Coarse-Grained Modeling of Genetic Circuits as a Function of the Inherent Time Scales

TL;DR

This paper investigates how inherent time scales in genetic circuits influence their bifurcation patterns, showing that common motifs do not always lead to universal dynamic behaviors, especially when gene binding rates are comparable to protein decay times.

Contribution

It introduces a coarse-grained modeling approach that accounts for different time scales, revealing how these scales affect bifurcation structures in genetic circuits.

Findings

Bifurcation patterns depend on the ratio of binding rates to protein decay times.

Regular limit cycles diminish when gene binding rates are slow.

Common circuit motifs do not guarantee universal dynamic features.

Abstract

From a coarse-grained perspective the motif of a self-activating species, activating a second species which acts as its own repressor, is widely found in biological systems, in particular in genetic systems with inherent oscillatory behavior. Here we consider a specific realization of this motif as a genetic circuit, in which genes are described as directly producing proteins, leaving out the intermediate step of mRNA production. We focus on the effect that inherent time scales on the underlying fine-grained scale can have on the bifurcation patterns on a coarser scale in time. Time scales are set by the binding and unbinding rates of the transcription factors to the promoter regions of the genes. Depending on the ratio of these rates to the decay times of the proteins, the appropriate averaging procedure for obtaining a coarse-grained description changes and leads to sets of deterministic equations, which differ in their bifurcation structure. In particular the desired intermediate range of regular limit cycles fades away when the binding rates of genes are of the same order or less than the decay time of at least one of the proteins. Our analysis illustrates that the common topology of the widely found motif alone does not necessarily imply universal features in the dynamics.