Models Of Gene Regulatory Networks Research Articles

Using phenotypic plasticity to understand the structure and evolution of the genotype–phenotype map

Deciphering the genotype-phenotype map necessitates relating variation at the genetic level to variation at the phenotypic level. This endeavour is inherently limited by the availability of standing genetic variation, the rate of spontaneous mutation to novo genetic variants, and possible biases associated with induced mutagenesis. An interesting alternative is to instead rely on the environment as a source of variation. Many phenotypic traits change plastically in response to the environment, and these changes are generally underlain by changes in gene expression. Relating gene expression plasticity to the phenotypic plasticity of more integrated organismal traits thus provides useful information about which genes influence the development and expression of which traits, even in the absence of genetic variation. We here appraise the prospects and limits of such an environment-for-gene substitution for investigating the genotype-phenotype map. We review models of gene regulatory networks, and discuss the different ways in which they can incorporate the environment to mechanistically model phenotypic plasticity and its evolution. We suggest that substantial progress can be made in deciphering this genotype-environment-phenotype map, by connecting theory on gene regulatory network to empirical patterns of gene co-expression, and by more explicitly relating gene expression to the expression and development of phenotypes, both theoretically and empirically.

On the almost periodicity in discontinuous impulsive gene regulatory networks

In this paper, the almost periodic solutions for discontinuous impulsive gene regulatory networks (GRNs) are investigated. Firstly, the concept of almost periodicity is introduced for the impulsive model under consideration. Secondly, sufficient conditions are presented for the existence, uniqueness, and global exponential stability of almost periodic solutions. To this end, an estimate of the Cauchy matrix of the model of GRNs is established. Finally, the obtained results as well as the control power of the impulses are demonstrated via examples. This research contributes to the development of the qualitative theory of impulsive GRNs in almost periodic environment.

GRAND: a database of gene regulatory network models across human conditions.

Gene regulation plays a fundamental role in shaping tissue identity, function, and response to perturbation. Regulatory processes are controlled by complex networks of interacting elements, including transcription factors, miRNAs and their target genes. The structure of these networks helps to determine phenotypes and can ultimately influence the development of disease or response to therapy. We developed GRAND (https://grand.networkmedicine.org) as a database for computationally-inferred, context-specific gene regulatory network models that can be compared between biological states, or used to predict which drugs produce changes in regulatory network structure. The database includes 12 468 genome-scale networks covering 36 human tissues, 28 cancers, 1378 unperturbed cell lines, as well as 173 013 TF and gene targeting scores for 2858 small molecule-induced cell line perturbation paired with phenotypic information. GRAND allows the networks to be queried using phenotypic information and visualized using a variety of interactive tools. In addition, it includes a web application that matches disease states to potentially therapeutic small molecule drugs using regulatory network properties.

Bursting and complex oscillatory patterns in a gene regulatory network model

Bursting is a dynamical behavior that has been widely observed in biological, chemical, and physical systems. It is well-known that the bursting behavior can occur in systems exhibiting distinct fast and slow time scales. Here, we show that bursting can happen in gene regulatory network systems without distinct fast and slow time scales. We perform bifurcation analyses to unravel the mechanisms underlying bursting behaviors in this model. We demonstrate that the bursting behavior is originated from a secondary Hopf bifurcation of a limit cycle, and terminated at a saddle-node bifurcation on an invariant circle. During the bursting cycle, the system evolves from the vicinity of a ghost point due to a disappeared stable fixed point to an unstable focus, then from the unstable focus to an unstable limit cycle, and finally from the unstable limit cycle back to the vicinity of the ghost point again. Our study provides a new mechanism for bursting dynamics in complex systems.

Landscape and kinetic path quantify critical transitions in epithelial-mesenchymal transition

Epithelial-mesenchymal transition (EMT), a basic developmental process that might promote cancer metastasis, has been studied from various perspectives. Recently, the early warning theory has been used to anticipate critical transitions in EMT from mathematical modeling. However, the underlying mechanisms of EMT involving complex molecular networks remain to be clarified. Especially, how to quantify the global stability and stochastic transition dynamics of EMT and what the underlying mechanism for early warning theory in EMT is remain to be fully clarified. To address these issues, we constructed a comprehensive gene regulatory network model for EMT and quantified the corresponding potential landscape. The landscape for EMT displays multiple stable attractors, which correspond to E, M, and some other intermediate states. Based on the path-integral approach, we identified the most probable transition paths of EMT, which are supported by experimental data. Correspondingly, the results of transition actions demonstrated that intermediate states can accelerate EMT, consistent with recent studies. By integrating the landscape and path with early warning concept, we identified the potential barrier height from the landscape as a global and more accurate measure for early warning signals to predict critical transitions in EMT. The landscape results also provide an intuitive and quantitative explanation for the early warning theory. Overall, the landscape and path results advance our mechanistic understanding of dynamical transitions and roles of intermediate states in EMT, and the potential barrier height provides a new, to our knowledge, measure for critical transitions and quantitative explanations for the early warning theory.

Modeling gene regulatory networks using neural network architectures.

Gene regulatory networks (GRNs) encode the complex molecular interactions that govern cell identity. Here we propose DeepSEM, a deep generative model that can jointly infer GRNs and biologically meaningful representation of single-cell RNA sequencing (scRNA-seq) data. In particular, we developed a neural network version of the structural equation model (SEM) to explicitly model the regulatory relationships among genes. Benchmark results show that DeepSEM achieves comparable or better performance on a variety of single-cell computational tasks, such as GRN inference, scRNA-seq data visualization, clustering and simulation, compared with the state-of-the-art methods. In addition, the gene regulations predicted by DeepSEM on cell-type marker genes in the mouse cortex can be validated by epigenetic data, which further demonstrates the accuracy and efficiency of our method. DeepSEM can provide a useful and powerful tool to analyze scRNA-seq data and infer a GRN.

Impulsive Fractional Differential Inclusions and Almost Periodic Waves

In the present paper, the concept of almost periodic waves is introduced to discontinuous impulsive fractional inclusions involving Caputo fractional derivative. New results on the existence and uniqueness are established by using the theory of operator semigroups, Hausdorff measure of noncompactness, fixed point theorems and fractional calculus techniques. Applications to a class of fractional-order impulsive gene regulatory network (GRN) models are proposed to illustrate the results.

An IRF1-IRF4 Toggle-Switch Controls Tolerogenic and Immunogenic Transcriptional Programming in Human Langerhans Cells.

Langerhans cells (LCs) reside in the epidermis as a dense network of immune system sentinels, coordinating both immunogenic and tolerogenic immune responses. To determine molecular switches directing induction of LC immune activation, we performed mathematical modelling of gene regulatory networks identified by single cell RNA sequencing of LCs exposed to TNF-alpha, a key pro-inflammatory signal produced by the skin. Our approach delineated three programmes of LC phenotypic activation (immunogenic, tolerogenic or ambivalent), and confirmed that TNF-alpha enhanced LC immunogenic programming. Through regulon analysis followed by mutual information modelling, we identified IRF1 as the key transcription factor for the regulation of immunogenicity in LCs. Application of a mathematical toggle switch model, coupling IRF1 with tolerance-inducing transcription factors, determined the key set of transcription factors regulating the switch between tolerance and immunogenicity, and correctly predicted LC behaviour in LCs derived from different body sites. Our findings provide a mechanistic explanation of how combinatorial interactions between different transcription factors can coordinate specific transcriptional programmes in human LCs, interpreting the microenvironmental context of the local tissue microenvironments.

Prediction and Boolean logical modelling of synergistic microRNA regulatory networks during reprogramming of male germline pluripotent stem cells

Unipotent male germline stem (GS) cells can undergo spontaneous reprogramming to germline pluripotent stem (GPS) cells during in vitro culture. In our previous study, we proposed a Boolean logical model of gene regulatory network (GRN) during reprogramming of GS cells to GPS cells. This study was designed to predict and model synergistic microRNA (miRNA) regulatory network during reprogramming of GS cells into GPS cells. The miRNAs targeting differentially expressed genes (DEGs) among GS and GPS cells were predicted by a novel Gene Ontology (GO) enrichment analysis to construct miRNA synergistic networks (MSN) and identify regulatory miRNA modules. Qualitative Boolean logical model of synergistic miRNAs and its regulated genes was then constructed by considering discrete, asynchronous, multivalued logical formalism using the GINsim modeling and simulation tools. Topology, functional and community overlap studies revealed that mmu-miR-200b-3p, mmu-miR-429–3p and mmu-miR-141–3p, mmu-miR-200a-3p and mmu-miR-200c-3p in MSN belongs to the family of miR-200/429/141 and conjectured to control the pluripotency and reprogramming by promoting Mesenchymal to Epithelial Transition (MET). Synergistic network involving mmu-miR-20b-5p, mmu-miR-20a-5p, mmu-miR-106a-5p, mmu-miR-106b-5p, and mmu-miR-17–5p were found to be essential for the maintenance of GS cells. Logical miRNA regulatory network modelling showed that synergistic miRNAs regulates the gene dynamics of MET during GS-GPS reprogramming, as confirmed by perturbation analysis. Taken together, our study predicted novel synergistic miRNAs involved in the regulation of reprogramming and pluripotency in GPS cells. The Boolean logical model of synergistic miRNAs regulatory network further confirms our previous study that gene dynamics of MET regulates GS-GPS reprogramming.

Identifying molecular targets for reverse aging using integrated network analysis of transcriptomic and epigenomic changes during aging

Aging is associated with widespread physiological changes, including skeletal muscle weakening, neuron system degeneration, hair loss, and skin wrinkling. Previous studies have identified numerous molecular biomarkers involved in these changes, but their regulatory mechanisms and functional repercussions remain elusive. In this study, we conducted next-generation sequencing of DNA methylation and RNA sequencing of blood samples from 51 healthy adults between 20 and 74 years of age and identified aging-related epigenetic and transcriptomic biomarkers. We also identified candidate molecular targets that can reversely regulate the transcriptomic biomarkers of aging by reconstructing a gene regulatory network model and performing signal flow analysis. For validation, we screened public experimental data including gene expression profiles in response to thousands of chemical perturbagens. Despite insufficient data on the binding targets of perturbagens and their modes of action, curcumin, which reversely regulated the biomarkers in the experimental dataset, was found to bind and inhibit JUN, which was identified as a candidate target via signal flow analysis. Collectively, our results demonstrate the utility of a network model for integrative analysis of omics data, which can help elucidate inter-omics regulatory mechanisms and develop therapeutic strategies against aging.

Evolution of dominance in gene expression pattern associated with phenotypic robustness

BackgroundMendelian inheritance is a fundamental law of genetics. When we consider two genomes in a diploid cell, a heterozygote’s phenotype is dominated by a particular homozygote according to the law of dominance. Classical Mendelian dominance is concerned with which proteins are dominant, and is usually based on simple genotype–phenotype relationship in which one gene regulates one phenotype. However, in reality, some interactions between genes can exist, resulting in deviations from Mendelian dominance. Whether and how Mendelian dominance is generalized to the phenotypes of gene expression determined by gene regulatory networks (GRNs) remains elusive.ResultsHere, by using the numerical evolution of diploid GRNs, we discuss whether the dominance of phenotype evolves beyond the classical Mendelian case of one-to-one genotype–phenotype relationship. We examine whether complex genotype–phenotype relationship can achieve Mendelian dominance at the expression level by a pair of haplotypes through the evolution of the GRN with interacting genes. This dominance is defined via a pair of haplotypes that differ from each other but have a common phenotype given by the expression of target genes. We numerically evolve the GRN model for a diploid case, in which two GRN matrices are added to give gene expression dynamics and simulate evolution with meiosis and recombination. Our results reveal that group Mendelian dominance evolves even under complex genotype–phenotype relationship. Calculating the degree of dominance shows that it increases through the evolution, correlating closely with the decrease in phenotypic fluctuations and the increase in robustness to initial noise. We also demonstrate that the dominance of gene expression patterns evolves concurrently. This evolution of group Mendelian dominance and pattern dominance is associated with phenotypic robustness against meiosis-induced genome mixing, whereas sexual recombination arising from the mixing of genomes from the parents further enhances dominance and robustness. Due to this dominance, the robustness to genetic differences increases, while optimal fitness is sustained to a significant difference between the two genomes.ConclusionGroup Mendelian dominance and gene-expression pattern dominance are achieved associated with the increase in phenotypic robustness to noise.

A KMT2A-AFF1 gene regulatory network highlights the role of core transcription factors and reveals the regulatory logic of key downstream target genes.

Regulatory interactions mediated by transcription factors (TFs) make up complex networks that control cellular behavior. Fully understanding these gene regulatory networks (GRNs) offers greater insight into the consequences of disease-causing perturbations than can be achieved by studying single TF binding events in isolation. Chromosomal translocations of the lysine methyltransferase 2A (KMT2A) gene produce KMT2A fusion proteins such as KMT2A-AFF1 (previously MLL-AF4), causing poor prognosis acute lymphoblastic leukemias (ALLs) that sometimes relapse as acute myeloid leukemias (AMLs). KMT2A-AFF1 drives leukemogenesis through direct binding and inducing the aberrant overexpression of key genes, such as the anti-apoptotic factor BCL2 and the proto-oncogene MYC. However, studying direct binding alone does not incorporate possible network-generated regulatory outputs, including the indirect induction of gene repression. To better understand the KMT2A-AFF1-driven regulatory landscape, we integrated ChIP-seq, patient RNA-seq, and CRISPR essentiality screens to generate a model GRN. This GRN identified several key transcription factors such as RUNX1 that regulate target genes downstream of KMT2A-AFF1 using feed-forward loop (FFL) and cascade motifs. A core set of nodes are present in both ALL and AML, and CRISPR screening revealed several factors that help mediate response to the drug venetoclax. Using our GRN, we then identified a KMT2A-AFF1:RUNX1 cascade that represses CASP9, as well as KMT2A-AFF1-driven FFLs that regulate BCL2 and MYC through combinatorial TF activity. This illustrates how our GRN can be used to better connect KMT2A-AFF1 behavior to downstream pathways that contribute to leukemogenesis, and potentially predict shifts in gene expression that mediate drug response.

Inferring gene regulatory network from single-cell transcriptomic data by integrating multiple prior networks

Gene regulatory network models the interactions between transcription factors and target genes. Reconstructing gene regulation network is critically important to understand gene function in a particular cellular context, providing key insights into complex biological systems. We develop a new computational method, named iMPRN, which integrates multiple prior networks to infer regulatory network. Based on the network component analysis model, iMPRN adopts linear regression, graph embedding, and elastic networks to optimize each prior network in line with specific biological context. For each rewired prior networks, iMPRN evaluate the confidence of the regulatory edges in each network based on B scores and finally integrated these optimized networks. We validate the effectiveness of iMPRN by comparing it with four widely-used gene regulatory network reconstruction algorithms on a simulation data set. The results show that iMPRN can infer the gene regulatory network more accurately. Further, on a real scRNA-seq dataset, iMPRN is respectively applied to reconstruct gene regulatory networks for malignant and nonmalignant head and neck tumor cells, demonstrating distinctive differences in their corresponding regulatory networks.

A multiscale compartment-based model of stochastic gene regulatory networks using hitting-time analysis.

Spatial stochastic models of single cell kinetics are capable of capturing both fluctuations in molecular numbers and the spatial dependencies of the key steps of intracellular regulatory networks. The spatial stochastic model can be simulated both on a detailed microscopic level using particle tracking and on a mesoscopic level using the reaction–diffusion master equation. However, despite substantial progress on simulation efficiency for spatial models in the last years, the computational cost quickly becomes prohibitively expensive for tasks that require repeated simulation of thousands or millions of realizations of the model. This limits the use of spatial models in applications such as multicellular simulations, likelihood-free parameter inference, and robustness analysis. Further approximation of the spatial dynamics is needed to accelerate such computational engineering tasks. We here propose a multiscale model where a compartment-based model approximates a detailed spatial stochastic model. The compartment model is constructed via a first-exit time analysis on the spatial model, thus capturing critical spatial aspects of the fine-grained simulations, at a cost close to the simple well-mixed model. We apply the multiscale model to a canonical model of negative-feedback gene regulation, assess its accuracy over a range of parameters, and demonstrate that the approximation can yield substantial speedups for likelihood-free parameter inference.

Inference of dynamic spatial GRN models with multi-GPU evolutionary computation.

Reverse engineering mechanistic gene regulatory network (GRN) models with a specific dynamic spatial behavior is an inverse problem without analytical solutions in general. Instead, heuristic machine learning algorithms have been proposed to infer the structure and parameters of a system of equations able to recapitulate a given gene expression pattern. However, these algorithms are computationally intensive as they need to simulate millions of candidate models, which limits their applicability and requires high computational resources. Graphics processing unit (GPU) computing is an affordable alternative for accelerating large-scale scientific computation, yet no method is currently available to exploit GPU technology for the reverse engineering of mechanistic GRNs from spatial phenotypes. Here we present an efficient methodology to parallelize evolutionary algorithms using GPU computing for the inference of mechanistic GRNs that can develop a given gene expression pattern in a multicellular tissue area or cell culture. The proposed approach is based on multi-CPU threads running the lightweight crossover, mutation and selection operators and launching GPU kernels asynchronously. Kernels can run in parallel in a single or multiple GPUs and each kernel simulates and scores the error of a model using the thread parallelism of the GPU. We tested this methodology for the inference of spatiotemporal mechanistic gene regulatory networks (GRNs)-including topology and parameters-that can develop a given 2D gene expression pattern. The results show a 700-fold speedup with respect to a single CPU implementation. This approach can streamline the extraction of knowledge from biological and medical datasets and accelerate the automatic design of GRNs for synthetic biology applications.

Temporal dynamics of a CSF1R signaling gene regulatory network involved in epilepsy.

Colony Stimulating Factor 1 Receptor (CSF1R) is a potential target for anti-epileptic drugs. However, inhibition of CSF1R is not well tolerated by patients, thereby prompting the need for alternative targets. To develop a framework for identification of such alternatives, we here develop a mathematical model of a pro-inflammatory gene regulatory network (GRN) involved in epilepsy and centered around CSF1R. This GRN comprises validated transcriptional and post-transcriptional regulations involving STAT1, STAT3, NFκB, IL6R, CSF3R, IRF8, PU1, C/EBPα, TNFR1, CSF1 and CSF1R. The model was calibrated on mRNA levels of all GRN components in lipopolysaccharide (LPS)-treated mouse microglial BV-2 cells, and allowed to predict that STAT1 and STAT3 have the strongest impact on the expression of the other GRN components. Microglial BV-2 cells were selected because, the modules from which the GRN was deduced are enriched for microglial marker genes. The function of STAT1 and STAT3 in the GRN was experimentally validated in BV-2 cells. Further, in silico analysis of the GRN dynamics predicted that a pro-inflammatory stimulus can induce irreversible bistability whereby the expression level of GRN components occurs as two distinct states. The irreversibility of the switch may enforce the need for chronic inhibition of the CSF1R GRN in order to achieve therapeutic benefit. The cell-to-cell heterogeneity driven by the bistability may cause variable therapeutic response. In conclusion, our modeling approach uncovered a GRN controlling CSF1R that is predominantly regulated by STAT1 and STAT3. Irreversible inflammation-induced bistability and cell-to-cell heterogeneity of the GRN provide a theoretical foundation to the need for chronic GRN control and the limited potential for disease modification via inhibition of CSF1R.

Phase transitions and assortativity in models of gene regulatory networks evolved under different selection processes.

We study a simplified model of gene regulatory network evolution in which links (regulatory interactions) are added via various selection rules that are based on the structural and dynamical features of the network nodes (genes). Similar to well-studied models of 'explosive' percolation, in our approach, links are selectively added so as to delay the transition to large-scale damage propagation, i.e. to make the network robust to small perturbations of gene states. We find that when selection depends only on structure, evolved networks are resistant to widespread damage propagation, even without knowledge of individual gene propensities for becoming 'damaged'. We also observe that networks evolved to avoid damage propagation tend towards disassortativity (i.e. directed links preferentially connect high degree 'source' genes to low degree 'target' genes and vice versa). We compare our simulations to reconstructed gene regulatory networks for several different species, with genes and links added over evolutionary time, and we find a similar bias towards disassortativity in the reconstructed networks.

Emergence of co-expression in gene regulatory networks.

Transcriptomes are known to organize themselves into gene co-expression clusters or modules where groups of genes display distinct patterns of coordinated or synchronous expression across independent biological samples. The functional significance of these co-expression clusters is suggested by the fact that highly coexpressed groups of genes tend to be enriched in genes involved in common functions and biological processes. While gene co-expression is widely assumed to reflect close regulatory proximity, the validity of this assumption remains unclear. Here we use a simple synthetic gene regulatory network (GRN) model and contrast the resulting co-expression structure produced by these networks with their known regulatory architecture and with the co-expression structure measured in available human expression data. Using randomization tests, we found that the levels of co-expression observed in simulated expression data were, just as with empirical data, significantly higher than expected by chance. When examining the source of correlated expression, we found that individual regulators, both in simulated and experimental data, fail, on average, to display correlated expression with their immediate targets. However, highly correlated gene pairs tend to share at least one common regulator, while most gene pairs sharing common regulators do not necessarily display correlated expression. Our results demonstrate that widespread co-expression naturally emerges in regulatory networks, and that it is a reliable and direct indicator of active co-regulation in a given cellular context.

Striking parallels between dorsoventral patterning in Drosophila and Gryllus reveal a complex evolutionary history behind a model gene regulatory network.

Dorsoventral pattering relies on Toll and BMP signalling in all insects studied so far, with variations in the relative contributions of both pathways. Drosophila and the beetle Tribolium share extensive dependence on Toll, while representatives of more distantly related lineages like the wasp Nasonia and bug Oncopeltus rely more strongly on BMP signalling. Here, we show that in the cricket Gryllus bimaculatus, an evolutionarily distant outgroup, Toll has, like in Drosophila, a direct patterning role for the ventral half of the embryo. In addition, Toll polarises BMP signalling, although this does not involve the conserved BMP inhibitor Sog/Chordin. Finally, Toll activation relies on ovarian patterning mechanisms with striking similarity to Drosophila. Our data suggest two surprising hypotheses: (1) that Toll's patterning function in Gryllus and Drosophila is the result of convergent evolution or (2) a Drosophila-like system arose early in insect evolution and was extensively altered in multiple independent lineages.

A computer-guided design tool to increase the efficiency of cellular conversions

Human cell conversion technology has become an important tool for devising new cell transplantation therapies, generating disease models and testing gene therapies. However, while transcription factor over-expression-based methods have shown great promise in generating cell types in vitro, they often endure low conversion efficiency. In this context, great effort has been devoted to increasing the efficiency of current protocols and the development of computational approaches can be of great help in this endeavor. Here we introduce a computer-guided design tool that combines a computational framework for prioritizing more efficient combinations of instructive factors (IFs) of cellular conversions, called IRENE, with a transposon-based genomic integration system for efficient delivery. Particularly, IRENE relies on a stochastic gene regulatory network model that systematically prioritizes more efficient IFs by maximizing the agreement of the transcriptional and epigenetic landscapes between the converted and target cells. Our predictions substantially increased the efficiency of two established iPSC-differentiation protocols (natural killer cells and melanocytes) and established the first protocol for iPSC-derived mammary epithelial cells with high efficiency.