Gene Regulatory Network Inference Research Articles

Inferring gene regulatory networks from single-cell transcriptomics based on graph embedding.

Gene regulatory networks (GRNs) encode gene regulation in living organisms, and have become a critical tool to understand complex biological processes. However, due to the dynamic and complex nature of gene regulation, inferring GRNs from scRNA-seq data is still a challenging task. Existing computational methods usually focus on the close connections between genes, and ignore the global structure and distal regulatory relationships. In this study, we develop a supervised deep learning framework, IGEGRNS, to infer GRNs from scRNA-seq data based on graph embedding. In the framework, contextual information of genes is captured by GraphSAGE, which aggregates gene features and neighborhood structures to generate low-dimensional embedding for genes. Then, the k most influential nodes in the whole graph are filtered through Top-k pooling. Finally, potential regulatory relationships between genes are predicted by stacking CNNs. Compared with nine competing supervised and unsupervised methods, our method achieves better performance on six time-series scRNA-seq datasets. Our method IGEGRNS is implemented in Python using the Pytorch machine learning library, and it is freely available at https://github.com/DHUDBlab/IGEGRNS.

Organ-delimited gene regulatory networks provide high accuracy in candidate transcription factor selection across diverse processes

Organ-specific gene expression datasets that include hundreds to thousands of experiments allow the reconstruction of organ-level gene regulatory networks (GRNs). However, creating such datasets is greatly hampered by the requirements of extensive and tedious manual curation. Here, we trained a supervised classification model that can accurately classify the organ-of-origin for a plant transcriptome. This K-Nearest Neighbor-based multiclass classifier was used to create organ-specific gene expression datasets for the leaf, root, shoot, flower, and seed in Arabidopsis thaliana. A GRN inference approach was used to determine the: i. influential transcription factors (TFs) in each organ and, ii. most influential TFs for specific biological processes in that organ. These genome-wide, organ-delimited GRNs (OD-GRNs), recalled many known regulators of organ development and processes operating in those organs. Importantly, many previously unknown TF regulators were uncovered as potential regulators of these processes. As a proof-of-concept, we focused on experimentally validating the predicted TF regulators of lipid biosynthesis in seeds, an important food and biofuel trait. Of the top 20 predicted TFs, eight are known regulators of seed oil content, e.g., WRI1, LEC1, FUS3. Importantly, we validated our prediction of MybS2, TGA4, SPL12, AGL18, and DiV2 as regulators of seed lipid biosynthesis. We elucidated the molecular mechanism of MybS2 and show that it induces purple acid phosphatase family genes and lipid synthesis genes to enhance seed lipid content. This general approach has the potential to be extended to any species with sufficiently large gene expression datasets to find unique regulators of any trait-of-interest.

Topological benchmarking of algorithms to infer gene regulatory networks from single-cell RNA-seq data.

In recent years, many algorithms for inferring gene regulatory networks from single-cell transcriptomic data have been published. Several studies have evaluated their accuracy in estimating the presence of an interaction between pairs of genes. However, these benchmarking analyses do not quantify the algorithms' ability to capture structural properties of networks, which are fundamental, e.g., for studying the robustness of a gene network to external perturbations. Here, we devise a three-step benchmarking pipeline called STREAMLINE that quantifies the ability of algorithms to capture topological properties of networks and identify hubs. To this aim, we use data simulated from different types of networks as well as experimental data from three different organisms. We apply our benchmarking pipeline to four inference algorithms and provide guidance on which algorithm should be used depending on the global network property of interest. STREAMLINE is available at https://github.com/ScialdoneLab/STREAMLINE. The data generated in this study are available at https://doi.org/10.5281/zenodo.10710444.

Inferring gene regulatory networks from single-cell multiome data using atlas-scale external data.

Existing methods for gene regulatory network (GRN) inference rely on gene expression data alone or on lower resolution bulk data. Despite the recent integration of chromatin accessibility and RNA sequencing data, learning complex mechanisms from limited independent data points still presents a daunting challenge. Here we present LINGER (Lifelong neural network for gene regulation), a machine-learning method to infer GRNs from single-cell paired gene expression and chromatin accessibility data. LINGER incorporates atlas-scale external bulk data across diverse cellular contexts and prior knowledge of transcription factor motifs as a manifold regularization. LINGER achieves a fourfold to sevenfold relative increase in accuracy over existing methods and reveals a complex regulatory landscape of genome-wide association studies, enabling enhanced interpretation of disease-associated variants and genes. Following the GRN inference from reference single-cell multiome data, LINGER enables the estimation of transcription factor activity solely from bulk or single-cell gene expression data, leveraging the abundance of available gene expression data to identify driver regulators from case-control studies.

A Meta-Analysis Approach to Gene Regulatory Network Inference Identifies Key Regulators of Cardiovascular Diseases.

Cardiovascular diseases (CVDs) represent a major concern for global health, whose mechanistic understanding is complicated by a complex interplay between genetic predisposition and environmental factors. Specifically, heart failure (HF), encompassing dilated cardiomyopathy (DC), ischemic cardiomyopathy (ICM), and hypertrophic cardiomyopathy (HCM), is a topic of substantial interest in basic and clinical research. Here, we used a Partial Correlation Coefficient-based algorithm (PCC) within the context of a meta-analysis framework to construct a Gene Regulatory Network (GRN) that identifies key regulators whose activity is perturbed in Heart Failure. By integrating data from multiple independent studies, our approach unveiled crucial regulatory associations between transcription factors (TFs) and structural genes, emphasizing their pivotal roles in regulating metabolic pathways, such as fatty acid metabolism, oxidative stress response, epithelial-to-mesenchymal transition, and coagulation. In addition to known associations, our analysis also identified novel regulators, including the identification of TFs FPM315 and OVOL2, which are implicated in dilated cardiomyopathies, and TEAD1 and TEAD2 in both dilated and ischemic cardiomyopathies. Moreover, we uncovered alterations in adipogenesis and oxidative phosphorylation pathways in hypertrophic cardiomyopathy and discovered a role for IL2 STAT5 signaling in heart failure. Our findings underscore the importance of TF activity in the initiation and progression of cardiac disease, highlighting their potential as pharmacological targets.

Evolutionary and developmental specialization of foveal cell types in the marmoset

In primates, high-acuity vision is mediated by the fovea, a small specialized central region of the retina. The fovea, unique to the anthropoid lineage among mammals, undergoes notable neuronal morphological changes during postnatal maturation. However, the extent of cellular similarity across anthropoid foveas and the molecular underpinnings of foveal maturation remain unclear. Here, we used high-throughput single-cell RNA sequencing to profile retinal cells of the common marmoset (Callithrix jacchus), an early divergent in anthropoid evolution from humans, apes, and macaques. We generated atlases of the marmoset fovea and peripheral retina for both neonates and adults. Our comparative analysis revealed that marmosets share almost all their foveal types with both humans and macaques, highlighting a conserved cellular structure among primate foveas. Furthermore, by tracing the developmental trajectory of cell types in the foveal and peripheral retina, we found distinct maturation paths for each. In-depth analysis of gene expression differences demonstrated that cone photoreceptors and Müller glia (MG), among others, show the greatest molecular divergence between these two regions. Utilizing single-cell ATAC-seq and gene-regulatory network inference, we uncovered distinct transcriptional regulations differentiating foveal cones from their peripheral counterparts. Further analysis of predicted ligand-receptor interactions suggested a potential role for MG in supporting the maturation of foveal cones. Together, these results provide valuable insights into foveal development, structure, and evolution.

PMF-GRN: a variational inference approach to single-cell gene regulatory network inference using probabilistic matrix factorization.

Inferring gene regulatory networks (GRNs) from single-cell data is challenging due to heuristic limitations. Existing methods also lack estimates of uncertainty. Here we present Probabilistic Matrix Factorization for Gene Regulatory Network Inference (PMF-GRN). Using single-cell expression data, PMF-GRN infers latent factors capturing transcription factor activity and regulatory relationships. Using variational inference allows hyperparameter search for principled model selection and direct comparison to other generative models. We extensively test and benchmark our method using real single-cell datasets and synthetic data. We show that PMF-GRN infers GRNs more accurately than current state-of-the-art single-cell GRN inference methods, offering well-calibrated uncertainty estimates.

Abstract NG08: Dissecting and quantifying pancreatic cancer plasticity using single-cell multiomics, lineage tracing and functional genomics reveals novel mediators of therapy resistance

Abstract NG08: Dissecting and quantifying pancreatic cancer plasticity using single-cell multiomics, lineage tracing and functional genomics reveals novel mediators of therapy resistance

DeepFGRN: inference of gene regulatory network with regulation type based on directed graph embedding.

The inference of gene regulatory networks (GRNs) from gene expression profiles has been a key issue in systems biology, prompting many researchers to develop diverse computational methods. However, most of these methods do not reconstruct directed GRNs with regulatory types because of the lack of benchmark datasets or defects in the computational methods. Here, we collect benchmark datasets and propose a deep learning-based model, DeepFGRN, for reconstructing fine gene regulatory networks (FGRNs) with both regulation types and directions. In addition, the GRNs of real species are always large graphs with direction and high sparsity, which impede the advancement of GRN inference. Therefore, DeepFGRN builds a node bidirectional representation module to capture the directed graph embedding representation of the GRN. Specifically, the source and target generators are designed to learn the low-dimensional dense embedding of the source and target neighbors of a gene, respectively. An adversarial learning strategy is applied to iteratively learn the real neighbors of each gene. In addition, because the expression profiles of genes with regulatory associations are correlative, a correlation analysis module is designed. Specifically, this module not only fully extracts gene expression features, but also captures the correlation between regulators and target genes. Experimental results show that DeepFGRN has a competitive capability for both GRN and FGRN inference. Potential biomarkers and therapeutic drugs for breast cancer, liver cancer, lung cancer and coronavirus disease 2019 are identified based on the candidate FGRNs, providing a possible opportunity to advance our knowledge of disease treatments.

Investigating the mechanisms underlying resistance to chemotherapy and to CRISPR-Cas9 in cancer cell lines

Cancer is one of the major causes of death worldwide and the development of multidrug resistance (MDR) in cancer cells is the principal cause of chemotherapy failure. To gain insights into the specific mechanisms of MDR in cancer cell lines, we developed a novel method for the combined analysis of recently published datasets on drug sensitivity and CRISPR loss-of-function screens for the same set of cancer cell lines. For our analysis, we first selected cell lines that consistently exhibit drug resistance across several classes of compounds. We then identified putative resistance genes for each class of compound and used inferred gene regulatory networks (GRNs) to study possible mechanisms underlying the development of MDR in the identified cancer cell lines. We show that the same method of analysis can also be used to identify cell lines that consistently exhibit resistance to the gene knockout effect of the CRISPR-Cas9 technique and to study the possible underlying mechanisms. In the GRN associated to the drug resistant cell lines, we identify genes previously associated with resistance (UHMK1, RALYL, MGST3, USP9X, and ESRG), genes for which an indirect association can be identified (SPINK13, LINC00664, MRPL38, and EMILIN3), and genes that are found to be overexpressed in non-resistant cancer cell lines (MRPL38, EMILIN3 and RALYL). In the GRNs associated to the CRISPR-Cas9 resistance mechanism, none of the identified genes has been previously reported in the admittedly sparse literature on the subject. However, some of these genes have a common role: APBB2, RUNX1T1, ZBTB7C, and ISX regulate transcription, while APBB2, BTG3, ZBTB7C, SZRD1 and LEF1 have a function in regulating proliferation, suggesting a role for these two pathways. While our results are specific for the lung cancer cell lines we selected for this work, our method of analysis can be applied to cell lines from other tissues and for which the required data is available.

Dynamic Model Inference of Gene Regulatory Network based on Hybrid Parallel Genetic Algorithm and Threshold Qualification Method

Gene regulation is the process by which various substances in cells regulate the behaviour of gene expression, thereby controlling almost all cellular activities. Therefore, studying gene regulation not only helps to uncover the internal laws governing life processes but also plays a crucial role in predicting, diagnosing, treating, and designing drugs for genetic diseases. By utilizing multi-source biological information such as gene expression profiles, transcription factor information, and protein interaction data, a network model can be developed to depict the regulatory relationships between genes, facilitating further research. To address the limitations of traditional gene regulatory network construction methods, a novel dynamic model has been created by combining hybrid genetics and threshold restriction. This model comprises two parts: solution space reduction and parameter fitting. During solution space reduction, singular value decomposition is employed to define a mathematically feasible gene regulatory network, reducing unnecessary calculations. Subsequently, the control genes of each gene are constrained within a certain range using threshold limitation, enhancing computational efficiency while adhering to bioinformatics principles. In the parameter fitting phase, parallel genetic algorithms are utilized to expediently optimize the entire solution space. The mountain climbing method is then applied to solve problems meticulously within a limited scope, improving calculation accuracy. In this study, this approach was applied to establish genetic regulatory systems for complex skin melanoma and type 2 diabetes. Through comparison with actual networks, the validity of the method was confirmed. Compared to traditional genetic and particle swarm optimization methods, the effectiveness of the proposed method was verified. This paper models the intricate mechanism of gene regulation and elucidates the regulatory process involving genes, proteins, and small biological molecules in greater detail than other models, aligning more closely with intracellular dynamics laws.

ScGREAT: Transformer-based deep-language model for gene regulatory network inference from single-cell transcriptomics

Gene regulatory networks (GRNs) involve complex and multi-layer regulatory interactions between regulators and their target genes. Precise knowledge of GRNs is important in understanding cellular processes and molecular functions. Recent breakthroughs in single-cell sequencing technology made it possible to infer GRNs at single-cell level. Existing methods, however, are limited by expensive computations, and sometimes simplistic assumptions. To overcome these obstacles, we propose scGREAT, a framework to infer GRN using gene embeddings and transformer from single-cell transcriptomics. scGREAT starts by constructing gene expression and gene biotext dictionaries from scRNA-seq data and gene text information. The representation of TF gene pairs is learned through optimizing embedding space by transformer-based engine. Results illustrated scGREAT outperformed other contemporary methods on benchmarks. Besides, gene representations from scGREAT provide valuable gene regulation insights, and external validation on spatial transcriptomics illuminated the mechanism behind scGREAT annotation. Moreover, scGREAT identified several TF target regulations corroborated in studies.

Quantifying Landscape-Flux via Single-Cell Transcriptomics Uncovers the Underlying Mechanism of Cell Cycle.

Recent developments in single-cell sequencing technology enable the acquisition of entire transcriptome data. Understanding the underlying mechanism and identifying the driving force of transcriptional regulation governing cell function directly from these data remains challenging. This study reconstructs a continuous vector field of the cell cycle based on discrete single-cell RNA velocity to quantify the single-cell global nonequilibrium dynamic landscape-flux. It reveals that large fluctuations disrupt the global landscape and genetic perturbations alter landscape-flux, thus identifying key genes in maintaining cell cycle dynamics and predicting associated functional effects. Additionally, it quantifies the fundamental energy cost of the cell cycle initiation and unveils that sustaining the cell cycle requires curl flux and dissipation to maintain the oscillatory phase coherence. This study enables the inference of the cell cycle gene regulatory networks directly from the single-cell transcriptomic data, including the feedback mechanisms and interaction intensity. This provides a golden opportunity to experimentally verify the landscape-flux theory and also obtain its associated quantifications. It also offers a unique framework for combining the landscape-flux theory and single-cell high-through sequencing experiments for understanding the underlying mechanisms of the cell cycle and can be extended to other nonequilibrium biological processes, such as differentiation development and disease pathogenesis.

Prediction of protein-RNA interactions from single-cell transcriptomic data.

Proteins are crucial in regulating every aspect of RNA life, yet understanding their interactions with coding and noncoding RNAs remains limited. Experimental studies are typically restricted to a small number of cell lines and a limited set of RNA-binding proteins (RBPs). Although computational methods based on physico-chemical principles can predict protein-RNA interactions accurately, they often lack the ability to consider cell-type-specific gene expression and the broader context of gene regulatory networks (GRNs). Here, we assess the performance of several GRN inference algorithms in predicting protein-RNA interactions from single-cell transcriptomic data, and propose a pipeline, called scRAPID (single-cell transcriptomic-based RnA Protein Interaction Detection), that integrates these methods with the catRAPID algorithm, which can identify direct physical interactions between RBPs and RNA molecules. Our approach demonstrates that RBP-RNA interactions can be predicted from single-cell transcriptomic data, with performances comparable or superior to those achieved for the well-established task of inferring transcription factor-target interactions. The incorporation of catRAPID significantly enhances the accuracy of identifying interactions, particularly with long noncoding RNAs, and enables the identification of hub RBPs and RNAs. Additionally, we show that interactions between RBPs can be detected based on their inferred RNA targets. The software is freely available at https://github.com/tartaglialabIIT/scRAPID.

Inference of Gene Regulatory Networks Based on Multi-view Hierarchical Hypergraphs.

Since gene regulation is a complex process in which multiple genes act simultaneously, accurately inferring gene regulatory networks (GRNs) is a long-standing challenge in systems biology. Although graph neural networks can formally describe intricate gene expression mechanisms, current GRN inference methods based on graph learning regard only transcription factor (TF)-target gene interactions as pairwise relationships, and cannot model the many-to-many high-order regulatory patterns that prevail among genes. Moreover, these methods often rely on limited prior regulatory knowledge, ignoring the structural information of GRNs in gene expression profiles. Therefore, we propose a multi-view hierarchical hypergraphs GRN (MHHGRN) inference model. Specifically, multiple heterogeneous biological information is integrated to construct multi-view hierarchical hypergraphs of TFs and target genes, using hypergraph convolution networks to model higher order complex regulatory relationships. Meanwhile, the coupled information diffusion mechanism and the cross-domain messaging mechanism facilitate the information sharing between genes to optimise gene embedding representations. Finally, a unique channel attention mechanism is used to adaptively learn feature representations from multiple views for GRN inference. Experimental results show that MHHGRN achieves better results than the baseline methods on the E. coli and S. cerevisiae benchmark datasets of the DREAM5 challenge, and it has excellent cross-species generalization, achieving comparable or better performance on scRNA-seq datasets from five mouse and two human cell lines.

Gene regulatory network inference from gene expression data based on knowledge matrix and improved rotation forest

Research on gene expression, as well as the regulatory interactions governing it, has been considered one of the significant challenges in recent decades. The process of regulating gene expression determines which genes should be turned on and turned off at specific times. Microarray data provide a wealth of information regarding gene expression levels. Due to the large volume of such data, their analysis requires robust computational methods for identifying and analyzing gene regulation networks. However, scholars in this field encounter numerous challenges, including the high number of genes to be considered, the limited number of samples, and the inherently noisy nature of the data. Accordingly, the main purpose of the present study is to propose a modeling approach for inferring gene regulatory networks using regression-based and rotation forest methods. In this method, after initial processing, the data are divided into different clusters using clustering approaches. This categorization is utilized in the next step to extract the knowledge matrix. Subsequently, regulatory interactions governing genes are identified using an improved version of rotation forest based on t-SNE. Furthermore, the proposed approach has been compared with some significant methods commonly used in this discipline to evaluate its efficiency. The analysis results demonstrate that, due to the incorporation of hidden biological knowledge within the dataset during the network modeling process, the proposed model excels in identifying regulatory mechanisms. It not only aligns with top methods in the discipline but can also, at times, outperform them in identifying gene regulatory networks.

Statistical inference on qualitative differences in the magnitude of an effect.

Qualitative interactions occur when a treatment effect or measure of association varies in sign by sub-population. Of particular interest in many biomedical settings are absence/presence qualitative interactions, which occur when an effect is present in one sub-population but absent in another. Absence/presence interactions arise in emerging applications in precision medicine, where the objective is to identify a set of predictive biomarkers that have prognostic value for clinical outcomes in some sub-population but not others. They also arise naturally in gene regulatory network inference, where the goal is to identify differences in networks corresponding to diseased and healthy individuals, or to different subtypes of disease; such differences lead to identification of network-based biomarkers for diseases. In this paper, we argue that while the absence/presence hypothesis is important, developing a statistical test for this hypothesis is an intractable problem. To overcome this challenge, we approximate the problem in a novel inference framework. In particular, we propose to make inferences about absence/presence interactions by quantifying the relative difference in effect size, reasoning that when the relative difference is large, an absence/presence interaction occurs. The proposed methodology is illustrated through a simulation study as well as an analysis of breast cancer data from the Cancer Genome Atlas.

Application of Single-Cell Assay for Transposase-Accessible Chromatin with High Throughput Sequencing in Plant Science: Advances, Technical Challenges, and Prospects.

The Single-cell Assay for Transposase-Accessible Chromatin with high throughput sequencing (scATAC-seq) has gained increasing popularity in recent years, allowing for chromatin accessibility to be deciphered and gene regulatory networks (GRNs) to be inferred at single-cell resolution. This cutting-edge technology now enables the genome-wide profiling of chromatin accessibility at the cellular level and the capturing of cell-type-specific cis-regulatory elements (CREs) that are masked by cellular heterogeneity in bulk assays. Additionally, it can also facilitate the identification of rare and new cell types based on differences in chromatin accessibility and the charting of cellular developmental trajectories within lineage-related cell clusters. Due to technical challenges and limitations, the data generated from scATAC-seq exhibit unique features, often characterized by high sparsity and noise, even within the same cell type. To address these challenges, various bioinformatic tools have been developed. Furthermore, the application of scATAC-seq in plant science is still in its infancy, with most research focusing on root tissues and model plant species. In this review, we provide an overview of recent progress in scATAC-seq and its application across various fields. We first conduct scATAC-seq in plant science. Next, we highlight the current challenges of scATAC-seq in plant science and major strategies for cell type annotation. Finally, we outline several future directions to exploit scATAC-seq technologies to address critical challenges in plant science, ranging from plant ENCODE(The Encyclopedia of DNA Elements) project construction to GRN inference, to deepen our understanding of the roles of CREs in plant biology.

P167 Remodelling of the colonic molecular landscape in patients failing anti-TNF therapy highlights dysregulation of the extracellular matrix in ulcerative colitis

Abstract Background In patients with ulcerative colitis (UC) who previously failed anti-TNF therapy, subsequent treatment with other advanced therapies is generally less effective than they are in anti-TNF naïve patients. Since anti-TNF drugs are frequently used first-line in UC, drug sequencing depreciation poses a major clinical challenge. To understand potential underlying mechanisms, we compared the clinical and molecular phenotype of UC patients who failed anti-TNF therapy with those who were anti-TNF naïve. Methods Clinical information and mucosal gene expression profiles were collected from 262 anti-TNF naïve and 275 anti-TNF exposed individuals with moderate to severe UC enrolled in the UNIFI clinical trial programme. We assessed differences between the groups in terms of clinical parameters, gene expression levels, pathway and transcription factor activity, as well as cellular composition. Results Anti-TNF exposed patients had significantly increased disease duration (p=0. 000009), CRP (p=0.03), and histological severity[PN1] (p=0.002). After adjusting for these factors, we identified 1,592 genes differentially expressed (FDR < 0.05), although the expression changes were quite modest. Pathway analysis linked previous anti-TNF exposure to significant downregulation of TNF and NFkB signalling and up-regulation of extracellular matrix components, stroma-related signatures, and growth factor receptor (EGFR, MAPK, PI3K) and TGFb signalling. These data were in line with results from cellular deconvolution methods, which showed an increase in stromal cell abundance and T cell depletion following anti-TNF failure. Gene regulatory network inference suggested that the observed gene expression differences were driven by increased activity of many transcriptional regulators, including those downstream of RUNX1 and RUNX3. Conclusion In patients with active UC, prior anti-TNF failure is associated with molecular remodelling of the colon characterised by dysregulated ECM organisation and shifts in stromal compartments. These data provide new insights into potential mechanisms of drug sequencing depreciation and could inform novel strategies to overcome this challenging clinical phenomenon.

GMFGRN: a matrix factorization and graph neural network approach for gene regulatory network inference.

The recent advances of single-cell RNA sequencing (scRNA-seq) have enabled reliable profiling of gene expression at the single-cell level, providing opportunities for accurate inference of gene regulatory networks (GRNs) on scRNA-seq data. Most methods for inferring GRNs suffer from the inability to eliminate transitive interactions or necessitate expensive computational resources. To address these, we present a novel method, termed GMFGRN, for accurate graph neural network (GNN)-based GRN inference from scRNA-seq data. GMFGRN employs GNN for matrix factorization and learns representative embeddings for genes. For transcription factor-gene pairs, it utilizes the learned embeddings to determine whether they interact with each other. The extensive suite of benchmarking experiments encompassing eight static scRNA-seq datasets alongside several state-of-the-art methods demonstrated mean improvements of 1.9 and 2.5% over the runner-up in area under the receiver operating characteristic curve (AUROC) and area under the precision-recall curve (AUPRC). In addition, across four time-series datasets, maximum enhancements of 2.4 and 1.3% in AUROC and AUPRC were observed in comparison to the runner-up. Moreover, GMFGRN requires significantly less training time and memory consumption, with time and memory consumed <10% compared to the second-best method. These findings underscore the substantial potential of GMFGRN in the inference of GRNs. It is publicly available at https://github.com/Lishuoyy/GMFGRN.