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

© 2018 The Author(s)..

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.

Medienart:

E-Artikel

Erscheinungsjahr:

2018

Erschienen:

2018

Enthalten in:

Zur Gesamtaufnahme - volume:15

Enthalten in:

Journal of the Royal Society, Interface - 15(2018), 138 vom: 13. Jan.

Sprache:

Englisch

Beteiligte Personen:

Lin, Yen Ting [VerfasserIn]
Buchler, Nicolas E [VerfasserIn]

Links:

Volltext

Themen:

Circadian rhythm
Gene expression
Intrinsic noise
Journal Article
Mathematical model
Research Support, N.I.H., Extramural
Research Support, Non-U.S. Gov't
Stochastic cycles

Anmerkungen:

Date Completed 25.06.2019

Date Revised 25.06.2019

published: Print

Citation Status MEDLINE

doi:

10.1098/rsif.2017.0804

funding:

Förderinstitution / Projekttitel:

PPN (Katalog-ID):

NLM280464290