Boolean Models of Bistable Biological Systems

TL;DR

This paper introduces an algorithm to approximate delay differential equation-based biological systems with Boolean networks, effectively capturing bistability in molecular switches for easier analysis.

Contribution

The work presents a novel method for modeling bistable biological systems using Boolean networks derived from delay differential equations.

Findings

Boolean models successfully capture bistability in biological switches.

The method is validated on lac operon and phage lambda systems.

Boolean models simplify understanding complex biological dynamics.

Abstract

This paper presents an algorithm for approximating certain types of dynamical systems given by a system of ordinary delay differential equations by a Boolean network model. Often Boolean models are much simpler to understand than complex differential equations models. The motivation for this work comes from mathematical systems biology. While Boolean mechanisms do not provide information about exact concentration rates or time scales, they are often sufficient to capture steady states and other key dynamics. Due to their intuitive nature, such models are very appealing to researchers in the life sciences. This paper is focused on dynamical systems that exhibit bistability and are desc ribedby delay equations. It is shown that if a certain motif including a feedback loop is present in the wiring diagram of the system, the Boolean model captures the bistability of molecular switches. The method is appl ied to two examples from biology, the lac operon and the phage lambda lysis/lysogeny switch.