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Dynamics of Canalizing Boolean Networks

Paul, Elijah and Pogudin, Gleb and Qin, William and Laubenbacher, Reinhard (2020) Dynamics of Canalizing Boolean Networks. Complexity, 2020 . Art. No. 3687961. ISSN 1076-2787. doi:10.1155/2020/3687961.

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Boolean networks are a popular modeling framework in computational biology to capture the dynamics of molecular networks, such as gene regulatory networks. It has been observed that many published models of such networks are defined by regulatory rules driving the dynamics that have certain so-called canalizing properties. In this paper, we investigate the dynamics of a random Boolean network with such properties using analytical methods and simulations. From our simulations, we observe that Boolean networks with higher canalizing depth have generally fewer attractors, the attractors are smaller, and the basins are larger, with implications for the stability and robustness of the models. These properties are relevant to many biological applications. Moreover, our results show that, from the standpoint of the attractor structure, high canalizing depth, compared to relatively small positive canalizing depth, has a very modest impact on dynamics. Motivated by these observations, we conduct mathematical study of the attractor structure of a random Boolean network of canalizing depth one (i.e., the smallest positive depth). For every positive integer , we give an explicit formula for the limit of the expected number of attractors of length in an n-state random Boolean network as n goes to infinity.

Item Type:Article
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URLURL TypeDescription ItemCode
Paul, Elijah0000-0002-8042-8474
Pogudin, Gleb0000-0002-5731-8242
Qin, William0000-0001-6090-6953
Laubenbacher, Reinhard0000-0002-9143-9451
Additional Information:© 2020 Elijah Paul et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Received 13 September 2019; Accepted 6 November 2019; Published 20 January 2020. The authors are grateful to Claus Kadelka, Christian Krattenthaler, and Doron Zeilberger for helpful discussions. GP was partially supported by NSF grants CCF-1564132, CCF-1563942, DMS-1760448, DMS-1853482, and DMS-1853650 by PSC-CUNY grants #69827-0047 and #60098-0048. RL was partially supported by Grants NIH 1U01EB024501-01 and NSF CBET-1750183. EP, GP, and WQ are grateful to the New York Math Circle, where their collaboration started. Data Availability: Python/sage code and the results of simulations used to support the findings of this study have been deposited at The authors declare that they have no conflicts of interest.
Funding AgencyGrant Number
City University of New York69827-0047
City University of New York60098-0048
Record Number:CaltechAUTHORS:20200305-133947216
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:101727
Deposited By: Tony Diaz
Deposited On:05 Mar 2020 23:21
Last Modified:16 Nov 2021 18:05

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