Stochastic Simulations of the Repressilator Circuit

TL;DR

This paper investigates the stochastic behavior of the genetic repressilator circuit, revealing how fluctuations influence oscillation conditions, amplitude, and period, especially under low-copy number scenarios, using master equations and Monte Carlo simulations.

Contribution

It introduces a stochastic analysis of the repressilator circuit, highlighting the impact of fluctuations and specific features like cooperative binding on oscillation properties.

Findings

Fluctuations alter oscillation conditions and characteristics.

Deterministic and stochastic models agree only at high copy numbers.

Features like cooperative binding significantly affect oscillation behavior.

Abstract

The genetic repressilator circuit consists of three transcription factors, or repressors, which negatively regulate each other in a cyclic manner. This circuit was synthetically constructed on plasmids in {\it Escherichia coli} and was found to exhibit oscillations in the concentrations of the three repressors. Since the repressors and their binding sites often appear in low copy numbers, the oscillations are noisy and irregular. Therefore, the repressilator circuit cannot be fully analyzed using deterministic methods such as rate-equations. Here we perform stochastic analysis of the repressilator circuit using the master equation and Monte Carlo simulations. It is found that fluctuations modify the range of conditions in which oscillations appear as well as their amplitude and period, compared to the deterministic equations. The deterministic and stochastic approaches coincide only in the limit in which all the relevant components, including free proteins, plasmids and bound proteins, appear in high copy numbers. We also find that subtle features such as cooperative binding and bound-repressor degradation strongly affect the existence and properties of the oscillations.