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Nonidentifiability of the Source of Intrinsic Noise in Gene Expression from Single-Burst Data

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      Abstract

      Over the last few years, experimental data on the fluctuations in gene activity between individual cells and within the same cell over time have confirmed that gene expression is a “noisy” process. This variation is in part due to the small number of molecules taking part in some of the key reactions that are involved in gene expression. One of the consequences of this is that protein production often occurs in bursts, each due to a single promoter or transcription factor binding event. Recently, the distribution of the number of proteins produced in such bursts has been experimentally measured, offering a unique opportunity to study the relative importance of different sources of noise in gene expression. Here, we provide a derivation of the theoretical probability distribution of these bursts for a wide variety of different models of gene expression. We show that there is a good fit between our theoretical distribution and that obtained from two different published experimental datasets. We then prove that, irrespective of the details of the model, the burst size distribution is always geometric and hence determined by a single parameter. Many different combinations of the biochemical rates for the constituent reactions of both transcription and translation will therefore lead to the same experimentally observed burst size distribution. It is thus impossible to identify different sources of fluctuations purely from protein burst size data or to use such data to estimate all of the model parameters. We explore methods of inferring these values when additional types of experimental data are available.

      Author Summary

      Recent experimental data showing fluctuations in gene activity between individual cells and within the same cell over time confirm that gene expression is a “noisy” process. This variation is partly due to the small number of molecules involved in gene expression. One consequence is that protein production often occurs in bursts, each due to the binding of a single transcription factor. Recently, the distribution of the number of proteins produced in such bursts has been experimentally measured, offering a unique opportunity to study the relative importance of different sources of noise in gene expression. We derive the theoretical probability distribution of these bursts for a wide variety of gene expression models. We show a good fit between our theoretical distribution and experimental data and prove that, irrespective of the model details, the burst size distribution always has the same shape, determined by a single parameter. As different combinations of the reaction rates lead to the same observed distribution, it is impossible to estimate all kinetic parameters from protein burst size data. When additional data, such as protein equilibrium distributions, are available, these can be used to infer additional parameters. We present one approach to this, demonstrating its application to published data.

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      Exact stochastic simulation of coupled chemical reactions

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        Stochastic gene expression in a single cell.

        Clonal populations of cells exhibit substantial phenotypic variation. Such heterogeneity can be essential for many biological processes and is conjectured to arise from stochasticity, or noise, in gene expression. We constructed strains of Escherichia coli that enable detection of noise and discrimination between the two mechanisms by which it is generated. Both stochasticity inherent in the biochemical process of gene expression (intrinsic noise) and fluctuations in other cellular components (extrinsic noise) contribute substantially to overall variation. Transcription rate, regulatory dynamics, and genetic factors control the amplitude of noise. These results establish a quantitative foundation for modeling noise in genetic networks and reveal how low intracellular copy numbers of molecules can fundamentally limit the precision of gene regulation.
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          Noise in gene expression: origins, consequences, and control.

          Genetically identical cells and organisms exhibit remarkable diversity even when they have identical histories of environmental exposure. Noise, or variation, in the process of gene expression may contribute to this phenotypic variability. Recent studies suggest that this noise has multiple sources, including the stochastic or inherently random nature of the biochemical reactions of gene expression. In this review, we summarize noise terminology and comment on recent investigations into the sources, consequences, and control of noise in gene expression.
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            Author and article information

            Affiliations
            [1 ]Department of Mathematics, Imperial College London, London, United Kingdom
            [2 ]Centre for Integrative Systems Biology at Imperial College, Imperial College London, London, United Kingdom
            [3 ]Theoretical Genomics Group, Centre for Bioinformatics, Division of Molecular Biosciences, Imperial College London, London, United Kingdom
            University of California San Diego, United States of America
            Author notes

            Conceived and designed the experiments: PJI MPHS JS. Wrote the paper: PJI JS. Performed the analysis: PJI.

            Contributors
            Role: Editor
            Journal
            PLoS Comput Biol
            plos
            ploscomp
            PLoS Computational Biology
            Public Library of Science (San Francisco, USA )
            1553-734X
            1553-7358
            October 2008
            October 2008
            10 October 2008
            : 4
            : 10
            2538572
            18846201
            06-PLCB-RA-0408R6
            10.1371/journal.pcbi.1000192
            (Editor)
            Ingram 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.
            Counts
            Pages: 10
            Categories
            Research Article
            Cell Biology
            Computational Biology
            Computational Biology/Systems Biology

            Quantitative & Systems biology

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