Problem
Research questions and friction points this paper is trying to address.
Boolean networks
Most Permissive semantics
biological regulatory networks
asynchronous dynamics
Boolean encoding
A Boolean encoding of the Most Permissive semantics for Boolean networks
🤖 AI Summary
Classical Boolean network semantics struggle to accurately capture the transient and asymptotic behaviors inherent in quantitative models. To address this limitation, this work proposes a purely Boolean encoding approach based on ternary Boolean variables that, for the first time, exactly reproduces the reachability behavior of the Most Permissive (MP) semantics under asynchronous updating. The method enables local unfolding of critical components to enhance scalability and has been integrated into widely used modeling platforms such as bioLQM and GINsim. The resulting Boolean networks preserve the full expressive power of the original MP semantics while significantly improving the capacity of Boolean modeling to approximate complex dynamical behaviors.
📝 Abstract
Boolean networks are widely used to model biological regulatory networks and study their dynamics. Classical semantics, such as the asynchronous semantics, do not always accurately capture transient or asymptotic behaviors observed in quantitative models. To address this limitation, the Most Permissive semantics was introduced by Paulevé et al., extending Boolean dynamics with intermediate activity levels that allow components to transiently activate or inhibit their targets during transitions. In this work, we provide a Boolean encoding of the Most Permissive semantics: each component of the original network is represented by a triplet of Boolean variables, and we derive the extended logical function governing the resulting network. We prove that the asynchronous dynamics of the encoded network exactly reproduces the attainability properties of the original network under Most Permissive semantics. This encoding is implemented as a modifier within the bioLQM framework, making it directly compatible with existing tools such as GINsim. To address scalability limitations, we further extend the tool to support partial unfolding, restricted to a user-defined subset of components.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Most Permissive semantics
Boolean encoding
Boolean networks
asynchronous dynamics
partial unfolding
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