Abstract formulations of the regulation of gene expression as random Boolean switching networks have been studied extensively over the past three decades. These models have been developed to make statistical predictions of the types of dynamics observed in biological networks based on network topology and interaction bias, p. For values of mean connectivity chosen to correspond to real biological networks, these models predict disordered dynamics. However, chaotic dynamics seems to be absent from the functioning of a normal cell. While these models use a fixed number of inputs for each element in the network, recent experimental evidence suggests that several biological networks have distributions in connectivity. We therefore study randomly constructed Boolean networks with distributions in the number of inputs, K, to each element. We study three distributions: delta function, Poisson, and power law (scale free). We analytically show that the critical value of the interaction bias parameter, p, above which steady state behavior is observed, is independent of the distribution in the limit of the number of elements We also study these networks numerically. Using three different measures (types of attractors, fraction of elements that are active, and length of period), we show that finite, scale-free networks are more ordered than either the Poisson or delta function networks below the critical point. Thus the topology of scale-free biochemical networks, characterized by a wide distribution in the number of inputs per element, may provide a source of order in living cells.
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December 2001
Research Article|
December 01 2001
From topology to dynamics in biochemical networks
Jeffrey J. Fox;
Jeffrey J. Fox
IGERT Program in Nonlinear Systems, Cornell University, Ithaca, New York 14853
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Colin C. Hill
Colin C. Hill
Laboratory of Atomic & Solid State Physics, Cornell University, Ithaca, New York 14853
Gene Network Sciences, Inc., 2359 North Triphammer Road, Ithaca, New York 14850
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Chaos 11, 809–815 (2001)
Article history
Received:
February 28 2001
Accepted:
August 27 2001
Citation
Jeffrey J. Fox, Colin C. Hill; From topology to dynamics in biochemical networks. Chaos 1 December 2001; 11 (4): 809–815. https://doi.org/10.1063/1.1414882
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