Modularity in the evolution of yeast protein interaction network

Protein interaction networks are known to exhibit remarkable structures: scale-free and small-world and modular structures. To explain the evolutionary processes of protein interaction networks possessing scale-free and small-world structures, preferential attachment and duplication-divergence models have been proposed as mathematical models. Protein interaction networks are also known to exhibit another remarkable structural characteristic, modular structure. How the protein interaction networks became to exhibit modularity in their evolution? Here, we propose a hypothesis of modularity in the evolution of yeast protein interaction network based on molecular evolutionary evidence. We assigned yeast proteins into six evolutionary ages by constructing a phylogenetic profile. We found that all the almost half of hub proteins are evolutionarily new. Examining the evolutionary processes of protein complexes, functional modules and topological modules, we also found that member proteins of these modules tend to appear in one or two evolutionary ages. Moreover, proteins in protein complexes and topological modules show significantly low evolutionary rates than those not in these modules. Our results suggest a hypothesis of modularity in the evolution of yeast protein interaction network as systems evolution.     

Analysis of feedback loops and robustness in network evolution based on Boolean models

Background  

Many biological networks such as protein-protein interaction networks, signaling networks, and metabolic networks have topological characteristics of a scale-free degree distribution. Preferential attachment has been considered as the most plausible evolutionary growth model to explain this topological property. Although various studies have been undertaken to investigate the structural characteristics of a network obtained using this growth model, its dynamical characteristics have received relatively less attention.     

Phylogenetic signal, evolutionary process, and rate

A recent advance in the phylogenetic comparative analysis of continuous traits has been explicit, model-based measurement of "phylogenetic signal" in data sets composed of observations collected from species related by a phylogenetic tree. Phylogenetic signal is a measure of the statistical dependence among species' trait values due to their phylogenetic relationships. Although phylogenetic signal is a measure of pattern (statistical dependence), there has nonetheless been a widespread propensity in the literature to attribute this pattern to aspects of the evolutionary process or rate. This may be due, in part, to the perception that high evolutionary rate necessarily results in low phylogenetic signal; and, conversely, that low evolutionary rate or stabilizing selection results in high phylogenetic signal (due to the resulting high resemblance between related species). In this study, we use individual-based numerical simulations on stochastic phylogenetic trees to clarify the relationship between phylogenetic signal, rate, and evolutionary process. Under the simplest model for quantitative trait evolution, homogeneous rate genetic drift, there is no relation between evolutionary rate and phylogenetic signal. For other circumstances, such as functional constraint, fluctuating selection, niche conservatism, and evolutionary heterogeneity, the relationship between process, rate, and phylogenetic signal is complex. For these reasons, we recommend against interpretations of evolutionary process or rate based on estimates of phylogenetic signal.     

Application of phylogenetic networks in evolutionary studies

The evolutionary history of a set of taxa is usually represented by a phylogenetic tree, and this model has greatly facilitated the discussion and testing of hypotheses. However, it is well known that more complex evolutionary scenarios are poorly described by such models. Further, even when evolution proceeds in a tree-like manner, analysis of the data may not be best served by using methods that enforce a tree structure but rather by a richer visualization of the data to evaluate its properties, at least as an essential first step. Thus, phylogenetic networks should be employed when reticulate events such as hybridization, horizontal gene transfer, recombination, or gene duplication and loss are believed to be involved, and, even in the absence of such events, phylogenetic networks have a useful role to play. This article reviews the terminology used for phylogenetic networks and covers both split networks and reticulate networks, how they are defined, and how they can be interpreted. Additionally, the article outlines the beginnings of a comprehensive statistical framework for applying split network methods. We show how split networks can represent confidence sets of trees and introduce a conservative statistical test for whether the conflicting signal in a network is treelike. Finally, this article describes a new program, SplitsTree4, an interactive and comprehensive tool for inferring different types of phylogenetic networks from sequences, distances, and trees.     

Discriminating Different Classes of Biological Networks by Analyzing the Graphs Spectra Distribution

The brain''s structural and functional systems, protein-protein interaction, and gene networks are examples of biological systems that share some features of complex networks, such as highly connected nodes, modularity, and small-world topology. Recent studies indicate that some pathologies present topological network alterations relative to norms seen in the general population. Therefore, methods to discriminate the processes that generate the different classes of networks (e.g., normal and disease) might be crucial for the diagnosis, prognosis, and treatment of the disease. It is known that several topological properties of a network (graph) can be described by the distribution of the spectrum of its adjacency matrix. Moreover, large networks generated by the same random process have the same spectrum distribution, allowing us to use it as a “fingerprint”. Based on this relationship, we introduce and propose the entropy of a graph spectrum to measure the “uncertainty” of a random graph and the Kullback-Leibler and Jensen-Shannon divergences between graph spectra to compare networks. We also introduce general methods for model selection and network model parameter estimation, as well as a statistical procedure to test the nullity of divergence between two classes of complex networks. Finally, we demonstrate the usefulness of the proposed methods by applying them to (1) protein-protein interaction networks of different species and (2) on networks derived from children diagnosed with Attention Deficit Hyperactivity Disorder (ADHD) and typically developing children. We conclude that scale-free networks best describe all the protein-protein interactions. Also, we show that our proposed measures succeeded in the identification of topological changes in the network while other commonly used measures (number of edges, clustering coefficient, average path length) failed.     

Detecting phylogenetic signal in mutualistic interaction networks using a Markov process model

Ecological interaction networks, such as those describing the mutualistic interactions between plants and their pollinators or between plants and their frugivores, exhibit non‐random structural properties that cannot be explained by simple models of network formation. One factor affecting the formation and eventual structure of such a network is its evolutionary history. We argue that this, in many cases, is closely linked to the evolutionary histories of the species involved in the interactions. Indeed, empirical studies of interaction networks along with the phylogenies of the interacting species have demonstrated significant associations between phylogeny and network structure. To date, however, no generative model explaining the way in which the evolution of individual species affects the evolution of interaction networks has been proposed. We present a model describing the evolution of pairwise interactions as a branching Markov process, drawing on phylogenetic models of molecular evolution. Using knowledge of the phylogenies of the interacting species, our model yielded a significantly better fit to 21% of a set of plant–pollinator and plant–frugivore mutualistic networks. This highlights the importance, in a substantial minority of cases, of inheritance of interaction patterns without excluding the potential role of ecological novelties in forming the current network architecture. We suggest that our model can be used as a null model for controlling evolutionary signals when evaluating the role of other factors in shaping the emergence of ecological networks.     

Parsimony Score of Phylogenetic Networks: Hardness Results and a Linear-Time Heuristic

Phylogenies—the evolutionary histories of groups of organisms—play a major role in representing the interrelationships among biological entities. Many methods for reconstructing and studying such phylogenies have been proposed, almost all of which assume that the underlying history of a given set of species can be represented by a binary tree. Although many biological processes can be effectively modeled and summarized in this fashion, others cannot: recombination, hybrid speciation, and horizontal gene transfer result in networks of relationships rather than trees of relationships. In previous works, we formulated a maximum parsimony (MP) criterion for reconstructing and evaluating phylogenetic networks, and demonstrated its quality on biological as well as synthetic data sets. In this paper, we provide further theoretical results as well as a very fast heuristic algorithm for the MP criterion of phylogenetic networks. In particular, we provide a novel combinatorial definition of phylogenetic networks in terms of “forbidden cycles,” and provide detailed hardness and hardness of approximation proofs for the "small” MP problem. We demonstrate the performance of our heuristic in terms of time and accuracy on both biological and synthetic data sets. Finally, we explain the difference between our model and a similar one formulated by Nguyen et al., and describe the implications of this difference on the hardness and approximation results.     

Maximum Parsimony on Phylogenetic networks

Background

Phylogenetic networks are generalizations of phylogenetic trees, that are used to model evolutionary events in various contexts. Several different methods and criteria have been introduced for reconstructing phylogenetic trees. Maximum Parsimony is a character-based approach that infers a phylogenetic tree by minimizing the total number of evolutionary steps required to explain a given set of data assigned on the leaves. Exact solutions for optimizing parsimony scores on phylogenetic trees have been introduced in the past.

Results

In this paper, we define the parsimony score on networks as the sum of the substitution costs along all the edges of the network; and show that certain well-known algorithms that calculate the optimum parsimony score on trees, such as Sankoff and Fitch algorithms extend naturally for networks, barring conflicting assignments at the reticulate vertices. We provide heuristics for finding the optimum parsimony scores on networks. Our algorithms can be applied for any cost matrix that may contain unequal substitution costs of transforming between different characters along different edges of the network. We analyzed this for experimental data on 10 leaves or fewer with at most 2 reticulations and found that for almost all networks, the bounds returned by the heuristics matched with the exhaustively determined optimum parsimony scores.

Conclusion

The parsimony score we define here does not directly reflect the cost of the best tree in the network that displays the evolution of the character. However, when searching for the most parsimonious network that describes a collection of characters, it becomes necessary to add additional cost considerations to prefer simpler structures, such as trees over networks. The parsimony score on a network that we describe here takes into account the substitution costs along the additional edges incident on each reticulate vertex, in addition to the substitution costs along the other edges which are common to all the branching patterns introduced by the reticulate vertices. Thus the score contains an in-built cost for the number of reticulate vertices in the network, and would provide a criterion that is comparable among all networks. Although the problem of finding the parsimony score on the network is believed to be computationally hard to solve, heuristics such as the ones described here would be beneficial in our efforts to find a most parsimonious network.     

Evolution at the system level: the natural history of protein interaction networks

Recent work leading to new insights into the molecular architecture underlying complex cellular phenotypes enables researchers to investigate evolutionary processes in unprecedented detail. Protein interaction network data, which are now available for an increasing number of species, promise new insights and there have been many recent studies investigating evolutionary aspects of these interaction networks, from mathematical studies of growing networks to detailed phylogenetic surveys of proteins in their interaction network context. Here, we review the spectrum of such approaches, and assess issues associated with analyzing such data from an evolutionary perspective. Currently, such analyses are statistically challenging, but could link present initiatives in systems biology with results and methodologies that have developed in evolutionary biology over the past 60 years.     

Comparison of Tree-Child Phylogenetic Networks

Phylogenetic networks are a generalization of phylogenetic trees that allow for the representation of nontreelike evolutionary events, like recombination, hybridization, or lateral gene transfer. While much progress has been made to find practical algorithms for reconstructing a phylogenetic network from a set of sequences, all attempts to endorse a class of phylogenetic networks (strictly extending the class of phylogenetic trees) with a well-founded distance measure have, to the best of our knowledge and with the only exception of the bipartition distance on regular networks, failed so far. In this paper, we present and study a new meaningful class of phylogenetic networks, called tree-child phylogenetic networks, and we provide an injective representation of these networks as multisets of vectors of natural numbers, their path multiplicity vectors. We then use this representation to define a distance on this class that extends the well-known Robinson-Foulds distance for phylogenetic trees and to give an alignment method for pairs of networks in this class. Simple polynomial algorithms for reconstructing a tree-child phylogenetic network from its path multiplicity vectors, for computing the distance between two tree-child phylogenetic networks and for aligning a pair of tree-child phylogenetic networks, are provided. They have been implemented as a Perl package and a Java applet, which can be found at http://bioinfo.uib.es/~recerca/phylonetworks/mudistance/.     

Reconstructing the evolutionary history of polyploids from multilabeled trees

In recent studies, phylogenetic networks have been derived from so-called multilabeled trees in order to understand the origins of certain polyploids. Although the trees used in these studies were constructed using sophisticated techniques in phylogenetic analysis, the presented networks were inferred using ad hoc arguments that cannot be easily extended to larger, more complicated examples. In this paper, we present a general method for constructing such networks, which takes as input a multilabeled phylogenetic tree and outputs a phylogenetic network with certain desirable properties. To illustrate the applicability of our method, we discuss its use in reconstructing the evolutionary history of plant allopolyploids. We conclude with a discussion concerning possible future directions. The network construction method has been implemented and is freely available for use from http://www.uea.ac.uk/ approximately a043878/padre.html.     

The probability of a gene tree topology within a phylogenetic network with applications to hybridization detection

Gene tree topologies have proven a powerful data source for various tasks, including species tree inference and species delimitation. Consequently, methods for computing probabilities of gene trees within species trees have been developed and widely used in probabilistic inference frameworks. All these methods assume an underlying multispecies coalescent model. However, when reticulate evolutionary events such as hybridization occur, these methods are inadequate, as they do not account for such events. Methods that account for both hybridization and deep coalescence in computing the probability of a gene tree topology currently exist for very limited cases. However, no such methods exist for general cases, owing primarily to the fact that it is currently unknown how to compute the probability of a gene tree topology within the branches of a phylogenetic network. Here we present a novel method for computing the probability of gene tree topologies on phylogenetic networks and demonstrate its application to the inference of hybridization in the presence of incomplete lineage sorting. We reanalyze a Saccharomyces species data set for which multiple analyses had converged on a species tree candidate. Using our method, though, we show that an evolutionary hypothesis involving hybridization in this group has better support than one of strict divergence. A similar reanalysis on a group of three Drosophila species shows that the data is consistent with hybridization. Further, using extensive simulation studies, we demonstrate the power of gene tree topologies at obtaining accurate estimates of branch lengths and hybridization probabilities of a given phylogenetic network. Finally, we discuss identifiability issues with detecting hybridization, particularly in cases that involve extinction or incomplete sampling of taxa.     

Testing for treeness: lateral gene transfer,phylogenetic inference,and model selection

A phylogeny that allows for lateral gene transfer (LGT) can be thought of as a strictly branching tree (all of whose branches are vertical) to which lateral branches have been added. Given that the goal of phylogenetics is to depict evolutionary history, we should look for the best supported phylogenetic network and not restrict ourselves to considering trees. However, the obvious extensions of popular tree-based methods such as maximum parsimony and maximum likelihood face a serious problem—if we judge networks by fit to data alone, networks that have lateral branches will always fit the data at least as well as any network that restricts itself to vertical branches. This is analogous to the well-studied problem of overfitting data in the curve-fitting problem. Analogous problems often have analogous solutions and we propose to treat network inference as a case of model selection and use the Akaike Information Criterion (AIC). Strictly tree-like networks are more parsimonious than those that postulate lateral as well as vertical branches. This leads to the conclusion that we should not always infer LGT events whenever it would improve our fit-to-data, but should do so only when the improved fit is larger than the penalty for adding extra lateral branches.     

Investigations into the relationship between feedback loops and functional importance of a signal transduction network based on Boolean network modeling

Background  

A number of studies on biological networks have been carried out to unravel the topological characteristics that can explain the functional importance of network nodes. For instance, connectivity, clustering coefficient, and shortest path length were previously proposed for this purpose. However, there is still a pressing need to investigate another topological measure that can better describe the functional importance of network nodes. In this respect, we considered a feedback loop which is ubiquitously found in various biological networks.     

Distinguishing terminal monophyletic groups from reticulate taxa: performance of phenetic, tree-based, and network procedures

Hybridization is a well-documented, natural phenomenon that is common at low taxonomic levels in the higher plants and other groups. In spite of the obvious potential for gene flow via hybridization to cause reticulation in an evolutionary tree, analytical methods based on a strictly bifurcating model of evolution have frequently been applied to data sets containing taxa known to hybridize in nature. Using simulated data, we evaluated the relative performance of phenetic, tree-based, and network approaches for distinguishing between taxa with known reticulate history and taxa that were true terminal monophyletic groups. In all methods examined, type I error (the erroneous rejection of the null hypothesis that a taxon of interest is not monophyletic) was likely during the early stages of introgressive hybridization. We used the gradual erosion of type I error with continued gene flow as a metric for assessing relative performance. Bifurcating tree-based methods performed poorly, with highly supported, incorrect topologies appearing during some phases of the simulation. Based on our model, we estimate that many thousands of gene flow events may be required in natural systems before reticulate taxa will be reliably detected using tree-based methods of phylogeny reconstruction. We conclude that the use of standard bifurcating tree-based methods to identify terminal monophyletic groups for the purposes of defining or delimiting phylogenetic species, or for prioritizing populations for conservation purposes, is difficult to justify when gene flow between sampled taxa is possible. As an alternative, we explored the use of two network methods. Minimum spanning networks performed worse than most tree-based methods and did not yield topologies that were easily interpretable as phylogenies. The performance of NeighborNet was comparable to parsimony bootstrap analysis. NeighborNet and reverse successive weighting were capable of identifying an ephemeral signature of reticulate evolution during the early stages of introgression by revealing conflicting phylogenetic signal. However, when gene flow was topologically complex, the conflicting phylogenetic signal revealed by these methods resulted in a high probability of type II error (inferring that a monophyletic taxon has a reticulate history). Lastly, we present a novel application of an existing nonparametric clustering procedure that, when used against a density landscape derived from principal coordinate data, showed superior performance to the tree-based and network procedures tested.     

An Adaptive Complex Network Model for Brain Functional Networks

Brain functional networks are graph representations of activity in the brain, where the vertices represent anatomical regions and the edges their functional connectivity. These networks present a robust small world topological structure, characterized by highly integrated modules connected sparsely by long range links. Recent studies showed that other topological properties such as the degree distribution and the presence (or absence) of a hierarchical structure are not robust, and show different intriguing behaviors. In order to understand the basic ingredients necessary for the emergence of these complex network structures we present an adaptive complex network model for human brain functional networks. The microscopic units of the model are dynamical nodes that represent active regions of the brain, whose interaction gives rise to complex network structures. The links between the nodes are chosen following an adaptive algorithm that establishes connections between dynamical elements with similar internal states. We show that the model is able to describe topological characteristics of human brain networks obtained from functional magnetic resonance imaging studies. In particular, when the dynamical rules of the model allow for integrated processing over the entire network scale-free non-hierarchical networks with well defined communities emerge. On the other hand, when the dynamical rules restrict the information to a local neighborhood, communities cluster together into larger ones, giving rise to a hierarchical structure, with a truncated power law degree distribution.     

Comparative bioacoustics: a roadmap for quantifying and comparing animal sounds across diverse taxa

Animals produce a wide array of sounds with highly variable acoustic structures. It is possible to understand the causes and consequences of this variation across taxa with phylogenetic comparative analyses. Acoustic and evolutionary analyses are rapidly increasing in sophistication such that choosing appropriate acoustic and evolutionary approaches is increasingly difficult. However, the correct choice of analysis can have profound effects on output and evolutionary inferences. Here, we identify and address some of the challenges for this growing field by providing a roadmap for quantifying and comparing sound in a phylogenetic context for researchers with a broad range of scientific backgrounds. Sound, as a continuous, multidimensional trait can be particularly challenging to measure because it can be hard to identify variables that can be compared across taxa and it is also no small feat to process and analyse the resulting high-dimensional acoustic data using approaches that are appropriate for subsequent evolutionary analysis. Additionally, terminological inconsistencies and the role of learning in the development of acoustic traits need to be considered. Phylogenetic comparative analyses also have their own sets of caveats to consider. We provide a set of recommendations for delimiting acoustic signals into discrete, comparable acoustic units. We also present a three-stage workflow for extracting relevant acoustic data, including options for multivariate analyses and dimensionality reduction that is compatible with phylogenetic comparative analysis. We then summarize available phylogenetic comparative approaches and how they have been used in comparative bioacoustics, and address the limitations of comparative analyses with behavioural data. Lastly, we recommend how to apply these methods to acoustic data across a range of study systems. In this way, we provide an integrated framework to aid in quantitative analysis of cross-taxa variation in animal sounds for comparative phylogenetic analysis. In addition, we advocate the standardization of acoustic terminology across disciplines and taxa, adoption of automated methods for acoustic feature extraction, and establishment of strong data archival practices for acoustic recordings and data analyses. Combining such practices with our proposed workflow will greatly advance the reproducibility, biological interpretation, and longevity of comparative bioacoustic studies.     

Exploring phylogenetic hypotheses via Gibbs sampling on evolutionary networks

Background

Phylogenetic networks are leaf-labeled graphs used to model and display complex evolutionary relationships that do not fit a single tree. There are two classes of phylogenetic networks: Data-display networks and evolutionary networks. While data-display networks are very commonly used to explore data, they are not amenable to incorporating probabilistic models of gene and genome evolution. Evolutionary networks, on the other hand, can accommodate such probabilistic models, but they are not commonly used for exploration.

Results

In this work, we show how to turn evolutionary networks into a tool for statistical exploration of phylogenetic hypotheses via a novel application of Gibbs sampling. We demonstrate the utility of our work on two recently available genomic data sets, one from a group of mosquitos and the other from a group of modern birds. We demonstrate that our method allows the use of evolutionary networks not only for explicit modeling of reticulate evolutionary histories, but also for exploring conflicting treelike hypotheses. We further demonstrate the performance of the method on simulated data sets, where the true evolutionary histories are known.

Conclusion

We introduce an approach to explore phylogenetic hypotheses over evolutionary phylogenetic networks using Gibbs sampling. The hypotheses could involve reticulate and non-reticulate evolutionary processes simultaneously as we illustrate on mosquito and modern bird genomic data sets.