On Analysis and Generation of some Biologically Important Boolean Functions

Boolean networks are used to model biological networks such as gene regulatory networks. Often Boolean networks show very chaotic behaviour which is sensitive to any small perturbations. In order to reduce the chaotic behaviour and to attain stability in the gene regulatory network, nested Canalizing Functions (NCFs) are best suited. NCFs and its variants have a wide range of applications in systems biology. Previously, many works were done on the application of canalizing functions, but there were fewer methods to check if any arbitrary Boolean function is canalizing or not. In this paper, by using Karnaugh Map this problem is solved and also it has been shown that when the canalizing functions of variable is given, all the canalizing functions of variable could be generated by the method of concatenation. In this paper we have uniquely identified the number of NCFs having a particular Hamming Distance (H.D) generated by each variable as starting canalizing input. Partially NCFs of 4 variables has also been studied in this paper.