The Influence of Canalization on the Robustness of Boolean Networks
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2016
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| _version_ | 1866910299993407488 |
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| author | Kadelka, Claus Kuipers, Jack Laubenbacher, Reinhard |
| author_facet | Kadelka, Claus Kuipers, Jack Laubenbacher, Reinhard |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1607_04474 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | The Influence of Canalization on the Robustness of Boolean Networks Kadelka, Claus Kuipers, Jack Laubenbacher, Reinhard Dynamical Systems Chaotic Dynamics Biological Physics Molecular 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 $k$-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. |
| title | The Influence of Canalization on the Robustness of Boolean Networks |
| topic | Dynamical Systems Chaotic Dynamics Biological Physics Molecular Networks |
| url | https://arxiv.org/abs/1607.04474 |