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Constructing the Energy Landscape for Genetic Switching System Driven by Intrinsic Noise

1 , 2 , 1 , 3 , * , 2 , 4 , *


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      Genetic switching driven by noise is a fundamental cellular process in genetic regulatory networks. Quantitatively characterizing this switching and its fluctuation properties is a key problem in computational biology. With an autoregulatory dimer model as a specific example, we design a general methodology to quantitatively understand the metastability of gene regulatory system perturbed by intrinsic noise. Based on the large deviation theory, we develop new analytical techniques to describe and calculate the optimal transition paths between the on and off states. We also construct the global quasi-potential energy landscape for the dimer model. From the obtained quasi-potential, we can extract quantitative results such as the stationary distributions of mRNA, protein and dimer, the noise strength of the expression state, and the mean switching time starting from either stable state. In the final stage, we apply this procedure to a transcriptional cascades model. Our results suggest that the quasi-potential energy landscape and the proposed methodology are general to understand the metastability in other biological systems with intrinsic noise.

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      Most cited references 13

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      Protein and messenger RNA (mRNA) copy numbers vary from cell to cell in isogenic bacterial populations. However, these molecules often exist in low copy numbers and are difficult to detect in single cells. We carried out quantitative system-wide analyses of protein and mRNA expression in individual cells with single-molecule sensitivity using a newly constructed yellow fluorescent protein fusion library for Escherichia coli. We found that almost all protein number distributions can be described by the gamma distribution with two fitting parameters which, at low expression levels, have clear physical interpretations as the transcription rate and protein burst size. At high expression levels, the distributions are dominated by extrinsic noise. We found that a single cell's protein and mRNA copy numbers for any given gene are uncorrelated.
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        Control of stochasticity in eukaryotic gene expression.

        Noise, or random fluctuations, in gene expression may produce variability in cellular behavior. To measure the noise intrinsic to eukaryotic gene expression, we quantified the differences in expression of two alleles in a diploid cell. We found that such noise is gene-specific and not dependent on the regulatory pathway or absolute rate of expression. We propose a model in which the balance between promoter activation and transcription influences the variability in messenger RNA levels. To confirm the predictions of our model, we identified both cis- and trans-acting mutations that alter the noise of gene expression. These mutations suggest that noise is an evolvable trait that can be optimized to balance fidelity and diversity in eukaryotic gene expression.
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          Phenotypic diversity, population growth, and information in fluctuating environments.

          Organisms in fluctuating environments must constantly adapt their behavior to survive. In clonal populations, this may be achieved through sensing followed by response or through the generation of diversity by stochastic phenotype switching. Here we show that stochastic switching can be favored over sensing when the environment changes infrequently. The optimal switching rates then mimic the statistics of environmental changes. We derive a relation between the long-term growth rate of the organism and the information available about its fluctuating environment.

            Author and article information

            [1 ]School of Physics, Peking University, Beijing, China
            [2 ]LMAM and School of Mathematical Sciences, Peking University, Beijing, China
            [3 ]Center of Quantitative Biology, Peking University, Beijing, China
            [4 ]Beijing International Center for Mathematical Research, Beijing, China
            University of Adelaide, Australia
            Author notes

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

            Conceived and designed the experiments: FL TL. Performed the experiments: CL XL. Wrote the paper: CL XL FL TL.

            Role: Editor
            PLoS One
            PLoS ONE
            PLoS ONE
            Public Library of Science (San Francisco, USA )
            13 February 2014
            : 9
            : 2
            3923795 PONE-D-13-39012 10.1371/journal.pone.0088167

            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.

            Pages: 10
            The work is supported by NSFC grants no. 11174011, 11021463 (F.Li), 11171009 and 91130005 and the National Science Foundation for Excellent Young Scholars (Grant No. 11222114) (T.Li). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
            Research Article
            Computational biology
            Molecular genetics
            Gene regulation
            Gene expression
            Computer science
            Applied mathematics
            Complex systems
            Probability theory
            Stochastic processes



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