Oscillations in the expression of a self-repressed gene induced by a slow transcriptional dynamics

TL;DR

This paper investigates how slow transcriptional dynamics in a self-repressed gene can induce sustained oscillations, providing analytical criteria and comparing deterministic and stochastic models.

Contribution

It introduces a minimal genetic oscillator model with slow transcriptional regulation and derives conditions for oscillation onset, highlighting less nonlinear degradation requirements.

Findings

Oscillations occur with less nonlinear degradation mechanisms.

Analytical criteria for oscillation onset are established.

Deterministic and stochastic models show consistent behaviors.

Abstract

We revisit the dynamics of a gene repressed by its own protein in the case where the transcription rate does not adapt instantaneously to protein concentration but is a dynamical variable. We derive analytical criteria for the appearance of sustained oscillations and find that they require degradation mechanisms much less nonlinear than for infinitely fast regulation. Deterministic predictions are also compared with stochastic simulations of this minimal genetic oscillator.