Mean-field vs. stochastic models for transcriptional regulation

TL;DR

This paper compares mean-field and stochastic models for transcriptional regulatory networks, highlighting their differences through detailed analysis of specific gene circuits like the repressilator and bistable circuits.

Contribution

It introduces a minimal model framework and systematically compares deterministic and stochastic approaches for transcriptional regulation dynamics.

Findings

Mean-field and stochastic models can yield different results depending on network complexity.

The level of detail in the model influences the accuracy of predictions.

Specific gene circuits exhibit distinct behaviors under different modeling assumptions.

Abstract

We introduce a minimal model description for the dynamics of transcriptional regulatory networks. It is studied within a mean-field approximation, i.e., by deterministic ode's representing the reaction kinetics, and by stochastic simulations employing the Gillespie algorithm. We elucidate the different results both approaches can deliver, depending on the network under study, and in particular depending on the level of detail retained in the respective description. Two examples are addressed in detail: the repressilator, a transcriptional clock based on a three-gene network realized experimentally in E. coli, and a bistable two-gene circuit under external driving, a transcriptional network motif recently proposed to play a role in cellular development.