Using Likelihood-Free Inference to Compare Evolutionary Dynamics of the Protein Networks of H. pylori and P. falciparum
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{"title"=>"Using likelihood-free inference to compare evolutionary dynamics of the protein networks of H. pylori and P. falciparum", "type"=>"journal", "authors"=>[{"first_name"=>"Oliver", "last_name"=>"Ratmann", "scopus_author_id"=>"23052436300"}, {"first_name"=>"Ole", "last_name"=>"Jørgensen", "scopus_author_id"=>"57197628743"}, {"first_name"=>"Trevor", "last_name"=>"Hinkley", "scopus_author_id"=>"23050628100"}, {"first_name"=>"Michael", "last_name"=>"Stumpf", "scopus_author_id"=>"7006271146"}, {"first_name"=>"Sylvia", "last_name"=>"Richardson", "scopus_author_id"=>"7202589117"}, {"first_name"=>"Carsten", "last_name"=>"Wiuf", "scopus_author_id"=>"7003496015"}], "year"=>2007, "source"=>"PLoS Computational Biology", "identifiers"=>{"scopus"=>"2-s2.0-36949017519", "pui"=>"350241950", "pmid"=>"18052538", "issn"=>"1553734X", "isbn"=>"1553-7358 (Electronic)\\r1553-734X (Linking)", "doi"=>"10.1371/journal.pcbi.0030230", "sgr"=>"36949017519"}, "id"=>"bee3f083-e5bf-32fc-9835-a380ead88333", "abstract"=>"Gene duplication with subsequent interaction divergence is one of the primary driving forces in the evolution of genetic systems. Yet little is known about the precise mechanisms and the role of duplication divergence in the evolution of protein networks from the prokaryote and eukaryote domains. We developed a novel, model-based approach for Bayesian inference on biological network data that centres on approximate Bayesian computation, or likelihood-free inference. Instead of computing the intractable likelihood of the protein network topology, our method summarizes key features of the network and, based on these, uses a MCMC algorithm to approximate the posterior distribution of the model parameters. This allowed us to reliably fit a flexible mixture model that captures hallmarks of evolution by gene duplication and subfunctionalization to protein interaction network data of Helicobacter pylori and Plasmodium falciparum. The 80% credible intervals for the duplication-divergence component are [0.64, 0.98] for H. pylori and [0.87, 0.99] for P. falciparum. The remaining parameter estimates are not inconsistent with sequence data. An extensive sensitivity analysis showed that incompleteness of PIN data does not largely affect the analysis of models of protein network evolution, and that the degree sequence alone barely captures the evolutionary footprints of protein networks relative to other statistics. Our likelihood-free inference approach enables a fully Bayesian analysis of a complex and highly stochastic system that is otherwise intractable at present. Modelling the evolutionary history of PIN data, it transpires that only the simultaneous analysis of several global aspects of protein networks enables credible and consistent inference to be made from available datasets. Our results indicate that gene duplication has played a larger part in the network evolution of the eukaryote than in the prokaryote, and suggests that single gene duplications with immediate divergence alone may explain more than 60% of biological network data in both domains.", "link"=>"http://www.mendeley.com/research/using-likelihoodfree-inference-compare-evolutionary-dynamics-protein-networks-h-pylori-p-falciparum", "reader_count"=>76, "reader_count_by_academic_status"=>{"Professor > Associate Professor"=>10, "Researcher"=>29, "Student > Doctoral Student"=>1, "Student > Ph. D. Student"=>16, "Other"=>2, "Student > Master"=>10, "Lecturer"=>2, "Professor"=>6}, "reader_count_by_user_role"=>{"Professor > Associate Professor"=>10, "Researcher"=>29, "Student > Doctoral Student"=>1, "Student > Ph. D. Student"=>16, "Other"=>2, "Student > Master"=>10, "Lecturer"=>2, "Professor"=>6}, "reader_count_by_subject_area"=>{"Unspecified"=>4, "Engineering"=>3, "Environmental Science"=>2, "Biochemistry, Genetics and Molecular Biology"=>3, "Mathematics"=>11, "Agricultural and Biological Sciences"=>40, "Medicine and Dentistry"=>3, "Physics and Astronomy"=>2, "Computer Science"=>8}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>3}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>3}, "Physics and Astronomy"=>{"Physics and Astronomy"=>2}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>40}, "Computer Science"=>{"Computer Science"=>8}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>3}, "Mathematics"=>{"Mathematics"=>11}, "Unspecified"=>{"Unspecified"=>4}, "Environmental Science"=>{"Environmental Science"=>2}}, "reader_count_by_country"=>{"Czech Republic"=>1, "United States"=>6, "Brazil"=>1, "United Kingdom"=>4, "France"=>1, "Kenya"=>1, "Switzerland"=>2}, "group_count"=>2}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/941232"], "description"=>"<div><p>(A–C) The 2D histograms of the posterior parameters to the H. pylori PIN dataset, obtained from LFI based on WR + DIA + CC + \n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t + FRAG. Posterior mass clearly centers on a tight cloud in parameter space.\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t</p><p>(D–F) For comparison, we ran LFI based on ND alone, adjusted to yield a similar empirical acceptance probability. Although <i>ɛ</i><sub>min</sub> could be chosen stringently, the 2D histograms are diffuse. The regions of highest posterior density of LFI using ND are inconsistent with those of LFI using WR + DIA + CC + \n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t + FRAG.\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t</p></div>", "links"=>[], "tags"=>["inference", "lfi", "summaries"], "article_id"=>611651, "categories"=>["Mathematics", "Biological Sciences", "Evolutionary Biology"], "users"=>["Oliver Ratmann", "Ole Jørgensen", "Trevor Hinkley", "Michael Stumpf", "Sylvia Richardson", "Carsten Wiuf"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.0030230.g004", "stats"=>{"downloads"=>0, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Comparison_of_Inference_with_LFI_Using_One_versus_Four_Summaries_for_the_H_pylori_PIN_Data_/611651", "title"=>"Comparison of Inference with LFI Using One versus Four Summaries for the H. pylori PIN Data", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2007-11-30 00:27:31"}
  • {"files"=>["https://ndownloader.figshare.com/files/941559"], "description"=>"<p>Randomly Growing Graphs</p>", "links"=>[], "tags"=>["Computational biology", "Evolutionary biology", "mathematics"], "article_id"=>611975, "categories"=>["Mathematics", "Biological Sciences", "Evolutionary Biology"], "users"=>["Oliver Ratmann", "Ole Jørgensen", "Trevor Hinkley", "Michael Stumpf", "Sylvia Richardson", "Carsten Wiuf"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.0030230.g007", "stats"=>{"downloads"=>1, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Randomly_Growing_Graphs_/611975", "title"=>"Randomly Growing Graphs", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2007-11-30 00:32:55"}
  • {"files"=>["https://ndownloader.figshare.com/files/463558", "https://ndownloader.figshare.com/files/463591", "https://ndownloader.figshare.com/files/463627", "https://ndownloader.figshare.com/files/463642", "https://ndownloader.figshare.com/files/463665"], "description"=>"<div><p>Gene duplication with subsequent interaction divergence is one of the primary driving forces in the evolution of genetic systems. Yet little is known about the precise mechanisms and the role of duplication divergence in the evolution of protein networks from the prokaryote and eukaryote domains. We developed a novel, model-based approach for Bayesian inference on biological network data that centres on approximate Bayesian computation, or likelihood-free inference. Instead of computing the intractable likelihood of the protein network topology, our method summarizes key features of the network and, based on these, uses a MCMC algorithm to approximate the posterior distribution of the model parameters. This allowed us to reliably fit a flexible mixture model that captures hallmarks of evolution by gene duplication and subfunctionalization to protein interaction network data of Helicobacter pylori and Plasmodium falciparum. The 80% credible intervals for the duplication–divergence component are [0.64, 0.98] for H. pylori and [0.87, 0.99] for P. falciparum. The remaining parameter estimates are not inconsistent with sequence data. An extensive sensitivity analysis showed that incompleteness of PIN data does not largely affect the analysis of models of protein network evolution, and that the degree sequence alone barely captures the evolutionary footprints of protein networks relative to other statistics. Our likelihood-free inference approach enables a fully Bayesian analysis of a complex and highly stochastic system that is otherwise intractable at present. Modelling the evolutionary history of PIN data, it transpires that only the simultaneous analysis of several global aspects of protein networks enables credible and consistent inference to be made from available datasets. Our results indicate that gene duplication has played a larger part in the network evolution of the eukaryote than in the prokaryote, and suggests that single gene duplications with immediate divergence alone may explain more than 60% of biological network data in both domains.</p></div>", "links"=>[], "tags"=>["likelihood-free", "inference", "evolutionary", "networks"], "article_id"=>151367, "categories"=>["Mathematics", "Biological Sciences", "Evolutionary Biology"], "users"=>["Oliver Ratmann", "Ole Jørgensen", "Trevor Hinkley", "Michael Stumpf", "Sylvia Richardson", "Carsten Wiuf"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.0030230.sg001", "https://dx.doi.org/10.1371/journal.pcbi.0030230.sg002", "https://dx.doi.org/10.1371/journal.pcbi.0030230.sg003", "https://dx.doi.org/10.1371/journal.pcbi.0030230.sg004", "https://dx.doi.org/10.1371/journal.pcbi.0030230.sd001"], "stats"=>{"downloads"=>16, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/Using_Likelihood_Free_Inference_to_Compare_Evolutionary_Dynamics_of_the_Protein_Networks_of_H_pylori_and_P_falciparum_/151367", "title"=>"Using Likelihood-Free Inference to Compare Evolutionary Dynamics of the Protein Networks of H. pylori and P. falciparum", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2007-11-30 00:22:47"}
  • {"files"=>["https://ndownloader.figshare.com/files/941497"], "description"=>"<p>For increasingly incomplete PIN datasets of P. falciparum, four MCMC chains were run for 75,000 iterations according to LFI based on WR + DIA + CC + \n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t + FRAG. We present the marginal posterior densities of the mixture parameter <i>α</i> for two PIN datasets: (A) LFI on four random subsets of order 900 for <i>ρ</i> = 0.17 of the P. falciparum PIN dataset (each corresponding to one Markov chain), and (B) LFI on the full P. falciparum PIN dataset for <i>ρ</i> = 0.24. The chains were tempered to the minimal threshold values before iteration 800, and converged well onto posterior support. After iteration 800, the chains were taken to represent samples from the posterior, which produced the displayed kernel density estimate. Although LFI is sensitive to the randomly withheld data points, the estimated posteriors of each chain in (A) largely agree with the posterior on the full dataset. This indicates that randomly omitting 500 proteins does not seriously affect algorithm LFI.\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t</p>", "links"=>[], "tags"=>["incompleteness"], "article_id"=>611916, "categories"=>["Mathematics", "Biological Sciences", "Evolutionary Biology"], "users"=>["Oliver Ratmann", "Ole Jørgensen", "Trevor Hinkley", "Michael Stumpf", "Sylvia Richardson", "Carsten Wiuf"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.0030230.g006", "stats"=>{"downloads"=>1, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_Effect_of_Increasing_Incompleteness_on_Summaries_/611916", "title"=>"The Effect of Increasing Incompleteness on Summaries", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2007-11-30 00:31:56"}
  • {"files"=>["https://ndownloader.figshare.com/files/940920"], "description"=>"<p>The standardized mean gradient smd is plotted as a function of <i>α.</i> Fifty networks corresponding to H. pylori (grown to 1,500 nodes and subsampled to 675) were generated as described in the text with <i>θ</i> ∈ [0.1, 0.7] × [0, 0.5] × [0.1, 0.6] in steps of 0.025; all mean summaries were computed for each <i>θ</i>. The marginal smd(α) is plotted for (A) summary statistics and (B) summary distributions. Together with cv in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0030230#pcbi-0030230-sg004\" target=\"_blank\">Figure S4</a>, smd characterizes the sensitivity and variability of single summary statistics on simulated data. All summaries except ND have smd not close to zero, whereas TRIA, FRAG, and CC are extremely variable. Results for the other two parameters are very similar (unpublished data). The range of CC was truncated for display purposes.</p>", "links"=>[], "tags"=>["summaries", "characterization"], "article_id"=>611343, "categories"=>["Mathematics", "Biological Sciences", "Evolutionary Biology"], "users"=>["Oliver Ratmann", "Ole Jørgensen", "Trevor Hinkley", "Michael Stumpf", "Sylvia Richardson", "Carsten Wiuf"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.0030230.g001", "stats"=>{"downloads"=>1, "page_views"=>1, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Choosing_Appropriate_Summaries_with_a_Characterization_of_Genuine_Change_/611343", "title"=>"Choosing Appropriate Summaries with a Characterization of Genuine Change", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2007-11-30 00:22:23"}
  • {"files"=>["https://ndownloader.figshare.com/files/941127"], "description"=>"<div><p>For the H. pylori PIN dataset, four MCMC chains were run for 75,000 iterations according to LFI based on the summaries WR + DIA + CC + \n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t + FRAG.\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t</p><p>(A) The four chains for the parameter <i>δ</i><sub>Div</sub> ∈ [0,1] over the first 30,000 iterations. During burn-in, the chains moved quickly from overdispersed starting values and converged toward the same narrow support. Before iteration 800 (vertical line), <i>ɛ</i> was cooled to the minimal temperature; thereafter, accepted parameters were recorded, representing samples from the approximate posterior (<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0030230#pcbi-0030230-e004\" target=\"_blank\">Equation 4</a>).</p><p>(B) Accepted parameters after convergence were pooled over the four chains and used to estimate the posterior density. For <i>δ</i><sub>Div</sub>, the marginal posterior is displayed (black line); in addition, posteriors were calculated for each chain and are overlaid, showing that the four sets of posterior samples overlapped well.</p></div>", "links"=>[], "tags"=>["Computational biology", "Evolutionary biology", "mathematics"], "article_id"=>611542, "categories"=>["Mathematics", "Biological Sciences", "Evolutionary Biology"], "users"=>["Oliver Ratmann", "Ole Jørgensen", "Trevor Hinkley", "Michael Stumpf", "Sylvia Richardson", "Carsten Wiuf"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.0030230.g003", "stats"=>{"downloads"=>2, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_LFI_on_the_H_pylori_PIN_/611542", "title"=>"LFI on the H. pylori PIN", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2007-11-30 00:25:42"}
  • {"files"=>["https://ndownloader.figshare.com/files/941020"], "description"=>"<div><p>To compare different distance functions on sets of summaries, we analyzed the two-dimensional posterior support of <i>θ</i> for the H. pylori PIN dataset.</p><p>(A) <i>α</i> versus <i>δ</i><sub>Div</sub> and (B) <i>α</i> versus <i>δ</i><sub>Att</sub>. Using LFI with the set of summaries WR + DIA + CC + \n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t + FRAG, we recorded after burn-in the accepted parameters when each mean summary differed from the observed summary within the respective thresholds <i>ɛ<sub>k</sub></i>,<sub>min</sub> (<i>d</i><sub>∩</sub>, red), and when the sum of these differences did not exceed the sum Σ<i><sub>k</sub>ɛ<sub>k</sub></i>,<sub>min</sub> of these thresholds (<i>d</i><sub>Σ</sub>, blue). In both cases, we used an average of shifted histograms to estimate the two-dimensional posterior support. When using <i>d</i><sub>∩</sub>, the posterior support was more restricted, prompting us to use <i>d</i><sub>∩</sub> in LFI.\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t</p></div>", "links"=>[], "tags"=>["functions"], "article_id"=>611439, "categories"=>["Mathematics", "Biological Sciences", "Evolutionary Biology"], "users"=>["Oliver Ratmann", "Ole Jørgensen", "Trevor Hinkley", "Michael Stumpf", "Sylvia Richardson", "Carsten Wiuf"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.0030230.g002", "stats"=>{"downloads"=>1, "page_views"=>1, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Comparing_Distance_Functions_on_a_Set_of_Summaries_/611439", "title"=>"Comparing Distance Functions on a Set of Summaries.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2007-11-30 00:23:59"}
  • {"files"=>["https://ndownloader.figshare.com/files/941392"], "description"=>"<div><p>(Left) posterior modes (5,636 and 43,835, dashed line and dot-dashed line, respectively) were consistent with the estimator presented in [<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0030230#pcbi-0030230-b022\" target=\"_blank\">22</a>] (6,082 and 45,940, respectively; black horizontal lines). The 80% credible interval of the predicted network size for the H. pylori PIN was [2,915, ,536], and the one for the P. falciparum PIN was [18,689, 84,205], illustrating the high variability in the posterior estimate, in particular when the sampling fraction is low (<i>ρ</i> = 0.45 and 0.24, respectively).</p><p>(Right) for the P. falciparum PIN, LFI was repeated using the same set of summaries at relaxed threshold values as indicated in the legend. For display purposes, the <i>y</i>-axis was magnified relative to the left figure. As expected, larger thresholds yielded less-confident approximations (<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0030230#pcbi-0030230-e004\" target=\"_blank\">Equation 4</a>).</p></div>", "links"=>[], "tags"=>["densities", "pins", "lfi", "wr", "dia", "cc"], "article_id"=>611806, "categories"=>["Mathematics", "Biological Sciences", "Evolutionary Biology"], "users"=>["Oliver Ratmann", "Ole Jørgensen", "Trevor Hinkley", "Michael Stumpf", "Sylvia Richardson", "Carsten Wiuf"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.0030230.g005", "stats"=>{"downloads"=>1, "page_views"=>10, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Posterior_Densities_of_the_Predicted_Network_Size_for_the_Complete_H_pylori_and_P_falciparum_PINs_with_LFI_Based_on_WR_DIA_CC_FRAG_/611806", "title"=>"Posterior Densities of the Predicted Network Size for the Complete <i>H. pylori</i> and <i>P. falciparum</i> PINs with LFI Based on WR + DIA + CC + + FRAG", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2007-11-30 00:30:06"}

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Relative Metric

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