Efficient analysis of stochastic gene dynamics in the non-adiabatic regime using piecewise deterministic Markov processes
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. 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. Finally, we show how noise-induced oscillation previously observedmore »
- Authors:
-
[1];
[2]
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. of Manchester, Manchester (United Kingdom)
- Duke Univ., Durham, NC (United States); Center for Genomic and Computational Biology, Durham, NC (United States)
- Publication Date:
- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE Laboratory Directed Research and Development (LDRD) Program
- OSTI Identifier:
- 1419760
- Report Number(s):
- LA-UR-17-29798
Journal ID: ISSN 1742-5689
- Grant/Contract Number:
- AC52-06NA25396
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Interface
- Additional Journal Information:
- Journal Volume: 15; Journal Issue: 138; Journal ID: ISSN 1742-5689
- Publisher:
- The Royal Society
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 59 BASIC BIOLOGICAL SCIENCES; Biological Science; Mathematics; gene expression, circadian rhythm, intrinsic noise, stochastic cycles
Citation Formats
Lin, Yen Ting, and Buchler, Nicolas E. Efficient analysis of stochastic gene dynamics in the non-adiabatic regime using piecewise deterministic Markov processes. United States: N. p., 2018.
Web. doi:10.1098/rsif.2017.0804.
Lin, Yen Ting, & Buchler, Nicolas E. Efficient analysis of stochastic gene dynamics in the non-adiabatic regime using piecewise deterministic Markov processes. United States. doi:10.1098/rsif.2017.0804.
Lin, Yen Ting, and Buchler, Nicolas E. Wed .
"Efficient analysis of stochastic gene dynamics in the non-adiabatic regime using piecewise deterministic Markov processes". United States. doi:10.1098/rsif.2017.0804. https://www.osti.gov/servlets/purl/1419760.
@article{osti_1419760,
title = {Efficient analysis of stochastic gene dynamics in the non-adiabatic regime using piecewise deterministic Markov processes},
author = {Lin, Yen Ting and Buchler, Nicolas E.},
abstractNote = {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. Finally, 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.},
doi = {10.1098/rsif.2017.0804},
journal = {Interface},
number = 138,
volume = 15,
place = {United States},
year = {2018},
month = {1}
}
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