Dynamics Of Gene Regulatory Networks Research Articles

Effect of cell heterogeneity on isogenic populations with the synthetic genetic toggle switch network: Bifurcation analysis of two-dimensional cell population balance models

The dynamics of gene regulatory networks are often modeled with the assumption of cellular homogeneity. However, this assumption contradicts the plethora of experimental results in a variety of systems, which designates that cell populations are heterogeneous systems in the sense that properties such as size, shape, and DNA/RNA content are unevenly distributed amongst their individuals. In order to address the implications of heterogeneity, we utilize the so-called cell population balance (CPB) models. Here, we solve numerically multivariable CPB models to study the effect of heterogeneity on populations carrying the toggle switch network, which features nonlinear behavior at the single-cell level. In order to answer whether this nonlinear behavior is inherited to the heterogeneous population level, we perform bifurcation analysis on the steady-state solutions of the CPB model. We show that bistability is present at the population level with the pertinent bistability region shrinking when the impact of heterogeneity is enhanced.

Modelling and Control of Gene Regulatory Networks for Perturbation Mitigation.

Synthetic Biologists are increasingly interested in the idea of using synthetic feedback control circuits for the mitigation of perturbations to gene regulatory networks that may arise due to disease and/or environmental disturbances. Models employing Michaelis-Menten kinetics with Hill-type nonlinearities are typically used to represent the dynamics of gene regulatory networks. Here, we identify some fundamental problems with such models from the point of view of control system design, and argue that an alternative formalism, based on so-called S-System models, is more suitable. Using tools from system identification, we show how to build S-System models that capture the key dynamics of an example gene regulatory network, and design a genetic feedback controller with the objective of rejecting an external perturbation. Using a sine sweeping method, we show how the S-System model can be approximated by a linear transfer function and, based on this transfer function, we design our controller. Simulation results using the full nonlinear S-System model of the network show that the synthetic control circuit is able to mitigate the effect of external perturbations. Our study is the first to highlight the usefulness of the S-System modelling formalism for the design of synthetic control circuits for gene regulatory networks.

Modeling multi-valued biological interaction networks using fuzzy answer set programming

Fuzzy Answer Set Programming (FASP) is an extension of the popular Answer Set Programming (ASP) paradigm that allows for modeling and solving combinatorial search problems in continuous domains. The recent development of practical solvers for FASP has enabled its applicability to real-world problems. In this paper, we investigate the application of FASP in modeling the dynamics of Gene Regulatory Networks (GRNs). A commonly used simplifying assumption to model the dynamics of GRNs is to assume only Boolean levels of activation of each node. Our work extends this Boolean network formalism by allowing multi-valued activation levels. We show how FASP can be used to model the dynamics of such networks. We experimentally assess the efficiency of our method using real biological networks found in the literature, as well as on randomly-generated synthetic networks. The experiments demonstrate the applicability and usefulness of our proposed method to find network attractors.

Graphics Processing Unit-Enhanced Genetic Algorithms for Solving the Temporal Dynamics of Gene Regulatory Networks.

Understanding the regulation of gene expression is one of the key problems in current biology. A promising method for that purpose is the determination of the temporal dynamics between known initial and ending network states, by using simple acting rules. The huge amount of rule combinations and the nonlinear inherent nature of the problem make genetic algorithms an excellent candidate for finding optimal solutions. As this is a computationally intensive problem that needs long runtimes in conventional architectures for realistic network sizes, it is fundamental to accelerate this task. In this article, we study how to develop efficient parallel implementations of this method for the fine-grained parallel architecture of graphics processing units (GPUs) using the compute unified device architecture (CUDA) platform. An exhaustive and methodical study of various parallel genetic algorithm schemes—master-slave, island, cellular, and hybrid models, and various individual selection methods (roulette, elitist)—is carried out for this problem. Several procedures that optimize the use of the GPU’s resources are presented. We conclude that the implementation that produces better results (both from the performance and the genetic algorithm fitness perspectives) is simulating a few thousands of individuals grouped in a few islands using elitist selection. This model comprises 2 mighty factors for discovering the best solutions: finding good individuals in a short number of generations, and introducing genetic diversity via a relatively frequent and numerous migration. As a result, we have even found the optimal solution for the analyzed gene regulatory network (GRN). In addition, a comparative study of the performance obtained by the different parallel implementations on GPU versus a sequential application on CPU is carried out. In our tests, a multifold speedup was obtained for our optimized parallel implementation of the method on medium class GPU over an equivalent sequential single-core implementation running on a recent Intel i7 CPU. This work can provide useful guidance to researchers in biology, medicine, or bioinformatics in how to take advantage of the parallelization on massively parallel devices and GPUs to apply novel metaheuristic algorithms powered by nature for real-world applications (like the method to solve the temporal dynamics of GRNs).

Efficient simulation of stochastic gene regulatory networks

Gene expression is inherently stochastic, and the dynamics of gene regulatory networks (GRNs) is governed by the Chemical Master Equation (CME). In most cases, the solution of the CME is not available, and the stochastic simulation algorithm (SSA) requires a high computational effort. In this work we illustrate the performance of a method recently developed for the simulation of stochastic gene regulatory networks that allows computational speeds up to 6500 times higher than SSA. Exploiting intrinsic structural properties of GRNs, the method accurately approximates the Chemical Master Equation (CME) with a Partial Integral Differential Equation (PIDE), which is solved numerically by means of a semi-lagrangian method. The method is available within the toolbox SELANSI https://sites.google.com/view/selansi.

Identifying the dynamic gene regulatory network during latent HIV-1 reactivation using high-dimensional ordinary differential equations.

Reactivation of latently infected cells has emerged as an important strategy for eradication of HIV. However, genetic mechanisms of regulation after reactivation remain unclear. We describe a five-step pipeline to study the dynamics of the gene regulatory network following a viral reactivation using high-dimensional ordinary differential equations. Our pipeline implements a combination of five different methods, by detecting temporally differentially expressed genes (step 1), clustering genes with similar temporal expression patterns into a small number of response modules (step2), performing a functional enrichment analysis within each gene response module (step 3), identifying a network structure based on the gene response modules using ordinary differential equations (ODE) and a high-dimensional variable selection technique (step 4), and obtaining a gene regulatory model based on refined parameter estimates using nonlinear least squares (step 5). We applied our pipeline to a time course gene expression data of latently infected T-cells following a latency-reversion.

Identifying the dynamic gene regulatory network during latent HIV-1 reactivation using high-dimensional ordinary differential equations

Reactivation of latently infected cells has emerged as an important strategy for eradication of HIV. However, genetic mechanisms of regulation after reactivation remain unclear. We describe a five-step pipeline to study the dynamics of the gene regulatory network following a viral reactivation using high-dimensional ordinary differential equations. Our pipeline implements a combination of five different methods, by detecting temporally differentially expressed genes (step 1), clustering genes with similar temporal expression patterns into a small number of response modules (step 2), performing a functional enrichment analysis within each gene response module (step 3), identifying a network structure based on the gene response modules using ordinary differential equations (ODE) and a high-dimensional variable selection technique (step 4), and obtaining a gene regulatory model based on refined parameter estimates using nonlinear least squares (step 5). We applied our pipeline to a time course gene expression data of latently infected T-cells following a latency-reversion.

Model checking optimal finite-horizon control for probabilistic gene regulatory networks

BackgroundProbabilistic Boolean networks (PBNs) have been proposed for analyzing external control in gene regulatory networks with incorporation of uncertainty. A context-sensitive PBN with perturbation (CS-PBNp), extending a PBN with context-sensitivity to reflect the inherent biological stability and random perturbations to express the impact of external stimuli, is considered to be more suitable for modeling small biological systems intervened by conditions from the outside. In this paper, we apply probabilistic model checking, a formal verification technique, to optimal control for a CS-PBNp that minimizes the expected cost over a finite control horizon.ResultsWe first describe a procedure of modeling a CS-PBNp using the language provided by a widely used probabilistic model checker PRISM. We then analyze the reward-based temporal properties and the computation in probabilistic model checking; based on the analysis, we provide a method to formulate the optimal control problem as minimum reachability reward properties. Furthermore, we incorporate control and state cost information into the PRISM code of a CS-PBNp such that automated model checking a minimum reachability reward property on the code gives the solution to the optimal control problem. We conduct experiments on two examples, an apoptosis network and a WNT5A network. Preliminary experiment results show the feasibility and effectiveness of our approach.ConclusionsThe approach based on probabilistic model checking for optimal control avoids explicit computation of large-size state transition relations associated with PBNs. It enables a natural depiction of the dynamics of gene regulatory networks, and provides a canonical form to formulate optimal control problems using temporal properties that can be automated solved by leveraging the analysis power of underlying model checking engines. This work will be helpful for further utilization of the advances in formal verification techniques in system biology.

SELANSI: a toolbox for simulation of stochastic gene regulatory networks.

MotivationGene regulation is inherently stochastic. In many applications concerning Systems and Synthetic Biology such as the reverse engineering and the de novo design of genetic circuits, stochastic effects (yet potentially crucial) are often neglected due to the high computational cost of stochastic simulations. With advances in these fields there is an increasing need of tools providing accurate approximations of the stochastic dynamics of gene regulatory networks (GRNs) with reduced computational effort.ResultsThis work presents SELANSI (SEmi-LAgrangian SImulation of GRNs), a software toolbox for the simulation of stochastic multidimensional gene regulatory networks. SELANSI exploits intrinsic structural properties of gene regulatory networks to accurately approximate the corresponding Chemical Master Equation with a partial integral differential equation that is solved by a semi-lagrangian method with high efficiency. Networks under consideration might involve multiple genes with self and cross regulations, in which genes can be regulated by different transcription factors. Moreover, the validity of the method is not restricted to a particular type of kinetics. The tool offers total flexibility regarding network topology, kinetics and parameterization, as well as simulation options.Availability and implementationSELANSI runs under the MATLAB environment, and is available under GPLv3 license at https://sites.google.com/view/selansi.

Evaluation of artificial time series microarray data for dynamic gene regulatory network inference

High-throughput technology like microarrays is widely used in the inference of gene regulatory networks (GRNs). We focused on time series data since we are interested in the dynamics of GRNs and the identification of dynamic networks. We evaluated the amount of information that exists in artificial time series microarray data and the ability of an inference process to produce accurate models based on them. We used dynamic artificial gene regulatory networks in order to create artificial microarray data. Key features that characterize microarray data such as the time separation of directly triggered genes, the percentage of directly triggered genes and the triggering function type were altered in order to reveal the limits that are imposed by the nature of microarray data on the inference process. We examined the effect of various factors on the inference performance such as the network size, the presence of noise in microarray data, and the network sparseness. We used a system theory approach and examined the relationship between the pole placement of the inferred system and the inference performance. We examined the relationship between the inference performance in the time domain and the true system parameter identification. Simulation results indicated that time separation and the percentage of directly triggered genes are crucial factors. Also, network sparseness, the triggering function type and noise in input data affect the inference performance. When two factors were simultaneously varied, it was found that variation of one parameter significantly affects the dynamic response of the other. Crucial factors were also examined using a real GRN and acquired results confirmed simulation findings with artificial data. Different initial conditions were also used as an alternative triggering approach. Relevant results confirmed that the number of datasets constitutes the most significant parameter with regard to the inference performance.

Design of experiment for nonlinear dynamic gene regulatory network identification

ABSTRACTThe gene regulatory network (GRN) is critical for understanding the regulatory interaction between genes. Time-course microarray experiments provide ample information for constructing GRN. The designs for microarray experiments serve different purposes. However, the experiment design specifically for GRN identification is still sparse. In this article, we use a simulation-based approach to deal with design problems in the framework of nonparametric differential equations. We investigate a number of feasible designs. In particular, we evaluate whether earlier samplings can result in more useful information for GRN identification. We also evaluate the effectiveness of two strategies: more frequent samplings per replicate with fewer replicates versus fewer samplings per replicate with more replicates while keeping the total number of samplings constant. The results of our investigation provide quantitative guidance for designing and selecting microarray experiments for the purpose of GRN identification.

Dynamic Gene Regulatory Networks of Human Myeloid Differentiation

The reconstruction of gene regulatory networks underlying cell differentiation from high-throughput gene expression and chromatin data remains a challenge. Here, we derive dynamic gene regulatory networks for human myeloid differentiation using a 5-day time series of RNA-seq and ATAC-seq data. We profile HL-60 promyelocytes differentiating into macrophages, neutrophils, monocytes, and monocyte-derived macrophages. We find a rapid response in the expression of key transcription factors and lineage markers that only regulate a subset of their targets at a given time, which is followed by chromatin accessibility changes that occur later along with further gene expression changes. We observe differences between promyelocyte- and monocyte-derived macrophages at both the transcriptional and chromatin landscape level, despite using the same differentiation stimulus, which suggest that the path taken by cells in the differentiation landscape defines their end cell state. More generally, our approach of combining neighboring time points and replicates to achieve greater sequencing depth can efficiently infer footprint-based regulatory networks from long series data.

Applying attractor dynamics to infer gene regulatory interactions involved in cellular differentiation

The dynamics of gene regulatory networks (GRNs) guide cellular differentiation. Determining the ways regulatory genes control expression of their targets is essential to understand and control cellular differentiation. The way a regulatory gene controls its target can be expressed as a gene regulatory function. Manual derivation of these regulatory functions is slow, error-prone and difficult to update as new information arises. Automating this process is a significant challenge and the subject of intensive effort. This work presents a novel approach to discovering biologically plausible gene regulatory interactions that control cellular differentiation. This method integrates known cell type expression data, genetic interactions, and knowledge of the effects of gene knockouts to determine likely GRN regulatory functions. We employ a genetic algorithm to search for candidate GRNs that use a set of transcription factors that control differentiation within a lineage. Nested canalyzing functions are used to constrain the search space to biologically plausible networks. The method identifies an ensemble of GRNs whose dynamics reproduce the gene expression pattern for each cell type within a particular lineage. The method's effectiveness was tested by inferring consensus GRNs for myeloid and pancreatic cell differentiation and comparing the predicted gene regulatory interactions to manually derived interactions. We identified many regulatory interactions reported in the literature and also found differences from published reports. These discrepancies suggest areas for biological studies of myeloid and pancreatic differentiation. We also performed a study that used defined synthetic networks to evaluate the accuracy of the automated search method and found that the search algorithm was able to discover the regulatory interactions in these defined networks with high accuracy. We suggest that the GRN functions derived from the methods described here can be used to fill gaps in knowledge about regulatory interactions and to offer hypotheses for experimental testing of GRNs that control differentiation and other biological processes.

NetLand: quantitative modeling and visualization of Waddington's epigenetic landscape using probabilistic potential.

SummaryWaddington’s epigenetic landscape is a powerful metaphor for cellular dynamics driven by gene regulatory networks (GRNs). Its quantitative modeling and visualization, however, remains a challenge, especially when there are more than two genes in the network. A software tool for Waddington’s landscape has not been available in the literature. We present NetLand, an open-source software tool for modeling and simulating the kinetic dynamics of GRNs, and visualizing the corresponding Waddington’s epigenetic landscape in three dimensions without restriction on the number of genes in a GRN. With an interactive and graphical user interface, NetLand can facilitate the knowledge discovery and experimental design in the study of cell fate regulation (e.g. stem cell differentiation and reprogramming).Availability and ImplementationNetLand can run under operating systems including Windows, Linux and OS X. The executive files and source code of NetLand as well as a user manual, example models etc. can be downloaded from http://netland-ntu.github.io/NetLand/.Supplementary information Supplementary data are available at Bioinformatics online.

Plasma MicroRNAs Relate to Atrial Fibrillation Recurrence after Catheter Ablation: Longitudinal Findings from the MiRhythm Study

Introduction: Genetic and transcriptomic factors play important roles as mediators of new-onset and recurrent atrial fibrillation (AF). MicroRNAs (miRNAs) regulate expression of gene networks involved in key aspects of atrial remodeling. Associations between circulating miRNAs and AF recurrence are unknown. We tested the hypothesis that cardiac miRNAs associated with electrical and structural remodeling predict recurrent AF rhythm in post-ablation patients. Methods: We quantified plasma expression of 86 cardiac miRNAs using RT-qPCR in 83 consenting participants undergoing ablation for AF. MiRNA expression was re-measured 1-month post-ablation in a subset of 43 of 83 study participants. Then all 83 patients were followed over a 12-month period for AF recurrence and plasma miRNA expression was compared between baseline and 1-month post-ablation and between those with and without an AF recurrence. Results: The mean age of study participants was 59 years, 34% were female, and 63% had paroxysmal AF. Plasma levels of miRNAs 125a-5p and 10b were 3-fold lower after ablation compared to pre-ablation (p<0.01). Pre-ablation plasma expression of miRNAs 125a and 10b, as well as miRNAs 60, 30a-3p and 199b, were higher among patients with an AF recurrence compared to those without recurrence after ablation (p<0.05) even after adjustment for clinical risk factors. Conclusion: The plasma miRnome is dynamic after AF ablation and associated with AF recurrence. Higher pre-ablation levels of circulating gene regulators implicated in atrial remodeling and AF, including miRNAs 125a-5p and 10b, were associated with AF recurrence and that these same miRNAs decreased post-ablation. Our investigation highlights dynamic gene regulatory networks in patients undergoing ablation and identifies potentially new AF treatment targets.

In Silico Methods for Cell Annotation, Quantification of Gene Expression, and Cell Geometry at Single-Cell Resolution Using 3DCellAtlas.

A comprehensive understanding of plant growth and development requires the integration of the spatial and temporal dynamics of gene regulatory networks with changes in cellular geometry during 3D organ growth. 3DCellAtlas is an integrative computational pipeline that semi-automatically identifies cell type and position within radially symmetric plant organs, and simultaneously quantifies 3D cell anisotropy and reporter abundance at single-cell resolution. It is a powerful tool that generates digital single-cell cellular atlases of plant organs and enables 3D cell geometry and reporter abundance (gene/protein/biosensor) from multiple samples to be integrated at single-cell resolution across whole organs. Here we describe how to use 3DCellAtlas to process and analyze radially symmetric organs, and to identify cell types and extract geometric cell data within these 3D cellular datasets. We detail how to use two statistical tools in 3DCellAtlas to compare cellular geometries, and to analyze reporter abundance at single-cell resolution.

Reconstructed cell fate-regulatory programs in stem cells reveal hierarchies and key factors of neurogenesis.

Cell lineages, which shape the body architecture and specify cell functions, derive from the integration of a plethora of cell intrinsic and extrinsic signals. These signals trigger a multiplicity of decisions at several levels to modulate the activity of dynamic gene regulatory networks (GRNs), which ensure both general and cell-specific functions within a given lineage, thereby establishing cell fates. Significant knowledge about these events and the involved key drivers comes from homogeneous cell differentiation models. Even a single chemical trigger, such as the morphogen all-trans retinoic acid (RA), can induce the complex network of gene-regulatory decisions that matures a stem/precursor cell to a particular step within a given lineage. Here we have dissected the GRNs involved in the RA-induced neuronal or endodermal cell fate specification by integrating dynamic RXRA binding, chromatin accessibility, epigenetic promoter epigenetic status, and the transcriptional activity inferred from RNA polymerase II mapping and transcription profiling. Our data reveal how RA induces a network of transcription factors (TFs), which direct the temporal organization of cognate GRNs, thereby driving neuronal/endodermal cell fate specification. Modeling signal transduction propagation using the reconstructed GRNs indicated critical TFs for neuronal cell fate specification, which were confirmed by CRISPR/Cas9-mediated genome editing. Overall, this study demonstrates that a systems view of cell fate specification combined with computational signal transduction models provides the necessary insight in cellular plasticity for cell fate engineering. The present integrated approach can be used to monitor the in vitro capacity of (engineered) cells/tissues to establish cell lineages for regenerative medicine.

Inferring gene regulatory networks using a time-delayed mass action model.

This paper demonstrates a new time-delayed mass action model which applies a set of delay differential equations (DDEs) to represent the dynamics of gene regulatory networks (GRNs). The mass action model is a classical model which is often used to describe the kinetics of biochemical processes, so it is fit for GRN modeling. The ability to incorporate time-delayed parameters in this model enables different time delays of interaction between genes. Moreover, an efficient learning method which employs population-based incremental learning (PBIL) algorithm and trigonometric differential evolution (TDE) algorithm TDE is proposed to automatically evolve the structure of the network and infer the optimal parameters from observed time-series gene expression data. Experiments on three well-known motifs of GRN and a real budding yeast cell cycle network show that the proposal can not only successfully infer the network structure and parameters but also has a strong anti-noise ability. Compared with other works, this method also has a great improvement in performances.

Diffusion driven oscillations in gene regulatory networks

Gene regulatory networks (GRNs) play an important role in maintaining cellular function by correctly timing key processes such as cell division and apoptosis. GRNs are known to contain similar structural components, which describe how genes and proteins within a network interact - typically by feedback. In many GRNs, proteins bind to gene-sites in the nucleus thereby altering the transcription rate. If the binding reduces the transcription rate there is a negative feedback leading to oscillatory behaviour in mRNA and protein levels, both spatially (e.g. by observing fluorescently labelled molecules in single cells) and temporally (e.g. by observing protein/mRNA levels over time). Mathematical modelling of GRNs has focussed on such oscillatory behaviour. Recent computational modelling has demonstrated that spatial movement of the molecules is a vital component of GRNs, while it has been proved rigorously that the diffusion coefficient of the protein/mRNA acts as a bifurcation parameter and gives rise to a Hopf-bifurcation. In this paper we consider the spatial aspect further by considering the specific location of gene and protein production, showing that there is an optimum range for the distance between an mRNA gene-site and a protein production site in order to achieve oscillations. We first present a model of a well-known GRN, the Hes1 system, and then extend the approach to examine spatio-temporal models of synthetic GRNs e.g. n-gene repressilator and activator–repressor systems. By incorporating the idea of production sites into such models we show that the spatial component is vital to fully understand GRN dynamics.

Super-transient scaling in time-delay autonomous Boolean network motifs.

Autonomous Boolean networks are commonly used to model the dynamics of gene regulatory networks and allow for the prediction of stable dynamical attractors. However, most models do not account for time delays along the network links and noise, which are crucial features of real biological systems. Concentrating on two paradigmatic motifs, the toggle switch and the repressilator, we develop an experimental testbed that explicitly includes both inter-node time delays and noise using digital logic elements on field-programmable gate arrays. We observe transients that last millions to billions of characteristic time scales and scale exponentially with the amount of time delays between nodes, a phenomenon known as super-transient scaling. We develop a hybrid model that includes time delays along network links and allows for stochastic variation in the delays. Using this model, we explain the observed super-transient scaling of both motifs and recreate the experimentally measured transient distributions.