Canalization of genetic regulatory networks has been argued to be favored byevolutionary processes due to the stability that it can confer to phenotypeexpression. We explore whether a significant amount of canalization and partialcanalization can arise in purely random networks in the absence of evolutionarypressures. We use a mapping of the Boolean functions in the Kauffman N-K modelfor genetic regulatory networks onto a k-dimensional Ising hypercube to showthat the functions can be divided into different classes strictly due togeometrical constraints. The classes can be counted and their propertiesdetermined using results from group theory and isomer chemistry. We demonstratethat partially canalized functions completely dominate all possible Booleanfunctions, particularly for higher k. This indicates that partial canalizationis extremely common, even in randomly chosen networks, and has implications forhow much information can be obtained in experiments on native state geneticregulatory networks.
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