Biology – Quantitative Biology – Molecular Networks
Scientific paper
2008-11-01
Biology
Quantitative Biology
Molecular Networks
10 pages for the main article, 33 pages for detailed proofs of the main results, 4 figures
Scientific paper
It is an increasingly important problem to study conditions on the structure of a network that guarantee a given behavior for its underlying dynamical system. In this paper we report that a Boolean network may fall within the chaotic regime, even under the simultaneous assumption of several conditions which in randomized studies have been separately shown to correlate with ordered behavior. These properties include using at most two inputs for every variable, using biased and canalyzing regulatory functions, and restricting the number of negative feedback loops. We also prove for n-dimensional Boolean networks that if in addition the number of outputs for each variable is bounded and there exist periodic orbits of length c^n for c sufficiently close to 2, any network with these properties must have a large proportion of variables that simply copy previous values of other variables. Such systems share a structural similarity to a relatively small Turing machine acting on one or several tapes.
Enciso German
Just Winfried
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