Dynamic modeling of genetic networks using genetic algorithm and S-system

Motivation: The modeling of system dynamics of genetic networks, metabolic networks or signal transduction cascades from time-course data is formulated as a reverse-problem. Previous studies focused on the estimation of only network structures, and they were ineffective in inferring a network structure with feedback loops. We previously proposed a method to predict not only the network structure but also its dynamics using a Genetic Algorithm (GA) and an S-system formalism. However, it could predict only a small number of parameters and could rarely obtain essential structures. In this work, we propose a unified extension of the basic method. Notable improvements are as follows: (1) an additional term in its evaluation function that aims at eliminating futile parameters; (2) a crossover method called Simplex Crossover (SPX) to improve its optimization ability; and (3) a gradual optimization strategy to increase the number of predictable parameters. Results: The proposed method is implemented as a C program called PEACE1 (Predictor by Evolutionary Algorithms and Canonical Equations 1). Its performance was compared with the basic method. The comparison showed that: (1) the convergence rate increased about 5-fold; (2) the optimization speed was raised about 1.5-fold; and (3) the number of predictable parameters was increased about 5-fold. Moreover, we successfully inferred the dynamics of a small genetic network constructed with 60 parameters for 5 network variables and feedback loops using only time-course data of gene expression.