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      Stochastic simulation and statistical inference platform for visualization and estimation of transcriptional kinetics

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          Abstract

          Recent advances in single-molecule fluorescent imaging have enabled quantitative measurements of transcription at a single gene copy, yet an accurate understanding of transcriptional kinetics is still lacking due to the difficulty of solving detailed biophysical models. Here we introduce a stochastic simulation and statistical inference platform for modeling detailed transcriptional kinetics in prokaryotic systems, which has not been solved analytically. The model includes stochastic two-state gene activation, mRNA synthesis initiation and stepwise elongation, release to the cytoplasm, and stepwise co-transcriptional degradation. Using the Gillespie algorithm, the platform simulates nascent and mature mRNA kinetics of a single gene copy and predicts fluorescent signals measurable by time-lapse single-cell mRNA imaging, for different experimental conditions. To approach the inverse problem of estimating the kinetic parameters of the model from experimental data, we develop a heuristic optimization method based on the genetic algorithm and the empirical distribution of mRNA generated by simulation. As a demonstration, we show that the optimization algorithm can successfully recover the transcriptional kinetics of simulated and experimental gene expression data. The platform is available as a MATLAB software package at https://data.caltech.edu/records/1287.

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          Most cited references32

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          Probing transcription factor dynamics at the single-molecule level in a living cell.

          Transcription factors regulate gene expression through their binding to DNA. In a living Escherichia coli cell, we directly observed specific binding of a lac repressor, labeled with a fluorescent protein, to a chromosomal lac operator. Using single-molecule detection techniques, we measured the kinetics of binding and dissociation of the repressor in response to metabolic signals. Furthermore, we characterized the nonspecific binding to DNA, one-dimensional (1D) diffusion along DNA segments, and 3D translocation among segments through cytoplasm at the single-molecule level. In searching for the operator, a lac repressor spends approximately 90% of time nonspecifically bound to and diffusing along DNA with a residence time of <5 milliseconds. The methods and findings can be generalized to other nucleic acid binding proteins.
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            Systematic identification of signal-activated stochastic gene regulation.

            Although much has been done to elucidate the biochemistry of signal transduction and gene regulatory pathways, it remains difficult to understand or predict quantitative responses. We integrate single-cell experiments with stochastic analyses, to identify predictive models of transcriptional dynamics for the osmotic stress response pathway in Saccharomyces cerevisiae. We generate models with varying complexity and use parameter estimation and cross-validation analyses to select the most predictive model. This model yields insight into several dynamical features, including multistep regulation and switchlike activation for several osmosensitive genes. Furthermore, the model correctly predicts the transcriptional dynamics of cells in response to different environmental and genetic perturbations. Because our approach is general, it should facilitate a predictive understanding for signal-activated transcription of other genes in other pathways or organisms.
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              Bayesian parameter inference for stochastic biochemical network models using particle Markov chain Monte Carlo.

              Computational systems biology is concerned with the development of detailed mechanistic models of biological processes. Such models are often stochastic and analytically intractable, containing uncertain parameters that must be estimated from time course data. In this article, we consider the task of inferring the parameters of a stochastic kinetic model defined as a Markov (jump) process. Inference for the parameters of complex nonlinear multivariate stochastic process models is a challenging problem, but we find here that algorithms based on particle Markov chain Monte Carlo turn out to be a very effective computationally intensive approach to the problem. Approximations to the inferential model based on stochastic differential equations (SDEs) are considered, as well as improvements to the inference scheme that exploit the SDE structure. We apply the methodology to a Lotka-Volterra system and a prokaryotic auto-regulatory network.
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                Author and article information

                Contributors
                Role: ConceptualizationRole: Formal analysisRole: Funding acquisitionRole: InvestigationRole: MethodologyRole: SoftwareRole: ValidationRole: VisualizationRole: Writing – original draftRole: Writing – review & editing
                Role: ConceptualizationRole: Funding acquisitionRole: SoftwareRole: Writing – review & editing
                Role: ConceptualizationRole: Formal analysisRole: Funding acquisitionRole: InvestigationRole: MethodologyRole: Project administrationRole: SupervisionRole: ValidationRole: VisualizationRole: Writing – original draftRole: Writing – review & editing
                Role: ConceptualizationRole: Formal analysisRole: Funding acquisitionRole: InvestigationRole: MethodologyRole: Project administrationRole: ResourcesRole: SupervisionRole: ValidationRole: VisualizationRole: Writing – original draftRole: Writing – review & editing
                Role: Editor
                Journal
                PLoS One
                PLoS ONE
                plos
                plosone
                PLoS ONE
                Public Library of Science (San Francisco, CA USA )
                1932-6203
                26 March 2020
                2020
                : 15
                : 3
                : e0230736
                Affiliations
                [1 ] Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California, United States of America
                [2 ] Department of Physics, Grainger College of Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois, United States of America
                [3 ] Center for the Physics of Living Cells, University of Illinois at Urbana-Champaign, Urbana, Illinois, United States of America
                [4 ] School of Physics and Astronomy, Shanghai Jiao Tong University, Minhang District, Shanghai, China
                [5 ] Institute of Natural Sciences, Shanghai Jiao Tong University, Minhang District, Shanghai, China
                Universitat Pompeu Fabra, SPAIN
                Author notes

                Competing Interests: The authors have declared that no competing interests exist.

                Author information
                http://orcid.org/0000-0001-6097-2029
                Article
                PONE-D-19-31981
                10.1371/journal.pone.0230736
                7098607
                32214380
                bcf9cf98-6a45-42b9-919d-31ab449cca91
                © 2020 Gorin et al

                This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

                History
                : 18 November 2019
                : 6 March 2020
                Page count
                Figures: 2, Tables: 0, Pages: 12
                Funding
                Funded by: National Institutes of Health (US)
                Award ID: U19MH114830
                Award Recipient :
                Funded by: National Institutes of Health (US)
                Award ID: R01 GM082837
                Award Recipient :
                Funded by: National Science Foundation (US)
                Award ID: PHY 1430124
                Award Recipient :
                Funded by: National Key R&D Program of China
                Award ID: 2018YFC0310803
                Award Recipient :
                Funded by: funder-id http://dx.doi.org/10.13039/501100001809, National Natural Science Foundation of China;
                Award ID: 11774225
                Award Recipient :
                Funded by: Thousand Talents Plan of China
                Award ID: Program for Young Professionals
                Award Recipient :
                Funded by: National Science Foundation of Shanghai
                Award ID: 18ZR1419800
                Award Recipient :
                Funded by: funder-id http://dx.doi.org/10.13039/100000861, Burroughs Wellcome Fund;
                Award ID: 1013907
                Award Recipient :
                Funded by: funder-id http://dx.doi.org/10.13039/100005598, Chao Center for Asian Studies, Rice University;
                Award ID: U-ASIA 2017
                Award Recipient :
                The authors were funded by the following sources during the completion of this research: GG: NIH U19MH114830. National Institutes of Health. nih.gov. GG: Undergraduate Asian Studies Internship Award (U-ASIA) 2017. Rice University Chao Center for Asian Studies. chaocenter.rice.edu. MW, IG: R01 GM082837. National Institutes of Health. nih.gov. MW, IG: PHY 1430124. National Science Foundation. nsf.gov. HX: 2018YFC0310803. National Key R&D Program of China. http://most.gov.cn/ HX: 11774225. National Natural Science Foundation of China. nsfc.gov.cn. HX: Thousand Talents Plan of China, Program for Young Professionals. 1000plan.org.cn. HX: 18ZR1419800. National Science Foundation of Shanghai. stcsm.sh.gov.cn. HX: 1013907. Burroughs Wellcome Fund Career Award at the Scientific Interface. bwfund.org. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
                Categories
                Research Article
                Biology and life sciences
                Biochemistry
                Nucleic acids
                RNA
                Messenger RNA
                Biology and life sciences
                Genetics
                Gene expression
                DNA transcription
                Research and Analysis Methods
                Simulation and Modeling
                Physical Sciences
                Mathematics
                Applied Mathematics
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                DNA-binding proteins
                Nucleases
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                Ribonucleases
                Biology and Life Sciences
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                Biology and Life Sciences
                Biophysics
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                Physical Sciences
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