Collectively canalizing Boolean functions

This paper studies the mathematical properties of collectively canalizing Boolean functions, a class of functions that has arisen from applications in systems biology. Boolean networks are an increasingly popular modeling framework for regulatory networks, and the class of functions studied here captures a key feature of biological network dynamics, namely that a subset of one or more variables, under certain conditions, can dominate the value of a Boolean function, to the exclusion of all others. These functions have rich mathematical properties to be explored. The paper shows how the number and type of such sets influence a function's behavior and define a new measure for the canalizing strength of any Boolean function. We further connect the concept of collective canalization with the well-studied concept of the average sensitivity of a Boolean function. The relationship between Boolean functions and the dynamics of the networks they form is important in a wide range of applications beyond biology, such as computer science, and has been studied with statistical and simulation -based methods. But the rich relationship between structure and dynamics remains largely unexplored, and this paper is intended as a contribution to its mathematical foundation. (c) 2022 Elsevier Inc. All rights reserved.

Automated summary

This paper investigates the mathematical properties of collectively canalizing Boolean functions, which are a class of functions derived from applications in systems biology. The functions studied capture an important aspect of biological network dynamics, where a subset of variables can dominate a Boolean function's value under certain conditions. The paper explores the influence of the number and type of these subsets on a function's behavior and introduces a new measure for canalizing strength.