Boolean networks with robust and reliable trajectories

TL;DR

This paper designs Boolean networks that reliably follow a specific trajectory despite noise and fluctuations, using evolutionary algorithms to optimize robustness with minimal connections, achieving near-perfect stability.

Contribution

It introduces a method to construct and optimize Boolean networks for robustness against noise, ensuring reliable trajectories with minimal connections.

Findings

Robustness approaches 100% during optimization

Optimized networks have state space dominated by the reliable trajectory's basin

Minimal connection networks can achieve high robustness

Abstract

We construct and investigate Boolean networks that follow a given reliable trajectory in state space, which is insensitive to fluctuations in the updating schedule, and which is also robust against noise. Robustness is quantified as the probability that the dynamics return to the reliable trajectory after a perturbation of the state of a single node. In order to achieve high robustness, we navigate through the space of possible update functions by using an evolutionary algorithm. We constrain the networks to having the minimum number of connections required to obtain the reliable trajectory. Surprisingly, we find that robustness always reaches values close to 100 percent during the evolutionary optimization process. The set of update functions can be evolved such that it differs only slightly from that of networks that were not optimized with respect to robustness. The state space of the optimized networks is dominated by the basin of attraction of the reliable trajectory.