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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 references 43

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          Exact stochastic simulation of coupled chemical reactions

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            A general method for numerically simulating the stochastic time evolution of coupled chemical reactions

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              Real-time kinetics of gene activity in individual bacteria.

              Protein levels have been shown to vary substantially between individual cells in clonal populations. In prokaryotes, the contribution to such fluctuations from the inherent randomness of gene expression has largely been attributed to having just a few transcripts of the corresponding mRNAs. By contrast, eukaryotic studies tend to emphasize chromatin remodeling and burst-like transcription. Here, we study single-cell transcription in Escherichia coli by measuring mRNA levels in individual living cells. The results directly demonstrate transcriptional bursting, similar to that indirectly inferred for eukaryotes. We also measure mRNA partitioning at cell division and correlate mRNA and protein levels in single cells. Partitioning is approximately binomial, and mRNA-protein correlations are weaker earlier in the cell cycle, where cell division has recently randomized the relative concentrations. Our methods further extend protein-based approaches by counting the integer-valued number of transcript with single-molecule resolution. This greatly facilitates kinetic interpretations in terms of the integer-valued random processes that produce the fluctuations.
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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
                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.

                Article
                PONE-D-19-31981
                10.1371/journal.pone.0230736
                7098607
                32214380
                © 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.

                Page count
                Figures: 2, Tables: 0, Pages: 12
                Product
                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
                Algorithms
                Research and Analysis Methods
                Simulation and Modeling
                Algorithms
                Biology and Life Sciences
                Biochemistry
                Biochemical Simulations
                Biology and Life Sciences
                Computational Biology
                Biochemical Simulations
                Physical Sciences
                Mathematics
                Applied Mathematics
                Algorithms
                Genetic Algorithms
                Research and Analysis Methods
                Simulation and Modeling
                Algorithms
                Genetic Algorithms
                Biology and life sciences
                Biochemistry
                Proteins
                DNA-binding proteins
                Nucleases
                Ribonucleases
                Biology and Life Sciences
                Biochemistry
                Enzymology
                Enzymes
                Hydrolases
                Nucleases
                Ribonucleases
                Biology and Life Sciences
                Biochemistry
                Proteins
                Enzymes
                Hydrolases
                Nucleases
                Ribonucleases
                Biology and Life Sciences
                Biophysics
                Biophysical Simulations
                Physical Sciences
                Physics
                Biophysics
                Biophysical Simulations
                Biology and Life Sciences
                Computational Biology
                Biophysical Simulations
                Custom metadata
                All relevant data are within the manuscript and its Supporting Information files.

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