Parameter identification of canalyzing Boolean functions with ternary vectors for gene networks

In gene dynamics modeling, parameters of Boolean networks are identified from continuous data under various assumptions expressed by logical constraints. These constraints may restrict the dynamics of the network to the subclass of canalyzing functions, which are known to be appropriate for genetic networks. This paper introduces a high performance algorithm, which solves the parameter identification problem by so called Zhegalkin identification and exploits the restriction to canalyzing functions resulting in reduced calculation time. The canalyzing constraint is formulated in terms of orthogonal ternary vector lists - which are intrinsically used in a Branch-and-Cut algorithm obeying this constraint. The algorithm is applied to mRNA micro array data from mice under different contaminant conditions and good correspondence to a known apoptotic pathway can be shown.