Functional geometry of protein interactomes

Motivation Protein–protein interactions (PPIs) are usually modeled as networks. These networks have extensively been studied using graphlets, small induced subgraphs capturing the local wiring patterns around nodes in networks. They revealed that proteins involved in similar functions tend to be similarly wired. However, such simple models can only represent pairwise relationships and cannot fully capture the higher-order organization of protein interactomes, including protein complexes. Results To model the multi-scale organization of these complex biological systems, we utilize simplicial complexes from computational geometry. The question is how to mine these new representations of protein interactomes to reveal additional biological information. To address this, we define simplets, a generalization of graphlets to simplicial complexes. By using simplets, we define a sensitive measure of similarity between simplicial complex representations that allows for clustering them according to their data types better than clustering them by using other state-of-the-art measures, e.g. spectral distance, or facet distribution distance. We model human and baker’s yeast protein interactomes as simplicial complexes that capture PPIs and protein complexes as simplices. On these models, we show that our newly introduced simplet-based methods cluster proteins by function better than the clustering methods that use the standard PPI networks, uncovering the new underlying functional organization of the cell. We demonstrate the existence of the functional geometry in the protein interactome data and the superiority of our simplet-based methods to effectively mine for new biological information hidden in the complexity of the higher-order organization of protein interactomes.This work was supported by the European Research Council (ERC) Starting Independent Researcher Grant 278212, the European Research Council (ERC) Consolidator Grant 770827, the Serbian Ministry of Education and Science Project III44006, the Slovenian Research Agency project J1-8155 and the awards to establish the Farr Institute of Health Informatics Research, London, from the Medical Research Council, Arthritis Research UK, British Heart Foundation, Cancer Research UK, Chief Scientist Office, Economic and Social Research Council, Engineering and Physical Sciences Research Council, National Institute for Health Research, National Institute for Social Care and Health Research, and Wellcome Trust (grant MR/K006584/1).Peer ReviewedPostprint (author's final draft

Omics Data Fusion for Understanding Molecular Complexity Enabling Precision Medicine

We are flooded by increasing volumes of heterogeneous, interconnected, systems-level, molecular (multi-omic) data. They provide complementary information about cells, tissues and diseases. We need to utilize them to better stratify patients into risk groups, discover new biomarkers, and repurpose known and discover new drugs to personalize medical treatment. This is nontrivial, because of computational intractability of many underlying problems, necessitating the development of algorithms for finding approximate solutions (heuristics). We develop a versatile data fusion (integration) machine learning (ML) framework to address key challenges in precision medicine from these data: better stratification of patients, prediction of biomarkers, and re-purposing of approved drugs to particular patient groups, applied to cancer, Covid-19, rare thrombophilia and Parkinson’s Disease. Our new methods stem from graph-regularized non-negative matrix tri-factorization (NMTF), a machine learning technique for dimensionality reduction, inference and coclustering of heterogeneous datasets, coupled with novel network science algorithms. We utilize our new framework to develop methodologies for improving the understanding the molecular organization and disease from the omics data embedding space.Book of abstract: 4th Belgrade Bioinformatics Conference, June 19-23, 202

GraphCrunch: A tool for large network analyses

<p>Abstract</p> <p>Background</p> <p>The recent explosion in biological and other real-world network data has created the need for improved tools for large network analyses. In addition to well established <it>global </it>network properties, several new mathematical techniques for analyzing <it>local </it>structural properties of large networks have been developed. Small over-represented subgraphs, called network <it>motifs</it>, have been introduced to identify simple building blocks of complex networks. Small induced subgraphs, called <it>graphlets</it>, have been used to develop "network signatures" that summarize network topologies. Based on these network signatures, two new highly sensitive measures of network local structural similarities were designed: the <it>relative graphlet frequency distance </it>(<it>RGF-distance</it>) and the <it>graphlet degree distribution agreement </it>(<it>GDD-agreement</it>).</p> <p>Finding adequate null-models for biological networks is important in many research domains. Network properties are used to assess the fit of network models to the data. Various network models have been proposed. To date, there does not exist a software tool that measures the above mentioned local network properties. Moreover, none of the existing tools compare real-world networks against a series of network models with respect to these local as well as a multitude of global network properties.</p> <p>Results</p> <p>Thus, we introduce GraphCrunch, a software tool that finds well-fitting network models by comparing large real-world networks against random graph models according to various network structural similarity measures. It has unique capabilities of finding computationally expensive RGF-distance and GDD-agreement measures. In addition, it computes several standard global network measures and thus supports the largest variety of network measures thus far. Also, it is the first software tool that compares real-world networks against a series of network models and that has built-in parallel computing capabilities allowing for a user specified list of machines on which to perform compute intensive searches for local network properties. Furthermore, GraphCrunch is easily extendible to include additional network measures and models.</p> <p>Conclusion</p> <p>GraphCrunch is a software tool that implements the latest research on biological network models and properties: it compares real-world networks against a series of random graph models with respect to a multitude of local and global network properties. We present GraphCrunch as a comprehensive, parallelizable, and easily extendible software tool for analyzing and modeling large biological networks. The software is open-source and freely available at <url>http://www.ics.uci.edu/~bio-nets/graphcrunch/</url>. It runs under Linux, MacOS, and Windows Cygwin. In addition, it has an easy to use on-line web user interface that is available from the above web page.</p

GraphCrunch 2: Software tool for network modeling, alignment and clustering

<p>Abstract</p> <p>Background</p> <p>Recent advancements in experimental biotechnology have produced large amounts of protein-protein interaction (PPI) data. The topology of PPI networks is believed to have a strong link to their function. Hence, the abundance of PPI data for many organisms stimulates the development of computational techniques for the modeling, comparison, alignment, and clustering of networks. In addition, finding representative models for PPI networks will improve our understanding of the cell just as a model of gravity has helped us understand planetary motion. To decide if a model is representative, we need quantitative comparisons of model networks to real ones. However, exact network comparison is computationally intractable and therefore several heuristics have been used instead. Some of these heuristics are easily computable "network properties," such as the degree distribution, or the clustering coefficient. An important special case of network comparison is the network alignment problem. Analogous to sequence alignment, this problem asks to find the "best" mapping between regions in two networks. It is expected that network alignment might have as strong an impact on our understanding of biology as sequence alignment has had. Topology-based clustering of nodes in PPI networks is another example of an important network analysis problem that can uncover relationships between interaction patterns and phenotype.</p> <p>Results</p> <p>We introduce the GraphCrunch 2 software tool, which addresses these problems. It is a significant extension of GraphCrunch which implements the most popular random network models and compares them with the data networks with respect to many network properties. Also, GraphCrunch 2 implements the GRAph ALigner algorithm ("GRAAL") for purely topological network alignment. GRAAL can align any pair of networks and exposes large, dense, contiguous regions of topological and functional similarities far larger than any other existing tool. Finally, GraphCruch 2 implements an algorithm for clustering nodes within a network based solely on their topological similarities. Using GraphCrunch 2, we demonstrate that eukaryotic and viral PPI networks may belong to different graph model families and show that topology-based clustering can reveal important functional similarities between proteins within yeast and human PPI networks.</p> <p>Conclusions</p> <p>GraphCrunch 2 is a software tool that implements the latest research on biological network analysis. It parallelizes computationally intensive tasks to fully utilize the potential of modern multi-core CPUs. It is open-source and freely available for research use. It runs under the Windows and Linux platforms.</p

Dominating Biological Networks

Proteins are essential macromolecules of life that carry out most cellular processes. Since proteins aggregate to perform function, and since protein-protein interaction (PPI) networks model these aggregations, one would expect to uncover new biology from PPI network topology. Hence, using PPI networks to predict protein function and role of protein pathways in disease has received attention. A debate remains open about whether network properties of “biologically central (BC)” genes (i.e., their protein products), such as those involved in aging, cancer, infectious diseases, or signaling and drug-targeted pathways, exhibit some topological centrality compared to the rest of the proteins in the human PPI network

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

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(N2) where N is the number of proteins.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

Optimized Null Model for Protein Structure Networks

Much attention has recently been given to the statistical significance of topological features observed in biological networks. Here, we consider residue interaction graphs (RIGs) as network representations of protein structures with residues as nodes and inter-residue interactions as edges. Degree-preserving randomized models have been widely used for this purpose in biomolecular networks. However, such a single summary statistic of a network may not be detailed enough to capture the complex topological characteristics of protein structures and their network counterparts. Here, we investigate a variety of topological properties of RIGs to find a well fitting network null model for them. The RIGs are derived from a structurally diverse protein data set at various distance cut-offs and for different groups of interacting atoms. We compare the network structure of RIGs to several random graph models. We show that 3-dimensional geometric random graphs, that model spatial relationships between objects, provide the best fit to RIGs. We investigate the relationship between the strength of the fit and various protein structural features. We show that the fit depends on protein size, structural class, and thermostability, but not on quaternary structure. We apply our model to the identification of significantly over-represented structural building blocks, i.e., network motifs, in protein structure networks. As expected, choosing geometric graphs as a null model results in the most specific identification of motifs. Our geometric random graph model may facilitate further graph-based studies of protein conformation space and have important implications for protein structure comparison and prediction. The choice of a well-fitting null model is crucial for finding structural motifs that play an important role in protein folding, stability and function. To our knowledge, this is the first study that addresses the challenge of finding an optimized null model for RIGs, by comparing various RIG definitions against a series of network models

Fitting a geometric graph to a protein-protein interaction network

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(N2) where N is the number of proteins.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