STATIONARITY AND INFERENCE IN MULTISTATE PROMOTER MODELS OF STOCHASTIC GENE EXPRESSION VIA STICK-BREAKING MEASURES

William Lippitt; Sunder Sethuraman; Xueying Tang

doi:10.1137/21M1440876

STATIONARITY AND INFERENCE IN MULTISTATE PROMOTER MODELS OF STOCHASTIC GENE EXPRESSION VIA STICK-BREAKING MEASURES

William Lippitt, Sunder Sethuraman, Xueying Tang

Research output: Contribution to journal › Article › peer-review

Abstract

In a general stochastic multistate promoter model of dynamic messenger ribonucleic acid (mRNA)/protein interactions, we identify the stationary joint distribution of the promoter state, mRNA, and protein levels through an explicit ``stick-breaking"" construction perhaps of interest in itself. This derivation is a constructive advance over previous work where the stationary distribution is solved only in restricted cases. Moreover, the stick-breaking construction allows us to sample directly from the stationary distribution, permitting inference procedures and model selection. In this context, we discuss numerical Bayesian experiments to illustrate the results.

Original language	English (US)
Pages (from-to)	1953-1986
Number of pages	34
Journal	SIAM Journal on Applied Mathematics
Volume	82
Issue number	6
DOIs	https://doi.org/10.1137/21M1440876
State	Published - 2022

Keywords

Bayesian
Dirichlet
Markovian
constructive
inference
mRNA
model validation
multistate
promoter
protein
stationary distribution
stick-breaking

ASJC Scopus subject areas

Applied Mathematics

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10.1137/21M1440876

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title = "STATIONARITY AND INFERENCE IN MULTISTATE PROMOTER MODELS OF STOCHASTIC GENE EXPRESSION VIA STICK-BREAKING MEASURES",

abstract = "In a general stochastic multistate promoter model of dynamic messenger ribonucleic acid (mRNA)/protein interactions, we identify the stationary joint distribution of the promoter state, mRNA, and protein levels through an explicit ``stick-breaking{"}{"} construction perhaps of interest in itself. This derivation is a constructive advance over previous work where the stationary distribution is solved only in restricted cases. Moreover, the stick-breaking construction allows us to sample directly from the stationary distribution, permitting inference procedures and model selection. In this context, we discuss numerical Bayesian experiments to illustrate the results.",

keywords = "Bayesian, Dirichlet, Markovian, constructive, inference, mRNA, model validation, multistate, promoter, protein, stationary distribution, stick-breaking",

author = "William Lippitt and Sunder Sethuraman and Xueying Tang",

note = "Funding Information: \ast Received by the editors August 16, 2021; accepted for publication (in revised form) July 22, 2022; published electronically December 9, 2022. https://doi.org/10.1137/21M1440876 Funding: This work was partially supported by the Army Research Office grant ARO-W911NF-18-1-0311. \dagger Department of Biostatistics and Informatics, University of Colorado Anschutz Medical Campus, Aurora, CO 80045 USA (william.lippitt@cuanschutz.edu). \ddagger Department of Mathematics, University of Arizona, Tucson, AZ 85721 USA (sethuram@ math.arizona.edu, xytang@math.arizona.edu). Publisher Copyright: {\textcopyright} 2022 Society for Industrial and applied Mathematics.",

year = "2022",

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AU - Sethuraman, Sunder

AU - Tang, Xueying

N1 - Funding Information: \ast Received by the editors August 16, 2021; accepted for publication (in revised form) July 22, 2022; published electronically December 9, 2022. https://doi.org/10.1137/21M1440876 Funding: This work was partially supported by the Army Research Office grant ARO-W911NF-18-1-0311. \dagger Department of Biostatistics and Informatics, University of Colorado Anschutz Medical Campus, Aurora, CO 80045 USA (william.lippitt@cuanschutz.edu). \ddagger Department of Mathematics, University of Arizona, Tucson, AZ 85721 USA (sethuram@ math.arizona.edu, xytang@math.arizona.edu). Publisher Copyright: © 2022 Society for Industrial and applied Mathematics.

PY - 2022

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AB - In a general stochastic multistate promoter model of dynamic messenger ribonucleic acid (mRNA)/protein interactions, we identify the stationary joint distribution of the promoter state, mRNA, and protein levels through an explicit ``stick-breaking"" construction perhaps of interest in itself. This derivation is a constructive advance over previous work where the stationary distribution is solved only in restricted cases. Moreover, the stick-breaking construction allows us to sample directly from the stationary distribution, permitting inference procedures and model selection. In this context, we discuss numerical Bayesian experiments to illustrate the results.

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STATIONARITY AND INFERENCE IN MULTISTATE PROMOTER MODELS OF STOCHASTIC GENE EXPRESSION VIA STICK-BREAKING MEASURES

Abstract

Keywords

ASJC Scopus subject areas

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