TY - JOUR

T1 - Expected Number of Fixed Points in Boolean Networks with Arbitrary Topology

AU - Mori, Fumito

AU - Mochizuki, Atsushi

N1 - Funding Information:
This work was supported by the Creation of Fundamental Technologies for Understanding and Control of Biosystem Dynamics (JPMJCR13W6), a CREST grant from the Japan Science and Technology Agency (JST), and by the iTHEMS program/iTHES project of RIKEN.
Publisher Copyright:
© 2017 American Physical Society.

PY - 2017/7/14

Y1 - 2017/7/14

N2 - Boolean network models describe genetic, neural, and social dynamics in complex networks, where the dynamics depend generally on network topology. Fixed points in a genetic regulatory network are typically considered to correspond to cell types in an organism. We prove that the expected number of fixed points in a Boolean network, with Boolean functions drawn from probability distributions that are not required to be uniform or identical, is one, and is independent of network topology if only a feedback arc set satisfies a stochastic neutrality condition. We also demonstrate that the expected number is increased by the predominance of positive feedback in a cycle.

AB - Boolean network models describe genetic, neural, and social dynamics in complex networks, where the dynamics depend generally on network topology. Fixed points in a genetic regulatory network are typically considered to correspond to cell types in an organism. We prove that the expected number of fixed points in a Boolean network, with Boolean functions drawn from probability distributions that are not required to be uniform or identical, is one, and is independent of network topology if only a feedback arc set satisfies a stochastic neutrality condition. We also demonstrate that the expected number is increased by the predominance of positive feedback in a cycle.

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U2 - 10.1103/PhysRevLett.119.028301

DO - 10.1103/PhysRevLett.119.028301

M3 - Article

C2 - 28753377

AN - SCOPUS:85024477761

VL - 119

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 2

M1 - 028301

ER -