Fixed Points in Discrete Models for Regulatory Genetic Networks

EURASIP Journal on Bioinformatics and Systems Biology. 2007;2007(1):97356

 

Journal Homepage

Journal Title: EURASIP Journal on Bioinformatics and Systems Biology

ISSN: 1687-4145 (Print); 1687-4153 (Online)

Publisher: Springer

Society/Institution: European Association for Signal Processing (EURASIP)

LCC Subject Category: Technology: Electrical engineering. Electronics. Nuclear engineering | Science: Biology (General) | Medicine: Medicine (General): Computer applications to medicine. Medical informatics

Country of publisher: United Kingdom

Language of fulltext: English

Full-text formats available: PDF, HTML

 

AUTHORS

Orozco Edusmildo
Bollman Dorothy
Colón-Reyes Omar

EDITORIAL INFORMATION

Blind peer review

Editorial Board

Instructions for authors

Time From Submission to Publication: 13 weeks

 

Abstract | Full Text

<p/> <p>It is desirable to have efficient mathematical methods to extract information about regulatory iterations between genes from repeated measurements of gene transcript concentrations. One piece of information is of interest when the dynamics reaches a steady state. In this paper we develop tools that enable the detection of steady states that are modeled by fixed points in discrete finite dynamical systems. We discuss two algebraic models, a univariate model and a multivariate model. We show that these two models are equivalent and that one can be converted to the other by means of a discrete Fourier transform. We give a new, more general definition of a linear finite dynamical system and we give a necessary and sufficient condition for such a system to be a fixed point system, that is, all cycles are of length one. We show how this result for generalized linear systems can be used to determine when certain nonlinear systems (monomial dynamical systems over finite fields) are fixed point systems. We also show how it is possible to determine in polynomial time when an ordinary linear system (defined over a finite field) is a fixed point system. We conclude with a necessary condition for a univariate finite dynamical system to be a fixed point system.</p>