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{"title"=>"Bayesian Parameter Inference by Markov Chain Monte Carlo with Hybrid Fitness Measures: Theory and Test in Apoptosis Signal Transduction Network", "type"=>"journal", "authors"=>[{"first_name"=>"Yohei", "last_name"=>"Murakami", "scopus_author_id"=>"54993998900"}, {"first_name"=>"Shoji", "last_name"=>"Takada", "scopus_author_id"=>"7202611424"}], "year"=>2013, "source"=>"PLoS ONE", "identifiers"=>{"issn"=>"19326203", "sgr"=>"84884687789", "doi"=>"10.1371/journal.pone.0074178", "scopus"=>"2-s2.0-84884687789", "pui"=>"369903716", "pmid"=>"24086320"}, "id"=>"70c46494-6697-34af-ac0f-8419d0d1444d", "abstract"=>"When model parameters in systems biology are not available from experiments, they need to be inferred so that the resulting simulation reproduces the experimentally known phenomena. For the purpose, Bayesian statistics with Markov chain Monte Carlo (MCMC) is a useful method. Conventional MCMC needs likelihood to evaluate a posterior distribution of acceptable parameters, while the approximate Bayesian computation (ABC) MCMC evaluates posterior distribution with use of qualitative fitness measure. However, none of these algorithms can deal with mixture of quantitative, i.e., likelihood, and qualitative fitness measures simultaneously. Here, to deal with this mixture, we formulated Bayesian formula for hybrid fitness measures (HFM). Then we implemented it to MCMC (MCMC-HFM). We tested MCMC-HFM first for a kinetic toy model with a positive feedback. Inferring kinetic parameters mainly related to the positive feedback, we found that MCMC-HFM reliably infer them using both qualitative and quantitative fitness measures. Then, we applied the MCMC-HFM to an apoptosis signal transduction network previously proposed. For kinetic parameters related to implicit positive feedbacks, which are important for bistability and irreversibility of the output, the MCMC-HFM reliably inferred these kinetic parameters. In particular, some kinetic parameters that have experimental estimates were inferred without using these data and the results were consistent with experiments. Moreover, for some parameters, the mixed use of quantitative and qualitative fitness measures narrowed down the acceptable range of parameters.", "link"=>"http://www.mendeley.com/research/bayesian-parameter-inference-markov-chain-monte-carlo-hybrid-fitness-measures-theory-test-apoptosis", "reader_count"=>15, "reader_count_by_academic_status"=>{"Professor > Associate Professor"=>1, "Researcher"=>5, "Student > Ph. D. Student"=>3, "Student > Postgraduate"=>2, "Student > Bachelor"=>1, "Professor"=>3}, "reader_count_by_user_role"=>{"Professor > Associate Professor"=>1, "Researcher"=>5, "Student > Ph. D. Student"=>3, "Student > Postgraduate"=>2, "Student > Bachelor"=>1, "Professor"=>3}, "reader_count_by_subject_area"=>{"Environmental Science"=>2, "Biochemistry, Genetics and Molecular Biology"=>2, "Mathematics"=>1, "Agricultural and Biological Sciences"=>6, "Physics and Astronomy"=>1, "Chemical Engineering"=>1, "Psychology"=>1, "Neuroscience"=>1}, "reader_count_by_subdiscipline"=>{"Neuroscience"=>{"Neuroscience"=>1}, "Physics and Astronomy"=>{"Physics and Astronomy"=>1}, "Psychology"=>{"Psychology"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>6}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>2}, "Mathematics"=>{"Mathematics"=>1}, "Environmental Science"=>{"Environmental Science"=>2}, "Chemical Engineering"=>{"Chemical Engineering"=>1}}, "reader_count_by_country"=>{"United States"=>1, "Germany"=>1}, "group_count"=>0}

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• {"files"=>["https://ndownloader.figshare.com/files/1471293"], "description"=>"<p>The 95% credible intervals are represented by common logarithm of the ratio of upper bound and lower bound of 95% credible intervals. Blue bars represent the case with “BI”. Red bars represent the case with “BIT_e”. Green bars represent the case with “BI[Y]_{time = 100}”. Magenta bars represent the case with “BIT_e [Y]_{time = 100}”. Cyan bars represent the case with “BIT_e [Y]_{time = 100}” with weaker noise in quantitative fitness.</p>", "links"=>[], "tags"=>["Biochemistry", "enzymology", "Enzyme kinetics", "enzymes", "cell biology", "Signal transduction", "cell signaling", "Signaling cascades", "Apoptotic signaling cascade", "Apoptotic signaling", "Molecular cell biology", "Computational biology", "systems biology", "mathematics", "Probability theory", "Bayes theorem", "Markov models", "credible", "intervals", "inferred", "kinetic"], "article_id"=>1004704, "categories"=>["Biological Sciences"], "users"=>["Yohei Murakami", "Shoji Takada"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0074178.g004", "stats"=>{"downloads"=>0, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_95_credible_intervals_of_inferred_parameters_in_the_kinetic_toy_model_/1004704", "title"=>"95% credible intervals of inferred parameters in the kinetic toy model.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-09-27 11:03:19"}
• {"files"=>["https://ndownloader.figshare.com/files/1471288"], "description"=>"<p>Flow chart of parameter inference. Dotted arrows and box with dotted line correspond to a preparation process of quantitative fitness f_quant(z) specifically for the kinetic toy model. Bold arrows and box with bold line correspond to a general parameter inference process by MCMC-HFM.</p>", "links"=>[], "tags"=>["Biochemistry", "enzymology", "Enzyme kinetics", "enzymes", "cell biology", "Signal transduction", "cell signaling", "Signaling cascades", "Apoptotic signaling cascade", "Apoptotic signaling", "Molecular cell biology", "Computational biology", "systems biology", "mathematics", "Probability theory", "Bayes theorem", "Markov models", "parameter"], "article_id"=>1004699, "categories"=>["Biological Sciences"], "users"=>["Yohei Murakami", "Shoji Takada"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0074178.g001", "stats"=>{"downloads"=>0, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Flow_chart_of_parameter_inference_/1004699", "title"=>"Flow chart of parameter inference.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-09-27 11:03:19"}
• {"files"=>["https://ndownloader.figshare.com/files/1471305"], "description"=>"<p>The 95% credible intervals are represented by common logarithm of the ratio of upper bound and lower bound of 95% credible intervals. Blue bars represent the case with “B”. Red bars represent the case with “BI”. Green bars represent the case with “BIT_s”. Magenta bars represent the case with “BIT_e”. Cyan bars represent the case with “BIT_sT_e”.</p>", "links"=>[], "tags"=>["Biochemistry", "enzymology", "Enzyme kinetics", "enzymes", "cell biology", "Signal transduction", "cell signaling", "Signaling cascades", "Apoptotic signaling cascade", "Apoptotic signaling", "Molecular cell biology", "Computational biology", "systems biology", "mathematics", "Probability theory", "Bayes theorem", "Markov models", "credible", "intervals", "inferred", "apoptosis"], "article_id"=>1004716, "categories"=>["Biological Sciences"], "users"=>["Yohei Murakami", "Shoji Takada"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0074178.g013", "stats"=>{"downloads"=>0, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_95_credible_intervals_of_inferred_parameters_in_the_apoptosis_model_/1004716", "title"=>"95% credible intervals of inferred parameters in the apoptosis model.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-09-27 11:03:19"}
• {"files"=>["https://ndownloader.figshare.com/files/1471302"], "description"=>"<p>Histogram of switching time of caspase-3 activation calculated with “B” (A), that with “BI” (B), that with “BIT_s” (C), that with “BIT_e” (D), and that with “BIT_sT_e” (E). Blue bars represent calculated results. Red outline box bars represent the approximated histogram of the function shown in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0074178#pone-0074178-g005\" target=\"_blank\">Figure 5.E</a>.</p>", "links"=>[], "tags"=>["Biochemistry", "enzymology", "Enzyme kinetics", "enzymes", "cell biology", "Signal transduction", "cell signaling", "Signaling cascades", "Apoptotic signaling cascade", "Apoptotic signaling", "Molecular cell biology", "Computational biology", "systems biology", "mathematics", "Probability theory", "Bayes theorem", "Markov models", "histograms", "switching", "caspase-3"], "article_id"=>1004713, "categories"=>["Biological Sciences"], "users"=>["Yohei Murakami", "Shoji Takada"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0074178.g011", "stats"=>{"downloads"=>0, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Calculated_histograms_of_switching_time_of_caspase_3_activation_/1004713", "title"=>"Calculated histograms of switching time of caspase-3 activation.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-09-27 11:03:19"}
• {"files"=>["https://ndownloader.figshare.com/files/1471300"], "description"=>"<p>The same as captions in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0074178#pone-0074178-g008\" target=\"_blank\">Figure 8</a>.</p>", "links"=>[], "tags"=>["Biochemistry", "enzymology", "Enzyme kinetics", "enzymes", "cell biology", "Signal transduction", "cell signaling", "Signaling cascades", "Apoptotic signaling cascade", "Apoptotic signaling", "Molecular cell biology", "Computational biology", "systems biology", "mathematics", "Probability theory", "Bayes theorem", "Markov models", "probability", "distributions"], "article_id"=>1004711, "categories"=>["Biological Sciences"], "users"=>["Yohei Murakami", "Shoji Takada"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0074178.g010", "stats"=>{"downloads"=>1, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Marginal_probability_distributions_of_k_asso_X_AC9_/1004711", "title"=>"Marginal probability distributions of k_asso (X-AC9*).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-09-27 11:03:19"}
• {"files"=>["https://ndownloader.figshare.com/files/1471296"], "description"=>"<p>The same as captions in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0074178#pone-0074178-g006\" target=\"_blank\">Figure 6</a>.</p>", "links"=>[], "tags"=>["Biochemistry", "enzymology", "Enzyme kinetics", "enzymes", "cell biology", "Signal transduction", "cell signaling", "Signaling cascades", "Apoptotic signaling cascade", "Apoptotic signaling", "Molecular cell biology", "Computational biology", "systems biology", "mathematics", "Probability theory", "Bayes theorem", "Markov models", "probability", "distributions"], "article_id"=>1004707, "categories"=>["Biological Sciences"], "users"=>["Yohei Murakami", "Shoji Takada"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0074178.g007", "stats"=>{"downloads"=>0, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Marginal_probability_distributions_of_k_asso_X_C9_/1004707", "title"=>"Marginal probability distributions of k_asso (X-C9).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-09-27 11:03:19"}
• {"files"=>["https://ndownloader.figshare.com/files/1471295"], "description"=>"<p>Probability distribution with “B” (A), that with “BI” (B), that with “BIT_s” (C), that with “BIT_e” (D), and that with ”BIT_sT_e” (E). Red bars represent experimentally estimated values. Red arrows indicate the modes.</p>", "links"=>[], "tags"=>["Biochemistry", "enzymology", "Enzyme kinetics", "enzymes", "cell biology", "Signal transduction", "cell signaling", "Signaling cascades", "Apoptotic signaling cascade", "Apoptotic signaling", "Molecular cell biology", "Computational biology", "systems biology", "mathematics", "Probability theory", "Bayes theorem", "Markov models", "probability", "distributions"], "article_id"=>1004706, "categories"=>["Biological Sciences"], "users"=>["Yohei Murakami", "Shoji Takada"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0074178.g006", "stats"=>{"downloads"=>0, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Marginal_probability_distributions_of_k_asso_X_C3_/1004706", "title"=>"Marginal probability distributions of k_asso (X-C3*).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-09-27 11:03:19"}
• {"files"=>["https://ndownloader.figshare.com/files/1471304"], "description"=>"<p>Histograms of execution time of caspase-3 activation calculated with “B” (A), that with “BI” (B), that with “BIT_s” (C), that with “BIT_e” (D), and that with “BIT_sT_e” (E). Blue bars represent calculated results. Red outline box bars represent the approximated histogram of the function shown in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0074178#pone-0074178-g005\" target=\"_blank\">Figure 5.F</a>.</p>", "links"=>[], "tags"=>["Biochemistry", "enzymology", "Enzyme kinetics", "enzymes", "cell biology", "Signal transduction", "cell signaling", "Signaling cascades", "Apoptotic signaling cascade", "Apoptotic signaling", "Molecular cell biology", "Computational biology", "systems biology", "mathematics", "Probability theory", "Bayes theorem", "Markov models", "histograms", "caspase-3"], "article_id"=>1004715, "categories"=>["Biological Sciences"], "users"=>["Yohei Murakami", "Shoji Takada"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0074178.g012", "stats"=>{"downloads"=>0, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Calculated_histograms_of_execution_time_of_caspase_3_activation_/1004715", "title"=>"Calculated histograms of execution time of caspase-3 activation.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-09-27 11:03:19"}
• {"files"=>["https://ndownloader.figshare.com/files/1471289"], "description"=>"<p>(A) Schematic diagram of the kinetic toy model. Y is a variable (protein). Arrows direct to Y represents production process. An arrow from Y represents degradation process. A lined circle represents a pool of Y. Equations correspond to the terms in the ordinary differential equation of the model. (B) Bifurcation diagram of the model. Red colored lines indicate stable steady states and the blue colored line indicates unstable steady state with “true” values of kinetic parameters θ_answer. “ks₀”, “ks_0.2”, “ks_0.3” and “ks₁” indicate the k_s values (k_s = 0, 0.2, 0.3, 1.0 respectively) used as the conditions to infer kinetic parameters. (C) Time series of [Y]. T_e represents “execution time of Y production”. (D) Distribution of “execution time of Y production” abbreviated as “T_e”. (E) Distribution of “concentration of Y at time = 100” abbreviated as “[Y]_{time = 100}”.</p>", "links"=>[], "tags"=>["Biochemistry", "enzymology", "Enzyme kinetics", "enzymes", "cell biology", "Signal transduction", "cell signaling", "Signaling cascades", "Apoptotic signaling cascade", "Apoptotic signaling", "Molecular cell biology", "Computational biology", "systems biology", "mathematics", "Probability theory", "Bayes theorem", "Markov models", "kinetic"], "article_id"=>1004700, "categories"=>["Biological Sciences"], "users"=>["Yohei Murakami", "Shoji Takada"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0074178.g002", "stats"=>{"downloads"=>1, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Mathematical_model_of_the_kinetic_toy_model_/1004700", "title"=>"Mathematical model of the kinetic toy model.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-09-27 11:03:19"}
• {"files"=>["https://ndownloader.figshare.com/files/1471298"], "description"=>"<p>The same as captions in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0074178#pone-0074178-g008\" target=\"_blank\">Figure 8</a>.</p>", "links"=>[], "tags"=>["Biochemistry", "enzymology", "Enzyme kinetics", "enzymes", "cell biology", "Signal transduction", "cell signaling", "Signaling cascades", "Apoptotic signaling cascade", "Apoptotic signaling", "Molecular cell biology", "Computational biology", "systems biology", "mathematics", "Probability theory", "Bayes theorem", "Markov models", "probability", "distributions"], "article_id"=>1004709, "categories"=>["Biological Sciences"], "users"=>["Yohei Murakami", "Shoji Takada"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0074178.g009", "stats"=>{"downloads"=>0, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Marginal_probability_distributions_of_k_asso_X_C9_/1004709", "title"=>"Marginal probability distributions of k_asso (X-C9*).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-09-27 11:03:19"}
• {"files"=>["https://ndownloader.figshare.com/files/1471312", "https://ndownloader.figshare.com/files/1471313", "https://ndownloader.figshare.com/files/1471314", "https://ndownloader.figshare.com/files/1471315", "https://ndownloader.figshare.com/files/1471316", "https://ndownloader.figshare.com/files/1471317", "https://ndownloader.figshare.com/files/1471318", "https://ndownloader.figshare.com/files/1471319", "https://ndownloader.figshare.com/files/1471320", "https://ndownloader.figshare.com/files/1471321", "https://ndownloader.figshare.com/files/1471322", "https://ndownloader.figshare.com/files/1471323", "https://ndownloader.figshare.com/files/1471324", "https://ndownloader.figshare.com/files/1471325", "https://ndownloader.figshare.com/files/1471326", "https://ndownloader.figshare.com/files/1471327", "https://ndownloader.figshare.com/files/1471328", "https://ndownloader.figshare.com/files/1471329", "https://ndownloader.figshare.com/files/1471330"], "description"=>"<div><p>When exact values of model parameters in systems biology are not available from experiments, they need to be inferred so that the resulting simulation reproduces the experimentally known phenomena. For the purpose, Bayesian statistics with Markov chain Monte Carlo (MCMC) is a useful method. Biological experiments are often performed with cell population, and the results are represented by histograms. On another front, experiments sometimes indicate the existence of a specific bifurcation pattern. In this study, to deal with both type of such experimental results and information for parameter inference, we introduced functions to evaluate fitness to both type of experimental results, named quantitative and qualitative fitness measures respectively. We formulated Bayesian formula for those hybrid fitness measures (HFM), and implemented it to MCMC (MCMC-HFM). We tested MCMC-HFM first for a kinetic toy model with a positive feedback. Inferring kinetic parameters mainly related to the positive feedback, we found that MCMC-HFM reliably infer them with both qualitative and quantitative fitness measures. Then, we applied the MCMC-HFM to an apoptosis signal transduction network previously proposed. For kinetic parameters related to implicit positive feedbacks, which are important for bistability and irreversibility of the output, the MCMC-HFM reliably inferred these kinetic parameters. In particular, some kinetic parameters that have the experimental estimates were inferred without these data and the results were consistent with the experiments. Moreover, for some parameters, the mixed use of quantitative and qualitative fitness measures narrowed down the acceptable range of parameters. Taken together, our approach could reliably infer the kinetic parameters of the target systems.</p></div>", "links"=>[], "tags"=>["Biochemistry", "enzymology", "Enzyme kinetics", "enzymes", "cell biology", "Signal transduction", "cell signaling", "Signaling cascades", "Apoptotic signaling cascade", "Apoptotic signaling", "Molecular cell biology", "Computational biology", "systems biology", "mathematics", "Probability theory", "Bayes theorem", "Markov models", "parameter", "inference", "markov", "monte", "carlo", "hybrid", "apoptosis", "transduction"], "article_id"=>1004723, "categories"=>["Biological Sciences"], "users"=>["Yohei Murakami", "Shoji Takada"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0074178.s001", "https://dx.doi.org/10.1371/journal.pone.0074178.s002", "https://dx.doi.org/10.1371/journal.pone.0074178.s003", "https://dx.doi.org/10.1371/journal.pone.0074178.s004", "https://dx.doi.org/10.1371/journal.pone.0074178.s005", "https://dx.doi.org/10.1371/journal.pone.0074178.s006", "https://dx.doi.org/10.1371/journal.pone.0074178.s007", "https://dx.doi.org/10.1371/journal.pone.0074178.s008", "https://dx.doi.org/10.1371/journal.pone.0074178.s009", "https://dx.doi.org/10.1371/journal.pone.0074178.s010", "https://dx.doi.org/10.1371/journal.pone.0074178.s011", "https://dx.doi.org/10.1371/journal.pone.0074178.s012", "https://dx.doi.org/10.1371/journal.pone.0074178.s013", "https://dx.doi.org/10.1371/journal.pone.0074178.s014", "https://dx.doi.org/10.1371/journal.pone.0074178.s015", "https://dx.doi.org/10.1371/journal.pone.0074178.s016", "https://dx.doi.org/10.1371/journal.pone.0074178.s017", "https://dx.doi.org/10.1371/journal.pone.0074178.s018", "https://dx.doi.org/10.1371/journal.pone.0074178.s019"], "stats"=>{"downloads"=>61, "page_views"=>21, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Bayesian_Parameter_Inference_by_Markov_Chain_Monte_Carlo_with_Hybrid_Fitness_Measures_Theory_and_Test_in_Apoptosis_Signal_Transduction_Network_/1004723", "title"=>"Bayesian Parameter Inference by Markov Chain Monte Carlo with Hybrid Fitness Measures: Theory and Test in Apoptosis Signal Transduction Network", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2013-09-27 11:03:19"}
• {"files"=>["https://ndownloader.figshare.com/files/1471297"], "description"=>"<p>The same as captions in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0074178#pone-0074178-g006\" target=\"_blank\">Figure 6</a>, except for green bars represent the used value in Legewie et al's study but not experimentally estimated.</p>", "links"=>[], "tags"=>["Biochemistry", "enzymology", "Enzyme kinetics", "enzymes", "cell biology", "Signal transduction", "cell signaling", "Signaling cascades", "Apoptotic signaling cascade", "Apoptotic signaling", "Molecular cell biology", "Computational biology", "systems biology", "mathematics", "Probability theory", "Bayes theorem", "Markov models", "probability", "distributions"], "article_id"=>1004708, "categories"=>["Biological Sciences"], "users"=>["Yohei Murakami", "Shoji Takada"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0074178.g008", "stats"=>{"downloads"=>0, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Marginal_probability_distributions_of_k_asso_X_AC9_/1004708", "title"=>"Marginal probability distributions of k_asso (X-AC9).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-09-27 11:03:19"}
• {"files"=>["https://ndownloader.figshare.com/files/1471294"], "description"=>"<p>(A) Schematic diagram of the model. Solid arrows represent mass flows. Dotted arrows represent enhancement of the processes. One-way arrows between components represent irreversible processes. Two-way arrows between components represent reversible processes. Apaf-1 “A” is an input stimulus, and activated caspase-3 “C3*” is an output. Abbreviations are as follows: A: Apaf-1, C9: caspase-9, C3: caspse-3, X: XIAP. (B) Simplified diagram of the apoptosis signal transduction network at cytoplasm. Arrows represent activations. Lines with horizontal bar represent inhibition by binding and sequestering. Red colored interactions are implicit positive feedbacks. (C) Bifurcation diagram of the model. Red colored lines indicate stable steady states and the blue colored line indicates unstable steady state with the set of kinetic parameters used in Legewie et al's study. “A_0.001”, “A₂” and “A₂₀” indicate the Apaf-1 concentrations (Apaf-1  =  0.001, 2.0, 20.0 respectively) used as the conditions to infer kinetic parameters. (D) Time series of active caspase-3 (C3*) with kinetic parameters used in Legewie et al's study. T_s represents “switching time of caspase-3 activation”. T_e represents “execution time of caspase-3 activation”. (E) Assumed function of switching time of caspase-3 activation. (F) Assumed function of execution time of caspase-3 activation.</p>", "links"=>[], "tags"=>["Biochemistry", "enzymology", "Enzyme kinetics", "enzymes", "cell biology", "Signal transduction", "cell signaling", "Signaling cascades", "Apoptotic signaling cascade", "Apoptotic signaling", "Molecular cell biology", "Computational biology", "systems biology", "mathematics", "Probability theory", "Bayes theorem", "Markov models", "apoptosis", "transduction"], "article_id"=>1004705, "categories"=>["Biological Sciences"], "users"=>["Yohei Murakami", "Shoji Takada"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0074178.g005", "stats"=>{"downloads"=>1, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Mathematical_model_of_the_apoptosis_signal_transduction_network_/1004705", "title"=>"Mathematical model of the apoptosis signal transduction network.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-09-27 11:03:19"}
• {"files"=>["https://ndownloader.figshare.com/files/1471292"], "description"=>"<p>Probability distributions with “BI” (A), those with “BIT_e” (B), those with “BI[Y]_{time = 100}” (C), those with “BIT_e[Y]_{time = 100}” (D) and those with ”BIT_e[Y]_{time = 100}” with weaker noise in quantitative fitness (E). Red bars represent the “true” values or parameters. Red arrows indicate the modes.</p>", "links"=>[], "tags"=>["Biochemistry", "enzymology", "Enzyme kinetics", "enzymes", "cell biology", "Signal transduction", "cell signaling", "Signaling cascades", "Apoptotic signaling cascade", "Apoptotic signaling", "Molecular cell biology", "Computational biology", "systems biology", "mathematics", "Probability theory", "Bayes theorem", "Markov models", "probability", "distributions", "kinetic"], "article_id"=>1004703, "categories"=>["Biological Sciences"], "users"=>["Yohei Murakami", "Shoji Takada"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0074178.g003", "stats"=>{"downloads"=>0, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Marginal_probability_distributions_of_parameters_in_the_kinetic_toy_model_/1004703", "title"=>"Marginal probability distributions of parameters in the kinetic toy model.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-09-27 11:03:19"}

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Relative Metric

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F1000Prime