On Analysis And Generation Of Biologically Important Boolean Functions

TL;DR

This paper introduces a method using Karnaugh Maps to identify and generate nested canalizing Boolean functions, which are crucial for stabilizing biological gene regulatory networks, and explores their properties and variants.

Contribution

It presents a novel approach to determine canalizing functions using Karnaugh Maps and a method to generate higher-variable functions from lower-variable ones, advancing analysis in systems biology.

Findings

Karnaugh Map method effectively identifies canalizing functions.

All n+1 variable canalizing functions can be generated by concatenation.

Partially nested canalizing functions of 4 variables are characterized.

Abstract

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