Estimation and Discrimination of Stochastic Biochemical Circuits from Time-Lapse Microscopy Data
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{"title"=>"Estimation and Discrimination of Stochastic Biochemical Circuits from Time-Lapse Microscopy Data", "type"=>"journal", "authors"=>[{"first_name"=>"David", "last_name"=>"Thorsley"}, {"first_name"=>"Eric", "last_name"=>"Klavins"}], "year"=>2012, "source"=>"PLoS ONE", "identifiers"=>{"pui"=>"366400016", "doi"=>"10.1371/journal.pone.0047151", "pmid"=>"23139740", "issn"=>"1932-6203", "sgr"=>"84876431265", "scopus"=>"2-s2.0-84876431265", "isbn"=>"1932-6203 (Electronic) 1932-6203 (Linking)"}, "id"=>"832d365a-470f-3f26-bef3-dc98e2f12d91", "abstract"=>"The ability of systems and synthetic biologists to observe the dynamics of cellular behavior is hampered by the limitations of the sensors, such as fluorescent proteins, available for use in time-lapse microscopy. In this paper, we propose a generalized solution to the problem of estimating the state of a stochastic chemical reaction network from limited sensor information generated by microscopy. We mathematically derive an observer structure for cells growing under time-lapse microscopy and incorporates the effects of cell division in order to estimate the dynamically-changing state of each cell in the colony. Furthermore, the observer can be used to discrimate between models by treating model indices as states whose values do not change with time. We derive necessary and sufficient conditions that specify when stochastic chemical reaction network models, interpreted as continuous-time Markov chains, can be distinguished from each other under both continual and periodic observation. We validate the performance of the observer on the Thattai-van Oudenaarden model of transcription and translation. The observer structure is most effective when the system model is well-parameterized, suggesting potential applications in synthetic biology where standardized biological parts are available. However, further research is necessary to develop computationally tractable approximations to the exact generalized solution presented here.", "link"=>"http://www.mendeley.com/research/estimation-discrimination-stochastic-biochemical-circuits-timelapse-microscopy-data", "reader_count"=>21, "reader_count_by_academic_status"=>{"Professor > Associate Professor"=>3, "Researcher"=>8, "Student > Ph. D. Student"=>4, "Student > Master"=>3, "Other"=>2, "Professor"=>1}, "reader_count_by_user_role"=>{"Professor > Associate Professor"=>3, "Researcher"=>8, "Student > Ph. D. Student"=>4, "Student > Master"=>3, "Other"=>2, "Professor"=>1}, "reader_count_by_subject_area"=>{"Engineering"=>3, "Unspecified"=>1, "Biochemistry, Genetics and Molecular Biology"=>2, "Agricultural and Biological Sciences"=>6, "Medicine and Dentistry"=>1, "Physics and Astronomy"=>3, "Social Sciences"=>2, "Computer Science"=>2, "Immunology and Microbiology"=>1}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>3}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>1}, "Social Sciences"=>{"Social Sciences"=>2}, "Physics and Astronomy"=>{"Physics and Astronomy"=>3}, "Immunology and Microbiology"=>{"Immunology and Microbiology"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>6}, "Computer Science"=>{"Computer Science"=>2}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>2}, "Unspecified"=>{"Unspecified"=>1}}, "reader_count_by_country"=>{"United States"=>2, "United Kingdom"=>1, "Switzerland"=>1, "Germany"=>1, "India"=>1}, "group_count"=>0}

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  • {"files"=>["https://ndownloader.figshare.com/files/293355", "https://ndownloader.figshare.com/files/293546"], "description"=>"<div><p>The ability of systems and synthetic biologists to observe the dynamics of cellular behavior is hampered by the limitations of the sensors, such as fluorescent proteins, available for use in time-lapse microscopy. In this paper, we propose a generalized solution to the problem of estimating the state of a stochastic chemical reaction network from limited sensor information generated by microscopy. We mathematically derive an observer structure for cells growing under time-lapse microscopy and incorporates the effects of cell division in order to estimate the dynamically-changing state of each cell in the colony. Furthermore, the observer can be used to discrimate between models by treating model indices as states whose values do not change with time. We derive necessary and sufficient conditions that specify when stochastic chemical reaction network models, interpreted as continuous-time Markov chains, can be distinguished from each other under both continual and periodic observation. We validate the performance of the observer on the Thattai-van Oudenaarden model of transcription and translation. The observer structure is most effective when the system model is well-parameterized, suggesting potential applications in synthetic biology where standardized biological parts are available. However, further research is necessary to develop computationally tractable approximations to the exact generalized solution presented here.</p> </div>", "links"=>[], "tags"=>["estimation", "stochastic", "biochemical", "circuits", "time-lapse", "microscopy", "data"], "article_id"=>117752, "categories"=>["Biochemistry", "Mathematics", "Molecular Biology", "Biological Sciences"], "users"=>["David Thorsley", "Eric Klavins"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0047151.s001", "https://dx.doi.org/10.1371/journal.pone.0047151.s002"], "stats"=>{"downloads"=>3, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/Estimation_and_Discrimination_of_Stochastic_Biochemical_Circuits_from_Time_Lapse_Microscopy_Data__/117752", "title"=>"Estimation and Discrimination of Stochastic Biochemical Circuits from Time-Lapse Microscopy Data", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2012-11-06 02:09:12"}
  • {"files"=>["https://ndownloader.figshare.com/files/548309"], "description"=>"<p>We consider three models in this figure: , a standard Thattai-van Oudenaarden model of transcription and translation, , a structurally-identical model in which the rates of protein production and degradation are increased by a factor of 10, and , another structurally-identical model in which the rates of messenger RNA production and degradation are increased by a factor of 10. Each subfigure contains three plots: the unobserved mRNA number from a stochastic simulation run (top), the observed protein number from the same SSA run (middle), and the idealized observer estimates as to the posterior probabilities of each model (bottom). The system is observed continually. (a) Results from simulated data generated from . (b) Results from simulated data generated from . Note that the observer decision is very quick in this scenario, as the observable protein dynamics in differ from those of both and . (c) Results from simulated data generated from . Note that despite the similar appearance of the protein number trajectory here and in (a), the observer is able to determine which unobservable mRNA dynamics are responsible for the observed behavior.</p>", "links"=>[], "tags"=>["discriminate"], "article_id"=>218817, "categories"=>["Biochemistry", "Mathematics", "Molecular Biology", "Biological Sciences"], "users"=>["David Thorsley", "Eric Klavins"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0047151.g004", "stats"=>{"downloads"=>0, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Using_the_observer_to_discriminate_between_models_/218817", "title"=>"Using the observer to discriminate between models.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-11-06 02:26:57"}
  • {"files"=>["https://ndownloader.figshare.com/files/548104"], "description"=>"<p>(a) Run the forward observer on each cell, breaking up the lineage so that each segment is only counted once. (b) Run the backward observer on each cell and “pinch” together a cell and its ancestor when the birth of a cell is observed. One forward and backward sweep of the lineage determines the posterior probability distribution for , where is the first division time. Calculating this probability distribution is sufficient for parameter estimation. To calculate posterior state estimates for , run an additional forward sweep on each cell, integrating the colony estimate with the results of the forward and backward observer.</p>", "links"=>[], "tags"=>["integrating"], "article_id"=>218604, "categories"=>["Biochemistry", "Mathematics", "Molecular Biology", "Biological Sciences"], "users"=>["David Thorsley", "Eric Klavins"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0047151.g002", "stats"=>{"downloads"=>1, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Procedure_for_integrating_lineages_/218604", "title"=>"Procedure for integrating lineages.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-11-06 02:23:24"}
  • {"files"=>["https://ndownloader.figshare.com/files/548031"], "description"=>"<p>(a) Inputs to the observer algorithm. (i) The system model consists is a birth-death reaction of a single species . The initial distribution is the steady-state of this reaction network, a Poisson distribution with parameter . (ii) The sensor model partitions the state space into three sections with deterministic outputs. If the population of is less than or equal to 6, the observed output is “LOW”; if the population is between 7 and 13, the output is “MEDIUM.” Otherwise the output is “HIGH.” (iii) A sample time series trajectory of observed output. The process is observed intermittently with observations taken every.1 time units. (b) The time-varying probability distribution of the state estimate generated by the forward algorithm. At each observation point, there is a discontinuity in as new information is incorporated into the estimated probability mass function. The forward algorithm estimate lags the data, as it does not anticipate the values of future outputs. (c) The time-varying probability distribution of the state estimate generated by the backward algorithm. At each observation point, the state estimation is non-differentiable, but continuous. (d) Comparison of the evolution of the forward expectation and the backward expectation . The shaded area indicates plus or minus one standard deviation.</p>", "links"=>[], "tags"=>["molecular biology", "Computational biology", "Biochemistry", "mathematics"], "article_id"=>218529, "categories"=>["Biochemistry", "Mathematics", "Molecular Biology", "Biological Sciences"], "users"=>["David Thorsley", "Eric Klavins"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0047151.g001", "stats"=>{"downloads"=>1, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Implementation_of_the_observer_algorithms_/218529", "title"=>"Implementation of the observer algorithms.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-11-06 02:22:09"}
  • {"files"=>["https://ndownloader.figshare.com/files/548214"], "description"=>"<p>(a) The unobserved mRNA population from a Gillespie SSA run of a colony where cells divide every 20 minutes and the system is observed every minute. (b) The observed protein number from the same Gillespie SSA run. (c) The estimate of the mRNA population in each cell as a function of time generated by the forward observer. (d) The estimate of the mRNA population in each cell as a function of time generated by the backward observer. In this example, we assumed that, when the cell divides, each molecule of mRNA and protein was equally likely to join both daughter cells. Each cell’s ancestor is the cell lineage is indicated by a red vertical line connecting the plot for a daughter cell to that of its mother cell. Brighter shades of green indicates mRNA populations that are more probable.</p>", "links"=>[], "tags"=>["mrna"], "article_id"=>218719, "categories"=>["Biochemistry", "Mathematics", "Molecular Biology", "Biological Sciences"], "users"=>["David Thorsley", "Eric Klavins"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0047151.g003", "stats"=>{"downloads"=>1, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Using_the_observer_to_estimate_mRNA_population_/218719", "title"=>"Using the observer to estimate mRNA population.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-11-06 02:25:19"}

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Relative Metric

{"start_date"=>"2012-01-01T00:00:00Z", "end_date"=>"2012-12-31T00:00:00Z", "subject_areas"=>[{"subject_area"=>"/Biology and life sciences", "average_usage"=>[322, 550, 671, 773, 864, 955, 1048, 1135, 1223, 1308, 1387, 1465, 1534, 1602, 1673, 1744, 1813, 1885, 1955, 2026, 2093, 2160, 2228, 2290, 2349]}, {"subject_area"=>"/Biology and life sciences/Biochemistry", "average_usage"=>[316, 541, 663, 766, 856, 950, 1041, 1128, 1218, 1302, 1382, 1456, 1526, 1593, 1657, 1729, 1796, 1862, 1930, 1999, 2065, 2132, 2202, 2261, 2319]}, {"subject_area"=>"/Physical sciences", "average_usage"=>[304, 506, 616, 712, 799, 879, 968, 1052, 1134, 1212, 1284, 1357, 1427, 1494, 1557, 1621, 1689, 1756, 1823, 1883, 1944, 1997, 2056, 2118, 2171]}, {"subject_area"=>"/Physical sciences/Mathematics", "average_usage"=>[325, 522, 627, 718, 804, 884, 969, 1052, 1131, 1207, 1277, 1346, 1415, 1478, 1542, 1605, 1663, 1723, 1776, 1839, 1895, 1955, 2008, 2066, 2123]}]}
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