Boolean dynamics of biological networks with multiple coupled feedback loops

¹ Seoul National University

^* To whom correspondence should be addressed. E-mail: ckh-sb{at}snu.ac.kr.

Submitted on September 8, 2006
Revised on October 10, 2006
Accepted on 29 December 2006

	Abstract

Boolean networks have been frequently used to study the dynamics of biological networks. In particular, there have been various studies showing that the network connectivity and the update rule of logical functions affect the dynamics of Boolean networks. There has been, however, relatively a little attention to the dynamical role of a feedback loop which is a circular chain of interactions between Boolean variables. We note that such feedback loops are ubiquitously found in various biological systems as multiple coupled structures and they are often the primary cause of complex dynamics. In this paper, we investigate the relationship between the multiple coupled feedback loops and the dynamics of Boolean networks. We show that networks have a larger proportion of basins corresponding to fixed-point attractors as they have more coupled positive feedback loops and a larger proportion of basins for limit-cycle attractors as they have more coupled negative feedback loops.

Key Words: fixed-point attractor, limit-cycle attractor, negative feedback loop, network dynamics, positive feedback loop, randon Boolean network

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