Simulation Of Gene Regulatory Networks Research Articles

One model fits all: Combining inference and simulation of gene regulatory networks.

The rise of single-cell data highlights the need for a nondeterministic view of gene expression, while offering new opportunities regarding gene regulatory network inference. We recently introduced two strategies that specifically exploit time-course data, where single-cell profiling is performed after a stimulus: HARISSA, a mechanistic network model with a highly efficient simulation procedure, and CARDAMOM, a scalable inference method seen as model calibration. Here, we combine the two approaches and show that the same model driven by transcriptional bursting can be used simultaneously as an inference tool, to reconstruct biologically relevant networks, and as a simulation tool, to generate realistic transcriptional profiles emerging from gene interactions. We verify that CARDAMOM quantitatively reconstructs causal links when the data is simulated from HARISSA, and demonstrate its performance on experimental data collected on in vitro differentiating mouse embryonic stem cells. Overall, this integrated strategy largely overcomes the limitations of disconnected inference and simulation.

A Stable, Unified Density Controlled Memetic Algorithm for Gene Regulatory Network Reconstruction Based on Sparse Fuzzy Cognitive Maps

Gene regulatory networks (GRNs) denote the interrelation among genes in the genomic level. GRNs have a sparse network structures, and as a simulation of GRNs, the density of The Dialogue for Reverse Engineering Assessments and Methods (DREAM) challenge is less than 5%. So using sparse models to represent GRNs is a meaningful task. Fuzzy cognitive maps (FCMs) have been used to reconstruct GRNs. However, the networks learned by automated derivate-free methods is much denser than those in practical applications. Moreover, the performance of current sparse FCM learning algorithms is worse than what we expect. Therefore, proposing a fast, simple and sparse FCM learning algorithm is a realistic demand. Here, we propose a new unified algorithm: Density Controlled Memetic Algorithm (DC-MA) for learning sparse FCMs. As a simple and good-performance algorithm, memetic algorithm (MA) is chosen as the framework of DC-MA. In DC-MA, a new crossover operator and a mutation operator are designed to optimize the target, control the density and ensure the stability; the local search is used to improve the accuracy and a special self-learning operator is proposed to adjust density. To test the effectiveness of our algorithm, DC-MA is performed on synthetic data with varying sizes and densities. The results show that DC-MA obtains good performance in learning sparse FCMs from time series. On the benchmark datasets DREAM3, DREAM4 and large-scale GRN reconstruction DREAM5 dataset, DC-MA shows high accuracy. The good performance in learning sparse FCMs shows the effectiveness of DC-MA, and the simplicity and scalability of the framework ensure that DC-MA can be adapted to a wide range of needs.

SCANPY: large-scale single-cell gene expression data analysis

Scanpy is a scalable toolkit for analyzing single-cell gene expression data. It includes methods for preprocessing, visualization, clustering, pseudotime and trajectory inference, differential expression testing, and simulation of gene regulatory networks. Its Python-based implementation efficiently deals with data sets of more than one million cells (https://github.com/theislab/Scanpy). Along with Scanpy, we present AnnData, a generic class for handling annotated data matrices (https://github.com/theislab/anndata).

A Model-Based Tool for the Analysis and Design of Gene Regulatory Networks.

Computational and mathematical models have significantly contributed to the rapid progress in the study of gene regulatory networks (GRN), but researchers still lack a reliable model-based framework for computer-aided analysis and design. Such tool should both reveal the relation between network structure and dynamics and find parameter values and/or constraints that enable the simulated dynamics to reproduce specific behaviors. This paper addresses these issues and proposes a computational framework that facilitates network analysis or design. It follows a modeling cycle that alternates phases of hypothesis testing with parameter space refinement to ultimately propose a network that exhibits specified behaviors with the highest probability. Hypothesis testing is performed via qualitative simulation of GRNs modeled by a class of nonlinear and temporal multiscale ODEs, where regulation functions are expressed by steep sigmoid functions and incompletely known parameter values by order relations only. Parameter space refinement, grounded on a method that considers the intrinsic stochasticity of regulation by expressing network uncertainty with fluctuations in parameter values only, optimizes parameter stochastic values initialized by probability distributions with large variances. The power and ease of our framework is demonstrated by working out a benchmark synthetic network to get a synthetic oscillator.

Stochastic modeling and numerical simulation of gene regulatory networks with protein bursting

Gene expression is inherently stochastic. Advanced single-cell microscopy techniques together with mathematical models for single gene expression led to important insights in elucidating the sources of intrinsic noise in prokaryotic and eukaryotic cells. In addition to the finite size effects due to low copy numbers, translational bursting is a dominant source of stochasticity in cell scenarios involving few short lived mRNA transcripts with high translational efficiency (as is typically the case for prokaryotes), causing protein synthesis to occur in random bursts.In the context of gene regulation cascades, the Chemical Master Equation (CME) governing gene expression has in general no closed form solution, and the accurate stochastic simulation of the dynamics of complex gene regulatory networks is a major computational challenge. The CME associated to a single gene self regulatory motif has been previously approximated by a one dimensional time dependent partial integral differential equation (PIDE). However, to the best of our knowledge, multidimensional versions for such PIDE have not been developed yet. Here we propose a multidimensional PIDE model for regulatory networks involving multiple genes with self and cross regulations (in which genes can be regulated by different transcription factors) derived as the continuous counterpart of a CME with jump process. The model offers a reliable description of systems with translational bursting. In order to provide an efficient numerical solution, we develop a semilagrangian method to discretize the differential part of the PIDE, combined with a composed trapezoidal quadrature formula to approximate the integral term.We apply the model and numerical method to study sustained stochastic oscillations and the development of competence, a particular case of transient differentiation attained by certain bacterial cells under stress conditions. We found that the resulting probability distributions are distinguishable from those characteristic of other transient differentiation processes. In this way, they can be employed as markers or signatures that identify such phenomena from bacterial population experimental data, for instance. The computational efficiency of the semilagrangian method makes it suitable for purposes like model identification and parameter estimation from experimental data or, in combination with optimization routines, the design of gene regulatory networks under molecular noise.

MultiGrain/MAPPER: A distributed multiscale computing approach to modeling and simulating gene regulation networks

Modeling and simulation of gene-regulatory networks (GRNs) has become an important aspect of modern systems biology investigations into mechanisms underlying gene regulation. A key task in this area is the automated inference or reverse-engineering of dynamic mechanistic GRN models from gene expression time-course data. Besides a lack of suitable data (in particular multi-condition data from the same system), one of the key challenges of this task is the computational complexity involved. The more genes in the GRN system and the more parameters a GRN model has, the higher the computational load. The computational challenge is likely to increase substantially in the near future when we tackle larger GRN systems. The goal of this study was to develop a distributed computing framework and system for reverse-engineering of GRN models. We present the resulting software called MultiGrain/MAPPER. This software is based on a new architecture and tools supporting multiscale computing in a distributed computing environment. A key feature of MultiGrain/MAPPER is the realization of GRN reverse-engineering based on the underlying distributed computing framework and multi-swarm particle swarm optimization. We demonstrate some of the features of MultiGrain/MAPPER and evaluate its performance using both real and artificial gene expression data.

A two-stage inference algorithm for gene regulation network models

Modelling and simulation of gene-regulatory networks (GRNs) has become an important aspect of modern systems biology investigations. An important and unsolved problem in this area is the automated inference (reverse-engineering) of dynamic mechanistic GRN models from gene-expression time-course data. The conventional single-stage algorithm determines the values of all model parameters simultaneously, whereas recent two-stage algorithms can potentially improve the performance (accuracy) of single-stage approaches. The objective of this study is to compare the performance of the conventional single-stage and a novel version of the modern two-stage algorithm. We based this study on our implementation of a multi-swarm particle swarm optimisation process. A particular focus of this study is placed on the comparison of the computational performance of the single-stage vs. two-stage algorithm. Our results suggest that the 2-stage approach outperforms the single-stage methods by far in terms of model inference speed without loss of accuracy.

Kinetic Theory Modeling and Efficient Numerical Simulation of Gene Regulatory Networks Based on Qualitative Descriptions

In this work, we begin by considering the qualitative modeling of biological regulatory systems using process hitting, from which we define its probabilistic counterpart by considering the chemical master equation within a kinetic theory framework. The last equation is efficiently solved by considering a separated representation within the proper generalized decomposition framework that allows circumventing the so-called curse of dimensionality. Finally, model parameters can be added as extra-coordinates in order to obtain a parametric solution of the model.

CoGNaC: A Chaste Plugin for the Multiscale Simulation of Gene Regulatory Networks Driving the Spatial Dynamics of Tissues and Cancer.

We introduce a Chaste plugin for the generation and the simulation of Gene Regulatory Networks (GRNs) in multiscale models of multicellular systems. Chaste is a widely used and versatile computational framework for the multiscale modeling and simulation of multicellular biological systems. The plugin, named CoGNaC (Chaste and Gene Networks for Cancer), allows the linking of the regulatory dynamics to key properties of the cell cycle and of the differentiation process in populations of cells, which can subsequently be modeled using different spatial modeling scenarios. The approach of CoGNaC focuses on the emergent dynamical behavior of gene networks, in terms of gene activation patterns characterizing the different cellular phenotypes of real cells and, especially, on the overall robustness to perturbations and biological noise. The integration of this approach within Chaste’s modular simulation framework provides a powerful tool to model multicellular systems, possibly allowing for the formulation of novel hypotheses on gene regulation, cell differentiation, and, in particular, cancer emergence and development. In order to demonstrate the usefulness of CoGNaC over a range of modeling paradigms, two example applications are presented. The first of these concerns the characterization of the gene activation patterns of human T-helper cells. The second example is a multiscale simulation of a simplified intestinal crypt, in which, given certain conditions, tumor cells can emerge and colonize the tissue.

Evaluating a common semi-mechanistic mathematical model of gene-regulatory networks.

Modeling and simulation of gene-regulatory networks (GRNs) has become an important aspect of modern systems biology investigations into mechanisms underlying gene regulation. A key challenge in this area is the automated inference (reverse-engineering) of dynamic, mechanistic GRN models from gene expression time-course data. Common mathematical formalisms for representing such models capture two aspects simultaneously within a single parameter: (1) Whether or not a gene is regulated, and if so, the type of regulator (activator or repressor), and (2) the strength of influence of the regulator (if any) on the target or effector gene. To accommodate both roles, "generous" boundaries or limits for possible values of this parameter are commonly allowed in the reverse-engineering process. This approach has several important drawbacks. First, in the absence of good guidelines, there is no consensus on what limits are reasonable. Second, because the limits may vary greatly among different reverse-engineering experiments, the concrete values obtained for the models may differ considerably, and thus it is difficult to compare models. Third, if high values are chosen as limits, the search space of the model inference process becomes very large, adding unnecessary computational load to the already complex reverse-engineering process. In this study, we demonstrate that restricting the limits to the [−1, +1] interval is sufficient to represent the essential features of GRN systems and offers a reduction of the search space without loss of quality in the resulting models. To show this, we have carried out reverse-engineering studies on data generated from artificial and experimentally determined from real GRN systems.

The Influence of Network Topology on Reverse-engineering of Gene-regulatory Networks

Modeling and simulation of gene-regulatory networks (GRNs) has become an important aspect of modern computational biology investigations into gene regulation. A key challenge in this area is the automated inference (reverse-engineering) of dynamic, mechanistic GRN models from time-course gene expression data. Common mathematical formalisms used to represent such models capture both the relative weight or strength of a regulator gene and the type of the regulator (activator, repressor) with a single model parameter. The goal of this study is to quantify the role this parameter plays in terms of the computational performance of the reverse-engineering process and the predictive power of the inferred GRN models. We carried out three sets of computational experiments on a GRN system consisting of 22 genes. While more comprehensive studies of this kind are ultimately required, this computational study demonstrates that models with similar training (reverse-engineering) error that have been inferred under varying degrees of a priori known topology information, exhibit considerably different predictive performance. This study was performed with a newly developed multiscale modeling and simulation tool called MultiGrain/MAPPER.

GeNESiS: gene network evolution simulation software

BackgroundThere has been a lot of interest in recent years focusing on the modeling and simulation of Gene Regulatory Networks (GRNs). However, the evolutionary mechanisms that give rise to GRNs in the first place are still largely unknown. In an earlier work, we developed a framework to analyze the effect of objective functions, input types and starting populations on the evolution of GRNs with a specific emphasis on the robustness of evolved GRNs.ResultsIn this work, we present a parallel software package, GeNESiS for the modeling and simulation of the evolution of gene regulatory networks (GRNs). The software models the process of gene regulation through a combination of finite-state and stochastic models. The evolution of GRNs is then simulated by means of a genetic algorithm with the network connections represented as binary strings. The software allows users to simulate the evolution under varying selective pressures and starting conditions. We believe that the software provides a way for researchers to understand the evolutionary behavior of populations of GRNs.ConclusionWe believe that GeNESiS will serve as a useful tool for scientists interested in understanding the evolution of gene regulatory networks under a range of different conditions and selective pressures. Such modeling efforts can lead to a greater understanding of the network characteristics of GRNs.

Compositionality, stochasticity, and cooperativity in dynamic models of gene regulation

We present an approach for constructing dynamic models for the simulation of gene regulatory networks from simple computational elements. Each element is called a "gene gate" and defines an inputoutput relationship corresponding to the binding and production of transcription factors. The proposed reaction kinetics of the gene gates can be mapped onto stochastic processes and the standard ordinary differential equation (ODE) description. While the ODE approach requires fixing the system's topology before its correct implementation, expressing them in stochastic pi-calculus leads to a fully compositional scheme: network elements become autonomous and only the inputoutput relationships fix their wiring. The modularity of our approach allows to pass easily from a basic first-level description to refined models which capture more details of the biological system. As an illustrative application we present the stochastic repressilator, an artificial cellular clock, which oscillates readily without any cooperative effects.

Accelerating Gene Regulatory Network Modeling Using Grid-Based Simulation

Modeling gene regulatory networks has, in some cases, enabled biologists to predict cellular behavior long before such behavior can be experimentally validated. Unfortunately, the extent to which biologists can take advantage of these modeling techniques is limited by the computational complexity of gene regulatory network simulation algorithms. This study presents a new platform-independent, grid-based distributed computing environment that accelerates biological model simulation and, ultimately, development. Applying this environment to gene regulatory network simulation shows a significant reduction in execution time versus running simulation jobs locally. To analyze this improvement, a performance model of the distributed computing environment is built. Although this grid-based system was specifically developed for biological simulation, the techniques discussed are applicable to a variety of simulation performance problems.