A stochastic model for the evolution of metabolic networks with neighbor dependence

Abstract

Most current research in network evolution focuses on networks that follow a Duplication Attachment model where the network is only allowed to grow. The evolution of metabolic networks, however, is characterized by gain as well as loss of reactions. It would be desirable to have a biologically relevant model of network evolution that could be used to calculate the likelihood of homologous metabolic networks. We describe metabolic network evolution as a discrete space continuous time Markov process and introduce a neighbor-dependent model for the evolution of metabolic networks where the rates with which reactions are added or removed depend on the fraction of neighboring reactions present in the network. We also present a Gibbs sampler for estimating the parameters of evolution without exploring the whole search space by iteratively sampling from the conditional distributions of the paths and parameters. A Metropolis-Hastings algorithm for sampling paths between two networks and calculating the likelihood of evolution is also presented. The sampler is used to estimate the parameters of evolution of metabolic networks in the genus Pseudomonas. An implementation of the Gibbs sampler in Java is available at http://www.stats.ox.ac.uk/ approximately mithani/networkGibbs/. Supplementary data are available at the Bioinformatics online.