Boolean networks with veto functions

TL;DR

This paper studies a special class of Boolean functions with veto inputs that force the output to zero, providing analytical sensitivity expressions and evidence of their natural occurrence in biological regulatory networks.

Contribution

It introduces veto functions in Boolean networks, analyzes their sensitivity, and demonstrates their relevance in biological systems and existing models.

Findings

Veto functions are over-represented in natural signaling networks.

Analytical expressions for the sensitivity of veto functions are provided.

Veto functions can be integrated into existing biological network models with minimal modifications.

Abstract

Boolean networks are discrete dynamical systems for modeling regulation and signaling in living cells. We investigate a particular class of Boolean functions with inhibiting inputs exerting a veto (forced zero) on the output. We give analytical expressions for the sensitivity of these functions and provide evidence for their role in natural systems. In an intracellular signal transduction network [Helikar et al., PNAS (2008)], the functions with veto are over-represented by a factor exceeding the over-representation of threshold functions and canalyzing functions in the same system. In Boolean networks for control of the yeast cell cycle [Fangting Li et al., PNAS (2004), Davidich et al., PLoS One (2009)], none or minimal changes to the wiring diagrams are necessary to formulate their dynamics in terms of the veto functions introduced here.