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

Journal Article

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. In addition to slow chromatin and/or DNA looping dynamics, 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 analysing 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.

Full Text

Duke Authors

Cited Authors

  • Lin, YT; Buchler, NE

Published Date

  • January 2018

Published In

Volume / Issue

  • 15 / 138

PubMed ID

  • 29386401

Electronic International Standard Serial Number (EISSN)

  • 1742-5662

International Standard Serial Number (ISSN)

  • 1742-5689

Digital Object Identifier (DOI)

  • 10.1098/rsif.2017.0804

Language

  • eng