Boolean versus continuous dynamics on simple two-gene modules

TL;DR

This paper compares Boolean and continuous models of simple two-gene modules, identifying conditions for stable oscillations and highlighting differences in dynamical behavior between the two modeling approaches.

Contribution

It introduces a generalized framework to analyze various continuous models and regulatory functions, establishing criteria for oscillations in gene regulatory modules.

Findings

Not all Boolean oscillations translate to continuous models.

Oscillation conditions depend on time scales, cooperativity, and interaction signs.

Differences exist between Boolean and continuous dynamics in gene modules.

Abstract

We investigate the dynamical behavior of simple modules composed of two genes with two or three regulating connections. Continuous dynamics for mRNA and protein concentrations is compared to a Boolean model for gene activity. Using a generalized method, we study within a single framework different continuous models and different types of regulatory functions, and establish conditions under which the system can display stable oscillations. These conditions concern the time scales, the degree of cooperativity of the regulating interactions, and the signs of the interactions. Not all models that show oscillations under Boolean dynamics can have oscillations under continuous dynamics, and vice versa.