Elements of Computational Systems Biology

10

ANALYSIS AND CONTROL OF DETERMINISTIC AND PROBABILISTIC BOOLEAN NETWORKS

Tatsuya Akutsu

Kyoto University, Kyoto, JapanWai-Ki ChingThe University of Hong Kong, Hong Kong, China

10.1 INTRODUCTION

Analyses of genetic networks are important topics in computational systems biology. For that purpose, mathematical models of genetic networks are needed, and thus various models have been proposed or utilized, which include Bayesian networks, Boolean networks (BNs), and probabilistic BN, ordinary and partial differential equations, and qualitative differential equations [1]. Among them, a lot of studied have been done on the BN. BN is a very simple model [2]: Each node (e.g., gene) takes either 0 (inactive) or 1 (active), and the states of nodes change synchronously according to regulation rules given as Boolean functions. Although such binary expression is very simple, BN is considered to retain meaningful biological information contained in the real continuous domain gene expression patterns. Furthermore, a lot of theoretical studies have been done on the distribution of length and number of attractors for randomly generated BNs with average indegree K, where an attractor corresponds to a steady state of a cell. However, exact results have not yet been obtained.

In 2002, probabilistic Boolean network (PBN) was proposed as a stochastic extension of BN [3]. Although only one Boolean function is assigned to each node in a BN, multiple Boolean functions can be assigned to each node in a ...