Effect of memory in non-Markovian Boolean networks

TL;DR

This paper investigates how incorporating memory into Boolean networks, specifically through non-Markovian threshold functions, affects their dynamics, revealing more robust behavior in biological models like the cell cycle network.

Contribution

It introduces a non-Markovian extension to Boolean networks, demonstrating the impact of memory on dynamics and robustness in biological systems.

Findings

Memory induces power-law behavior in Boolean network dynamics

Non-Markovian models show increased robustness compared to Markovian ones

Memory effects can better capture biological phenomena

Abstract

One successful model of interacting biological systems is the Boolean network. 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 a cell cycle network, we discover a power law memory with a more robust dynamics than the Markovian dynamics.