The influence of canalization on the robustness of Boolean networks
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" role="presentation">-canalizing functions, a recently introduced class of Boolean functions that contains the well-studied class of nested canalizing functions. The variable activities and sensitivity of a function quantify the impact of input changes on the function output. This paper generalizes the latter concept to c" role="presentation">-sensitivity and provides formulas for the activities and c" role="presentation">-sensitivity of general k" role="presentation">-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" role="presentation">-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. Physica D: Nonlinear Phenomena 2017 Sep; 353-354:39-47.