On Analysis And Generation Of Biologically Important Boolean Functions
For researchers in systems biology using Boolean networks, this work provides new methods for analyzing and generating canalizing functions, which are important for modeling stable gene regulatory networks.
This paper addresses the problem of analyzing and generating biologically important Boolean functions, specifically nested canalizing functions (NCFs). Using Karnaugh maps, they developed a method to check if any Boolean function is canalizing and showed how to generate all canalizing functions of n+1 variables from those of n variables via concatenation. They also uniquely identified the number of NCFs with a given Hamming distance for each starting canalizing input and studied partially nested canalizing functions of 4 variables.
Boolean networks are used to model biological networks such as gene regulatory networks. Often Boolean networks show very chaotic behavior which is sensitive to any small perturbations.In order to reduce the chaotic behavior and to attain stability in the gene regulatory network,nested canalizing functions(NCF)are best suited NCF and its variants have a wide range of applications in system biology. Previously many work 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 gas been solved and also it has been shown that when the canalizing functions of n variable is given, all the canalizing functions of n+1 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 x as starting canalizing input. Partially nested canalizing functions of 4 variables have also been studied in this paper. Keywords: Karnaugh Map, Canalizing function, Nested canalizing function, Partially nested canalizing function,concatenation