Nataša Pržulj

Protein complex prediction via cost-based clustering

MOTIVATION Understanding principles of cellular organization and function can be enhanced if we detect known and predict still undiscovered protein complexes within the cells protein-protein interaction (PPI) network. Such predictions may be used as an inexpensive tool to direct biological experiments. The increasing amount of available PPI data necessitates an accurate and scalable approach to protein complex identification. RESULTS We have developed the Restricted Neighborhood Search Clustering Algorithm (RNSC) to efficiently partition networks into clusters using a cost function. We applied this cost-based clustering algorithm to PPI networks of Saccharomyces cerevisiae, Drosophila melanogaster and Caenorhabditis elegans to identify and predict protein complexes. We have determined functional and graph-theoretic properties of true protein complexes from the MIPS database. Based on these properties, we defined filters to distinguish between identified network clusters and true protein complexes. CONCLUSIONS Our application of the cost-based clustering algorithm provides an accurate and scalable method of detecting and predicting protein complexes within a PPI network.

Modeling interactome: scale-free or geometric?

MOTIVATION Networks have been used to model many real-world phenomena to better understand the phenomena and to guide experiments in order to predict their behavior. Since incorrect models lead to incorrect predictions, it is vital to have as accurate a model as possible. As a result, new techniques and models for analyzing and modeling real-world networks have recently been introduced. RESULTS One example of large and complex networks involves protein-protein interaction (PPI) networks. We analyze PPI networks of yeast Saccharomyces cerevisiae and fruitfly Drosophila melanogaster using a newly introduced measure of local network structure as well as the standardly used measures of global network structure. We examine the fit of four different network models, including Erdos-Renyi, scale-free and geometric random network models, to these PPI networks with respect to the measures of local and global network structure. We demonstrate that the currently accepted scale-free model of PPI networks fails to fit the data in several respects and show that a random geometric model provides a much more accurate model of the PPI data. We hypothesize that only the noise in these networks is scale-free. CONCLUSIONS We systematically evaluate how well-different network models fit the PPI networks. We show that the structure of PPI networks is better modeled by a geometric random graph than by a scale-free model. SUPPLEMENTARY INFORMATION Supplementary information is available at http://www.cs.utoronto.ca/~juris/data/data/ppiGRG04/

Biological network comparison using graphlet degree distribution

Motivation: Analogous to biological sequence comparison, comparing cellular networks is an important problem that could provide insight into biological understanding and therapeutics. For technical reasons, comparing large networks is computationally infeasible, and thus heuristics, suchas thedegreedistribution, clusteringcoefficient, diameter, and relative graphlet frequency distribution have been sought. It is easy to demonstrate that two networks are different by simply showing a short list of properties in which they differ. It is much harder to show that two networks are similar, as it requires demonstrating their similarity in all of their exponentially many properties. Clearly, it is computationally prohibitive to analyze all network properties, but the larger the number of constraints we impose in determining network similarity, the more likely it is that the networks will truly be similar. Results:We introduce a new systematic measure of a network’s local structure that imposes a large number of similarity constraints on networks being compared. In particular, we generalize the degree distribution, which measures the number of nodes ‘touching’ k edges, into distributions measuring the number of nodes ‘touching’ k graphlets, where graphlets are small connected non-isomorphic subgraphs of a large network. Our new measure of network local structure consists of 73 graphlet degree distributions of graphlets with 2–5 nodes, but it is easily extendible to a greater number of constraints (i.e. graphlets), if necessary, and the extensions are limited only by the available CPU. Furthermore, we show a way to combine the 73 graphlet degree distributions into a network ‘agreement’ measure which is a number between 0 and 1, where 1 means that networks have identical distributions and 0means that they are far apart. Based on this new network agreement measure, we show that almost all of the 14 eukaryotic PPI networks, including human, resulting from various high-throughput experimental techniques, aswell as from curated databases, are better modeled by geometric random graphs than by Erdös–Rény, random scale-free, or Barabási–Albert scale-free networks. Availability: Software executables are available upon request. Contact: natasha@ics.uci.edu

Functional topology in a network of protein interactions

MOTIVATION The building blocks of biological networks are individual protein-protein interactions (PPIs). The cumulative PPI data set in Saccharomyces cerevisiae now exceeds 78 000. Studying the network of these interactions will provide valuable insight into the inner workings of cells. RESULTS We performed a systematic graph theory-based analysis of this PPI network to construct computational models for describing and predicting the properties of lethal mutations and proteins participating in genetic interactions, functional groups, protein complexes and signaling pathways. Our analysis suggests that lethal mutations are not only highly connected within the network, but they also satisfy an additional property: their removal causes a disruption in network structure. We also provide evidence for the existence of alternate paths that bypass viable proteins in PPI networks, while such paths do not exist for lethal mutations. In addition, we show that distinct functional classes of proteins have differing network properties. We also demonstrate a way to extract and iteratively predict protein complexes and signaling pathways. We evaluate the power of predictions by comparing them with a random model, and assess accuracy of predictions by analyzing their overlap with MIPS database. CONCLUSIONS Our models provide a means for understanding the complex wiring underlying cellular function, and enable us to predict essentiality, genetic interaction, function, protein complexes and cellular pathways. This analysis uncovers structure-function relationships observable in a large PPI network.

Uncovering Biological Network Function via Graphlet Degree Signatures

Motivation Proteins are essential macromolecules of life and thus understanding their function is of great importance. The number of functionally unclassified proteins is large even for simple and well studied organisms such as bakers yeast. Methods for determining protein function have shifted their focus from targeting specific proteins based solely on sequence homology to analyses of the entire proteome based on protein-protein interaction (PPI) networks. Since proteins interact to perform a certain function, analyzing structural properties of PPI networks may provide useful clues about the biological function of individual proteins, protein complexes they participate in, and even larger subcellular machines. Results We design a sensitive graph theoretic method for comparing local structures of node neighborhoods that demonstrates that in PPI networks, biological function of a node and its local network structure are closely related. The method summarizes a proteins local topology in a PPI network into the vector of graphlet degrees called the signature of the protein and computes the signature similarities between all protein pairs. We group topologically similar proteins under this measure in a PPI network and show that these protein groups belong to the same protein complexes, perform the same biological functions, are localized in the same subcellular compartments, and have the same tissue expressions. Moreover, we apply our technique on a proteome-scale network data and infer biological function of yet unclassified proteins demonstrating that our method can provide valuable guidelines for future experimental research such as disease protein prediction. Availability Data is available upon request.

Topological network alignment uncovers biological function and phylogeny

Sequence comparison and alignment has had an enormous impact on our understanding of evolution, biology and disease. Comparison and alignment of biological networks will probably have a similar impact. Existing network alignments use information external to the networks, such as sequence, because no good algorithm for purely topological alignment has yet been devised. In this paper, we present a novel algorithm based solely on network topology, that can be used to align any two networks. We apply it to biological networks to produce by far the most complete topological alignments of biological networks to date. We demonstrate that both species phylogeny and detailed biological function of individual proteins can be extracted from our alignments. Topology-based alignments have the potential to provide a completely new, independent source of phylogenetic information. Our alignment of the protein–protein interaction networks of two very different species—yeast and human—indicate that even distant species share a surprising amount of network topology, suggesting broad similarities in internal cellular wiring across all life on Earth.

Integrative network alignment reveals large regions of global network similarity in yeast and human

MOTIVATION High-throughput methods for detecting molecular interactions have produced large sets of biological network data with much more yet to come. Analogous to sequence alignment, efficient and reliable network alignment methods are expected to improve our understanding of biological systems. Unlike sequence alignment, network alignment is computationally intractable. Hence, devising efficient network alignment heuristics is currently a foremost challenge in computational biology. RESULTS We introduce a novel network alignment algorithm, called Matching-based Integrative GRAph ALigner (MI-GRAAL), which can integrate any number and type of similarity measures between network nodes (e.g. proteins), including, but not limited to, any topological network similarity measure, sequence similarity, functional similarity and structural similarity. Hence, we resolve the ties in similarity measures and find a combination of similarity measures yielding the largest contiguous (i.e. connected) and biologically sound alignments. MI-GRAAL exposes the largest functional, connected regions of protein-protein interaction (PPI) network similarity to date: surprisingly, it reveals that 77.7% of proteins in the bakers yeast high-confidence PPI network participate in such a subnetwork that is fully contained in the human high-confidence PPI network. This is the first demonstration that species as diverse as yeast and human contain so large, continuous regions of global network similarity. We apply MI-GRAALs alignments to predict functions of un-annotated proteins in yeast, human and bacteria validating our predictions in the literature. Furthermore, using network alignment scores for PPI networks of different herpes viruses, we reconstruct their phylogenetic relationship. This is the first time that phylogeny is exactly reconstructed from purely topological alignments of PPI networks. AVAILABILITY Supplementary files and MI-GRAAL executables: http://bio-nets.doc.ic.ac.uk/MI-GRAAL/.

Not all scale free networks are Born equal: the role of the seed graph in PPI network emulation

The (asymptotic) degree distributions of the best-known “scale-free” network models are all similar and are independent of the seed graph used; hence, it has been tempting to assume that networks generated by these models are generally similar. In this paper, we observe that several key topological features of such networks depend heavily on the specific model and the seed graph used. Furthermore, we show that starting with the “right” seed graph (typically a dense subgraph of the protein–protein interaction network analyzed), the duplication model captures many topological features of publicly available protein–protein interaction networks very well.

Optimal Network Alignment with Graphlet Degree Vectors

Important biological information is encoded in the topology of biological networks. Comparative analyses of biological networks are proving to be valuable, as they can lead to transfer of knowledge between species and give deeper insights into biological function, disease, and evolution. We introduce a new method that uses the Hungarian algorithm to produce optimal global alignment between two networks using any cost function. We design a cost function based solely on network topology and use it in our network alignment. Our method can be applied to any two networks, not just biological ones, since it is based only on network topology. We use our new method to align protein-protein interaction networks of two eukaryotic species and demonstrate that our alignment exposes large and topologically complex regions of network similarity. At the same time, our alignment is biologically valid, since many of the aligned protein pairs perform the same biological function. From the alignment, we predict function of yet unannotated proteins, many of which we validate in the literature. Also, we apply our method to find topological similarities between metabolic networks of different species and build phylogenetic trees based on our network alignment score. The phylogenetic trees obtained in this way bear a striking resemblance to the ones obtained by sequence alignments. Our method detects topologically similar regions in large networks that are statistically significant. It does this independent of protein sequence or any other information external to network topology.

Fitting a geometric graph to a protein–protein interaction network

MOTIVATION Finding a good network null model for protein-protein interaction (PPI) networks is a fundamental issue. Such a model would provide insights into the interplay between network structure and biological function as well as into evolution. Also, network (graph) models are used to guide biological experiments and discover new biological features. It has been proposed that geometric random graphs are a good model for PPI networks. In a geometric random graph, nodes correspond to uniformly randomly distributed points in a metric space and edges (links) exist between pairs of nodes for which the corresponding points in the metric space are close enough according to some distance norm. Computational experiments have revealed close matches between key topological properties of PPI networks and geometric random graph models. In this work, we push the comparison further by exploiting the fact that the geometric property can be tested for directly. To this end, we develop an algorithm that takes PPI interaction data and embeds proteins into a low-dimensional Euclidean space, under the premise that connectivity information corresponds to Euclidean proximity, as in geometric-random graphs. We judge the sensitivity and specificity of the fit by computing the area under the Receiver Operator Characteristic (ROC) curve. The network embedding algorithm is based on multi-dimensional scaling, with the square root of the path length in a network playing the role of the Euclidean distance in the Euclidean space. The algorithm exploits sparsity for computational efficiency, and requires only a few sparse matrix multiplications, giving a complexity of O(N(2)) where N is the number of proteins. RESULTS The algorithm has been verified in the sense that it successfully rediscovers the geometric structure in artificially constructed geometric networks, even when noise is added by re-wiring some links. Applying the algorithm to 19 publicly available PPI networks of various organisms indicated that: (a) geometric effects are present and (b) two-dimensional Euclidean space is generally as effective as higher dimensional Euclidean space for explaining the connectivity. Testing on a high-confidence yeast data set produced a very strong indication of geometric structure (area under the ROC curve of 0.89), with this network being essentially indistinguishable from a noisy geometric network. Overall, the results add support to the hypothesis that PPI networks have a geometric structure. AVAILABILITY MATLAB code implementing the algorithm is available upon request.