Boolean models of bistable biological systems

Abstract

This paper presents an algorithm for approximating certain types of dynamicalsystems given by a system of ordinary delay differential equations bya Boolean network model. Often Boolean models are much simpler to understand thancomplex differential equations models. The motivation for this work comesfrom mathematical systems biology. While Boolean mechanisms do not provide information about exactconcentration rates or time scales, they are often sufficient tocapture steady states and other key dynamics. Due to their intuitive nature, suchmodels are very appealing to researchers in the life sciences.This paper is focused on dynamical systems that exhibit bistability and are describedby delay equations. It is shown that if a certain motifincluding a feedback loop is present in the wiring diagram of the system, theBoolean model captures the bistability of molecular switches. The method is applied totwo examples from biology, the lac operon and the phage $\lambda$lysis/lysogeny switch.