Analysis of Boolean functions based on Interaction graphsand their influence in System Biology

Biological regulatory network can be modeled through a set of Boolean functions. These set of functions enable graph representation of the network structure and hence the dynamics of the network can be seen easily. In this article, the regulations of such network have been explored in term of interaction graph. With the help of Boolean function decomposition this work presents an approach for construction of interaction graphs. This decomposition technique is also used to reduce the network state space of the cell cycle network Fission Yeast for finding the singleton attractors. Some special classes of Boolean functions with respect to the interaction graphs have been discussed. A unique recursive procedure is devised that uses the Cartesian product of sets starting from the set of one variable Boolean function. Interaction graphs generated with these Boolean functions have only positive/negative edges and the corresponding state spaces have periodic attractors with length one/two.