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arXiv · 1607.04474

The Influence of Canalization on the Robustness of Boolean Networks

Claus Kadelka·Jack Kuipers·Reinhard Laubenbacher
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Abstract

Time- and state-discrete dynamical systems are frequently used to model molecular networks. This paper provides a collection of mathematical and computational tools for the study of robustness in Boolean network models. The focus is on networks governed by $k$-canalizing functions, a recently introduced class of Boolean functions that contains the well-studied class of nested canalizing functions. The activities and sensitivity of a function quantify the impact of input changes on the function output. This paper generalizes the latter concept to $c$-sensitivity and provides formulas for the activities and $c$-sensitivity of general $k$-canalizing functions as well as canalizing functions with more precisely defined structure. A popular measure for the robustness of a network, the Derrida value, can be expressed as a weighted sum of the $c$-sensitivities of the governing canalizing functions, and can also be calculated for a stochastic extension of Boolean networks. These findings provide a computationally efficient way to obtain Derrida values of Boolean networks, deterministic or stochastic, that does not involve simulation.

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Claus Kadelka, Jack Kuipers, Reinhard Laubenbacher. 2016-07-15. The Influence of Canalization on the Robustness of Boolean Networks. https://doi.org/10.1016/j.physd.2017.05.002

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