Construction Method of Probabilistic Boolean Networks Based on Imperfect Information

Katsuaki Umiji,Koichi Kobayashi,Yuh Yamashita

doi:10.3390/a12120268

Abstract

A probabilistic Boolean network (PBN) is well known as one of the mathematical models of gene regulatory networks. In a Boolean network, expression of a gene is approximated by a binary value, and its time evolution is expressed by Boolean functions. In a PBN, a Boolean function is probabilistically chosen from candidates of Boolean functions. One of the authors has proposed a method to construct a PBN from imperfect information. However, there is a weakness that the number of candidates of Boolean functions may be redundant. In this paper, this construction method is improved to efficiently utilize given information. To derive Boolean functions and those selection probabilities, the linear programming problem is solved. Here, we introduce the objective function to reduce the number of candidates. The proposed method is demonstrated by a numerical example.

Highlights

One of the aims in systems biology is to develop a method for modeling, analysis, and control of gene regulatory networks
In a Boolean network (BN), dynamics such as interactions between genes are expressed by Boolean functions; that is, gene expression is expressed by a binary value (0 or 1)
In a probabilistic Boolean network (PBN), the candidates of f (i) are given, and for each xi, selecting one Boolean function is probabilistically independent at each time

Summary

Introduction

One of the aims in systems biology is to develop a method for modeling, analysis, and control of gene regulatory networks. For a PBN, controllability/reachability analysis [14,15,16,17] and optimal control [18,19,20,21,22] have been studied (see the survey paper [23]). We consider the problem of finding a PBN based on imperfect information such as the network structure, the sample mean, and the prescribed Boolean functions. Q}, define j∈J y j := y j1 ⊗ y j2 ⊗ · · · ⊗ y j p. Let 1m×n denote the m × n matrix whose elements are all one

Probabilistic Boolean Networks

Matrix-Based Representation for PBNs

Construction Problem and Its Solution Method

Example

Conclusions