Efficient analysis of stochastic gene dynamics in the nonadiabatic regime using piecewise deterministic Markov processes
Singlecell 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 longlived promoter states is the slow binding and unbinding kinetics of transcription factors to promoters, i.e. the nonadiabatic 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 nonadiabatic regime. We illustrate the utility of the PDMP on a nontrivial dynamical system by analysing the properties of a titrationbased oscillator in the nonadiabatic 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 repressorbased titration oscillators. We then generalize our PDMP analysis to more complicated versions of titrationbased oscillators to explain how multiple binding sites lengthen the period and improve coherence. Finally, we show how noiseinduced 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:
 Report Number(s):
 LAUR1729798
Journal ID: ISSN 17425689
 Grant/Contract Number:
 AC5206NA25396
 Type:
 Accepted Manuscript
 Journal Name:
 Interface
 Additional Journal Information:
 Journal Volume: 15; Journal Issue: 138; Journal ID: ISSN 17425689
 Publisher:
 The Royal Society
 Research Org:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org:
 USDOE Laboratory Directed Research and Development (LDRD) Program
 Country of Publication:
 United States
 Language:
 English
 Subject:
 59 BASIC BIOLOGICAL SCIENCES; Biological Science; Mathematics; gene expression, circadian rhythm, intrinsic noise, stochastic cycles
 OSTI Identifier:
 1419760
Lin, Yen Ting, and Buchler, Nicolas E. Efficient analysis of stochastic gene dynamics in the nonadiabatic regime using piecewise deterministic Markov processes. United States: N. p.,
Web. doi:10.1098/rsif.2017.0804.
Lin, Yen Ting, & Buchler, Nicolas E. Efficient analysis of stochastic gene dynamics in the nonadiabatic regime using piecewise deterministic Markov processes. United States. doi:10.1098/rsif.2017.0804.
Lin, Yen Ting, and Buchler, Nicolas E. 2018.
"Efficient analysis of stochastic gene dynamics in the nonadiabatic 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 nonadiabatic regime using piecewise deterministic Markov processes},
author = {Lin, Yen Ting and Buchler, Nicolas E.},
abstractNote = {Singlecell 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 longlived promoter states is the slow binding and unbinding kinetics of transcription factors to promoters, i.e. the nonadiabatic 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 nonadiabatic regime. We illustrate the utility of the PDMP on a nontrivial dynamical system by analysing the properties of a titrationbased oscillator in the nonadiabatic 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 repressorbased titration oscillators. We then generalize our PDMP analysis to more complicated versions of titrationbased oscillators to explain how multiple binding sites lengthen the period and improve coherence. Finally, we show how noiseinduced oscillation previously observed in a titrationbased oscillator arises from nonadiabatic 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}
}