Efficient analysis of stochastic gene dynamics in the non-adiabatic regime using piecewise deterministic Markov processes

TL;DR

This paper introduces a PDMP framework to analyze stochastic gene expression in the non-adiabatic regime, accurately capturing dynamics like oscillations and promoter state transitions in single-cell systems.

Contribution

The authors develop an analytical PDMP approach to model non-adiabatic gene regulation, extending understanding of stochastic gene dynamics beyond previous methods.

Findings

PDMP accurately models stochastic cycles in titration oscillators.

Multiple binding sites increase oscillation period and coherence.

Noise-induced oscillations arise from non-adiabatic promoter events.

Abstract

Single-cell experiments show that gene expression is stochastic and bursty, a feature that can emerge from slow switching between promoter states with different activities. One source of long-lived promoter states is the slow binding and unbinding kinetics of transcription factors to promoters, i.e. the non-adiabatic binding regime. Here, we introduce a simple analytical framework, known as a piecewise deterministic Markov process (PDMP), that accurately describes the stochastic dynamics of gene expression in the non-adiabatic regime. We illustrate the utility of the PDMP on a non-trivial dynamical system by analyzing the properties of a titration-based oscillator in the non-adiabatic limit. We first show how to transform the underlying Chemical Master Equation into a PDMP where the slow transitions between promoter states are stochastic, but whose rates depend upon the faster deterministic dynamics of the transcription factors regulated by these promoters. We show that the PDMP accurately describes the observed periods of stochastic cycles in activator and repressor-based titration oscillators. We then generalize our PDMP analysis to more complicated versions of titration-based oscillators to explain how multiple binding sites lengthen the period and improve coherence. Last, we show how noise-induced oscillation previously observed in a titration-based oscillator arises from non-adiabatic and discrete binding events at the promoter site.