Mathematics – Dynamical Systems
Scientific paper
2012-04-23
Mathematics
Dynamical Systems
19 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:1111.7217
Scientific paper
Boolean network models of molecular regulatory networks have been used successfully in computational systems biology. The Boolean functions that appear in published models tend to have special properties, in particular the property of being nested canalizing, a property inspired by the concept of canalization in evolutionary biology. It has been shown that networks comprised of nested canalizing functions have dynamic properties that make them suitable for modeling molecular regulatory networks, namely a small number of (large) attractors, as well as relatively short limit cycles. This paper contains a detailed analysis of this class of functions, based on a novel normal form as polynomial functions over the Boolean field. The concept of layer is introduced that stratifies variables into different classes depending on their level of dominance. Using this layer concept a closed form formula is derived for the number of nested canalizing functions with a given number of variables. Additional metrics analyzed include Hamming weight, the activity number of any variable, and the average sensitivity of the function. It is also shown that the average sensitivity of any nested canalizing function is between 0 and 2. This provides a rationale for why nested canalizing functions are stable, since a random Boolean function has average sensitivity n/2. The paper also contains experimental evidence that the layer number is an important factor in network stability.
Adeyeye John O.
Aguilar Boris
Laubenbacher Reinhard
Li Yuan
Murrugarra David
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