Qualitative simulation of genetic regulatory networks using piecewise-linear models (original) (raw)
Dealing with Discontinuities in the Qualitative Simulation of Genetic Regulatory Networks
2002
Methods developed for the qualitative simulation of dynamical systems have turned out to be powerful tools for studying genetic regulatory networks. We present a generalization of a simulation method based on piecewise-linear differential equation models that is able to deal with discontinuities. The method is sound and has been implemented in a computer tool called GNA.
Modeling gene regulatory networks with piecewise linear differential equations
European Journal of Operational Research, 2007
Microarray chips generate large amounts of data about a cell's state. In our work we want to analyze these data in order to describe the regulation processes within a cell. Therefore, we build a model which is capable of capturing the most relevant regulating interactions and present an approach how to calculate the parameters for the model from time-series data. This approach uses the discrete approximation method of least squares to solve a data fitting modeling problem. Furthermore, we analyze the features of our proposed system, i.e., which kinds of dynamical behaviors the system is able to show.
On Two Qualitative Representations of a Genetic Regulatory Network
There is an increasing interest in the study of genetic regulatory networks, and in addition to experimental tools, specific tools for modelling and simulation recently emerged, allowing systematic behaviour prediction of large complex systems. Since there is a usual lack of information of biochemical reaction networks, qualitative simulation tools, requiring only specification of inequality-like algebraic constraints, are preferred to quantitative ones. Starting from a simple piecewise- linear model of a two genes regulatory network (TGNR) described in the literature, this paper proposes an alternate qualitative modelling technique, which extends a hybrid control systems (HCS) framework from control engineering. The thresholds protein concentrations partition the state space into hyperrectangular open regions and the resulting qualitative model is basically a logical abstraction of the families of continuous trajectories mapped to this partition. The relations of this model to nume...
Simulation of genetic networks modelled by piecewise deterministic Markov processes
IET Systems Biology, 2008
The authors propose piecewise deterministic Markov processes as an alternative approach to model gene regulatory networks. A hybrid simulation algorithm is presented and discussed, and several standard regulatory modules are analysed by numerical means. It is shown that despite of the partial simplification of the mesoscopic nature of regulatory networks such processes are suitable to reveal the intrinsic noise effects because of the low copy numbers of genes.
Piecewise-linear Models of Genetic Regulatory Networks: Equilibria and their Stability
Journal of Mathematical Biology, 2006
A formalism based on piecewise-linear (PL) differential equations, originally due to Glass and Kauffman, has been shown to be well-suited to modelling genetic regulatory networks. However, the discontinuous vector field inherent in the PL models raises some mathematical problems in defining solutions on the surfaces of discontinuity. To overcome these difficulties we use the approach of Filippov, which extends the vector field to a differential inclusion. We study the stability of equilibria (called singular equilibrium sets) that lie on the surfaces of discontinuity. We prove several theorems that characterize the stability of these singular equilibria directly from the state transition graph, which is a qualitative representation of the dynamics of the system. We also formulate a stronger conjecture on the stability of these singular equilibrium sets.
Simulating Genetic Regulatory Networks Version 1.2
If we assume that the process modelled is stable over time, then we can represent the causal structure of the series with a time series graph that includes the smallest fragment of the series that repeats. The number of temporal slices in the time series graph is the longest lag of direct influence plus one. For example, the time series graph in Figure 2, 1 which represents the series in Figure 1, needs three temporal slices to represent a repeating sequence, because G2 has a direct effect on G3 with a temporal lag of two. time= i
2005
Methods developed for the qualitative simulation of dynamical systems have turned out to be powerful tools for studying genetic regulatory networks. A bottleneck in the application of these methods is the analysis of the simulation results. In this paper, we propose a combination of qualitative simulation and model-checking techniques to perform this task systematically and efficiently. We apply our approach to the analysis of the complex network controlling the nutritional stress response in the bacterium Escherichia coli.
Lecture Notes in Computer Science, 2008
A specific class of ODEs has been shown to be adequate to describe the essential features of the complex dynamics of Gene-Regulatory Networks (GRN). But, the effective exploitation of such models to predict the dynamics of specific GRNs by classical numerical schemes is greatly hampered by the current lack of precise and quantitative information on regulation mechanisms and kinetic parameters. Due to the size and complexity of large GRNs, classical qualitative analysis could be very hard, or even impracticable, to be carried out by hand, and conventional qualitative simulation approaches rapidly lead to an exponential growth of the generated behavior tree that, besides all possible sound behaviors, may also contain spurious ones. This paper discusses the work-in-progress of a research effort aiming at the design and implementation of a computational framework for qualitative simulation of the dynamics of a class of ODE models of GRNs. The algorithm we propose results from a set of symbolic computation algorithms that carry out the integration of qualitative reasoning techniques with singular perturbation analysis methods. The former techniques allow us to cope with uncertain and incomplete knowledge whereas the latter ones lay the mathematical groundwork for a sound and complete algorithm capable to deal with regulation processes that occur at different time scales.
INTERNATIONAL …, 2005
Methods developed for the qualitative simulation of dynamical systems have turned out to be powerful tools for studying genetic regulatory networks. A bottleneck in the application of these methods is the analysis of the simulation results. In this paper, we propose a combination of qualitative simulation and model-checking techniques to perform this task systematically and efficiently. We apply our approach to the analysis of the complex network controlling the nutritional stress response in the bacterium Escherichia coli.
Temporal constraints of a gene regulatory network: Refining a qualitative simulation
Biosystems, 2009
The modelling of gene regulatory networks (GRNs) has classically been addressed through very different approaches. Among others, extensions of Thomas's asynchronous Boolean approach have been proposed, to better fit the dynamics of biological systems: genes may reach different discrete expression levels, depending on the states of other genes, called the regulators: thus, activations and inhibitions are triggered conditionally on the proper expression levels of these regulators. In contrast, some fine-grained propositions have focused on the molecular level as modelling the evolution of biological compound concentrations through differential equation systems. Both approaches are limited. The first one leads to an oversimplification of the system, whereas the second is incapable to tackle large GRNs. In this context, hybrid paradigms, that mix discrete and continuous features underlying distinct biological properties, achieve significant advances for investigating biological properties. One of these hybrid formalisms proposes to focus, within a GRN abstraction, on the time delay to pass from a gene expression level to the next. Until now, no research work has been carried out, which attempts to benefit from the modelling of a GRN by differential equations, converting it into a multi-valued logical formalism of Thomas, with the aim of performing biological applications.
Logical modelling of regulatory networks with GINsim 2.3
Biosystems, 2009
Many important problems in cell biology require the consideration of dense nonlinear interactions between functional modules. The requirement of computer simulation for the understanding of cellular processes is now widely accepted, and a variety of modelling frameworks have been designed to meet this need. Here, we present a novel public release of the Gene Interaction Network simulation suite (GINsim), a software designed for the qualitative modelling and analysis of regulatory networks. The main functionalities of GINsim are illustrated through the analysis of a logical model for the core network controlling the fission yeast cell cycle. The last public release of GINsim (version 2.3), as well as development versions, can be downloaded from the dedicated website (http://gin.univ-mrs.fr/GINsim/), which further includes a model library, along with detailed tutorial and user manual.
Symbolic Modeling of Genetic Regulatory Networks
Journal of Bioinformatics and Computational Biology, 2007
Understanding the functioning of genetic regulatory networks supposes a modeling of biological processes in order to simulate behaviors and to reason on the model. Unfortunately, the modeling task is confronted to incomplete knowledge about the system. To deal with this problem we propose a methodology that uses the qualitative approach developed by R. Thomas. A symbolic transition system can represent the set of all possible models in a concise and symbolic way. We introduce a new method based on model-checking techniques and symbolic execution to extract constraints on parameters leading to dynamics coherent with known behaviors. Our method allows us to efficiently respond to two kinds of questions: is there any model coherent with a certain hypothetic behavior? Are there behaviors common to all selected models? The first question is illustrated with the example of the mucus production in Pseudomonas aeruginosa while the second one is illustrated with the example of immunity control in bacteriophage lambda.
Genetic Network Analyzer: qualitative simulation of genetic regulatory networks
Bioinformatics, 2003
Motivation: The study of genetic regulatory networks has received a major impetus from the recent development of experimental techniques allowing the measurement of patterns of gene expression in a massively parallel way. This experimental progress calls for the development of appropriate computer tools for the modeling and simulation of gene regulation processes. Results: We present Genetic Network Analyzer (GNA), a computer tool for the modeling and simulation of genetic regulatory networks. The tool is based on a qualitative simulation method that employs coarse-grained models of regulatory networks. The use of GNA is illustrated by a case study of the network of genes and interactions regulating the initiation of sporulation in Bacillus subtilis. Availability: GNA and the model of the sporulation network are available at http://www-helix.inrialpes.fr/gna Contact: Hidde.de-Jong@inrialpes.fr * To whom correspondence should be addressed.
Simulating genetic networks made easy: Network construction with simple building blocks
Bioinformatics, 2005
We present SIM-plex, a genetic network simulator with a very intuitive interface in which a user can easily specify interactions as simple 'if-then' statements. The simulator is based on the mathematical model of Piecewise Linear Differential Equations (PLDEs). With PLDEs, genetic interactions are approximated as acting in a switch-like manner.
Logical Modelling of Gene Regulatory Networks with GINsim
Bacterial Molecular Networks, 2011
Discrete mathematical formalisms are well adapted to model large biological networks, for which detailed kinetic data are scarce. This chapter introduces the reader to a well-established qualitative (logical) framework for the modelling of regulatory networks. Relying on GINsim, a software implementing this logical formalism, we guide the reader step by step towards the definition and the analysis of a simple model of the lysis-lysogeny decision in the bacteriophage l.
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2004
Genetic regulatory networks have the complex task of controlling all aspects of life. Using a model of gene expression by piecewise linear differential equations we show that this process can be considered as a process of computation. This is demonstrated by showing that this model can simulate memory bounded Turing machines. The simulation is robust with respect to perturbations of the system, an important property for both analog computers and biological systems. Robustness is achieved using a condition that ensures that the model equations, that are generally chaotic, follow a predictable dynamics.