Synchrony in a Boolean network model of the L-arabinose operon in Escherichia coli

TL;DR

This paper models the arabinose operon in E. coli using Boolean networks, verifying biological states and bistability, and compares synchronous versus asynchronous updates to reveal artificial cycles.

Contribution

It introduces a Boolean network model for the arabinose operon, capturing complex features and validating system states with computational algebra.

Findings

Single fixed point matches biological data in most initial conditions

The model predicts bistability under specific conditions

Synchronous updates produce artificial cycles not seen in asynchronous updates

Abstract

The lactose operon in Escherichia coli was the first known gene regulatory network, and it is frequently used as a prototype for new modeling paradigms. Historically, many of these modeling frameworks use differential equations. More recently, Stigler and Veliz-Cuba proposed a Boolean network model that captures the bistability of the system and all of the biological steady states. In this paper, we model the well-known arabinose operon in E. coli with a Boolean network. This has several complex features not found in the lac operon, such as a protein that is both an activator and repressor, a DNA looping mechanism for gene repression, and the lack of inducer exclusion by glucose. For 11 out of 12 choices of initial conditions, we use computational algebra and Sage to verify that the state space contains a single fixed point that correctly matches the biology. The final initial condition, medium levels of arabinose and no glucose, successfully predicts the system's bistability. Finally, we compare the state space under synchronous and asynchronous update, and see that the former has several artificial cycles that go away under a general asynchronous update.