Effect of memory in non-Markovian Boolean networks illustrated with a case study: A cell cycling process

¹ Bioinformatics, Institute for Computer Science, Leipzig University - Härtelstrasse 16-18, 04107 Leipzig, Germany
² Department of Physics, Shahid Beheshti University, G.C. - Evin, Tehran 19839, Iran
³ School of Business, University of Leicester - University Road, Leicester LE1 7RH, UK
⁴ GRAPES - rue de la Belle Jardiniere 483, B-4031, Angleur, Belgium
⁵ The Institute for Brain and Cognitive Science (IBCS), Shahid Beheshti University, G.C. - Evin, Tehran 19839, Iran
⁶ School of Biological Sciences, Institute for Research in Fundamental Sciences (IPM) - Tehran, Iran

Received: 9 August 2016
Accepted: 26 November 2016

Abstract

The Boolean network is one successful model to investigate discrete complex systems such as the gene interacting phenomenon. The dynamics of a Boolean network, controlled with Boolean functions, is usually considered to be a Markovian (memory-less) process. However, both self-organizing features of biological phenomena and their intelligent nature should raise some doubt about ignoring the history of their time evolution. Here, we extend the Boolean network Markovian approach: we involve the effect of memory on the dynamics. This can be explored by modifying Boolean functions into non-Markovian functions, for example, by investigating the usual non-Markovian threshold function —one of the most applied Boolean functions. By applying the non-Markovian threshold function on the dynamical process of the yeast cell cycle network, we discover a power-law-like memory with a more robust dynamics than the Markovian dynamics.