Activities and Sensitivities in Boolean Network Models

Ilya Shmulevich and Stuart A. Kauffman
Phys. Rev. Lett. 93, 048701 – Published 22 July 2004
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Abstract

We study how the notions of importance of variables in Boolean functions as well as the sensitivities of the functions to changes in these variables impact the dynamical behavior of Boolean networks. The activity of a variable captures its influence on the output of the function and is a measure of that variable's importance. The average sensitivity of a Boolean function captures the smoothness of the function and is related to its internal homogeneity. In a random Boolean network, we show that the expected average sensitivity determines the well-known critical transition curve. We also discuss canalizing functions and the fact that the canalizing variables enjoy higher importance, as measured by their activities, than the noncanalizing variables. Finally, we demonstrate the important role of the average sensitivity in determining the dynamical behavior of a Boolean network.

  • Figure
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  • Received 24 October 2003

DOI:https://doi.org/10.1103/PhysRevLett.93.048701

©2004 American Physical Society

Authors & Affiliations

Ilya Shmulevich1 and Stuart A. Kauffman2,1

  • 1Cancer Genomics Laboratory, University of Texas M. D. Anderson Cancer Center, Houston, Texas 77030, USA
  • 2Department of Cell Biology and Physiology, University of New Mexico Health Sciences Center, Albuquerque, New Mexico 87131, USA

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Issue

Vol. 93, Iss. 4 — 23 July 2004

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