BIOPHYSICAL THEORY AND MODELING |
The effect of negative feedback loops on the dynamics of Boolean networks
Eduardo Sontag 1*, Alan Veliz-Cuba 2, Reinhard Laubenbacher 2 and Abdul Salam Jarrah 2
1 Rutgers
2 Virginia Polytechnic Institute and State University
* To whom correspondence should be addressed. E-mail: sontag{at}math.rutgers.edu.
Submitted on November 1, 2007
Revised on December 29, 2007
Accepted on 8 February 2008
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Abstract |
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Feedback loops play an important role in determining the dynamics of biological networks. In order to study the role of negative feedback loops, this paper introduces the notion of "distance to positive feedback (PF-distance)" which in essence captures the number of "independent" negative feedback loops in the network, a property inherent in the network topology. Through a computational study using Boolean networks, it is shown that PF-distance has a strong influence on network dynamics and correlates very well with the number and length of limit cycles in the phase space of the network. To be precise, it is shown that, as the number of independent negative feedback loops increases, the number (length) of limit cycles tends to decrease (increase). These conclusions are consistent with the fact that certain natural biological networks exhibit generally regular behavior and have fewer negative feedback loops than randomized networks with the same numbers of nodes and connectivity.
Key Words:
Boolean networks, Feedback loops, gene regulatory networks, limit cycles
