Results 1  10
of
30
Modeling and simulation of genetic regulatory systems: A literature review
 Journal of Computational Biology
, 2002
"... In order to understand the functioning of organisms on the molecular level, we need to know which genes are expressed, when and where in the organism, and to which extent. The regulation of gene expression is achieved through genetic regulatory systems structured by networks of interactions between ..."
Abstract

Cited by 415 (9 self)
 Add to MetaCart
In order to understand the functioning of organisms on the molecular level, we need to know which genes are expressed, when and where in the organism, and to which extent. The regulation of gene expression is achieved through genetic regulatory systems structured by networks of interactions between DNA, RNA, proteins, and small molecules. As most genetic regulatory networks of interest involve many components connected through interlocking positive and negative feedback loops, an intuitive understanding of their dynamics is hard to obtain. As a consequence, formal methods and computer tools for the modeling and simulation of genetic regulatory networks will be indispensable. This paper reviews formalisms that have been employed in mathematical biology and bioinformatics to describe genetic regulatory systems, in particular directed graphs, Bayesian networks, Boolean networks and their generalizations, ordinary and partial differential equations, qualitative differential equations, stochastic equations, and rulebased formalisms. In addition, the paper discusses how these formalisms have been used in the simulation of the behavior of actual regulatory systems. Key words: genetic regulatory networks, mathematical modeling, simulation, computational biology.
Genetic Network Inference: From CoExpression Clustering To Reverse Engineering
, 2000
"... motivation: Advances in molecular biological, analytical and computational technologies are enabling us to systematically investigate the complex molecular processes underlying biological systems. In particular, using highthroughput gene expression assays, we are able to measure the output of the ge ..."
Abstract

Cited by 210 (0 self)
 Add to MetaCart
motivation: Advances in molecular biological, analytical and computational technologies are enabling us to systematically investigate the complex molecular processes underlying biological systems. In particular, using highthroughput gene expression assays, we are able to measure the output of the gene regulatory network. We aim here to review datamining and modeling approaches for conceptualizing and unraveling the functional relationships implicit in these datasets. Clustering of coexpression profiles allows us to infer shared regulatory inputs and functional pathways. We discuss various aspects of clustering, ranging from distance measures to clustering algorithms and multiplecluster memberships. More advanced analysis aims to infer causal connections between genes directly, i.e. who is regulating whom and how. We discuss several approaches to the problem of reverse engineering of genetic networks, from discrete Boolean networks, to continuous linear and nonlinear models. We conclude that the combination of predictive modeling with systematic experimental verification will be required to gain a deeper insight into living organisms, therapeutic targeting and bioengineering.
Qualitative Simulation of Genetic Regulatory Networks Using PiecewiseLinear Models
, 2001
"... In order to cope with the large amounts of data that have become available in genomics, mathematical tools for the analysis of networks of interactions between genes, proteins, and other molecules are indispensable. We present a method for the qualitative simulation of genetic regulatory networks ..."
Abstract

Cited by 130 (21 self)
 Add to MetaCart
In order to cope with the large amounts of data that have become available in genomics, mathematical tools for the analysis of networks of interactions between genes, proteins, and other molecules are indispensable. We present a method for the qualitative simulation of genetic regulatory networks, based on a class of piecewiselinear (PL) differential equations that has been wellstudied in mathematical biology. The simulation method is welladapted to stateoftheart measurement techniques in genomics, which often provide qualitative and coarsegrained descriptions of genetic regulatory networks. Given a qualitative model of a genetic regulatory network, consisting of a system of PL differential equations and inequality constraints on the parameter values, the method produces a graph of qualitative states and transitions between qualitative states, summarizing the qualitative dynamics of the system. The qualitative simulation method has been implemented in Java in the computer tool Genetic Network Analyzer.
F: Designer gene networks: Towards fundamental cellular control. Chaos: An Interdisciplinary
 Journal of Nonlinear Science
"... Submitted to ChaosABSTRACT The engineered control of cellular function through the design of synthetic genetic networks is becoming plausible. Here we show how a naturally occurring network can be used as a parts list for artificial network design, and how model formulation leads to computational an ..."
Abstract

Cited by 29 (2 self)
 Add to MetaCart
Submitted to ChaosABSTRACT The engineered control of cellular function through the design of synthetic genetic networks is becoming plausible. Here we show how a naturally occurring network can be used as a parts list for artificial network design, and how model formulation leads to computational and analytical approaches relevant to nonlinear dynamics and statistical physics. We first review the relevant work on synthetic gene networks, highlighting the important experimental findings with regard to genetic switches and oscillators. We then present the derivation of a deterministic model describing the temporal evolution of the concentration of protein in a singlegene network. Bistability in the steadystate protein concentration arises naturally as a consequence of autoregulatory feedback, and we focus on the hysteretic properties of the protein concentration as a function of the degradation rate. We then formulate the effect of an external noise source which interacts with the protein degradation rate. We demonstrate the utility of such a formulation by constructing a protein switch, whereby external noise pulses are used to switch the protein concentration between two values. Following the lead of earlier work, we show how the addition of a second network component can be used to construct a relaxation oscillator, whereby the system is driven
Discrete time piecewise affine model of genetic regulatory networks, Preprint CPT
, 2004
"... We introduce simple models of genetic regulatory networks and we proceed to the mathematical analysis of their dynamics. The models are discrete time dynamical systems generated by piecewise affine contracting mappings whose variables represent gene expression levels. When compared to other models o ..."
Abstract

Cited by 8 (2 self)
 Add to MetaCart
We introduce simple models of genetic regulatory networks and we proceed to the mathematical analysis of their dynamics. The models are discrete time dynamical systems generated by piecewise affine contracting mappings whose variables represent gene expression levels. When compared to other models of regulatory networks, these models have an additional parameter which is identified as quantifying interaction delays. In spite of their simplicity, their dynamics presents a rich variety of behaviours. This phenomenology is not limited to piecewise affine model but extends to smooth nonlinear discrete time models of regulatory networks. In a first step, our analysis concerns general properties of networks on arbitrary graphs (characterisation of the attractor, symbolic dynamics, Lyapunov stability, structural stability, symmetries, etc). In a second step, focus is made on simple circuits for which the attractor and its changes with parameters are described. In the negative circuit of 2 genes, a thorough study is presented which concern stable (quasi)periodic oscillations governed by rotations on the unit circle – with a rotation number depending continuously and monotonically on threshold parameters. These regular oscillations exist in negative circuits with arbitrary number of genes where they are most likely to be observed in genetic systems with nonnegligible delay effects. 1
A mathematical framework for the control of piecewise affine models of gene networks
, 2007
"... ..."
On matrices with common invariant cones with applications in neural and gene networks. Linear Algebra and its Applications
"... Motivated by a differential continuoustime switching model for gene and neural networks, we investigate matrix theoretic problems regarding the relative location and topology of the dominant eigenvectors of words constructed multiplicatively from two matrices A and B. These problems are naturally a ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
Motivated by a differential continuoustime switching model for gene and neural networks, we investigate matrix theoretic problems regarding the relative location and topology of the dominant eigenvectors of words constructed multiplicatively from two matrices A and B. These problems are naturally associated with the existence of common invariant subspaces and common invariant proper cones of A and B. The commuting case and the two dimensional case are rich and considered analytically. We also analyze and recast the problem of the existence of a common invariant polyhedral cone in a multilinear framework, as well as present necessary conditions for the existence of low dimensional common invariant cones.
Global Dynamics of Neural Nets With Infinite Gain.
, 1999
"... We consider a model of neural and gene networks where the nonlinearities in the system of differential equations are discontinuous and piecewise constant. We associate to the system a graph on a hypercube, which can be used to define a Morse decomposition of a related flow on the set of rays through ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
We consider a model of neural and gene networks where the nonlinearities in the system of differential equations are discontinuous and piecewise constant. We associate to the system a graph on a hypercube, which can be used to define a Morse decomposition of a related flow on the set of rays through the origin. We then discuss relationship between the invariant sets in the ray flow and the invariant sets in regular flow. We provide a sufficient conditions when there is a oneto one correspondence between these sets. Finally, we consider a subclass of gene networks, where under certain conditions we can determine the structure of the lowest (attracting) Morse set directly from the hypercube graph. Key words. Neural and gene networks, Morse decomposition, global dynamics. AMS subject classification 34C25, 68T10, 92B20,92D15. 1 Introduction In this paper we study a set of differential equations, introduced by L. Glass [1] x i = \Gammafl i x i + i (x 1 ; : : : ; x n ); i = 1; : : : ; n...