Models Of Gene Regulatory Networks Research Articles

A logic-incorporated gene regulatory network deciphers principles in cell fate decisions.

Organisms utilize gene regulatory networks (GRN) to make fate decisions, but the regulatory mechanisms of transcription factors (TF) in GRNs are exceedingly intricate. A longstanding question in this field is how these tangled interactions synergistically contribute to decision-making procedures. To comprehensively understand the role of regulatory logic in cell fate decisions, we constructed a logic-incorporated GRN model and examined its behavior under two distinct driving forces (noise-driven and signal-driven). Under the noise-driven mode, we distilled the relationship among fate bias, regulatory logic, and noise profile. Under the signal-driven mode, we bridged regulatory logic and progression-accuracy trade-off, and uncovered distinctive trajectories of reprogramming influenced by logic motifs. In differentiation, we characterized a special logic-dependent priming stage by the solution landscape. Finally, we applied our findings to decipher three biological instances: hematopoiesis, embryogenesis, and trans-differentiation. Orthogonal to the classical analysis of expression profile, we harnessed noise patterns to construct the GRN corresponding to fate transition. Our work presents a generalizable framework for top-down fate-decision studies and a practical approach to the taxonomy of cell fate decisions.

A logic-incorporated gene regulatory network deciphers principles in cell fate decisions

Organisms utilize gene regulatory networks (GRN) to make fate decisions, but the regulatory mechanisms of transcription factors (TF) in GRNs are exceedingly intricate. A longstanding question in this field is how these tangled interactions synergistically contribute to decision-making procedures. To comprehensively understand the role of regulatory logic in cell fate decisions, we constructed a logic-incorporated GRN model and examined its behavior under two distinct driving forces (noise-driven and signal-driven). Under the noise-driven mode, we distilled the relationship among fate bias, regulatory logic, and noise profile. Under the signal-driven mode, we bridged regulatory logic and progression-accuracy trade-off, and uncovered distinctive trajectories of reprogramming influenced by logic motifs. In differentiation, we characterized a special logic-dependent priming stage by the solution landscape. Finally, we applied our findings to decipher three biological instances: hematopoiesis, embryogenesis, and trans-differentiation. Orthogonal to the classical analysis of expression profile, we harnessed noise patterns to construct the GRN corresponding to fate transition. Our work presents a generalizable framework for top-down fate-decision studies and a practical approach to the taxonomy of cell fate decisions.

Effects of Small Random Perturbations in the Extended Glass–Kauffman Model of Gene Regulatory Networks

Effects of Small Random Perturbations in the Extended Glass–Kauffman Model of Gene Regulatory Networks

Data-driven modeling of core gene regulatory network underlying leukemogenesis in IDH mutant AML

Acute myeloid leukemia (AML) is characterized by uncontrolled proliferation of poorly differentiated myeloid cells, with a heterogenous mutational landscape. Mutations in IDH1 and IDH2 are found in 20% of the AML cases. Although much effort has been made to identify genes associated with leukemogenesis, the regulatory mechanism of AML state transition is still not fully understood. To alleviate this issue, here we develop a new computational approach that integrates genomic data from diverse sources, including gene expression and ATAC-seq datasets, curated gene regulatory interaction databases, and mathematical modeling to establish models of context-specific core gene regulatory networks (GRNs) for a mechanistic understanding of tumorigenesis of AML with IDH mutations. The approach adopts a new optimization procedure to identify the top network according to its accuracy in capturing gene expression states and its flexibility to allow sufficient control of state transitions. From GRN modeling, we identify key regulators associated with the function of IDH mutations, such as DNA methyltransferase DNMT1, and network destabilizers, such as E2F1. The constructed core regulatory network and outcomes of in-silico network perturbations are supported by survival data from AML patients. We expect that the combined bioinformatics and systems-biology modeling approach will be generally applicable to elucidate the gene regulation of disease progression.

Effects of mRNA conformational switching on translational noise in gene circuits.

Intragenic translational heterogeneity describes the variation in translation at the level of transcripts for an individual gene. A factor that contributes to this source of variation is the mRNA structure. Both the composition of the thermodynamic ensemble, i.e., the stationary distribution of mRNA structures, and the switching dynamics between those play a role. The effect of the switching dynamics on intragenic translational heterogeneity remains poorly understood. We present a stochastic translation model that accounts for mRNA structure switching and is derived from a Markov model via approximate stochastic filtering. We assess the approximation on various timescales and provide a method to quantify how mRNA structure dynamics contributes to translational heterogeneity. With our approach, we allow quantitative information on mRNA switching from biophysical experiments or coarse-grain molecular dynamics simulations of mRNA structures to be included in gene regulatory chemical reaction network models without an increase in the number of species. Thereby, our model bridges a gap between mRNA structure kinetics and gene expression models, which we hope will further improve our understanding of gene regulatory networks and facilitate genetic circuit design.

Biologically meaningful regulatory logic enhances the convergence rate in Boolean networks and bushiness of their state transition graph.

Boolean models of gene regulatory networks (GRNs) have gained widespread traction as they can easily recapitulate cellular phenotypes via their attractor states. Their overall dynamics are embodied in a state transition graph (STG). Indeed, two Boolean networks (BNs) with the same network structure and attractors can have drastically different STGs depending on the type of Boolean functions (BFs) employed. Our objective here is to systematically delineate the effects of different classes of BFs on the structural features of the STG of reconstructed Boolean GRNs while keeping network structure and biological attractors fixed, and explore the characteristics of BFs that drive those features. Using $10$ reconstructed Boolean GRNs, we generate ensembles that differ in BFs and compute from their STGs the dynamics' rate of contraction or 'bushiness' and rate of 'convergence', quantified with measures inspired from cellular automata (CA) that are based on the garden-of-Eden (GoE) states. We find that biologically meaningful BFs lead to higher STG 'bushiness' and 'convergence' than random ones. Obtaining such 'global' measures gets computationally expensive with larger network sizes, stressing the need for feasible proxies. So we adapt Wuensche's $Z$-parameter in CA to BFs in BNs and provide four natural variants, which, along with the average sensitivity of BFs computed at the network level, comprise our descriptors of local dynamics and we find some of them to be good proxies for bushiness. Finally, we provide an excellent proxy for the 'convergence' based on computing transient lengths originating at random states rather than GoE states.

Plasticity-led and mutation-led evolutions are different modes of the same developmental gene regulatory network.

The standard theory of evolution proposes that mutations cause heritable variations, which are naturally selected, leading to evolution. However, this mutation-led evolution (MLE) is being questioned by an alternative theory called plasticity-led evolution (PLE). PLE suggests that an environmental change induces adaptive phenotypes, which are later genetically accommodated. According to PLE, developmental systems should be able to respond to environmental changes adaptively. However, developmental systems are known to be robust against environmental and mutational perturbations. Thus, we expect a transition from a robust state to a plastic one. To test this hypothesis, we constructed a gene regulatory network (GRN) model that integrates developmental processes, hierarchical regulation, and environmental cues. We then simulated its evolution over different magnitudes of environmental changes. Our findings indicate that this GRN model exhibits PLE under large environmental changes and MLE under small environmental changes. Furthermore, we observed that the GRN model is susceptible to environmental or genetic fluctuations under large environmental changes but is robust under small environmental changes. This indicates a breakdown of robustness due to large environmental changes. Before the breakdown of robustness, the distribution of phenotypes is biased and aligned to the environmental changes, which would facilitate rapid adaptation should a large environmental change occur. These observations suggest that the evolutionary transition from mutation-led to plasticity-led evolution is due to a developmental transition from robust to susceptible regimes over increasing magnitudes of environmental change. Thus, the GRN model can reconcile these conflicting theories of evolution.

COMPARATIVE ANALYSIS OF MODELS OF GENETIC AND NEURONAL NETWORKS

The comparative analysis of systems of ordinary differential equations, modeling gene regulatory networks and neuronal networks, is provided. In focus of the study are asymptotical behavior of solutions, types of attractors. Emphasis is made on the chaotic behavior of solutions.

Set stabilization of logical control networks: A minimum node control approach

In network systems, control using minimum nodes or pinning control can be effectively used for stabilization problems to cut down the cost of control. In this paper, we investigate the set stabilization problem of logical control networks. In particular, we study the set stabilization problem of probabilistic Boolean networks (PBNs) and probabilistic Boolean control networks (PBCNs) via controlling minimal nodes. Firstly, an algorithm is given to search for the minimum index set of pinning nodes. Then, based on the analysis of its high computational complexity, we present optimized algorithms with lower computational complexity to ascertain the network control using minimum node sets. Moreover, some sufficient and necessary conditions are proposed to ensure the feasibility and effectiveness of the proposed algorithms. Furthermore, a theorem is presented for PBCNs to devise all state-feedback controllers corresponding to the set of pinning nodes. Finally, two models of gene regulatory networks are considered to show the efficacy of obtained results.

Preponderance of generalized chain functions in reconstructed Boolean models of biological networks

Boolean networks (BNs) have been extensively used to model gene regulatory networks (GRNs). The dynamics of BNs depend on the network architecture and regulatory logic rules (Boolean functions (BFs)) associated with nodes. Nested canalyzing functions (NCFs) have been shown to be enriched among the BFs in the large-scale studies of reconstructed Boolean models. The central question we address here is whether that enrichment is due to certain sub-types of NCFs. We build on one sub-type of NCFs, the chain functions (or chain-0 functions) proposed by Gat-Viks and Shamir. First, we propose two other sub-types of NCFs, namely, the class of chain-1 functions and generalized chain functions, the union of the chain-0 and chain-1 types. Next, we find that the fraction of NCFs that are chain-0 (also holds for chain-1) functions decreases exponentially with the number of inputs. We provide analytical treatment for this and other observations on BFs. Then, by analyzing three different datasets of reconstructed Boolean models we find that generalized chain functions are significantly enriched within the NCFs. Lastly we illustrate that upon imposing the constraints of generalized chain functions on three different GRNs we are able to obtain biologically viable Boolean models.

A neural network-based model framework for cell-fate decisions and development

Gene regulatory networks (GRNs) fulfill the essential function of maintaining the stability of cellular differentiation states by sustaining lineage-specific gene expression, while driving the progression of development. However, accounting for the relative stability of intermediate differentiation stages and their divergent trajectories remains a major challenge for models of developmental biology. Here, we develop an empirical data-based associative GRN model (AGRN) in which regulatory networks store multilineage stage-specific gene expression profiles as associative memory patterns. These networks are capable of responding to multiple instructive signals and, depending on signal timing and identity, can dynamically drive the differentiation of multipotent cells toward different cell state attractors. The AGRN dynamics can thus generate diverse lineage-committed cell populations in a robust yet flexible manner, providing an attractor-based explanation for signal-driven cell fate decisions during differentiation and offering a readily generalizable modelling tool that can be applied to a wide variety of cell specification systems.

Chaos in gene regulatory networks: Effects of time delays and interaction structure.

In biological system models, gene expression levels are typically described by regulatory feedback mechanisms. Many studies of gene network models focus on dynamical interactions between components, but often overlook time delays. Here we present an extended model for gene regulatory networks with time delayed negative feedback, which is described by delay differential equations. We analyze nonlinear properties of the model in terms of chaos and compare the conditions with the benchmark homogeneous gene regulatory network model. Chaotic dynamics depend strongly on the inclusion of time delays, but the minimum motifs that show chaos differ when both original and extended models are considered. Our results suggest that, for a particular higher order extension of the gene network, it is possible to observe chaotic dynamics in a two-gene system without adding any self-inhibition. This finding can be explained as a result of modification of the original benchmark model induced by previously unmodeled dynamics. We argue that the inclusion of additional parameters in regulatory gene circuit models substantially enhances the likelihood of observing non-periodic dynamics.

A Spatial Artificial Chemistry Implementation of a Gene Regulatory Network Aimed at Generating Protein Concentration Dynamics.

Gene regulatory networks are networks of interactions in organisms responsible for determining the production levels of proteins and peptides. Mathematical and computational models of gene regulatory networks have been proposed, some of them rather abstract and called artificial regulatory networks. In this contribution, a spatial model for gene regulatory networks is proposed that is biologically more realistic and incorporates an artificial chemistry to realize the interaction between regulatory proteins called the transcription factors and the regulatory sites of simulated genes. The result is a system that is quite robust while able to produce complex dynamics similar to what can be observed in nature. Here an analysis of the impact of the initial states of the system on the produced dynamics is performed, showing that such models are evolvable and can be directed toward producing desired protein dynamics.

A gene regulatory network model that recovers the abaxial-adaxial polarity in Arabidopsis thaliana leaf primordium

Megaphylls, present in the majority of vascular plants, show in many plant lineages an abaxial-adaxial polarity in their dorsoventral axis. This polarity commonly translates into different tissues developing on each side of the leaf blade. This is important because it promotes better photosynthetic efficiency as related to light absorption and gas exchange. Many researchers have studied the molecular bases of the emergence of leaf abaxial-adaxial polarity, showing that it is produced by the interaction and differential expression of particular genes and other molecules. However, until now, it is still unclear if the molecular components documented thus far are sufficient to explain the emergence of leaf polarity. In this work, we integrated the available experimental data to construct a graph of the Gene Regulatory Network (GRN) involved in the formation of abaxial-adaxial polarity in the leaf primordium of Arabidopsis thaliana. This graph consisted of 21 nodes and 47 regulations. We extracted the main components of the graph to obtain a Minimum Network consisting of six genes and 22 possible regulations. Then, we used the Boolean network (BN) formalism to describe the dynamics of this Minimum Network. We identified 1905 distinct BNs that comprised the regulations of the Minimum Network and exclusively generated the two attractors representing the abaxial and adaxial cell types. This highlights the fact that most graphs, including our network, can describe experimentally observed behaviors with many BN dynamics. By performing mutant simulations and robustness analysis, we found that two of the 1905 BNs better reproduce experimentally available information. To produce the expected attractors, both BNs predict the same missing regulations, which we propose should be experimentally analyzed to confirm their existence. Interestingly, these two BNs have low robustness to perturbations compared with previously analyzed GRNs. This was an unexpected result since abaxial-adaxial polarity is a robust biological trait, which suggests more components or regulations of the network are missing.

A Kinetic Finite Volume Discretization of the Multidimensional PIDE Model for Gene Regulatory Networks

In this paper, a finite volume discretization scheme for partial integro-differential equations (PIDEs) describing the temporal evolution of protein distribution in gene regulatory networks is proposed. It is shown that the obtained set of ODEs can be formally represented as a compartmental kinetic system with a strongly connected reaction graph. This allows the application of the theory of nonnegative and compartmental systems for the qualitative analysis of the approximating dynamics. In this framework, it is straightforward to show the existence, uniqueness and stability of equilibria. Moreover, the computation of the stationary probability distribution can be traced back to the solution of linear equations. The discretization scheme is presented for one and multiple dimensional models separately. Illustrative computational examples show the precision of the approach, and good agreement with previous results in the literature.

A meta-analysis of Boolean network models reveals design principles of gene regulatory networks.

Gene regulatory networks (GRNs) play a central role in cellular decision-making. Understanding their structure and how it impacts their dynamics constitutes thus a fundamental biological question. GRNs are frequently modeled as Boolean networks, which are intuitive, simple to describe, and can yield qualitative results even when data are sparse. We assembled the largest repository of expert-curated Boolean GRN models. A meta-analysis of this diverse set of models reveals several design principles. GRNs exhibit more canalization, redundancy, and stable dynamics than expected. Moreover, they are enriched for certain recurring network motifs. This raises the important question why evolution favors these design mechanisms.

Epigenetic OCT4 regulatory network: stochastic analysis of cellular reprogramming

Experimental studies have shown that chromatin modifiers have a critical effect on cellular reprogramming, i.e., the conversion of differentiated cells to pluripotent stem cells. Here, we develop a model of the OCT4 gene regulatory network that includes genes expressing chromatin modifiers TET1 and JMJD2, and the chromatin modification circuit on which these modifiers act. We employ this model to compare three reprogramming approaches that have been considered in the literature with respect to reprogramming efficiency and latency variability. These approaches are overexpression of OCT4 alone, overexpression of OCT4 with TET1, and overexpression of OCT4 with JMJD2. Our results show more efficient and less variable reprogramming when also JMJD2 and TET1 are overexpressed, consistent with previous experimental data. Nevertheless, TET1 overexpression can lead to more efficient reprogramming compared to JMJD2 overexpression. This is the case when the recruitment of DNA methylation by H3K9me3 is weak and the methyl-CpG-binding domain (MBD) proteins are sufficiently scarce such that they do not hamper TET1 binding to methylated DNA. The model that we developed provides a mechanistic understanding of existing experimental results and is also a tool for designing optimized reprogramming approaches that combine overexpression of cell-fate specific transcription factors (TFs) with targeted recruitment of epigenetic modifiers.

TMELand: An end-to-end Pipeline for Quantification and Visualization of Waddington's Epigenetic Landscape based on Gene Regulatory Network.

Waddington's epigenetic landscape is a framework depicting the processes of cell differentiation and reprogramming under the control of a gene regulatory network (GRN). Traditional model-driven methods for landscape quantification focus on the Boolean network or differential equation-based models of GRN, which need sophisticated prior knowledge and hence hamper their practical applications. To resolve this problem, we combine data-driven methods for inferring GRNs from gene expression data with model-driven approach to the landscape mapping. Specifically, we build an end-to-end pipeline to link data-driven and model-driven methods and develop a software tool named TMELand for GRN inference, visualizing Waddington's epigenetic landscape, and calculating state transition paths between attractors to uncover the intrinsic mechanism of cellular transition dynamics. By integrating GRN inference from real transcriptomic data with landscape modeling, TMELand can facilitate studies of computational systems biology, such as predicting cellular states and visualizing the dynamical trends of cell fate determination and transition dynamics from single-cell transcriptomic data. The source code of TMELand, a user manual, and model files of case studies can be downloaded freely from https://github.com/JieZheng-ShanghaiTech/TMELand.

Impulsive Controllers Design for the Practical Stability Analysis of Gene Regulatory Networks with Distributed Delays

This paper studies gene regulatory networks (GRNs) with distributed delays. The essential concept of practical stability of the genes is introduced. We investigate the problems of practical stability and global practical exponential stability of the GRN model under an impulsive control. New practical stability criteria are proposed by designing appropriate impulsive controllers via the Lyapunov functions approach. In the design of the impulsive controller, we consider the effect of impulsive perturbations at fixed times and distributed delays on the stability of the considered GRNs. Several numerical examples are also presented to justify the proposed criteria.

Pillars of biology: Boolean modeling of gene-regulatory networks

Boolean modeling is a mathematical modeling framework used for defining and studying gene-regulatory networks (GRNs). It serves as a means to develop mechanistic models, offering insights into the trajectories and dynamic properties of GRNs. In this review, I delve into seminal papers published in the Journal of Theoretical Biology that have spearheaded this field. Additionally, I explore the application of these modeling methods in the current era of data-intensive science.