Efficient estimation of graphlet frequency distributions in protein–protein interaction networks

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. 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. 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 is available at http://www.cs.utoronto.ca/~juris/data/data/ppiGRG04/

Advances in proteomic technologies combined with sophisticated computing and modeling methods have generated an unprecedented amount of high-throughput data for system-scale analysis. As a result, the study of protein-protein interaction (PPI) networks has garnered much attention in recent years. One of the most fundamental problems in studying PPI networks is to understand how their architecture originated and evolved to their current state. By investigating how proteins of different ages are connected in the yeast PPI networks, one can deduce their expansion procedure in evolution and how the ancient primitive network expanded and evolved. Studies have shown that proteins are often connected to other proteins of a similar age, suggesting a high degree of age preference between interacting proteins. Though several theories have been proposed to explain this phenomenon, none of them considered protein-clusters as a contributing factor. Here we first investigate the age-dependency of the proteins from the perspective of network motifs. Our analysis confirms that proteins of the same age groups tend to form interacting network motifs; furthermore, those proteins within motifs tend to be within protein complexes and the interactions among them largely contribute to the observed age preference in the yeast PPI networks. In light of these results, we describe a new modeling approach, based on "network motifs", whereby topologically connected protein clusters in the network are treated as single evolutionary units. Instead of modeling single proteins, our approach models the connections and evolutionary relationships of multiple related protein clusters or "network motifs" that are collectively integrated into an existing PPI network. Through simulation studies, we found that the "network motif" modeling approach can capture yeast PPI network properties better than if individual proteins were considered to be the simplest evolutionary units. Our approach provides a fresh perspective on modeling the evolution of yeast PPI networks, specifically that PPI networks may have a much higher age-dependency of interaction density than had been previously envisioned.

Identifying functional modules in protein-protein interaction (PPI) networks elucidates cellular organization and mechanism. Various methods have been proposed to identify the functional modules in PPI networks, but most of these methods do not consider the noisy links in PPI networks. They achieve a competitive performance on the PPI networks without noisy links, but the performance of these methods considerably deteriorates in the noisy PPI networks. Furthermore, the noisy links are inevitable in the PPI networks. In this paper, we propose a novel link-driven label propagation algorithm (LLPA) to identify functional modules in PPI networks. The LLPA first find link clusters in PPI networks, and then the functional modules are identified from the link clusters. Two strategies aimed to ensure the robustness of LLPA are proposed. One strategy involves the proposed LLPA updating the link labels in accordance with the designed weight of the link, which can reduce the incidence of noisy links. The other strategy involves the filtration of some noisy labels from the link clusters to further reduce the influence of noisy links. The performance evaluation on three real PPI networks shows that LLPA outperforms other eight state-of-the-art detection algorithms in terms of accuracy and robustness.

The Impact of Gene Expression Regulation on Evolution of Extracellular Signaling Pathways

Signal flow direction is one of the most important features of the protein-protein interactions in signaling networks. However, almost all the outcomes of current high-throughout techniques for protein-protein interactions mapping are usually supposed to be non-directional. Based on the pairwise interaction domains, here we defined a novel parameter protein interaction directional score and then used it to predict the direction of signal flow between proteins in proteome-wide signaling networks. Using 5-fold cross-validation, our approach obtained a satisfied performance with the accuracy 89.79%, coverage 48.08%, and error ratio 16.91%. As an application, we established an integrated human directional protein interaction network, including 2,237 proteins and 5,530 interactions, and inferred a large amount of novel signaling pathways. Directional protein interaction network was strongly supported by the known signaling pathways literature (with the 87.5% accuracy) and further analyses on the biological annotation, subcellular localization, and network topology property. Thus, this study provided an effective method to define the upstream/downstream relations of interacting protein pairs and a powerful tool to unravel the unknown signaling pathways.

Graph clustering algorithms are widely used in the analysis of biological networks. Extracting functional modules in protein-protein interaction (PPI) networks is one such use. Most clustering algorithms whose focuses are on finding functional modules try either to find a clique like sub networks or to grow clusters starting from vertices with high degrees as seeds. These algorithms do not make any difference between a biological network and any other networks. In the current research, we present a new procedure to find functional modules in PPI networks. Our main idea is to model a biological concept and to use this concept for finding good functional modules in PPI networks. In order to evaluate the quality of the obtained clusters, we compared the results of our algorithm with those of some other widely used clustering algorithms on three high throughput PPI networks from Sacchromyces Cerevisiae, Homo sapiens and Caenorhabditis elegans as well as on some tissue specific networks. Gene Ontology (GO) analyses were used to compare the results of different algorithms. Each algorithm's result was then compared with GO-term derived functional modules. We also analyzed the effect of using tissue specific networks on the quality of the obtained clusters. The experimental results indicate that the new algorithm outperforms most of the others, and this improvement is more significant when tissue specific networks are used.

Protein-protein interaction (PPI) networks provide insights into understanding of biological processes, function and the underlying complex evolutionary mechanisms of the cell. Modeling PPI network is an important and fundamental problem in system biology, where it is still of major concern to find a better fitting model that requires less structural assumptions and is more robust against the large fraction of noisy PPIs. In this paper, we propose a new approach called t-logistic semantic embedding (t-LSE) to model PPI networks. t-LSE tries to adaptively learn a metric embedding under the simple geometric assumption of PPI networks, and a non-convex cost function was adopted to deal with the noise in PPI networks. The experimental results show the superiority of the fit of t-LSE over other network models to PPI data. Furthermore, the robust loss function adopted here leads to big improvements for dealing with the noise in PPI network. The proposed model could thus facilitate further graph-based studies of PPIs and may help infer the hidden underlying biological knowledge. The Matlab code implementing the proposed method is freely available from the web site: http://home.ustc.edu.cn/~yzh33108/PPIModel.htm.

The structure of protein-protein interaction (PPI) networks has been studied for over a decade. Many theoretical models have been proposed to model PPI network structure, but continuing noise and incompleteness in these networks make conclusions about their structure difficult. Using newer, larger networks from Sept. 2018 BioGRID and Jan. 2019 IID, we show the joint distribution of degree products and common neighbors has a greater impact on PPI edge connectivity than their individual distributions, and introduce two new models (CN and STICKY-CN) for PPI networks employing these features. Since graphlet-based measures are believed to be among the most discerning and sensitive network comparison tools available, we assess their overall global and local fits to PPI networks using Graphlet Kernel (GK). We fit 10 theoretical models to nine BioGRID networks and twelve Integrated Interactive Database (IID) networks and find: (1) STICKY and STICKY-CN are the overall globally best fitting models according to GK, (2) Hyperbolic Geometric Graph model is a better fit than any STICKY-based model on 4 species, (3) though STICKY-CN provides a better local fit than the STICKY model, the CN model provides the greatest local fit over most species. We conclude that the inclusion of CN into STICKY-CN makes it the best overall fit for PPI networks as it is a good fit locally and globally.

Accumulating evidence suggests that biological systems are composed of interacting, separable, functional modules-groups of vertices within which connections are dense but between which they are sparse. Identifying these modules is likely through capturing the biologically meaningful interactions. In recent years, many algorithms have been developed for detecting such structures. These algorithms, however, are computationally demanding, which limits their applications. In this paper, we propose a fast iterative-clique percolation method (ICPM) for identifying overlapping functional modules in protein-protein interaction (PPI) networks. Our method is based on clique percolation method (CPM), and it not only considers the degree of nodes to minimize the search space (the vertices in k-cliques must have the degree of k − 1 at least), but also converts k-cliques to (k − 1)-cliques. It finds k-cliques by appending one node to (k − 1)-cliques. By testing our method on PPI networks, our analysis of the yeast PPI network suggests that most of these modules have well-supported biological significance.

In network and systems medicine, active module identification methods (AMIMs) are widely used for discovering candidate molecular disease mechanisms. To this end, AMIMs combine network analysis algorithms with molecular profiling data, most commonly, by projecting gene expression data onto generic protein-protein interaction (PPI) networks. Although active module identification has led to various novel insights into complex diseases, there is increasing awareness in the field that the combination of gene expression data and PPI network is problematic because up-to-date PPI networks have a very small diameter and are subject to both technical and literature bias. In this paper, we report the results of an extensive study where we analyzed for the first time whether widely used AMIMs really benefit from using PPI networks. Our results clearly show that, except for the recently proposed AMIM DOMINO, the tested AMIMs do not produce biologically more meaningful candidate disease modules on widely used PPI networks than on random networks with the same node degrees. AMIMs hence mainly learn from the node degrees and mostly fail to exploit the biological knowledge encoded in the edges of the PPI networks. This has far-reaching consequences for the field of active module identification. In particular, we suggest that novel algorithms are needed which overcome the degree bias of most existing AMIMs and/or work with customized, context-specific networks instead of generic PPI networks.

With an ever-increasing amount of available data on protein-protein interaction (PPI) networks and research revealing that these networks evolve at a modular level, discovery of conserved patterns in these networks becomes an important problem. Although available data on protein-protein interactions is currently limited, recently developed algorithms have been shown to convey novel biological insights through employment of elegant mathematical models. The main challenge in aligning PPI networks is to define a graph theoretical measure of similarity between graph structures that captures underlying biological phenomena accurately. In this respect, modeling of conservation and divergence of interactions, as well as the interpretation of resulting alignments, are important design parameters. In this paper, we develop a framework for comprehensive alignment of PPI networks, which is inspired by duplication/divergence models that focus on understanding the evolution of protein interactions. We propose a mathematical model that extends the concepts of match, mismatch, and gap in sequence alignment to that of match, mismatch, and duplication in network alignment and evaluates similarity between graph structures through a scoring function that accounts for evolutionary events. By relying on evolutionary models, the proposed framework facilitates interpretation of resulting alignments in terms of not only conservation but also divergence of modularity in PPI networks. Furthermore, as in the case of sequence alignment, our model allows flexibility in adjusting parameters to quantify underlying evolutionary relationships. Based on the proposed model, we formulate PPI network alignment as an optimization problem and present fast algorithms to solve this problem. Detailed experimental results from an implementation of the proposed framework show that our algorithm is able to discover conserved interaction patterns very effectively, in terms of both accuracies and computational cost.

The protein-protein interaction (PPI) networks can be regarded as powerful platforms to elucidate the principle and mechanism of cellular organization. Uncovering protein complexes from PPI networks will lead to a better understanding of the science of biological function in cellular systems. In recent decades, numerous computational algorithms have been developed to identify protein complexes. However, the majority of them primarily concern the topological structure of PPI networks and lack of the consideration for the native organized structure among protein complexes. The PPI networks generated by high-throughput technology include a fraction of false protein interactions which make it difficult to identify protein complexes efficiently. To tackle these challenges, we propose a novel semi-supervised protein complex detection model based on non-negative matrix tri-factorization, which not only considers topological structure of a PPI network but also makes full use of available high quality known protein pairs with must-link constraints. We propose non-overlapping (NSSNMTF) and overlapping (OSSNMTF) protein complex detection algorithms to identify the significant protein complexes with clear module structures from PPI networks. In addition, the proposed two protein complex detection algorithms outperform a diverse range of state-of-the-art protein complex identification algorithms on both synthetic networks and human related PPI networks.

Spermatogonial stem cells (SSCs) are responsible for sustained spermatogenesis throughout the reproductive life of the male. Extensive studies of SSCs have identified dozens of genes that play important roles in sustaining or controlling the pool of SSCs in the mammalian testis. However, there is still limited knowledge of whether or how these key genes interact with each other during SSC self-renewal. Here, we constructed a protein-protein interaction (PPI) network for SSC self-renewal based on interactions between 23 genes essential for SSC self-renewal, which were obtained from a text mining system, and the interacting partners of the 23 key genes, which were differentially expressed in SSCs. The SSC self-renewal PPI network consisted of 246 nodes connected by 844 edges. Topological analyses of the PPI network were conducted to identify genes essential for maintenance of SSC self-renewal. The subnetwork of the SSC self-renewal network suggested that the 23 key genes involved in SSC self-renewal were connected together through other 94 genes. Clustering of the whole network and subnetwork of SSC self-renewal revealed several densely connected regions, implying significant molecular interaction modules essential for SSC self-renewal. Notably, we found the 23 genes to be responsible for SSC self-renewal by forming a continuous PPI network centered on Pou5f1. Our study indicates that it is feasible to explore important proteins and regulatory pathways in biological activities by combining a PPI database with the high-throughput data of gene expression profiles.

Protein-protein interaction (PPI) networks provide a well-established framework for elucidating structural properties. In contrast, much greater effort is required to identify useful and/or hidden information using the approach because of the complexity of the networks. Accordingly, an appropriate methodology that allows characterization of a simple, but core, sub-network of a complex network would be a potentially valuable alternative approach. Here, we employed k-core decomposition as a useful tool for obtaining core sub-networks from the complex PPI network in yeast. To apply a k-core value to the complex yeast PPI network, we constructed cytoplasmic and nuclear core sub-networks. We measured the lethality of proteins and the ratio of hub to non-hub core sub-network proteins at each k-core value step. With increasing k-core value, the values of the two parameters gradually increased. Application of 6- and 7-core values to cytoplasmic and nuclear PPI networks yielded modular, structured core sub-networks that were functionally specialized. We also elucidated a false hub: a structural hub exhibiting no functional roles or lethal properties in the network. By employing k-core decomposition to cytoplasmic and nuclear PPI networks in yeast, we obtained useful and/or hidden information during the core sub-network construction process, indicating that k-core decomposition is a useful tool for structural and informational network studies. Notably, we found false hub proteins that might provide insight into protein networks and clues to understanding network evolution.

We know that protein-protein interaction (PPI) network is an extremely important biological molecular relationship network in life activities, at present, it has become an important research topic in bioinformatics to detect functional modules from PPI network by computational methods. In this context, this paper studies the implementation of fast algorithm based on GN algorithm in PPI network. Based on GN algorithm, this paper proposes a fast algorithm based on GN algorithm and applies it to PPI network. In the research, we first analyze the performance of the fast algorithm based on GN algorithm, and select MIPS database as PPI data set, compare the proposed method with GN algorithm, and evaluate the accuracy, recall rate, F measure, sensitivity, positive prediction rate and coverage. The results show that the F measure of the fast algorithm based on GN algorithm is 0.70, and the recall rate of GN algorithm is 0.63. The F measure of this algorithm is larger than that of GN algorithm. In addition, the fast algorithm based on GN algorithm is better than GN algorithm in other evaluation indexes. It can be seen that this method has great advantages in the implementation of PPI network.KeywordsGN algorithmFast algorithmPPI networkF measure