameworks must similarly evolve to capture their specific capabilities, such as identifying cooperative TF interactions or predicting context-specific regulatory activities. Future benchmarking efforts may need to incorporate additional metrics beyond AUC and AUPR to fully characterize method performance on these advanced tasks.

G gt Ground Truth Data chipseq ChIP-seq (TF Binding) gt->chipseq eqtl eQTL Data (Cis-regulation) gt->eqtl perturbation Genetic Perturbation (Causality) gt->perturbation model_org Model Organism Databases gt->model_org metrics Performance Metrics chipseq->metrics eqtl->metrics perturbation->metrics model_org->metrics auc AUC (Overall Ranking) metrics->auc aupr AUPR (Positive Prediction) metrics->aupr ratio AUPR Ratio (Improvement vs Random) metrics->ratio

Figure 2: Hierarchy of evaluation framework components showing the relationship between ground truth data types and performance metrics in GRN inference benchmarking.

Rigorous evaluation of GRN inference methods using AUC, AUPR, and comprehensive ground truth comparisons is essential for advancing single-cell multi-omics research in evolutionary developmental biology. The protocols and frameworks presented here provide researchers with standardized approaches for assessing method performance, enabling informed selection of appropriate computational tools for investigating gene regulatory mechanisms in development and disease. As the field continues to evolve with emerging technologies and more sophisticated algorithms, these evaluation principles will remain fundamental for validating biological discoveries and ensuring computational reproducibility.

In the field of evolutionary developmental biology, understanding the gene regulatory networks (GRNs) that govern cell identity and fate is paramount. Single-cell multi-omics technologies now enable the joint profiling of chromatin accessibility and gene expression in individual cells, providing an unprecedented opportunity to decipher enhancer-driven GRNs that underlie developmental processes [65]. The computational inference of these networks is a central problem in biology, with implications for understanding evolution, development, and disease mechanisms [3].

Several advanced computational methods have emerged to leverage single-cell multi-omics data for GRN inference. This application note provides a comparative analysis of three leading tools—LINGER, SCENIC+, and cRegulon—framed within the context of single-cell multi-omics GRN inference for evolutionary developmental biology research. We evaluate their methodologies, performance, and practical applications to guide researchers and drug development professionals in selecting appropriate tools for their specific research needs.

SCENIC+: Enhancer-Driven GRN Inference

SCENIC+ is a comprehensive computational framework designed specifically for inferring enhancer-driven GRNs from single-cell multi-omics data. The method predicts genomic enhancers alongside candidate upstream transcription factors (TFs) and links these enhancers to candidate target genes [65].

  • Workflow: SCENIC+ implements a three-step workflow:

    • Identifies candidate enhancers from single-cell ATAC-seq data using pycisTopic, which identifies sets of co-accessible regions (topics) across cell types or states.
    • Discovers enriched TF-binding motifs in candidate enhancers using pycisTarget, which employs two algorithms: the cisTarget ranking-and-recovery-based algorithm and a Wilcoxon rank-sum test called differential enrichment of motifs (DEM). This step leverages a massive curated collection of 32,765 unique motifs spanning 1,553 TFs.
    • Links TFs to enhancers and target genes using GRNBoost2 to quantify the importance of both TFs and enhancer candidates for target genes and infers the direction of regulation [65].

  • Key Output: The output is a set of enhancer-driven regulons (eRegulons), each comprising a TF with its set of target regions and genes, which together form the complete eGRN [65].

LINGER: Lifelong Learning for GRN Inference

LINGER (Lifelong neural network for gene regulation) represents a paradigm shift in GRN inference by incorporating atlas-scale external bulk data across diverse cellular contexts as a manifold regularization. This approach addresses the challenge of learning complex regulatory mechanisms from limited independent data points in single-cell experiments [3].

  • Workflow: LINGER employs a three-step process centered on lifelong machine learning:

    • Pre-training on External Bulk Data: A neural network model (BulkNN) is pre-trained on external bulk data from sources like the ENCODE project, which contains hundreds of samples covering diverse cellular contexts.
    • Refinement on Single-Cell Data: The model is refined on single-cell multiome data using elastic weight consolidation (EWC) loss, which uses the bulk data parameters as a prior to prevent catastrophic forgetting and ensure stable learning.
    • Regulatory Strength Inference: After training, the regulatory strength of TF-target gene (TF-TG) and regulatory element-target gene (RE-TG) interactions is inferred using Shapley values, which estimate the contribution of each feature for each gene [3].

  • Key Advantage: This unique approach allows LINGER to achieve a fourfold to sevenfold relative increase in accuracy over existing methods, as validated by ChIP-seq data and expression quantitative trait loci (eQTL) studies [3].

cRegulon: Modeling Combinatorial Regulation

cRegulon addresses a critical limitation in existing GRN inference methods by modeling combinatorial regulation of transcription factors. While methods like SCENIC+ infer regulons for single TFs, cRegulon identifies regulatory modules where multiple TFs work together to regulate common target genes, which is fundamental for understanding cell fate decisions [12].

  • Core Concept: A cRegulon is defined as a set of TF pairs (a TF module), a corresponding set of binding regulatory elements (REs), and a set of target genes whose expressions are co-regulated by these TFs and REs.
  • Methodology: The method takes single-cell multi-omics data and constructs cluster-specific GRNs. It then computes a matrix of pairwise combinatorial effects for TF pairs, considering both co-regulation effects and activity specificities. cRegulon assumes this matrix can be approximated by a mixture of rank-1 matrices, each corresponding to a module of co-regulating TFs, and solves an optimization model to identify these TF modules across all cell clusters [12].
  • Biological Significance: This approach captures the cooperative nature of gene regulation observed in key developmental processes, such as the collaboration of Sox2, Nanog, and Pou5f1 in pluripotency maintenance in embryonic stem cells [12].

Comparative Workflow Visualization

The following diagram illustrates the core methodological differences and shared workflow stages among SCENIC+, LINGER, and cRegulon:

GRN_Workflow_Comparison cluster_preprocess Data Preprocessing & Integration cluster_core_method Core Inference Method cluster_output Network Output start Input: scMulti-ome Data (RNA-seq + ATAC-seq) preprocess Cell Clustering & Feature Identification start->preprocess scenic_method SCENIC+: Motif Enrichment & Region-Gene Linking preprocess->scenic_method linger_method LINGER: Lifelong Learning with External Data Integration preprocess->linger_method scenic_output eRegulons (TF + Enhancers + Genes) scenic_method->scenic_output linger_output Cell-Type Specific GRNs (TF-TG + RE-TG + TF-RE) linger_method->linger_output cregulon_method cRegulon: Combinatorial TF Module Identification cregulon_output cRegulons (TF Modules + REs + Genes) cregulon_method->cregulon_output pregraph pregraph

Performance Benchmarking and Comparative Analysis

Quantitative Performance Metrics

Independent benchmarking studies provide critical insights into the performance of GRN inference methods. The table below summarizes key performance characteristics of SCENIC+, LINGER, and cRegulon based on published evaluations.

Table 1: Performance Comparison of GRN Inference Tools

Metric SCENIC+ LINGER cRegulon
Accuracy Improvement Outperforms CellOracle, Pando, FigR, GRaNIE, and SCENIC in TF and target region prediction [65] 4-7x relative increase in accuracy over existing methods [3] Outperforms existing approaches in identifying TF combinatorial modules [12]
TF Recovery Best recovery of differentially expressed TFs and TFs with direct ChIP-seq peaks [65] High recovery of biologically relevant TFs validated by ChIP-seq [3] Specialized in identifying cooperative TF pairs with validated biological relevance [12]
Precision/Recall High precision and recall for predicted target regions based on ChIP-seq validation [65] Significantly higher AUC and AUPR ratio across validation datasets [3] Precise capture of known cooperative TF interactions [12]
Experimental Validation Strong overlap with EBF1, PAX5, and POU2F2 ChIP-seq data in PBMCs; high enhancer activity by STARR-seq [65] Consistency with eQTL data from GTEx and eQTLGen; validation against ChIP-seq ground truth [3] Validation on in-silico data and real cell line mixtures confirming biological properties [12]
Scalability 1h-44h running time and 21GB-461GB memory for tested datasets [65] Efficient utilization of large-scale external data improves learning from limited single-cell data [3] Designed to reduce GRN complexity through modularity, enabling genome-scale analysis [12]

Methodological Comparison

Table 2: Methodological Approaches of GRN Inference Tools

Feature SCENIC+ LINGER cRegulon
Primary Innovation Large motif collection (32,765 motifs) and enhancer-focused GRNs [65] Lifelong learning incorporating external bulk data [3] Combinatorial TF module identification [12]
Data Requirements Paired scRNA-seq + scATAC-seq (can work with integrated data) [17] Paired scRNA-seq + scATAC-seq with cell type annotations [3] Paired or unpaired scRNA-seq + scATAC-seq [12]
Regulatory Unit eRegulon (single TF + enhancers + target genes) [65] Triple interactions (TF-TG, RE-TG, TF-RE) [3] cRegulon (TF modules + REs + target genes) [12]
Modeling Approach Linear modeling with frequentist framework [17] Neural network with Bayesian-inspired refinement [3] Matrix optimization and modularity analysis [12]
Key Applications Master regulator identification; conserved regulation across species; differentiation trajectories [65] Disease-relevant cell type and driver regulator identification; GWAS interpretation [3] Cell type annotation; developmental process analysis; cooperative TF identification [12]

Experimental Protocols

Protocol 1: SCENIC+ for Enhancer-Driven GRN Inference in Developmental Systems

Purpose: To identify enhancer-driven gene regulatory networks governing cell fate decisions in developing tissues.

Materials:

  • Single-cell multiome data (scRNA-seq + scATAC-seq) from developing tissue
  • Reference genome (human, mouse, or fly)
  • SCENIC+ installation (scenicplus.readthedocs.io)

Procedure:

  • Data Preprocessing:
    • Process scATAC-seq data using pycisTopic to identify co-accessible regions (topics) across cell types.
    • Identify differentially accessible regions (DARs) between cell states.
    • Use both topics and DARs as candidate enhancers.

  • Motif Enrichment Analysis:

    • Scan candidate enhancers using the curated motif collection (32,765 motifs) via pycisTarget.
    • Apply both cisTarget and DEM algorithms to identify significantly enriched TF-binding motifs.

  • Region-to-Gene Linking:

    • Use GRNBoost2 to infer relationships between TFs, enhancer candidates, and potential target genes.
    • Combine motif enrichment results with GRNBoost2 inferences to form eRegulons.

  • Downstream Analysis:

    • Visualize eRegulon enrichment scores across cell types to identify master regulators.
    • Analyze conservation of TFs, enhancers, and GRNs across species (e.g., human vs. mouse cerebral cortex).
    • Study dynamics of gene regulation along differentiation trajectories.

Validation: Compare predicted target regions with available ChIP-seq data and assess enhancer activity using STARR-seq data [65].

Protocol 2: LINGER for Disease-Relevant GRN Inference

Purpose: To infer GRNs from single-cell multiome data using atlas-scale external data for enhanced accuracy, particularly for disease applications.

Materials:

  • Single-cell multiome data with cell type annotations
  • External bulk multi-omics data (e.g., from ENCODE)
  • LINGER installation

Procedure:

  • Data Preparation:
    • Preprocess single-cell multiome data to obtain count matrices for gene expression and chromatin accessibility.
    • Annotate cell types using standard clustering approaches.

  • Model Pre-training:

    • Pre-train the BulkNN neural network model on external bulk data from diverse cellular contexts.
    • This establishes prior knowledge of regulatory relationships.

  • Lifelong Learning Refinement:

    • Refine the pre-trained model on single-cell data using Elastic Weight Consolidation (EWC) loss.
    • The EWC regularization preserves knowledge from bulk data while adapting to single-cell specifics.

  • GRN Extraction:

    • Infer regulatory strengths of TF-TG and RE-TG interactions using Shapley values.
    • Generate TF-RE binding strength from correlation of learned parameters.
    • Construct cell type-specific and cell-level GRNs.

  • Disease Application:

    • Integrate with GWAS data to identify disease-relevant cell types and TFs.
    • Estimate TF activity from external bulk or single-cell gene expression data to identify driver regulators in case-control studies [3].

Validation: Validate trans-regulatory predictions against ChIP-seq data and cis-regulatory predictions against eQTL data from GTEx and eQTLGen [3].

Protocol 3: cRegulon for Combinatorial Regulation Analysis

Purpose: To identify combinatorial TF modules that co-regulate target genes and define cell identities.

Materials:

  • Single-cell multi-omics data (paired or unpaired scRNA-seq and scATAC-seq)
  • cRegulon installation

Procedure:

  • Initial GRN Construction:
    • Preprocess single-cell multi-omics data and perform cell clustering.
    • Construct initial GRNs for each cell cluster using a base method (e.g., region-to-gene links and motif matching).

  • Combinatorial Effect Calculation:

    • For each cluster-specific GRN, compute a combinatorial effect matrix for TF pairs that considers both co-regulation effect and activity specificity.

  • TF Module Identification:

    • Apply the optimization model to approximate the combinatorial effect matrix as a mixture of rank-1 matrices.
    • Extract TF modules from the decomposition, where each module represents a set of co-regulating TFs.

  • cRegulon Construction:

    • For each TF module, identify the corresponding set of regulatory elements and target genes to form complete cRegulons.
    • Annotate cell types by the cRegulons they utilize.

  • Biological Interpretation:

    • Identify cRegulons associated with specific biological processes or cell states.
    • Validate known cooperative TF interactions (e.g., Sox2-Nanog-Pou5f1 in pluripotency).
    • Analyze how cRegulons are shared or specialized across different cell types [12].

Validation: Apply to in-silico simulated data and real cell line mixtures to validate the biological properties of identified regulatory units [12].

The Scientist's Toolkit: Essential Research Reagents

Table 3: Key Research Reagents for Single-Cell Multi-omics GRN Inference

Reagent/Resource Function Example Applications
10x Genomics Single-Cell Multiome Kit Simultaneous measurement of gene expression and chromatin accessibility in the same single cell Generating input data for all three tools; PBMC analysis for benchmarking [3]
ENCODE Project Data Comprehensive collection of functional genomic datasets across diverse cell types External bulk data for pre-training LINGER; validation of predictions [3]
CisTarget Databases Curated collections of transcription factor binding motifs and regulatory interactions Motif enrichment analysis in SCENIC+; improved TF identification [65]
ChIP-seq Reference Data Genome-wide mapping of transcription factor binding sites Validation of predicted TF-target region relationships [65] [3]
eQTL Data (GTEx/eQTLGen) Catalog of genetic variants associated with gene expression levels Validation of predicted region-to-gene links [3]
STARR-seq Data High-throughput assessment of enhancer activity Validation of predicted enhancer regions [65]

Application in Evolutionary Developmental Biology

The following diagram illustrates how these tools can be integrated to unravel gene regulatory networks in evolutionary developmental biology, from data acquisition to biological insight:

EvoDevo_GRN_Pipeline tissue Developing Tissue (e.g., Embryonic Brain) tech Single-Cell Multi-ome Sequencing tissue->tech scenic SCENIC+ tech->scenic linger LINGER tech->linger cregulon cRegulon tech->cregulon enhancers Conserved Enhancers & Master TFs scenic->enhancers dynamics Differentiation Dynamics scenic->dynamics linger->dynamics disease Disease-Associated Regulatory Variants linger->disease comb_reg Combinatorial TF Logic in Cell Fate cregulon->comb_reg

SCENIC+, LINGER, and cRegulon represent distinct but complementary approaches to GRN inference from single-cell multi-omics data. SCENIC+ excels in enhancer-centric network inference with its extensive motif collection and established workflow. LINGER demonstrates groundbreaking accuracy through its lifelong learning approach that leverages external data. cRegulon addresses the critical dimension of combinatorial regulation that is largely overlooked by other methods.

For evolutionary developmental biology research, the choice of tool depends on the specific biological question:

  • SCENIC+ is recommended for studies focusing on enhancer function, conservation across species, and differentiation trajectories.
  • LINGER is ideal for disease-focused research requiring high accuracy and integration with GWAS data.
  • cRegulon is essential for understanding cooperative TF interactions in cell fate determination and reprogramming.

As the field advances, integration of these complementary approaches may provide the most comprehensive understanding of the gene regulatory networks that underlie developmental processes and their evolution.

Cross-Species Validation and Application in Evolutionary Studies

In evolutionary developmental biology, the inference of Gene Regulatory Networks (GRNs) from single-cell multi-omics data has become a powerful approach for understanding the molecular basis of phenotypic divergence. However, a significant challenge persists: the computational predictions of regulatory interactions, especially those identified through cross-species comparisons, require robust experimental validation to confirm their biological relevance. Cross-species validation ensures that identified regulatory elements and network architectures are genuine drivers of evolutionary change rather than technical artifacts or species-specific peculiarities.

The integration of single-cell technologies has revolutionized GRN inference by enabling the profiling of chromatin accessibility, gene expression, and epigenetic states at unprecedented resolution [85] [86]. These advances allow researchers to move beyond static network models toward dynamic representations of regulatory changes across evolutionary timescales. Nevertheless, the accuracy of inferred networks depends heavily on the validation strategies employed, particularly when comparing distantly related species with distinct genomic architectures.

Core Methodologies for Cross-Species Validation

Oligo-FISH for Chromosome-Level Genome Validation

Recent work on the Tasmanian snow skink (Carinascincus ocellatus) demonstrates an innovative approach to chromosome-level genome validation using Oligo-FISH (Fluorescence In Situ Hybridization) [87]. This methodology provides direct cytogenetic confirmation of computational genome assemblies, which is particularly crucial for accurately resolving microchromosomes that are prevalent in reptilian genomes and notoriously difficult to assemble.

Table 1: Key Components of the Oligo-FISH Validation Protocol

Component Specification Function in Validation
Oligonucleotide Probes Thousands of short probes designed from genome assembly Provide specific binding sites for chromosomal visualization
Metaphase Spread Preparation Single C. ocellatus metaphase slide Enables chromosomal visualization at condensed state
Hybridization Conditions Standardized buffer and temperature conditions Ensure specific probe binding to chromosomal targets
Imaging & Analysis Fluorescence microscopy with appropriate filters Visualize and confirm all 15 chromosomes including microchromosomes

The protocol involves designing thousands of short oligonucleotide probes directly from the genome assembly itself, then hybridizing them to metaphase chromosome spreads. This single-step approach provides independent cytogenetic confirmation of computational assemblies and has demonstrated utility across multiple skink species, highlighting its potential for comparative genomic studies [87]. The method is particularly valuable for resolving evolutionary rearrangements and validating conserved syntenic blocks across species boundaries.

Single-Cell Multi-Omics GRN Inference Frameworks

The emergence of single-cell multi-omics technologies has prompted development of novel computational frameworks for GRN inference that leverage both transcriptomic and chromatin accessibility data [85] [86]. These methods overcome limitations of traditional bulk sequencing by capturing cellular heterogeneity while providing insights into regulatory changes that drive evolutionary adaptations.

Table 2: Benchmarking Metrics for GRN Inference Methods in Evolutionary Studies

Method Category Key Principles Strengths Limitations for Cross-Species Studies
Tree-Based Methods Inference of regulatory relationships using tree models Handles non-linear relationships; robust to noise May require species-specific parameter tuning
Correlation-Based Networks Weighted gene co-expression network analysis (WGCNA) Identifies co-regulated modules; preserves network topology Cannot distinguish direct vs. indirect regulation
Integration Methods Combining ChIP-seq/ATAC-seq with transcriptome data Provides direct evidence of TF binding Requires cross-species compatible epigenomic data
Multimodal Integration Simultaneous measurement of transcriptome and epigenome in same cell Reduces spurious correlations from cellular heterogeneity Technical challenges in cross-species application

These inference methods can be applied to cross-species comparisons by analyzing homologous cell types or tissues across evolutionary lineages. For example, studies of craniofacial development in marsupials have revealed significant divergence in cis-regulatory elements despite high conservation of protein-coding genes [88]. Such approaches help identify which aspects of GRN architecture are evolutionarily stable versus those that contribute to phenotypic diversification.

Experimental Protocols

Detailed Protocol: Chromosome-Level Genome Assembly Validation with Oligo-FISH

This protocol describes the validation of chromosome-scale genome assemblies using oligonucleotide-based FISH, adapted from Saunders et al. [87] for cross-species applications.

Sample Preparation:

  • Cell Culture and Metaphase Spread Preparation:
    • Culture fibroblasts from skin biopsies in RPMI-1640 medium supplemented with 15% fetal bovine serum at 28°C with 5% COâ‚‚.
    • Add colcemid (0.1 μg/mL) to log-phase cultures for 45 minutes to arrest cells in metaphase.
    • Harvest cells using trypsin-EDTA treatment followed by hypotonic shock with 0.075 M KCl for 20 minutes at 37°C.
    • Fix cells with 3:1 methanol:acetic acid, with three changes of fixative over 30 minutes.
    • Drop cell suspension onto clean glass slides and age overnight at room temperature.

  • Oligonucleotide Probe Design and Labeling:

    • Design 45-50mer oligonucleotide probes targeting conserved syntenic regions across species using software such as OligoArray or OligoMiner.
    • Include approximately 2,000-5,000 probes per chromosome to ensure adequate coverage.
    • Label probes with fluorophores (e.g., Cy3, Cy5, or FITC) using nick translation or random priming methods.
    • Purify labeled probes using column purification to remove unincorporated nucleotides.

  • In Situ Hybridization:

    • Denature chromosomal DNA on slides by incubating in 70% formamide/2× SSC at 75°C for 5 minutes.
    • Dehydrate slides through ethanol series (70%, 85%, 100%) and air dry.
    • Prepare hybridization mixture containing labeled probes (50-100 ng/μL), competitor DNA (500-1000 ng/μL), and hybridization buffer.
    • Denature probe mixture at 75°C for 10 minutes, then pre-anneal at 37°C for 30-60 minutes.
    • Apply probe mixture to denatured slides, cover with coverslip, and seal with rubber cement.
    • Hybridize in a humid chamber at 37°C for 16-48 hours.

  • Post-Hybridization Washes and Detection:

    • Remove coverslips and wash slides three times in 50% formamide/2× SSC at 45°C.
    • Perform additional washes in 2× SSC and 1× SSC at 45°C.
    • Counterstain with DAPI (125 ng/mL) and mount with antifade medium.
    • Visualize using fluorescence microscopy with appropriate filter sets.

  • Image Analysis and Interpretation:

    • Capture images using a cooled CCD camera on an epifluorescence microscope.
    • Process images using software such as MetaSystems or Cytovision.
    • Verify probe signals correspond to predicted chromosomal locations based on genome assembly.
    • Identify any discrepancies between computational assembly and cytogenetic mapping.
Detailed Protocol: Cross-Species GRN Inference from Single-Cell Multi-Omics

This protocol outlines the inference of gene regulatory networks from single-cell multi-omics data for cross-species evolutionary comparisons, based on methodologies reviewed by Badia-I-Mompel et al. [85] [86].

Experimental Design:

  • Sample Selection and Single-Cell Sequencing:
    • Identify homologous tissues or cell types across target species (e.g., neural crest cells in vertebrate craniofacial development).
    • Isolate single-cell suspensions using standard dissociation protocols appropriate for each tissue type.
    • Process cells using a multi-ome platform (e.g., 10x Genomics Multiome ATAC + Gene Expression) to simultaneously profile chromatin accessibility and gene expression.
    • Sequence libraries following manufacturer recommendations, aiming for >20,000 reads per cell for gene expression and >10,000 reads per cell for chromatin accessibility.

  • Computational Analysis of Single-Cell Data:

    • Preprocess sequencing data using Cell Ranger ARC or similar pipelines.
    • Perform quality control to remove low-quality cells (high mitochondrial percentage, low unique molecular identifiers).
    • Integrate datasets across species using harmony or Seurat integration methods to correct for technical batch effects.
    • Annotate cell types using conserved marker genes and reference datasets.

  • GRN Inference and Cross-Species Comparison:

    • Identify regions of conserved open chromatin using peak calling algorithms (MACS2) and alignment to syntenic regions.
    • Calculate gene activity scores by combining gene expression with adjacent chromatin accessibility.
    • Infer regulatory networks using tools specifically designed for single-cell multi-omics data (e.g., Pando, FigR, SCENIC+).
    • Compare network topology across species focusing on transcription factor binding sites in conserved accessible regions.
    • Validate key regulatory interactions using orthogonal methods (e.g., CUT&Tag, reporter assays).

The Scientist's Toolkit: Essential Research Reagents and Materials

Table 3: Research Reagent Solutions for Cross-Species Validation Studies

Reagent/Material Function Example Application Considerations for Cross-Species Work
Oligo-FISH Probe Sets Chromosomal visualization and genome validation Validating chromosome-scale assemblies [87] Probe design must account for sequence divergence between species
Single-Cell Multiome Kits Simultaneous profiling of gene expression and chromatin accessibility GRN inference across species [85] [86] Protocol optimization may be needed for different species
Transposition Enzyme (Tn5) Tagmentation of accessible chromatin regions ATAC-seq for regulatory element identification Enzyme efficiency may vary across species; titration may be required
Cross-Species Harmony Integration Algorithms Computational integration of multi-species single-cell data Aligning homologous cell types across evolutionary lineages Requires careful parameterization to preserve biological variation
CUT&Tag Reagents Profiling transcription factor binding and histone modifications Validation of predicted TF-binding sites Antibody compatibility across species must be verified
Epigenome Editing Tools (CRISPR-dCas9) Functional validation of regulatory elements Testing enhancer activity across species Requires species-specific guide RNA design and delivery optimization

Workflow Visualization

Cross-Species GRN Inference and Validation Workflow

workflow start Sample Collection from Multiple Species multiome Single-Cell Multi-omics Profiling start->multiome preprocessing Data Preprocessing & Quality Control multiome->preprocessing integration Cross-Species Data Integration preprocessing->integration grn_inference GRN Inference (Pando, SCENIC+) integration->grn_inference comparison Network Comparison & Topology Analysis grn_inference->comparison prediction Identify Divergent & Conserved Interactions comparison->prediction validation Experimental Validation prediction->validation oligo_fish Oligo-FISH Genome Validation validation->oligo_fish functional Functional Assays (CRISPR, Reporters) validation->functional insights Evolutionary Insights & Models oligo_fish->insights functional->insights

Oligo-FISH Chromosome Validation Process

oligofish genome_assembly Draft Genome Assembly probe_design Oligonucleotide Probe Design genome_assembly->probe_design probe_labeling Probe Labeling with Fluorophores probe_design->probe_labeling hybridization In Situ Hybridization probe_labeling->hybridization metaphase Metaphase Spread Preparation metaphase->hybridization imaging Fluorescence Microscopy hybridization->imaging analysis Image Analysis & Signal Mapping imaging->analysis validation Chromosome Model Validation analysis->validation microchromosomes Microchromosome Confirmation analysis->microchromosomes

Application Notes for Evolutionary Studies

The integration of cross-species validation approaches with single-cell multi-omics has yielded significant insights into evolutionary mechanisms. For example, studies of craniofacial development have demonstrated that while genes involved in this process are highly conserved between marsupials and placental mammals, their cis-regulatory elements show significant divergence that likely reflects species-specific developmental processes [88]. Similarly, research on trained immunity has revealed evolutionarily conserved transcription factor networks that encode innate immune memory in long-lived stem cells across mammalian species [88].

These approaches are particularly powerful when applied to understanding human evolutionary history. Genomic investigations of ancient West Eurasians have identified signatures of positive selection related to adaptation to M. tuberculosis, revealing how autoimmune trade-offs have shaped modern genetic risk profiles for inflammatory bowel disease [89]. Such findings demonstrate the value of combining evolutionary genomics with functional validation to understand the health implications of our evolutionary past.

When implementing these protocols, researchers should consider that different taxonomic groups may present specific challenges. For example, studies of skinks and other reptiles must account for the presence of microchromosomes that require specialized assembly and validation approaches [87]. Similarly, cross-species comparisons of GRNs must distinguish genuine regulatory rewiring from technical artifacts arising from sequence divergence that affects probe hybridization or antibody binding in validation experiments.

Functional Enrichment and Linking GWAS Variants to Regulatory Mechanisms

Genome-wide association studies (GWAS) have successfully identified thousands of genetic variants associated with complex traits and diseases. However, over 90% of these variants lie in non-coding regions of the genome, obscuring their functional mechanisms and causal genes [90] [91]. This gap impedes the translation of genetic discoveries into biological insights and therapeutic interventions. Functional genomics approaches, particularly those utilizing single-cell multi-omics data, now enable researchers to map these non-coding variants to cell-type-specific regulatory mechanisms and gene networks.

The integration of single-cell RNA sequencing (scRNA-seq) and single-cell ATAC sequencing (scATAC-seq) provides unprecedented resolution for mapping enhancer-gene interactions and inferring gene regulatory networks (GRNs) across diverse cell types [90] [3]. These advancements are crucial for evolutionary developmental biology research, as they reveal how genetic variation shapes regulatory programs across cell types and developmental trajectories. This application note details computational protocols and experimental frameworks for linking GWAS variants to regulatory mechanisms through functional enrichment analysis and GRN inference.

Key Computational Methods for GRN Inference and Enhancer Mapping

Table 1: Computational Methods for Regulatory Mechanism Inference

Method Name Primary Function Key Innovation Data Input Requirements
scMultiMap [90] Infers cell-type-specific enhancer-gene pairs from multi-omics data Joint latent-variable model with analytical p-values; 100x faster than existing methods Paired scRNA-seq and scATAC-seq from same cells
LINGER [3] Infers gene regulatory networks (GRNs) using lifelong learning Incorporates atlas-scale external bulk data as manifold regularization Single-cell multiome data (paired gene expression & chromatin accessibility)
cRegulon [12] Identifies combinatorial TF regulatory modules Models TF cooperativity beyond single-TF regulons scRNA-seq and scATAC-seq (paired or unpaired)

Protocol: Linking GWAS Variants to Target Genes and Regulatory Mechanisms

The following diagram illustrates the comprehensive workflow for connecting GWAS variants to regulatory mechanisms and potential therapeutic targets:

G Start GWAS Variants (Non-coding) Step1 Cell Type Identification (Annotation Enrichment) Start->Step1 Step2 Multi-omics Data Collection (scRNA-seq + scATAC-seq) Step1->Step2 Step3 Enhancer-Gene Mapping (scMultiMap) Step2->Step3 Step4 GRN Inference (LINGER/cRegulon) Step3->Step4 Step5 Variant-to-Gene Linking (Colocalization/SMR) Step4->Step5 Step6 Functional Validation (Enhancer Assays) Step5->Step6 End Candidate Causal Genes & Regulatory Mechanisms Step6->End

Step-by-Step Protocol
Step 1: Identify Disease-Relevant Cell Types

Purpose: Determine which cell types show enrichment for GWAS signal and regulatory annotations.

Procedure:

  • Obtain GWAS summary statistics for your trait of interest from public repositories (GWAS Catalog, NIAGADS for neuropsychiatric traits)
  • Calculate enrichment of GWAS variants in cell-type-specific epigenetic markers using tools like LD Score Regression (LDSC)
  • Prioritize cell types with statistically significant enrichment (FDR < 0.05) for downstream analysis

Expected Output: Ranked list of cell types with enrichment p-values and fold-enrichment estimates.

Step 2: Generate or Access Single-Cell Multi-omics Data

Purpose: Acquire paired gene expression and chromatin accessibility data for prioritized cell types.

Procedure:

  • Sample preparation: Isolate nuclei from fresh or frozen tissue relevant to your disease context
  • Library preparation: Use multiome technologies (10x Multiome ATAC + Gene Expression) following manufacturer protocols
  • Sequencing: Aim for ≥10,000 cells per sample with ≥20,000 reads per cell for scRNA-seq and ≥10,000 reads per cell for scATAC-seq
  • Quality control: Filter cells with >20% mitochondrial reads (scRNA-seq) or TSS enrichment <4 (scATAC-seq)

Alternative Approach: Utilize public single-cell multi-omics datasets from resources like BRAIN Initiative Cell Census Network, Human Cell Atlas, or CellXGene.

Step 3: Map Enhancer-Gene Associations

Purpose: Identify statistical associations between regulatory elements and potential target genes.

Procedure:

  • Data preprocessing:
    • Create cell-by-gene (scRNA-seq) and cell-by-peak (scATAC-seq) matrices
    • Normalize for sequencing depth variations
    • Regress out technical covariates (mitochondrial percentage, nucleosome signal)
  • Run scMultiMap analysis:

  • Filter significant associations: Retain enhancer-gene pairs with FDR < 0.05 and correlation > 0.1

Validation: Compare associations with orthogonal datasets (Promoter Capture Hi-C, PLAC-seq) where available.

Step 4: Infer Gene Regulatory Networks

Purpose: Reconstruct comprehensive GRNs including TF-RE and TF-TG interactions.

Procedure:

  • Prepare input data:
    • Create pseudobulk profiles by aggregating cells within cell types or samples
    • Annotate TF-binding motifs in accessible chromatin regions
  • Run LINGER analysis:

  • Extract regulatory interactions: Use Shapley values to quantify TF-TG edge strengths

Alternative Approach: Apply cRegulon for combinatorial TF module identification [12].

Purpose: Connect non-coding GWAS variants to their regulated genes through statistical colocalization.

Procedure:

  • Perform colocalization analysis between GWAS signals and cell-type-specific eQTLs:

  • Apply Summary-data-based Mendelian Randomization (SMR) to test causal relationships between expression and traits
  • Integrate enhancer-gene links: Annotate GWAS variants falling within linked enhancers from Step 3

Interpretation: Prioritize gene-variant pairs with posterior probability of colocalization (PP4) > 0.8 and SMR p-value < 2.5×10^-6.

Step 6: Functional Validation and Prioritization

Purpose: Experimentally validate computational predictions and prioritize candidates for therapeutic development.

Procedure:

  • Enhancer activity assays: Clone putative enhancers containing GWAS variants into luciferase reporter vectors
  • CRISPR inhibition/activation: Target prioritized enhancers in relevant cell models and measure effects on candidate gene expression
  • Drug target prioritization:
    • Perform protein-protein interaction analysis for candidate genes
    • Conduct pathway enrichment (ERK1/2, PI3K/AKT signaling)
    • Query drug-gene databases (DSigDB) for repurposing opportunities

Table 2: Key Research Reagents and Computational Resources

Resource Type Specific Examples Function/Purpose Access Information
Reference Datasets ENCODE Epigenome Roadmap [3], GTEx eQTLs [3], BRAIN Initiative Cell Census Provide external regulatory annotations and expression quantitative trait loci for prioritization and validation Publicly available from respective consortia websites
Analysis Tools scMultiMap [90], LINGER [3], cRegulon [12], COLOC, SMR Perform statistical inference of enhancer-gene links, GRNs, and variant-to-function mapping GitHub repositories with documentation
Experimental Reagents 10x Genomics Multiome Kit, Luciferase Reporter Vectors, CRISPRa/i Systems Generate multi-omics data and validate computational predictions experimentally Commercial vendors (10x Genomics, Addgene, etc.)
Cell Type Markers Microglia (TMEM119, CX3CR1), Astrocytes (GFAP), Neuronal (RBFOX3) Annotate cell types in single-cell data and interpret cell-type-specific mechanisms Published cell type atlases and marker databases

Case Study: Application to Alzheimer's Disease Research

Alzheimer's Disease Regulatory Network Analysis

Recent applications in Alzheimer's disease demonstrate the power of this integrated approach. A multi-omics analysis of AD integrated five GWAS datasets with two single-cell eQTL datasets and one bulk eQTL dataset, identifying 28 candidate causal genes for AD [92]. The study revealed that microglia contributed the highest number of candidate genes, followed by excitatory neurons and astrocytes, highlighting the cell-type-specific nature of AD genetic architecture.

The analytical workflow employed SMR and Bayesian colocalization to prioritize genes, followed by enhancer activity analysis using H3K27ac and ATAC-seq data. This led to the discovery that AD-risk variants associated with candidate causal genes are frequently located near or within enhancers specifically active in disease-relevant cell types. For example, the novel candidate gene PABPC1 was found to be associated with an AD-risk variant located within an enhancer active only in astrocytes [92].

Signaling Pathways in Alzheimer's Disease

The following diagram illustrates key signaling pathways enriched for Alzheimer's disease risk genes identified through functional genomics approaches:

G Extracellular Extracellular Signals Membrane Membrane Receptors (Identified candidates) Extracellular->Membrane PI3K PI3K/AKT Signaling Membrane->PI3K ERK ERK1/2 Signaling Membrane->ERK Migration Cell Migration Pathways PI3K->Migration Organization Membrane Organization ERK->Organization Outcomes Disease Outcomes: Neurodegeneration & Cognitive Decline Migration->Outcomes Organization->Outcomes

The integration of single-cell multi-omics data with GWAS signals provides a powerful framework for mapping non-coding variants to cell-type-specific regulatory mechanisms. The protocols outlined here—from cell type identification and enhancer mapping to GRN inference and experimental validation—enable researchers to bridge the gap between genetic associations and biological mechanisms. For evolutionary developmental biology research, these approaches offer particular promise for understanding how genetic variation shapes regulatory programs across cell types and developmental trajectories, ultimately accelerating the identification of therapeutic targets for complex diseases.

Conclusion

The integration of single-cell multi-omics data with advanced computational models marks a paradigm shift in GRN inference, moving from correlative maps to predictive, mechanistic models of gene regulation. The key takeaways are the critical importance of leveraging large-scale external data, as demonstrated by LINGER, and the need to model combinatorial TF interactions, as enabled by cRegulon, to truly capture the logic of development and disease. While challenges in data sparsity, model interpretability, and standardization persist, the field is rapidly advancing through foundational models and federated computational ecosystems. Future directions point towards the integration of spatiotemporal data, the application of these networks for in silico drug perturbation screening, and the translation of these insights into clinically actionable strategies for precision medicine, ultimately bridging the gap between cellular omics and therapeutic innovation.

References