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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 ℓ , we give an explicit formula for the limit of the expected number of attractors of length ℓ in an n -state random Boolean network as n goes to infinity.
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Critical assessment of the ability of Boolean threshold models to describe gene regulatory network dynamics
Abstract The inference of gene regulatory networks (GRNs) from high-throughput data constitutes a fundamental and challenging task in systems biology. Boolean networks are a popular modeling framework to understand the dynamic nature of GRNs. In the absence of reliable methods to infer the regulatory logic of Boolean GRN models, researchers frequently assume threshold logic as a default. Using the largest repository of published expert-curated Boolean GRN models as best proxy of reality, we systematically compare the ability of two popular threshold formalisms, the Ising and the 01 formalism, to truthfully recover biological functions and biological system dynamics. While Ising rules match fewer biological functions exactly than 01 rules, they yield a better average agreement. In general, more complex regulatory logic proves harder to be represented by either threshold formalism. Informed by these results and a meta-analysis of regulatory logic, we propose modified versions for both formalisms, which provide a better function-level and dynamic agreement with biological GRN models than the usual threshold formalisms. For small biological GRN models with low connectivity, corresponding threshold networks exhibit similar dynamics. However, they generally fail to recover the dynamics of large networks or highly connected networks. In conclusion, this study provides new insights into an important question in computational systems biology: how truthfully do Boolean threshold networks capture the dynamics of GRNs?
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- Award ID(s):
- 2424632
- PAR ID:
- 10636911
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- PNAS Nexus
- Volume:
- 4
- Issue:
- 8
- ISSN:
- 2752-6542
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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