TY - JOUR
T1 - Expected Number of Fixed Points in Boolean Networks with Arbitrary Topology
AU - Mori, Fumito
AU - Mochizuki, Atsushi
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 -