TY - JOUR

T1 - Edgetic perturbations to eliminate fixed-point attractors in Boolean regulatory networks

AU - Campbell, Colin

AU - Albert, Réka

N1 - Funding Information:
C.C. gratefully acknowledges support from the Washington College. R.A.’s research on Boolean modeling is supported by the National Science Foundation (NSF) Grant Nos. MCB 1715826 and PHY 1545832. The authors are grateful to Jorge G.T. Zañudo, Xiao Gan, and Jordan Rozum for insightful feedback on a draft of the manuscript.
Publisher Copyright:
© 2019 Author(s).

PY - 2019/2/1

Y1 - 2019/2/1

N2 - The dynamics of complex biological networks may be modeled in a Boolean framework, where the state of each system component is either abundant (ON) or scarce/absent (OFF), and each component's dynamic trajectory is determined by a logical update rule involving the state(s) of its regulator(s). It is possible to encode the update rules in the topology of the so-called expanded graph, analysis of which reveals the long-term behavior, or attractors, of the network. Here, we develop an algorithm to perturb the expanded graph (or, equivalently, the logical update rules) to eliminate stable motifs: subgraphs that cause a subset of components to stabilize to one state. Depending on the topology of the expanded graph, these perturbations lead to the modification or loss of the corresponding attractor. While most perturbations of biological regulatory networks in the literature involve the knockout (fixing to OFF) or constitutive activation (fixing to ON) of one or more nodes, we here consider edgetic perturbations, where a node's update rule is modified such that one or more of its regulators is viewed as ON or OFF regardless of its actual state. We apply the methodology to two biological networks. In a network representing T-LGL leukemia, we identify edgetic perturbations that eliminate the cancerous attractor, leaving only the healthy attractor representing cell death. In a network representing drought-induced closure of plant stomata, we identify edgetic perturbations that modify the single attractor such that stomata, instead of being fixed in the closed state, oscillates between the open and closed states.

AB - The dynamics of complex biological networks may be modeled in a Boolean framework, where the state of each system component is either abundant (ON) or scarce/absent (OFF), and each component's dynamic trajectory is determined by a logical update rule involving the state(s) of its regulator(s). It is possible to encode the update rules in the topology of the so-called expanded graph, analysis of which reveals the long-term behavior, or attractors, of the network. Here, we develop an algorithm to perturb the expanded graph (or, equivalently, the logical update rules) to eliminate stable motifs: subgraphs that cause a subset of components to stabilize to one state. Depending on the topology of the expanded graph, these perturbations lead to the modification or loss of the corresponding attractor. While most perturbations of biological regulatory networks in the literature involve the knockout (fixing to OFF) or constitutive activation (fixing to ON) of one or more nodes, we here consider edgetic perturbations, where a node's update rule is modified such that one or more of its regulators is viewed as ON or OFF regardless of its actual state. We apply the methodology to two biological networks. In a network representing T-LGL leukemia, we identify edgetic perturbations that eliminate the cancerous attractor, leaving only the healthy attractor representing cell death. In a network representing drought-induced closure of plant stomata, we identify edgetic perturbations that modify the single attractor such that stomata, instead of being fixed in the closed state, oscillates between the open and closed states.

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U2 - 10.1063/1.5083060

DO - 10.1063/1.5083060

M3 - Article

C2 - 30823730

AN - SCOPUS:85062110312

SN - 1054-1500

VL - 29

JO - Chaos

JF - Chaos

IS - 2

M1 - 023130

ER -