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Using Likelihood-Free Inference to Compare Evolutionary Dynamics of the Protein Networks of H. pylori and P. falciparum

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      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.

      Author Summary

      The importance of gene duplication to biological evolution has been recognized since the 1930s. For more than a decade, substantial evidence has been collected from genomic sequence data in order to elucidate the importance and the mechanisms of gene duplication; however, most biological characteristics arise from complex interactions between the cell's numerous constituents. Recently, preliminary descriptions of the protein interaction networks have become available for species of different domains. Adapting novel techniques in stochastic simulation, the authors demonstrate that evolutionary inferences can be drawn from large-scale, incomplete network data by fitting a stochastic model of network growth that captures hallmarks of evolution by duplication and divergence. They have also analyzed the effect of summarizing protein networks in different ways, and show that a reliable and consistent analysis requires many aspects of network data to be considered jointly; in contrast to what is commonly done in practice. Their results indicate that duplication and divergence has played a larger role in the network evolution of the eukaryote P. falciparum than in the prokaryote H. pylori, and emphasize at least for the eukaryote the potential importance of subfunctionalization in network evolution.

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          The evolutionary fate and consequences of duplicate genes.

          Gene duplication has generally been viewed as a necessary source of material for the origin of evolutionary novelties, but it is unclear how often gene duplicates arise and how frequently they evolve new functions. Observations from the genomic databases for several eukaryotic species suggest that duplicate genes arise at a very high rate, on average 0.01 per gene per million years. Most duplicated genes experience a brief period of relaxed selection early in their history, with a moderate fraction of them evolving in an effectively neutral manner during this period. However, the vast majority of gene duplicates are silenced within a few million years, with the few survivors subsequently experiencing strong purifying selection. Although duplicate genes may only rarely evolve new functions, the stochastic silencing of such genes may play a significant role in the passive origin of new species.

            Author and article information

            [1 ] Department of Public Health and Epidemiology, Imperial College London, London, United Kingdom
            [2 ] Bioinformatics Research Center, University of Aarhus, Aarhus, Denmark
            [3 ] Institut für Integrative Biologie, ETH Zürich, Zürich, Switzerland
            [4 ] Theoretical Genomics Group, Centre for Bioinformatics, Division of Molecular Biosciences, Imperial College London, London, United Kingdom
            [5 ] Institute of Mathematical Sciences, Imperial College London, London, United Kingdom
            [6 ] Centre for Biostatistics, Imperial College London, London, United Kingdom
            [7 ] Molecular Diagnostic Laboratory, Aarhus University Hospital, Aarhus, Denmark
            ETH Zürich, Switzerland
            Author notes
            * To whom correspondence should be addressed. E-mail: oliver.ratmann@
            Role: Editor
            PLoS Comput Biol
            PLoS Computational Biology
            Public Library of Science (San Francisco, USA )
            November 2007
            30 November 2007
            9 October 2007
            : 3
            : 11
            07-PLCB-RA-0155R2 plcb-03-11-20
            Copyright: © 2007 Ratmann et al. 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: 13
            Research Article
            Computational Biology
            Evolutionary Biology
            Custom metadata
            Ratmann O, Jørgensen O, Hinkley T, Stumpf M, Richardson S, et al. (2007) Using likelihood-free inference to compare evolutionary dynamics of the protein networks of H. pylori and P. falciparum. PLoS Comput Biol 3(11): e230. doi: 10.1371/journal.pcbi.0030230

            Quantitative & Systems biology


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