The Influence of Canalization on the Robustness of Boolean Networks

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.

arXiv comment16 pages, 2 figures, 3 tables

References in corpus (9)

• The Yeast Cell-Cycle Network Is Robustly Designed
• Random Boolean Network Models and the Yeast Transcriptional Network
• Boolean network model predicts cell cycle sequence of fission yeast
• Genetic networks with canalyzing Boolean rules are always stable
• Modeling Stochasticity and Variability in Gene Regulatory Networks
• Boolean nested canalizing functions: a comprehensive analysis
• Canalization and control in automata networks: body segmentation in Drosophila melanogaster
• Regulatory patterns in molecular interaction networks
• Perturbation propagation in random and evolved Boolean networks

Cited by in corpus (7)

• A meta-analysis of Boolean network models reveals design principles of gene regulatory networks
• Revealing the canalizing structure of Boolean functions: Algorithms and applications
• Stability of Linear Boolean Networks
• Nested canalizing functions minimize sensitivity and simultaneously promote criticality
• Upper bound for the stability of Boolean networks
• Symmetry Properties of Nested Canalyzing Functions
• Dynamics of attractor transitions in Boolean networks under noise