Reconstruction of Network Evolutionary History from Extant Network Topology and Duplication History

Genome-wide protein-protein interaction (PPI) data are readily available thanks to recent breakthroughs in biotechnology. However, PPI networks of extant organisms are only snapshots of the network evolution. How to infer the whole evolution history becomes a challenging problem in computational biology. In this paper, we present a likelihood-based approach to inferring network evolution history from the topology of PPI networks and the duplication relationship among the paralogs. Simulations show that our approach outperforms the existing ones in terms of the accuracy of reconstruction. Moreover, the growth parameters of several real PPI networks estimated by our method are more consistent with the ones predicted in literature.Comment: 15 pages, 5 figures, submitted to ISBRA 201

Network Archaeology: Uncovering Ancient Networks from Present-day Interactions

Often questions arise about old or extinct networks. What proteins interacted in a long-extinct ancestor species of yeast? Who were the central players in the Last.fm social network 3 years ago? Our ability to answer such questions has been limited by the unavailability of past versions of networks. To overcome these limitations, we propose several algorithms for reconstructing a network's history of growth given only the network as it exists today and a generative model by which the network is believed to have evolved. Our likelihood-based method finds a probable previous state of the network by reversing the forward growth model. This approach retains node identities so that the history of individual nodes can be tracked. We apply these algorithms to uncover older, non-extant biological and social networks believed to have grown via several models, including duplication-mutation with complementarity, forest fire, and preferential attachment. Through experiments on both synthetic and real-world data, we find that our algorithms can estimate node arrival times, identify anchor nodes from which new nodes copy links, and can reveal significant features of networks that have long since disappeared.Comment: 16 pages, 10 figure

Algorithms for Visualizing Phylogenetic Networks

We study the problem of visualizing phylogenetic networks, which are extensions of the Tree of Life in biology. We use a space filling visualization method, called DAGmaps, in order to obtain clear visualizations using limited space. In this paper, we restrict our attention to galled trees and galled networks and present linear time algorithms for visualizing them as DAGmaps.Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016

A probabilistic model for gene content evolution with duplication, loss, and horizontal transfer

We introduce a Markov model for the evolution of a gene family along a phylogeny. The model includes parameters for the rates of horizontal gene transfer, gene duplication, and gene loss, in addition to branch lengths in the phylogeny. The likelihood for the changes in the size of a gene family across different organisms can be calculated in O(N+hM^2) time and O(N+M^2) space, where N is the number of organisms, $h$ is the height of the phylogeny, and M is the sum of family sizes. We apply the model to the evolution of gene content in Preoteobacteria using the gene families in the COG (Clusters of Orthologous Groups) database

Bayesian Inference for Duplication-Mutation with Complementarity Network Models

We observe an undirected graph $G$ without multiple edges and self-loops, which is to represent a protein-protein interaction (PPI) network. We assume that $G$ evolved under the duplication-mutation with complementarity (DMC) model from a seed graph, $G_0$, and we also observe the binary forest $\Gamma$ that represents the duplication history of $G$. A posterior density for the DMC model parameters is established, and we outline a sampling strategy by which one can perform Bayesian inference; that sampling strategy employs a particle marginal Metropolis-Hastings (PMMH) algorithm. We test our methodology on numerical examples to demonstrate a high accuracy and precision in the inference of the DMC model's mutation and homodimerization parameters

Uniqueness, intractability and exact algorithms: reflections on level-k phylogenetic networks

Phylogenetic networks provide a way to describe and visualize evolutionary histories that have undergone so-called reticulate evolutionary events such as recombination, hybridization or horizontal gene transfer. The level k of a network determines how non-treelike the evolution can be, with level-0 networks being trees. We study the problem of constructing level-k phylogenetic networks from triplets, i.e. phylogenetic trees for three leaves (taxa). We give, for each k, a level-k network that is uniquely defined by its triplets. We demonstrate the applicability of this result by using it to prove that (1) for all k of at least one it is NP-hard to construct a level-k network consistent with all input triplets, and (2) for all k it is NP-hard to construct a level-k network consistent with a maximum number of input triplets, even when the input is dense. As a response to this intractability we give an exact algorithm for constructing level-1 networks consistent with a maximum number of input triplets

Confounding factors in HGT detection: Statistical error, coalescent effects, and multiple solutions

Prokaryotic organisms share genetic material across species boundaries by means of a process known as horizontal gene transfer (HGT). This process has great significance for understanding prokaryotic genome diversification and unraveling their complexities. Phylogeny-based detection of HGT is one of the most commonly used methods for this task, and is based on the fundamental fact that HGT may cause gene trees to disagree with one another, as well as with the species phylogeny. Using these methods, we can compare gene and species trees, and infer a set of HGT events to reconcile the differences among these trees. In this paper, we address three factors that confound the detection of the true HGT events, including the donors and recipients of horizontally transferred genes. First, we study experimentally the effects of error in the estimated gene trees (statistical error) on the accuracy of inferred HGT events. Our results indicate that statistical error leads to overestimation of the number of HGT events, and that HGT detection methods should be designed with unresolved gene trees in mind. Second, we demonstrate, both theoretically and empirically, that based on topological comparison alone, the number of HGT scenarios that reconcile a pair of species/gene trees may be exponential. This number may be reduced when branch lengths in both trees are estimated correctly. This set of results implies that in the absence of additional biological information, and/or a biological model of how HGT occurs, multiple HGT scenarios must be sought, and efficient strategies for how to enumerate such solutions must be developed. Third, we address the issue of lineage sorting, how it confounds HGT detection, and how to incorporate it with HGT into a single stochastic framework that distinguishes between the two events by extending population genetics theories. This result is very important, particularly when analyzing closely related organisms, where coalescent effects may not be ignored when reconciling gene trees. In addition to these three confounding factors, we consider the problem of enumerating all valid coalescent scenarios that constitute plausible species/gene tree reconciliations, and develop a polynomial-time dynamic programming algorithm for solving it. This result bears great significance on reducing the search space for heuristics that seek reconciliation scenarios. Finally, we show, empirically, that the locality of incongruence between a pair of trees has an impact on the numbers of HGT and coalescent reconciliation scenarios