General method to find the attractors of discrete dynamic models of biological systems

Physical Review. E
Xiao Gan, Réka Albert

Abstract

Analyzing the long-term behaviors (attractors) of dynamic models of biological networks can provide valuable insight. We propose a general method that can find the attractors of multilevel discrete dynamical systems by extending a method that finds the attractors of a Boolean network model. The previous method is based on finding stable motifs, subgraphs whose nodes' states can stabilize on their own. We extend the framework from binary states to any finite discrete levels by creating a virtual node for each level of a multilevel node, and describing each virtual node with a quasi-Boolean function. We then create an expanded representation of the multilevel network, find multilevel stable motifs and oscillating motifs, and identify attractors by successive network reduction. In this way, we find both fixed point attractors and complex attractors. We implemented an algorithm, which we test and validate on representative synthetic networks and on published multilevel models of biological networks. Despite its primary motivation to analyze biological networks, our motif-based method is general and can be applied to any finite discrete dynamical system.

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Citations

Jan 18, 2019·Physical Biology·Jorge Gómez Tejeda ZañudoRéka Albert
Jan 11, 2020·Bulletin of Mathematical Biology·Luis Sordo VieiraDavid Murrugarra
Sep 10, 2020·Frontiers in Physiology·Parul MaheshwariReka Albert
Sep 22, 2018·Journal of Theoretical Biology·Jordan C Rozum, Réka Albert

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