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Modeling the Dynamics of Gene Regulatory Networks

其他書名	Piecewise Linear Differential Equations and Discrete Approaches
出版	2012
URL	http://books.google.com.hk/books?id=1uJHmwEACAAJ&hl=&source=gbs_api

註釋In order to describe the dynamic behavior of gene regulatory networks different formalisms have been introduced. In this thesis, we describe first the discrete approach of René Thomas and piecewise linear differential equations approach. Then we proposed a correspondence result between the two approaches and based on it we proposed an automatic computational technique to understand the global behavior of such complex systems using MAPLE programming language. The proposed code provides a way to compute the trajectories of the discrete version of a gene regulatory network model given an initial condition, in the same way as usual numerical algorithms give the "true" solution of a differential model from an initial condition. Knowing a discrete trajectory is less precise than knowing a true trajectory but correspondence theorems shows the link between the two approaches. Hence, it is a mathematical tool for analysing gene regulatory networks models. Finally, we illustrate both discrete and piecewise linear approaches, theircorrespondence and the use of our Maple code on a specific example: a mathematical model of the circadian clock. Our first two presented 8 and 4 variables models are the simplification of a model proposed by Leloup and Goldbeter. We deliberately choose to push the simplicity of the model as far as possible, focusing only on a few biological behaviors of interest. The hope is to get nevertheless the essential abstract causalities that govern these behaviors.