Exact and efficient hybrid Monte Carlo algorithm for accelerated Bayesian inference of gene expression models from snapshots of single-cell transcripts
Abstract
Single cells exhibit a significant amount of variability in transcript levels, which arises from slow, stochastic transitions between gene expression states. Elucidating the nature of these states and understanding how transition rates are affected by different regulatory mechanisms require state-of-the-art methods to infer underlying models of gene expression from single cell data. A Bayesian approach to statistical inference is the most suitable method for model selection and uncertainty quantification of kinetic parameters using small data sets. However, this approach is impractical because current algorithms are too slow to handle typical models of gene expression. To solve this problem, we first show that time-dependent mRNA distributions of discrete-state models of gene expression are dynamic Poisson mixtures, whose mixing kernels are characterized by a piecewise deterministic Markov process. Here, we combined this analytical result with a kinetic Monte Carlo algorithm to create a hybrid numerical method that accelerates the calculation of time-dependent mRNA distributions by 1000-fold compared to current methods. We then integrated the hybrid algorithm into an existing Monte Carlo sampler to estimate the Bayesian posterior distribution of many different, competing models in a reasonable amount of time. We demonstrate that kinetic parameters can be reasonably constrained for modestly sampled datamore »
- Authors:
-
[1];
[2]
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- North Carolina State Univ., Raleigh, 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:
- 1557757
- Alternate Identifier(s):
- OSTI ID: 1532586
- Report Number(s):
- LA-UR-18-31392
Journal ID: ISSN 0021-9606
- Grant/Contract Number:
- 89233218CNA000001
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Chemical Physics
- Additional Journal Information:
- Journal Volume: 151; Journal Issue: 2; Journal ID: ISSN 0021-9606
- Publisher:
- American Institute of Physics (AIP)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 59 BASIC BIOLOGICAL SCIENCES; Biological Science; Mathematics
Citation Formats
Lin, Yen Ting, and Buchler, Nicolas E. Exact and efficient hybrid Monte Carlo algorithm for accelerated Bayesian inference of gene expression models from snapshots of single-cell transcripts. United States: N. p., 2019.
Web. doi:10.1063/1.5110503.
Lin, Yen Ting, & Buchler, Nicolas E. Exact and efficient hybrid Monte Carlo algorithm for accelerated Bayesian inference of gene expression models from snapshots of single-cell transcripts. United States. doi:10.1063/1.5110503.
Lin, Yen Ting, and Buchler, Nicolas E. Sun .
"Exact and efficient hybrid Monte Carlo algorithm for accelerated Bayesian inference of gene expression models from snapshots of single-cell transcripts". United States. doi:10.1063/1.5110503. https://www.osti.gov/servlets/purl/1557757.
@article{osti_1557757,
title = {Exact and efficient hybrid Monte Carlo algorithm for accelerated Bayesian inference of gene expression models from snapshots of single-cell transcripts},
author = {Lin, Yen Ting and Buchler, Nicolas E.},
abstractNote = {Single cells exhibit a significant amount of variability in transcript levels, which arises from slow, stochastic transitions between gene expression states. Elucidating the nature of these states and understanding how transition rates are affected by different regulatory mechanisms require state-of-the-art methods to infer underlying models of gene expression from single cell data. A Bayesian approach to statistical inference is the most suitable method for model selection and uncertainty quantification of kinetic parameters using small data sets. However, this approach is impractical because current algorithms are too slow to handle typical models of gene expression. To solve this problem, we first show that time-dependent mRNA distributions of discrete-state models of gene expression are dynamic Poisson mixtures, whose mixing kernels are characterized by a piecewise deterministic Markov process. Here, we combined this analytical result with a kinetic Monte Carlo algorithm to create a hybrid numerical method that accelerates the calculation of time-dependent mRNA distributions by 1000-fold compared to current methods. We then integrated the hybrid algorithm into an existing Monte Carlo sampler to estimate the Bayesian posterior distribution of many different, competing models in a reasonable amount of time. We demonstrate that kinetic parameters can be reasonably constrained for modestly sampled data sets if the model is known a priori. If there are many competing models, Bayesian evidence can rigorously quantify the likelihood of a model relative to other models from the data. We demonstrate that Bayesian evidence selects the true model and outperforms approximate metrics typically used for model selection.},
doi = {10.1063/1.5110503},
journal = {Journal of Chemical Physics},
number = 2,
volume = 151,
place = {United States},
year = {2019},
month = {7}
}
Other availability
Search WorldCat to find libraries that may hold this journal
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Estimating the Dimension of a Model
journal, March 1978
- Schwarz, Gideon
- The Annals of Statistics, Vol. 6, Issue 2
Real-Time Kinetics of Gene Activity in Individual Bacteria
journal, December 2005
- Golding, Ido; Paulsson, Johan; Zawilski, Scott M.
- Cell, Vol. 123, Issue 6
Stochastic Gene Expression in a Single Cell
journal, August 2002
- Elowitz, M. B.
- Science, Vol. 297, Issue 5584
Stochastic Gene Expression with a Multistate Promoter: Breaking Down Exact Distributions
journal, January 2019
- Herbach, Ulysse
- SIAM Journal on Applied Mathematics, Vol. 79, Issue 3
The finite state projection algorithm for the solution of the chemical master equation
journal, January 2006
- Munsky, Brian; Khammash, Mustafa
- The Journal of Chemical Physics, Vol. 124, Issue 4
Single-cell analysis of transcription kinetics across the cell cycle
journal, January 2016
- Skinner, Samuel O.; Xu, Heng; Nagarkar-Jaiswal, Sonal
- eLife, Vol. 5
Single-RNA counting reveals alternative modes of gene expression in yeast
journal, November 2008
- Zenklusen, Daniel; Larson, Daniel R.; Singer, Robert H.
- Nature Structural & Molecular Biology, Vol. 15, Issue 12
Dichotomous Markov Noise: Exact Results for Out-Of-Equilibrium Systems
journal, August 2006
- Bena, Ioana
- International Journal of Modern Physics B, Vol. 20, Issue 20
Single-cell RNA sequencing technologies and bioinformatics pipelines
journal, August 2018
- Hwang, Byungjin; Lee, Ji Hyun; Bang, Duhee
- Experimental & Molecular Medicine, Vol. 50, Issue 8
Efficient analysis of stochastic gene dynamics in the non-adiabatic regime using piecewise deterministic Markov processes
journal, January 2018
- Lin, Yen Ting; Buchler, Nicolas E.
- Journal of The Royal Society Interface, Vol. 15, Issue 138
Distribution shapes govern the discovery of predictive models for gene regulation
journal, June 2018
- Munsky, Brian; Li, Guoliang; Fox, Zachary R.
- Proceedings of the National Academy of Sciences, Vol. 115, Issue 29
Mammalian Genes Are Transcribed with Widely Different Bursting Kinetics
journal, March 2011
- Suter, D. M.; Molina, N.; Gatfield, D.
- Science, Vol. 332, Issue 6028
Exact stochastic simulation of coupled chemical reactions
journal, December 1977
- Gillespie, Daniel T.
- The Journal of Physical Chemistry, Vol. 81, Issue 25
Universally Sloppy Parameter Sensitivities in Systems Biology Models
journal, January 2007
- Gutenkunst, Ryan N.; Waterfall, Joshua J.; Casey, Fergal P.
- PLoS Computational Biology, Vol. 3, Issue 10
Estimating the Marginal Likelihood Using the Arithmetic Mean Identity
journal, March 2017
- Pajor, Anna
- Bayesian Analysis, Vol. 12, Issue 1
Intrinsic noise in systems with switching environments
journal, May 2016
- Hufton, Peter G.; Lin, Yen Ting; Galla, Tobias
- Physical Review E, Vol. 93, Issue 5
Hybrid Monte Carlo
journal, September 1987
- Duane, Simon; Kennedy, A. D.; Pendleton, Brian J.
- Physics Letters B, Vol. 195, Issue 2
Transcription Factors Modulate c-Fos Transcriptional Bursts
journal, July 2014
- Senecal, Adrien; Munsky, Brian; Proux, Florence
- Cell Reports, Vol. 8, Issue 1
Accurate Chemical Master Equation Solution Using Multi-Finite Buffers
journal, January 2016
- Cao, Youfang; Terebus, Anna; Liang, Jie
- Multiscale Modeling & Simulation, Vol. 14, Issue 2
Piecewise-Deterministic Markov Processes: A General Class of Non-Diffusion Stochastic Models
journal, July 1984
- Davis, M. H. A.
- Journal of the Royal Statistical Society: Series B (Methodological), Vol. 46, Issue 3
State-dependent doubly weighted stochastic simulation algorithm for automatic characterization of stochastic biochemical rare events
journal, December 2011
- Roh, Min K.; Daigle, Bernie J.; Gillespie, Dan T.
- The Journal of Chemical Physics, Vol. 135, Issue 23
BayFish: Bayesian inference of transcription dynamics from population snapshots of single-molecule RNA FISH in single cells
journal, September 2017
- Gómez-Schiavon, Mariana; Chen, Liang-Fu; West, Anne E.
- Genome Biology, Vol. 18, Issue 1
A Growing Toolbox to Image Gene Expression in Single Cells: Sensitive Approaches for Demanding Challenges
journal, August 2018
- Pichon, Xavier; Lagha, Mounia; Mueller, Florian
- Molecular Cell, Vol. 71, Issue 3
Bursting noise in gene expression dynamics: linking microscopic and mesoscopic models
journal, January 2016
- Lin, Yen Ting; Galla, Tobias
- Journal of The Royal Society Interface, Vol. 13, Issue 114
Stochastic switching in biology: from genotype to phenotype
journal, February 2017
- Bressloff, Paul C.
- Journal of Physics A: Mathematical and Theoretical, Vol. 50, Issue 13
Weak convergence and optimal scaling of random walk Metropolis algorithms
journal, February 1997
- Roberts, G. O.; Gelman, A.; Gilks, W. R.
- The Annals of Applied Probability, Vol. 7, Issue 1
Exact Distributions for Stochastic Gene Expression Models with Bursting and Feedback
journal, December 2014
- Kumar, Niraj; Platini, Thierry; Kulkarni, Rahul V.
- Physical Review Letters, Vol. 113, Issue 26
A stochastic and dynamical view of pluripotency in mouse embryonic stem cells
journal, February 2018
- Lin, Yen Ting; Hufton, Peter G.; Lee, Esther J.
- PLOS Computational Biology, Vol. 14, Issue 2
A continuum model of transcriptional bursting
journal, February 2016
- Corrigan, Adam M.; Tunnacliffe, Edward; Cannon, Danielle
- eLife, Vol. 5
Nature, Nurture, or Chance: Stochastic Gene Expression and Its Consequences
journal, October 2008
- Raj, Arjun; van Oudenaarden, Alexander
- Cell, Vol. 135, Issue 2
Equation of State Calculations by Fast Computing Machines
journal, June 1953
- Metropolis, Nicholas; Rosenbluth, Arianna W.; Rosenbluth, Marshall N.
- The Journal of Chemical Physics, Vol. 21, Issue 6
Refining the weighted stochastic simulation algorithm
journal, May 2009
- Gillespie, Dan T.; Roh, Min; Petzold, Linda R.
- The Journal of Chemical Physics, Vol. 130, Issue 17
Bursty Gene Expression in the Intact Mammalian Liver
journal, April 2015
- Bahar Halpern, Keren; Tanami, Sivan; Landen, Shanie
- Molecular Cell, Vol. 58, Issue 1
Gene expression dynamics with stochastic bursts: Construction and exact results for a coarse-grained model
journal, February 2016
- Lin, Yen Ting; Doering, Charles R.
- Physical Review E, Vol. 93, Issue 2
mRNA-Seq whole-transcriptome analysis of a single cell
journal, April 2009
- Tang, Fuchou; Barbacioru, Catalin; Wang, Yangzhou
- Nature Methods, Vol. 6, Issue 5
What shapes eukaryotic transcriptional bursting?
journal, January 2017
- Nicolas, Damien; Phillips, Nick E.; Naef, Felix
- Molecular BioSystems, Vol. 13, Issue 7
Real-Time Observation of Transcription Initiation and Elongation on an Endogenous Yeast Gene
journal, April 2011
- Larson, D. R.; Zenklusen, D.; Wu, B.
- Science, Vol. 332, Issue 6028
Bayes Factors
journal, June 1995
- Kass, Robert E.; Raftery, Adrian E.
- Journal of the American Statistical Association, Vol. 90, Issue 430
Transcriptional Bursting Diversifies the Behaviour of a Toggle Switch: Hybrid Simulation of Stochastic Gene Expression
journal, January 2013
- Bokes, Pavol; King, John R.; Wood, Andrew T. A.
- Bulletin of Mathematical Biology, Vol. 75, Issue 2
Precise Developmental Gene Expression Arises from Globally Stochastic Transcriptional Activity
journal, August 2013
- Little, Shawn C.; Tikhonov, Mikhail; Gregor, Thomas
- Cell, Vol. 154, Issue 4
Stochastic mRNA Synthesis in Mammalian Cells
journal, September 2006
- Raj, Arjun; Peskin, Charles S.; Tranchina, Daniel
- PLoS Biology, Vol. 4, Issue 10
Non-equilibrium Thermodynamics of Piecewise Deterministic Markov Processes
journal, October 2009
- Faggionato, A.; Gabrielli, D.; Ribezzi Crivellari, M.
- Journal of Statistical Physics, Vol. 137, Issue 2
Gene expression distribution deconvolution in single-cell RNA sequencing
journal, June 2018
- Wang, Jingshu; Huang, Mo; Torre, Eduardo
- Proceedings of the National Academy of Sciences, Vol. 115, Issue 28
Modulation of transcriptional burst frequency by histone acetylation
journal, June 2018
- Nicolas, Damien; Zoller, Benjamin; Suter, David M.
- Proceedings of the National Academy of Sciences, Vol. 115, Issue 27
Enhancer Control of Transcriptional Bursting
journal, July 2016
- Fukaya, Takashi; Lim, Bomyi; Levine, Michael
- Cell, Vol. 166, Issue 2
Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems
journal, July 2008
- Toni, Tina; Welch, David; Strelkowa, Natalja
- Journal of The Royal Society Interface, Vol. 6, Issue 31
Computing the Bayes Factor from a Markov Chain Monte Carlo Simulation of the Posterior Distribution
journal, September 2012
- Weinberg, Martin D.
- Bayesian Analysis, Vol. 7, Issue 3
Bayesian inference on stochastic gene transcription from flow cytometry data
journal, September 2018
- Tiberi, Simone; Walsh, Mark; Cavallaro, Massimo
- Bioinformatics, Vol. 34, Issue 17
Reversible jump Markov chain Monte Carlo computation and Bayesian model determination
journal, January 1995
- Green, Peter J.
- Biometrika, Vol. 82, Issue 4
An efficient and exact stochastic simulation method to analyze rare events in biochemical systems
journal, October 2008
- Kuwahara, Hiroyuki; Mura, Ivan
- The Journal of Chemical Physics, Vol. 129, Issue 16
Integrating single-molecule experiments and discrete stochastic models to understand heterogeneous gene transcription dynamics
journal, September 2015
- Munsky, Brian; Fox, Zachary; Neuert, Gregor
- Methods, Vol. 85
Analytical distributions for stochastic gene expression
journal, November 2008
- Shahrezaei, V.; Swain, P. S.
- Proceedings of the National Academy of Sciences, Vol. 105, Issue 45
Accelerated maximum likelihood parameter estimation for stochastic biochemical systems
journal, January 2012
- Daigle, Bernie J.; Roh, Min K.; Petzold, Linda R.
- BMC Bioinformatics, Vol. 13, Issue 1
Systematic Identification of Signal-Activated Stochastic Gene Regulation
journal, January 2013
- Neuert, Gregor; Munsky, Brian; Tan, Rui Zhen
- Science, Vol. 339, Issue 6119
A general method for numerically simulating the stochastic time evolution of coupled chemical reactions
journal, December 1976
- Gillespie, Daniel T.
- Journal of Computational Physics, Vol. 22, Issue 4
Imaging individual mRNA molecules using multiple singly labeled probes
journal, September 2008
- Raj, Arjun; van den Bogaard, Patrick; Rifkin, Scott A.
- Nature Methods, Vol. 5, Issue 10
Monte Carlo Sampling Methods Using Markov Chains and Their Applications
journal, April 1970
- Hastings, W. K.
- Biometrika, Vol. 57, Issue 1
Enhancer Histone Acetylation Modulates Transcriptional Bursting Dynamics of Neuronal Activity-Inducible Genes
journal, January 2019
- Chen, Liang-Fu; Lin, Yen Ting; Gallegos, David A.
- Cell Reports, Vol. 26, Issue 5
Computational methods for Bayesian model choice
conference, January 2009
- Robert, C. P.; Wraith, D.; Goggans, Paul M.
- BAYESIAN INFERENCE AND MAXIMUM ENTROPY METHODS IN SCIENCE AND ENGINEERING: The 29th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, AIP Conference Proceedings
Regulation of noise in the expression of a single gene
journal, April 2002
- Ozbudak, Ertugrul M.; Thattai, Mukund; Kurtser, Iren
- Nature Genetics, Vol. 31, Issue 1
Bayes Factors
journal, June 1995
- Kass, Robert E.; Raftery, Adrian E.
- Journal of the American Statistical Association, Vol. 90, Issue 430