Dynamics Of Gene Regulatory Networks Research Articles

Repressive Gene Regulation Synchronizes Development with Cellular Metabolism

Metabolic conditions affect the developmental tempo of animals. Developmental gene regulatory networks (GRNs) must therefore synchronize their dynamics with a variable timescale. We find that layered repression of genes couples GRN output with variable metabolism. When repressors of transcription or mRNA and protein stability are lost, fewer errors in Drosophila development occur when metabolism is lowered. We demonstrate the universality of this phenomenon by eliminating the entire microRNA family of repressors and find that development to maturity can be largely rescued when metabolism is reduced. Using a mathematical model that replicates GRN dynamics, we find that lowering metabolism suppresses the emergence of developmental errors by curtailing the influence of auxiliary repressors on GRN output. We experimentally show that gene expression dynamics are less affected by loss of repressors when metabolism is reduced. Thus, layered repression provides robustness through error suppression and may provide an evolutionary route to a shorter reproductive cycle.

Analytical results for the distribution of shortest path lengths in directed random networks that grow by node duplication

We present exact analytical results for the distribution of shortest path lengths (DSPL) in a directed network model that grows by node duplication. Such models are useful in the study of the structure and growth dynamics of gene regulatory networks and scientific citation networks. Starting from an initial seed network, at each time step a random node, referred to as a mother node, is selected for duplication. Its daughter node is added to the network and duplicates each outgoing link of the mother node with probability $p$. In addition, the daughter node forms a directed link to the mother node itself. Thus, the model is referred to as the corded directed-node-duplication (DND) model. In this network not all pairs of nodes are connected by directed paths, in spite of the fact that the corresponding undirected network consists of a single connected component. More specifically, in the large network limit only a diminishing fraction of pairs of nodes are connected by directed paths. To calculate the DSPL between those pairs of nodes that are connected by directed paths we derive a master equation for the time evolution of the probability $P_t(L=\ell)$, $\ell=1,2,\dots$, where $\ell$ is the length of the shortest directed path. Solving the master equation, we obtain a closed form expression for $P_t(L=\ell)$. It is found that the DSPL at time $t$ consists of a convolution of the initial DSPL $P_0(L=\ell)$, with a Poisson distribution and a sum of Poisson distributions. The mean distance ${\mathbb E}_t[L|L<\infty]$ between pairs of nodes which are connected by directed paths is found to depend logarithmically on the network size $N_t$. However, since in the large network limit the fraction of pairs of nodes that are connected by directed paths is diminishingly small, the corded DND network is not a small-world network, unlike the corresponding undirected network.

Dynamics of gene regulatory networks and their dependence on network topology and quantitative parameters \u2013 the case of phage \u03bb

BackgroundGene regulatory networks can be modelled in various ways depending on the level of detail required and biological questions addressed. One of the earliest formalisms used for modeling is a Boolean network, although these models cannot describe most temporal aspects of a biological system. Differential equation models have also been used to model gene regulatory networks, but these frameworks tend to be too detailed for large models and many quantitative parameters might not be deducible in practice. Hybrid models bridge the gap between these two model classes – these are useful when concentration changes are important while the information about precise concentrations and binding site affinities is partial.ResultsIn this paper we study the stable behaviours of phage λ via a hybrid system based model. We identify wild type and mutant behaviours that arise for various orderings of binding site affinities. We propose experiments for detecting these behaviours: we suggest several ways of altering binding affinities with either mutations or genome rearrangements to achieve modified behaviours. The feasibility of these experiments is assessed. The interplay between the qualitative aspects of a network, e.g. network topology, and quantitative parameters, e.g. growth and degradation rates of proteins, is demonstrated. We also provide a software for exploring all feasible states of a hybrid system model and identifying all attractors.ConclusionsThe behaviours of phage λ are determined mainly by the topology of this network and by the mutual order of binding affinities. Exact affinities and growth and degradation rates of proteins fine tune the system. We show that only two stable behaviours are possible for phage λ if the main constraints of λ switch are preserved – these behaviours correspond to lysis and lysogeny. We identify several variants of both lysis and lysogeny – one wild type and one modified behaviour for each. We elucidate the necessary constraints for binding site affinities to achieve both wild type lysis and lysogeny. Our software is applicable to a wide range of biological models described as a hybrid system.

The regulatory pathway from genes directly activated by maternal factors to muscle structural genes in ascidian embryos

Striated muscle cells in the tail of ascidian tadpole larvae differentiate cell-autonomously. Although several key regulatory factors have been identified, the genetic regulatory pathway is not fully understood; comprehensive understanding of the regulatory pathway is essential for accurate modeling in order to deduce principles for gene regulatory network dynamics, and for comparative analysis on how ascidians have evolved the cell-autonomous gene regulatory mechanism. Here, we reveal regulatory interactions among three key regulatory factors, Zic-r.b, Tbx6-r.b and Mrf, and elucidate the mechanism by which these factors activate muscle structural genes. We reveal a cross-regulatory circuit among these regulatory factors, which maintains the expression of Tbx6-r.b and Mrf during gastrulation. Although these two factors combinatorially activate muscle structural genes in late-stage embryos, muscle structural genes are activated mainly by Tbx6-r.b before gastrulation. Time points when expression of muscle structural genes become first detectable are strongly correlated with the degree of Tbx6-r.b occupancy. Thus, the genetic pathway, starting with Tbx6-r.b and Zic-r.b, which are activated by maternal factors, and ending with expression of muscle structural genes, has been revealed.

Temporal enhancer profiling of parallel lineages identifies AHR and GLIS1 as regulators of mesenchymal multipotency.

Temporal data on gene expression and context-specific open chromatin states can improve identification of key transcription factors (TFs) and the gene regulatory networks (GRNs) controlling cellular differentiation. However, their integration remains challenging. Here, we delineate a general approach for data-driven and unbiased identification of key TFs and dynamic GRNs, called EPIC-DREM. We generated time-series transcriptomic and epigenomic profiles during differentiation of mouse multipotent bone marrow stromal cell line (ST2) toward adipocytes and osteoblasts. Using our novel approach we constructed time-resolved GRNs for both lineages and identifed the shared TFs involved in both differentiation processes. To take an alternative approach to prioritize the identified shared regulators, we mapped dynamic super-enhancers in both lineages and associated them to target genes with correlated expression profiles. The combination of the two approaches identified aryl hydrocarbon receptor (AHR) and Glis family zinc finger 1 (GLIS1) as mesenchymal key TFs controlled by dynamic cell type-specific super-enhancers that become repressed in both lineages. AHR and GLIS1 control differentiation-induced genes and their overexpression can inhibit the lineage commitment of the multipotent bone marrow-derived ST2 cells.

Architecture of gene regulatory networks controlling flower development in Arabidopsis thaliana

Floral homeotic transcription factors (TFs) act in a combinatorial manner to specify the organ identities in the flower. However, the architecture and the function of the gene regulatory network (GRN) controlling floral organ specification is still poorly understood. In particular, the interconnections of homeotic TFs, microRNAs (miRNAs) and other factors controlling organ initiation and growth have not been studied systematically so far. Here, using a combination of genome-wide TF binding, mRNA and miRNA expression data, we reconstruct the dynamic GRN controlling floral meristem development and organ differentiation. We identify prevalent feed-forward loops (FFLs) mediated by floral homeotic TFs and miRNAs that regulate common targets. Experimental validation of a coherent FFL shows that petal size is controlled by the SEPALLATA3-regulated miR319/TCP4 module. We further show that combinatorial DNA-binding of homeotic factors and selected other TFs is predictive of organ-specific patterns of gene expression. Our results provide a valuable resource for studying molecular regulatory processes underlying floral organ specification in plants.

A systems biology approach uncovers the core gene regulatory network governing iridophore fate choice from the neural crest.

Multipotent neural crest (NC) progenitors generate an astonishing array of derivatives, including neuronal, skeletal components and pigment cells (chromatophores), but the molecular mechanisms allowing balanced selection of each fate remain unknown. In zebrafish, melanocytes, iridophores and xanthophores, the three chromatophore lineages, are thought to share progenitors and so lend themselves to investigating the complex gene regulatory networks (GRNs) underlying fate segregation of NC progenitors. Although the core GRN governing melanocyte specification has been previously established, those guiding iridophore and xanthophore development remain elusive. Here we focus on the iridophore GRN, where mutant phenotypes identify the transcription factors Sox10, Tfec and Mitfa and the receptor tyrosine kinase, Ltk, as key players. Here we present expression data, as well as loss and gain of function results, guiding the derivation of an initial iridophore specification GRN. Moreover, we use an iterative process of mathematical modelling, supplemented with a Monte Carlo screening algorithm suited to the qualitative nature of the experimental data, to allow for rigorous predictive exploration of the GRN dynamics. Predictions were experimentally evaluated and testable hypotheses were derived to construct an improved version of the GRN, which we showed produced outputs consistent with experimentally observed gene expression dynamics. Our study reveals multiple important regulatory features, notably a sox10-dependent positive feedback loop between tfec and ltk driving iridophore specification; the molecular basis of sox10 maintenance throughout iridophore development; and the cooperation between sox10 and tfec in driving expression of pnp4a, a key differentiation gene. We also assess a candidate repressor of mitfa, a melanocyte-specific target of sox10. Surprisingly, our data challenge the reported role of Foxd3, an established mitfa repressor, in iridophore regulation. Our study builds upon our previous systems biology approach, by incorporating physiologically-relevant parameter values and rigorous evaluation of parameter values within a qualitative data framework, to establish for the first time the core GRN guiding specification of the iridophore lineage.

Monostability, bistability, periodicity and chaos in gene regulatory network

This letter gives a general review on the monostability, bistability, periodicity and chaos in gene regulatory network. Some simple motifs that generate monostability, bistability, periodicity and chaos are analytically and numerically reported. Further research directions of the nonlinear dynamics of gene regulatory network are discussed.

Single-Cell Transcriptomic Analysis of Cardiac Differentiation from Human PSCs Reveals HOPX-Dependent Cardiomyocyte Maturation

Cardiac differentiation of human pluripotent stem cells (hPSCs) requires orchestration of dynamic gene regulatory networks during stepwise fate transitions but often generates immature cell types that do not fully recapitulate properties of their adult counterparts, suggesting incomplete activation of key transcriptional networks. We performed extensive single-cell transcriptomic analyses to map fate choices and gene expression programs during cardiac differentiation of hPSCs and identified strategies to improve invitro cardiomyocyte differentiation. Utilizing genetic gain- and loss-of-function approaches, we found that hypertrophic signaling is not effectively activated during monolayer-based cardiac differentiation, thereby preventing expression of HOPX and its activation of downstream genes that govern late stages of cardiomyocyte maturation. This study therefore provides a key transcriptional roadmap of invitro cardiac differentiation at single-cell resolution, revealing fundamental mechanisms underlying heart development and differentiation of hPSC-derived cardiomyocytes.

Criticality Distinguishes the Ensemble of Biological Regulatory Networks.

The hypothesis that many living systems should exhibit near-critical behavior is well motivated theoretically, and an increasing number of cases have been demonstrated empirically. However, a systematic analysis across biological networks, which would enable identification of the network properties that drive criticality, has not yet been realized. Here, we provide a first comprehensive survey of criticality across a diverse sample of biological networks, leveraging a publicly available database of 67 Boolean models of regulatory circuits. We find all 67 networks to be near critical. By comparing to ensembles of random networks with similar topological and logical properties, we show that criticality in biological networks is not predictable solely from macroscale properties such as mean degree ⟨K⟩ and mean bias in the logic functions ⟨p⟩, as previously emphasized in theories of random Boolean networks. Instead, the ensemble of real biological circuits is jointly constrained by the local causal structure and logic of each node. In this way, biological regulatory networks are more distinguished from random networks by their criticality than by other macroscale network properties such as degree distribution, edge density, or fraction of activating conditions.

Stochastic hybrid models of gene regulatory networks – A PDE approach

A widely used approach to describe the dynamics of gene regulatory networks is based on the chemical master equation, which considers probability distributions over all possible combinations of molecular counts. The analysis of such models is extremely challenging due to their large discrete state space. We therefore propose a hybrid approximation approach based on a system of partial differential equations, where we assume a continuous-deterministic evolution for the protein counts. We discuss efficient analysis methods for both modeling approaches and compare their performance. We show that the hybrid approach yields accurate results for sufficiently large molecule counts, while reducing the computational effort from one ordinary differential equation for each state to one partial differential equation for each mode of the system. Furthermore, we give an analytical steady-state solution of the hybrid model for the case of a self-regulatory gene.

A Dynamic Co-expression Map of Early Inflorescence Development in Setaria viridis Provides a Resource for Gene Discovery and Comparative Genomics.

The morphological and functional diversity of plant form is governed by dynamic gene regulatory networks. In cereal crops, grain and/or pollen-bearing inflorescences exhibit vast architectural diversity and developmental complexity, yet the underlying genetic framework is only partly known. Setaria viridis is a small, rapidly growing grass species in the subfamily Panicoideae, a group that includes economically important cereal crops such as maize and sorghum. The S. viridis inflorescence displays complex branching patterns, but its early development is similar to that of other panicoid grasses, and thus is an ideal model for studying inflorescence architecture. Here we report a detailed transcriptional resource that captures dynamic transitions across six sequential stages of S. viridis inflorescence development, from reproductive onset to floral organ differentiation. Co-expression analyses identified stage-specific signatures of development, which include homologs of previously known developmental genes from maize and rice, suites of transcription factors and gene family members, and genes of unknown function. This spatiotemporal co-expression map and associated analyses provide a foundation for gene discovery in S. viridis inflorescence development, and a comparative model for exploring related architectural features in agronomically important cereals.

Rare-event sampling of epigenetic landscapes and phenotype transitions.

Stochastic simulation has been a powerful tool for studying the dynamics of gene regulatory networks, particularly in terms of understanding how cell-phenotype stability and fate-transitions are impacted by noisy gene expression. However, gene networks often have dynamics characterized by multiple attractors. Stochastic simulation is often inefficient for such systems, because most of the simulation time is spent waiting for rare, barrier-crossing events to occur. We present a rare-event simulation-based method for computing epigenetic landscapes and phenotype-transitions in metastable gene networks. Our computational pipeline was inspired by studies of metastability and barrier-crossing in protein folding, and provides an automated means of computing and visualizing essential stationary and dynamic information that is generally inaccessible to conventional simulation. Applied to a network model of pluripotency in Embryonic Stem Cells, our simulations revealed rare phenotypes and approximately Markovian transitions among phenotype-states, occurring with a broad range of timescales. The relative probabilities of phenotypes and the transition paths linking pluripotency and differentiation are sensitive to global kinetic parameters governing transcription factor-DNA binding kinetics. Our approach significantly expands the capability of stochastic simulation to investigate gene regulatory network dynamics, which may help guide rational cell reprogramming strategies. Our approach is also generalizable to other types of molecular networks and stochastic dynamics frameworks.

Use of chick neural tube for optimizing the PSM and epithelial somites electroporation parameters: A detailed protocol.

Somite myogenesis is one of the crucial early embryonic events that lead to the formation of muscular tissue. A complex of dynamic gene regulatory networks masters this event. To understand and analyze these networks, there remains a genuine need for the use of a reproducible and highly efficient gene transfer technique. In vivo electroporation has proven to be amongst the best approaches in achieving a high level of gene transfer. However, unoptimized electroporation conditions can directly cause varying degrees of cellular damage which may induce abnormal embryonic development as well as changes in the endogenous gene expression. Presegmented mesoderm and epithelial somites are not easy to electroporate. Chick neural tube has served in many functional studies as an ideal experimental model organ which is both robust and easily manipulated. In the current detailed protocol, the neural tube was used as a tool to optimize the electroporation conditions which were subsequently applied in the electroporation of the presegmented mesoderm and epithelial somites. The protocol highlights important notes and hints that enable reproducible results and could be applied in the in vivo electroporation of other chick embryo tissues.

A big data pipeline: Identifying dynamic gene regulatory networks from time-course Gene Expression Omnibus data with applications to influenza infection.

A biological host response to an external stimulus or intervention such as a disease or infection is a dynamic process, which is regulated by an intricate network of many genes and their products. Understanding the dynamics of this gene regulatory network allows us to infer the mechanisms involved in a host response to an external stimulus, and hence aids the discovery of biomarkers of phenotype and biological function. In this article, we propose a modeling/analysis pipeline for dynamic gene expression data, called Pipeline4DGEData, which consists of a series of statistical modeling techniques to construct dynamic gene regulatory networks from the large volumes of high-dimensional time-course gene expression data that are freely available in the Gene Expression Omnibus repository. This pipeline has a consistent and scalable structure that allows it to simultaneously analyze a large number of time-course gene expression data sets, and then integrate the results across different studies. We apply the proposed pipeline to influenza infection data from nine studies and demonstrate that interesting biological findings can be discovered with its implementation.

Independence screening for high dimensional nonlinear additive ODE models with applications to dynamic gene regulatory networks.

Mechanism-driven low-dimensional ordinary differential equation (ODE) models are often used to model viral dynamics at cellular levels and epidemics of infectious diseases. However, low-dimensional mechanism-based ODE models are limited for modeling infectious diseases at molecular levels such as transcriptomic or proteomic levels, which is critical to understand pathogenesis of diseases. Although linear ODE models have been proposed for gene regulatory networks (GRNs), nonlinear regulations are common in GRNs. The reconstruction of large-scale nonlinear networks from time-course gene expression data remains an unresolved issue. Here, we use high-dimensional nonlinear additive ODEs to model GRNs and propose a 4-step procedure to efficiently perform variable selection for nonlinear ODEs. To tackle the challenge of high dimensionality, we couple the 2-stage smoothing-based estimation method for ODEs and a nonlinear independence screening method to perform variable selection for the nonlinear ODE models. We have shown that our method possesses the sure screening property and it can handle problems with non-polynomialdimensionality. Numerical performance of the proposed method is illustrated with simulated data and a real data example for identifying the dynamic GRN of Saccharomyces cerevisiae.

Investigating the use of Boolean networks for the control of gene regulatory networks

The behaviour of biological cells emerges from complex patterns of interactions between genes and their products, known as gene regulatory networks (GRN). An important aim of biology is to control the dynamics of GRNs, in order to push a cell towards or away from certain behaviours. This could potentially be done by coupling a synthetic GRN to an existing biological GRN. In this work, we use Boolean networks, a methodology for modelling and simulating GRNs, to investigate the potential for doing this. Our results demonstrate that Boolean networks can be optimised to control other Boolean networks, and that the approach scales well as the target network size increases.

How Criticality of Gene Regulatory Networks Affects the Resulting Morphogenesis under Genetic Perturbations.

Whereas the relationship between criticality of gene regulatory networks (GRNs) and dynamics of GRNs at a single-cell level has been vigorously studied, the relationship between the criticality of GRNs and system properties at a higher level has not been fully explored. Here we aim at revealing a potential role of criticality of GRNs in morphogenesis, which is hard to uncover through the single-cell-level studies, especially from an evolutionary viewpoint. Our model simulated the growth of a cell population from a single seed cell. All the cells were assumed to have identical intracellular GRNs. We induced genetic perturbations to the GRN of the seed cell by adding, deleting, or switching a regulatory link between a pair of genes. From numerical simulations, we found that the criticality of GRNs facilitated the formation of nontrivial morphologies when the GRNs were critical in the presence of the evolutionary perturbations. Moreover, the criticality of GRNs produced topologically homogeneous cell clusters by adjusting the spatial arrangements of cells, which led to the formation of nontrivial morphogenetic patterns. Our findings correspond to an epigenetic viewpoint that heterogeneous and complex features emerge from homogeneous and less complex components through the interactions among them. Thus, our results imply that highly structured tissues or organs in morphogenesis of multicellular organisms might stem from the criticality of GRNs.

Gene regulatory network state estimation from arbitrary correlated measurements

BackgroundAdvancements in gene expression technology allow acquiring cheap and abundant data for analyzing cell behavior. However, these technologies produce noisy, and often correlated, measurements on the transcriptional states of genes. The Boolean network model has been shown to be effective in capturing the complex dynamics of gene regulatory networks (GRNs). It is important in many applications, such as anomaly detection and optimal intervention, to be able to track the evolution of the Boolean states of a gene regulatory network using noisy time-series transcriptional measurements, which may be correlated in time.ResultsWe propose efficient estimators for the Boolean states of GRNs using correlated time-series transcriptional measurements, where the nature of the correlation and of the measurements themselves are entirely arbitrary. More specifically, we propose new algorithms based on a hypothesis tree to compute optimal minimum mean square error (MMSE) filtering and smoothing state estimators for a Partially-Observed Boolean Dynamical System (POBDS) with correlated measurements. The algorithms are exact but may be computationally expensive for large state spaces or long time horizons, in which case a process for pruning the hypothesis tree is employed to obtain an approximation of the optimal MMSE estimators, while keeping computation tractable. Performance is assessed through a comprehensive set of numerical experiments based on the p53-MDM2 negative-feedback loop Boolean regulatory network, where the standard Boolean Kalman Filter (BKF) and Boolean Kalman Smoother (BKS) for uncorrelated measurements are compared to the corresponding new estimators for correlated measurements, called BKF-CORR and BKS-CORR, respectively.

Dynamics of gene regulatory networks with stochastic propensities

Gene regulatory networks (GRNs) control the production of proteins in cells. It is well-known that this process is not deterministic. Numerous studies employed a non-deterministic transition structure to model these networks. However, it is not realistic to expect state-to-state transition probabilities to remain constant throughout an organism’s lifetime. In this work, we focus on modeling GRN state transition (edge) variability using an ever-changing set of propensities. We suspect that the source of this variation is due to internal noise at the molecular level and can be modeled by introducing additional stochasticity into GRN models. We employ a beta distribution, whose parameters are estimated to capture the pattern inherent in edge behavior with minimum error. Additionally, we develop a method for obtaining propensities from a pre-determined network.