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

      research-article
      1 , 2 , 1 , 3 , * , 2 , 4 , *
      PLoS ONE
      Public Library of Science

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          Abstract

          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 references6

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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.
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            Noise in gene expression determines cell fate in Bacillus subtilis.

            Random cell-to-cell variations in gene expression within an isogenic population can lead to transitions between alternative states of gene expression. Little is known about how these variations (noise) in natural systems affect such transitions. In Bacillus subtilis, noise in ComK, the protein that regulates competence for DNA uptake, is thought to cause cells to transition to the competent state in which genes encoding DNA uptake proteins are expressed. We demonstrate that noise in comK expression selects cells for competence and that experimental reduction of this noise decreases the number of competent cells. We also show that transitions are limited temporally by a reduction in comK transcription. These results illustrate how such stochastic transitions are regulated in a natural system and suggest that noise characteristics are subject to evolutionary forces.
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              Ultrasensitivity and noise propagation in a synthetic transcriptional cascade.

              The precise nature of information flow through a biological network, which is governed by factors such as response sensitivities and noise propagation, greatly affects the operation of biological systems. Quantitative analysis of these properties is often difficult in naturally occurring systems but can be greatly facilitated by studying simple synthetic networks. Here, we report the construction of synthetic transcriptional cascades comprising one, two, and three repression stages. These model systems enable us to analyze sensitivity and noise propagation as a function of network complexity. We demonstrate experimentally steady-state switching behavior that becomes sharper with longer cascades. The regulatory mechanisms that confer this ultrasensitive response both attenuate and amplify phenotypical variations depending on the system's input conditions. Although noise attenuation allows the cascade to act as a low-pass filter by rejecting short-lived perturbations in input conditions, noise amplification results in loss of synchrony among a cell population. The experimental results demonstrating the above network properties correlate well with simulations of a simple mathematical model of the system.
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                Author and article information

                Contributors
                Role: Editor
                Journal
                PLoS One
                PLoS ONE
                plos
                plosone
                PLoS ONE
                Public Library of Science (San Francisco, USA )
                1932-6203
                2014
                13 February 2014
                : 9
                : 2
                : e88167
                Affiliations
                [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.

                Article
                PONE-D-13-39012
                10.1371/journal.pone.0088167
                3923795
                24551081
                2138a483-79a0-4bac-b9e0-240c8e3064f5
                Copyright @ 2014

                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
                : 21 September 2013
                : 3 January 2014
                Page count
                Pages: 10
                Funding
                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.
                Categories
                Research Article
                Biology
                Computational biology
                Molecular genetics
                Gene regulation
                Gene expression
                Computer science
                Algorithms
                Mathematics
                Applied mathematics
                Algorithms
                Complex systems
                Probability theory
                Stochastic processes

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                Uncategorized

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