Algorithms and Complexity Analyses for Control of Singleton Attractors in Boolean Networks

Morihiro Hayashida,Tatsuya Akutsu,Takeyuki Tamura,Shu-Qin Zhang,Wai-Ki Ching

doi:10.1155/2008/521407

Abstract

A Boolean network (BN) is a mathematical model of genetic networks. We propose several algorithms for control of singleton attractors in BN. We theoretically estimate the average-case time complexities of the proposed algorithms, and confirm them by computer experiments. The results suggest the importance of gene ordering. Especially, setting internal nodes ahead yields shorter computational time than setting external nodes ahead in various types of algorithms. We also present a heuristic algorithm which does not look for the optimal solution but for the solution whose computational time is shorter than that of the exact algorithms.

Highlights

One of the important challenges of computational systems biology and bioinformatics is to develop a control theory for biological systems [1, 2]
(ii) Output: a 0-1 assignment to external nodes, which maximizes the minimum score of singleton attractors, where the score of an attractor is given as vi∈V S(vi, a)
Output: 0-1 assignment to external nodes, which maximizes the minimum score of singleton attractors

Summary

Introduction

One of the important challenges of computational systems biology and bioinformatics is to develop a control theory for biological systems [1, 2]. For control of linear systems, extensive studies have been done, and rigorous theories and useful methods have been developed. Many of these methods have been applied to control various kinds of real systems. It is to be noted that Yamanaka et al introduced 4 transcription factors of Oct3/4, Sox, c-Myc, and Klf into fibroblast cells, whereas Thomson et al introduced 4 factors of OCT4, SOX2, NANOG, and LIN28 into somatic cells Though these seminal discoveries were achieved based on their knowledge, experience, and many experiments, systematic methods might help such kind of works. We focus on control of gene regulatory networks because these networks play a fundamental role in cells and may be efficiently controlled by overexpression and suppression of genes

Objectives

Methods

Conclusion