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Inferring distributions from observed mRNA and protein copy counts in genetic circuits

Komlan Atitey, Pavel Loskot Orcid Logo, Paul Rees Orcid Logo

Biomedical Physics & Engineering Express

Swansea University Authors: Pavel Loskot Orcid Logo, Paul Rees Orcid Logo

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DOI (Published version): 10.1088/2057-1976/aaef5c

Abstract

Defining distributions of molecule counts produced in the cell can elucidate stochastic dynamics of the underlying biological circuits. For genetic circuits, only a few distributions of messenger RNA and protein counts were reported in literature, so the task is to decide which of these candidate di...

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Published in: Biomedical Physics & Engineering Express
ISSN: 2057-1976
Published: 2018
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URI: https://cronfa.swan.ac.uk/Record/cronfa45470
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first_indexed 2018-11-06T20:16:27Z
last_indexed 2019-09-23T14:09:22Z
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spelling 2019-09-23T04:33:34.5565739 v2 45470 2018-11-06 Inferring distributions from observed mRNA and protein copy counts in genetic circuits bc7cba9ef306864239b9348c3aea4c3e 0000-0002-2773-2186 Pavel Loskot Pavel Loskot true false 537a2fe031a796a3bde99679ee8c24f5 0000-0002-7715-6914 Paul Rees Paul Rees true false 2018-11-06 EEN Defining distributions of molecule counts produced in the cell can elucidate stochastic dynamics of the underlying biological circuits. For genetic circuits, only a few distributions of messenger RNA and protein counts were reported in literature, so the task is to decide which of these candidate distributions best fit the observed data. In this paper, we present a statistical method to infer distributions of mRNA and protein counts from observed data. The main advantage of this method is that it does not require any prior assumptions or knowledge about underlying chemical reactions. In particular, a given distribution is fitted to the observed copy counts using a histogram with optimized bin sizes in order to reduce the fitting error. The goodness of fit is evaluated by Kolmogorov-Smirnov and chi-square statistical tests to accept or reject the hypothesis that observed molecule counts were generated from given distribution. The distribution fitting also yields the values of distribution parameters, or they can be estimated using the Bayes theorem. These parameters appear to be themselves random processes. The presented statistical framework for analyzing the observed mRNA and protein copy counts is illustrated for a simulated model of lac genetic circuit in Escherichia coli. For reaction rates assumed in the model, the results in literature predict that mRNA and protein counts at steady-state are gamma distributed. Our analysis shows that both mRNA and protein in the lac circuit model can be considered gamma distributed in at least 70% of times from the initial state until steady-state. The shape and scale parameters of observed gamma distributions are also gamma distributed, giving rise to double stochastic processes. More importantly, as shown previously, the distribution parameters are functions of transcription and translation rates, so presented statistical framework can be used to estimate or optimize reaction rates in biochemical systems. Journal Article Biomedical Physics & Engineering Express 2057-1976 31 12 2018 2018-12-31 10.1088/2057-1976/aaef5c COLLEGE NANME Engineering COLLEGE CODE EEN Swansea University 2019-09-23T04:33:34.5565739 2018-11-06T15:05:34.4695950 Faculty of Science and Engineering School of Engineering and Applied Sciences - Biomedical Engineering Komlan Atitey 1 Pavel Loskot 0000-0002-2773-2186 2 Paul Rees 0000-0002-7715-6914 3 0045470-06112018150805.pdf atitey2018(2).pdf 2018-11-06T15:08:05.4100000 Output 1198878 application/pdf Accepted Manuscript true 2019-11-08T00:00:00.0000000 true eng
title Inferring distributions from observed mRNA and protein copy counts in genetic circuits
spellingShingle Inferring distributions from observed mRNA and protein copy counts in genetic circuits
Pavel Loskot
Paul Rees
title_short Inferring distributions from observed mRNA and protein copy counts in genetic circuits
title_full Inferring distributions from observed mRNA and protein copy counts in genetic circuits
title_fullStr Inferring distributions from observed mRNA and protein copy counts in genetic circuits
title_full_unstemmed Inferring distributions from observed mRNA and protein copy counts in genetic circuits
title_sort Inferring distributions from observed mRNA and protein copy counts in genetic circuits
author_id_str_mv bc7cba9ef306864239b9348c3aea4c3e
537a2fe031a796a3bde99679ee8c24f5
author_id_fullname_str_mv bc7cba9ef306864239b9348c3aea4c3e_***_Pavel Loskot
537a2fe031a796a3bde99679ee8c24f5_***_Paul Rees
author Pavel Loskot
Paul Rees
author2 Komlan Atitey
Pavel Loskot
Paul Rees
format Journal article
container_title Biomedical Physics & Engineering Express
publishDate 2018
institution Swansea University
issn 2057-1976
doi_str_mv 10.1088/2057-1976/aaef5c
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Engineering and Applied Sciences - Biomedical Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Engineering and Applied Sciences - Biomedical Engineering
document_store_str 1
active_str 0
description Defining distributions of molecule counts produced in the cell can elucidate stochastic dynamics of the underlying biological circuits. For genetic circuits, only a few distributions of messenger RNA and protein counts were reported in literature, so the task is to decide which of these candidate distributions best fit the observed data. In this paper, we present a statistical method to infer distributions of mRNA and protein counts from observed data. The main advantage of this method is that it does not require any prior assumptions or knowledge about underlying chemical reactions. In particular, a given distribution is fitted to the observed copy counts using a histogram with optimized bin sizes in order to reduce the fitting error. The goodness of fit is evaluated by Kolmogorov-Smirnov and chi-square statistical tests to accept or reject the hypothesis that observed molecule counts were generated from given distribution. The distribution fitting also yields the values of distribution parameters, or they can be estimated using the Bayes theorem. These parameters appear to be themselves random processes. The presented statistical framework for analyzing the observed mRNA and protein copy counts is illustrated for a simulated model of lac genetic circuit in Escherichia coli. For reaction rates assumed in the model, the results in literature predict that mRNA and protein counts at steady-state are gamma distributed. Our analysis shows that both mRNA and protein in the lac circuit model can be considered gamma distributed in at least 70% of times from the initial state until steady-state. The shape and scale parameters of observed gamma distributions are also gamma distributed, giving rise to double stochastic processes. More importantly, as shown previously, the distribution parameters are functions of transcription and translation rates, so presented statistical framework can be used to estimate or optimize reaction rates in biochemical systems.
published_date 2018-12-31T03:57:16Z
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score 11.012924

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