BinTree seeking: a novel approach to mine both bi-sparse and cohesive modules in protein interaction networks

Modern science of networks has brought significant advances to our understanding of complex systems biology. As a representative model of systems biology, Protein Interaction Networks (PINs) are characterized by a remarkable modular structures, reflecting functional associations between their components. Many methods were proposed to capture cohesive modules so that there is a higher density of edges within modules than those across them. Recent studies reveal that cohesively interacting modules of proteins is not a universal organizing principle in PINs, which has opened up new avenues for revisiting functional modules in PINs. In this paper, functional clusters in PINs are found to be able to form unorthodox structures defined as bi-sparse module. In contrast to the traditional cohesive module, the nodes in the bi-sparse module are sparsely connected internally and densely connected with other bi-sparse or cohesive modules. We present a novel protocol called the BinTree Seeking (BTS) for mining both bi-sparse and cohesive modules in PINs based on Edge Density of Module (EDM) and matrix theory. BTS detects modules by depicting links and nodes rather than nodes alone and its derivation procedure is totally performed on adjacency matrix of networks. The number of modules in a PIN can be automatically determined in the proposed BTS approach. BTS is tested on three real PINs and the results demonstrate that functional modules in PINs are not dominantly cohesive but can be sparse. BTS software and the supporting information are available at: www.csbio.sjtu.edu.cn/bioinf/BTS/.     

Virtual identification of essential proteins within the protein interaction network of yeast

Topological analysis of large scale protein-protein interaction networks (PINs) is important for understanding the organizational and functional principles of individual proteins. The number of interactions that a protein has in a PIN has been observed to be correlated with its indispensability. Essential proteins generally have more interactions than the nonessential ones. We show here that the lethality associated with removal of a protein from the yeast proteome correlates with different centrality measures of the nodes in the PIN, such as the closeness of a protein to many other proteins, or the number of pairs of proteins which need a specific protein as an intermediary in their communications, or the participation of a protein in different protein clusters in the PIN. These measures are significantly better than random selection in identifying essential proteins in a PIN. Centrality measures based on graph spectral properties of the network, in particular the subgraph centrality, show the best performance in identifying essential proteins in the yeast PIN. Subgraph centrality gives important structural information about the role of individual proteins, and permits the selection of possible targets for rational drug discovery through the identification of essential proteins in the PIN.     

Coevolution is a short-distance force at the protein interaction level and correlates with the modular organization of protein networks

We investigated what roles coevolution plays in shaping yeast protein interaction network (PIN). We found that the extent of coevolution between two proteins decreases rapidly as their interacting distance on the PIN increases, suggesting coevolutionary constraint is a short-distance force at the molecular level. We also found that protein-protein interactions (PPIs) with strong coevolution tend to be enriched in interconnected clusters, whereas PPIs with weak coevolution are more frequently present at inter-cluster region. The findings indicate the close relationship between coevolution and modular organization of PINs, and may provide insights into evolution and modularity of cellular networks.     

Combining functional and topological properties to identify core modules in protein interaction networks

Advances in large-scale technologies in proteomics, such as yeast two-hybrid screening and mass spectrometry, have made it possible to generate large Protein Interaction Networks (PINs). Recent methods for identifying dense sub-graphs in such networks have been based solely on graph theoretic properties. Therefore, there is a need for an approach that will allow us to combine domain-specific knowledge with topological properties to generate functionally relevant sub-graphs from large networks. This article describes two alternative network measures for analysis of PINs, which combine functional information with topological properties of the networks. These measures, called weighted clustering coefficient and weighted average nearest-neighbors degree, use weights representing the strengths of interactions between the proteins, calculated according to their semantic similarity, which is based on the Gene Ontology terms of the proteins. We perform a global analysis of the yeast PIN by systematically comparing the weighted measures with their topological counterparts. To show the usefulness of the weighted measures, we develop an algorithm for identification of functional modules, called SWEMODE (Semantic WEights for MODule Elucidation), that identifies dense sub-graphs containing functionally similar proteins. The proposed method is based on the ranking of nodes, i.e., proteins, according to their weighted neighborhood cohesiveness. The highest ranked nodes are considered as seeds for candidate modules. The algorithm then iterates through the neighborhood of each seed protein, to identify densely connected proteins with high functional similarity, according to the chosen parameters. Using a yeast two-hybrid data set of experimentally determined protein-protein interactions, we demonstrate that SWEMODE is able to identify dense clusters containing proteins that are functionally similar. Many of the identified modules correspond to known complexes or subunits of these complexes.     

Topology of small-world networks of protein-protein complex structures

The majority of real examples of small-world networks exhibit a power law distribution of edges among the nodes, therefore not fitting into the wiring model proposed by Watts and Strogatz. However, protein structures can be modeled as small-world networks, with a distribution of the number of links decaying exponentially as in the case of this wiring model. We approach the protein-protein interaction mechanism by viewing it as a particular rewiring occurring in the system of two small-world networks represented by the monomers, where a re-arrangement of links takes place upon dimerization leaving the small-world character in the dimer network. Due to this rewiring, the most central residues at the complex interfaces tend to form clusters, which are not homogenously distributed. We show that these highly central residues are strongly correlated with the presence of hot spots of binding free energy. CONTACT: ao-mesa@fujirebio.co.jp SUPPLEMENTARY INFORMATION: http://www.fujirebio.co.jp/support/index.php (under construction).     

Structure of Protein Interaction Networks and Their Implications on Drug Design

Protein-protein interaction networks (PINs) are rich sources of information that enable the network properties of biological systems to be understood. A study of the topological and statistical properties of budding yeast and human PINs revealed that they are scale-rich and configured as highly optimized tolerance (HOT) networks that are similar to the router-level topology of the Internet. This is different from claims that such networks are scale-free and configured through simple preferential-attachment processes. Further analysis revealed that there are extensive interconnections among middle-degree nodes that form the backbone of the networks. Degree distributions of essential genes, synthetic lethal genes, synthetic sick genes, and human drug-target genes indicate that there are advantageous drug targets among nodes with middle- to low-degree nodes. Such network properties provide the rationale for combinatorial drugs that target less prominent nodes to increase synergetic efficacy and create fewer side effects.     

Context-specific protein network miner--an online system for exploring context-specific protein interaction networks from the literature

Background

Protein interaction networks (PINs) specific within a particular context contain crucial information regarding many cellular biological processes. For example, PINs may include information on the type and directionality of interaction (e.g. phosphorylation), location of interaction (i.e. tissues, cells), and related diseases. Currently, very few tools are capable of deriving context-specific PINs for conducting exploratory analysis.

Results

We developed a literature-based online system, Context-specific Protein Network Miner (CPNM), which derives context-specific PINs in real-time from the PubMed database based on a set of user-input keywords and enhanced PubMed query system. CPNM reports enriched information on protein interactions (with type and directionality), their network topology with summary statistics (e.g. most densely connected proteins in the network; most densely connected protein-pairs; and proteins connected by most inbound/outbound links) that can be explored via a user-friendly interface. Some of the novel features of the CPNM system include PIN generation, ontology-based PubMed query enhancement, real-time, user-queried, up-to-date PubMed document processing, and prediction of PIN directionality.

Conclusions

CPNM provides a tool for biologists to explore PINs. It is freely accessible at http://www.biotextminer.com/CPNM/.     

Functional Analysis of the Hydrophilic Loop in Intracellular Trafficking of Arabidopsis PIN-FORMED Proteins

Different PIN-FORMED proteins (PINs) contribute to intercellular and intracellular auxin transport, depending on their distinctive subcellular localizations. Arabidopsis thaliana PINs with a long hydrophilic loop (HL) (PIN1 to PIN4 and PIN7; long PINs) localize predominantly to the plasma membrane (PM), whereas short PINs (PIN5 and PIN8) localize predominantly to internal compartments. However, the subcellular localization of the short PINs has been observed mostly for PINs ectopically expressed in different cell types, and the role of the HL in PIN trafficking remains unclear. Here, we tested whether a long PIN-HL can provide its original molecular cues to a short PIN by transplanting the HL. The transplanted long PIN2-HL was sufficient for phosphorylation and PM trafficking of the chimeric PIN5:PIN2-HL but failed to provide the characteristic polarity of PIN2. Unlike previous observations, PIN5 showed clear PM localization in diverse cell types where PIN5 is natively or ectopically expressed and even polar PM localization in one cell type. Furthermore, in the root epidermis, the subcellular localization of PIN5 switched from PM to internal compartments according to the developmental stage. Our results suggest that the long PIN-HL is partially modular for the trafficking behavior of PINs and that the intracellular trafficking of PIN is plastic depending on cell type and developmental stage.     

Drug response prediction using graph representation learning and Laplacian feature selection

Background

Essential proteins are indispensable to the development and survival of cells. The identification of essential proteins not only is helpful for the understanding of the minimal requirements for cell survival, but also has practical significance in disease diagnosis, drug design and medical treatment. With the rapidly amassing of protein–protein interaction (PPI) data, computationally identifying essential proteins from protein–protein interaction networks (PINs) becomes more and more popular. Up to now, a number of various approaches for essential protein identification based on PINs have been developed.

Results

In this paper, we propose a new and effective approach called iMEPP to identify essential proteins from PINs by fusing multiple types of biological data and applying the influence maximization mechanism to the PINs. Concretely, we first integrate PPI data, gene expression data and Gene Ontology to construct weighted PINs, to alleviate the impact of high false-positives in the raw PPI data. Then, we define the influence scores of nodes in PINs with both orthological data and PIN topological information. Finally, we develop an influence discount algorithm to identify essential proteins based on the influence maximization mechanism.

Conclusions

We applied our method to identifying essential proteins from saccharomyces cerevisiae PIN. Experiments show that our iMEPP method outperforms the existing methods, which validates its effectiveness and advantage.

     

Interaction and domain networks of yeast

Data of currently available protein-protein interaction sets and protein domain sets of yeast are used to set up protein and domain interaction and domain sequence networks. All of them are far from being random or regular networks. In fact, they turn out to be sparse and locally well clustered indicating so-called scale-free and partially small-world topology. These subtle topologies display considerable indirect properties which are measured with a newly introduced transitivity coefficient. Fairly small sets of highly connected proteins and domains shape the topologies of the underlying networks, emphasizing a kind of backbone the nets are based on. The biological nature of these particular nodes is further investigated. Since highly connected proteins and domains accumulated a significant higher number of links by their important involvement in certain cellular aspects, their mutational effect on the cell is considered by a perturbation analysis. In comparison to domains of yeast, what factors force domains to accumulate links to other domains in protein sequences of higher eukaryotes are investigated.     

Protein bipartivity and essentiality in the yeast protein-protein interaction network

Protein-protein interaction networks (PINs) are structured by means of a few highly connected proteins linked to a large number of less-connected ones. Essential proteins have been found to be more abundant among these highly connected proteins. Here we demonstrate that the likelihood that removal of a protein in a PIN will prove lethal to yeast correlates with the lack of bipartivity of the protein. A protein is bipartite if it can be partitioned in such a way that there are two groups of proteins with intergroup, but not intragroup, interactions. The abundance of essential proteins found among the least bipartite proteins clearly exceeds that found among the most connected ones. For instance, among the top 50 proteins ranked by their lack of bipartivity 62% are essential proteins. However, this percentage is only 38% for proteins ranked according to their number of interactions. Protein bipartivity also surpasses another 5 measures of protein centrality in yeast PIN in identifying essential proteins and doubles the number of essential proteins selected at random. We propose a possible mechanism for the evolution of essential proteins in yeast PIN based on the duplication-divergence scheme. We conclude that a replica protein evolving from a nonbipartite target will also be nonbipartite with high probability. Consequently, these new replicas evolving from nonbipartite (essential) targets will with high probability be essential.     

Epidemic threshold and network structure: The interplay of probability of transmission and of persistence in small-size directed networks

A growing number of studies are investigating the effect of contact structure on the dynamics of epidemics in large-scale complex networks. Whether findings thus obtained apply also to networks of small size, and thus to many real-world biological applications, is still an open question. We use numerical simulations of disease spread in directed networks of 100 individual nodes with a constant number of links. We show that, no matter the type of network structure (local, small-world, random and scale-free), there is a linear threshold determined by the probability of infection transmission between connected nodes and the probability of infection persistence in an infected node. The threshold is significantly lower for scale-free networks compared to local, random and small-world ones only if super-connected nodes have a higher number of links both to and from other nodes. The starting point, the node at which the epidemic starts, does not affect the threshold conditions, but has a marked influence on the final size of the epidemic in all kinds of network. There is evidence that contact structure has an influence on the average final size of an epidemic across all starting nodes, with significantly lower values in scale-free networks at equilibrium. Simulations in scale-free networks show a distinctive time-series pattern, which, if found in a real epidemic, can be used to infer the underlying network structure. The findings have relevance also for meta-population ecology and species conservation.     

NetAlign: a web-based tool for comparison of protein interaction networks

NetAlign is a web-based tool designed to enable comparative analysis of protein interaction networks (PINs). NetAlign compares a query PIN with a target PIN by combining interaction topology and sequence similarity to identify conserved network substructures (CoNSs), which may derive from a common ancestor and disclose conserved topological organization of interactions in evolution. To exemplify the application of NetAlign, we perform two genome-scale comparisons with (1) the Escherichia coli PIN against the Helicobacter pylori PIN and (2) the Saccharomyces cerevisiae PIN against the Caenorrhabditis elegans PIN. Many of the identified CoNSs correspond to known complexes; therefore, cross-species PIN comparison provides a way for discovery of conserved modules. In addition, based on the species-to-species differences in CoNSs, we reformulate the problems of protein-protein interaction (PPI) prediction and species divergence from a network perspective. AVAILABILITY: http://www1.ustc.edu.cn/lab/pcrystal/NetAlign.     

Optimal link removal for epidemic mitigation: a two-way partitioning approach

The structure of the contact network through which a disease spreads may influence the optimal use of resources for epidemic control. In this work, we explore how to minimize the spread of infection via quarantining with limited resources. In particular, we examine which links should be removed from the contact network, given a constraint on the number of removable links, such that the number of nodes which are no longer at risk for infection is maximized. We show how this problem can be posed as a non-convex quadratically constrained quadratic program (QCQP), and we use this formulation to derive a link removal algorithm. The performance of our QCQP-based algorithm is validated on small Erd?s–Renyi and small-world random graphs, and then tested on larger, more realistic networks, including a real-world network of injection drug use. We show that our approach achieves near optimal performance and out-performs other intuitive link removal algorithms, such as removing links in order of edge centrality.     

Antagonism and bistability in protein interaction networks

A protein interaction network (PIN) is a set of proteins that modulate one another's activities by regulated synthesis and degradation, by reversible binding to form complexes, and by catalytic reactions (e.g., phosphorylation and dephosphorylation). Most PINs are so complex that their dynamical characteristics cannot be deduced accurately by intuitive reasoning alone. To predict the properties of such networks, many research groups have turned to mathematical models (differential equations based on standard biochemical rate laws, e.g., mass-action, Michaelis-Menten, Hill). When using Michaelis-Menten rate expressions to model PINs, care must be exercised to avoid making inconsistent assumptions about enzyme-substrate complexes. We show that an appealingly simple model of a PIN that functions as a bistable switch is compromised by neglecting enzyme-substrate intermediates. When the neglected intermediates are put back into the model, bistability of the switch is lost. The theory of chemical reaction networks predicts that bistability can be recovered by adding specific reaction channels to the molecular mechanism. We explore two very different routes to recover bistability. In both cases, we show how to convert the original 'phenomenological' model into a consistent set of mass-action rate laws that retains the desired bistability properties. Once an equivalent model is formulated in terms of elementary chemical reactions, it can be simulated accurately either by deterministic differential equations or by Gillespie's stochastic simulation algorithm.     

Differential Auxin-Transporting Activities of PIN-FORMED Proteins in Arabidopsis Root Hair Cells

The Arabidopsis (Arabidopsis thaliana) genome includes eight PIN-FORMED (PIN) members that are molecularly diverged. To comparatively examine their differences in auxin-transporting activity and subcellular behaviors, we expressed seven PIN proteins specifically in Arabidopsis root hairs and analyzed their activities in terms of the degree of PIN-mediated root hair inhibition or enhancement and determined their subcellular localization. Expression of six PINs (PIN1–PIN4, PIN7, and PIN8) in root hair cells greatly inhibited root hair growth, most likely by lowering auxin levels in the root hair cell by their auxin efflux activities. The auxin efflux activity of PIN8, which had not been previously demonstrated, was further confirmed using a tobacco (Nicotiana tabacum) cell assay system. In accordance with these results, those PINs were localized in the plasma membrane, where they likely export auxin to the apoplast and formed internal compartments in response to brefeldin A. These six PINs conferred different degrees of root hair inhibition and sensitivities to auxin or auxin transport inhibitors. Conversely, PIN5 mostly localized to internal compartments, and its expression in root hair cells rather slightly stimulated hair growth, implying that PIN5 enhanced internal auxin availability. These results suggest that different PINs behave differentially in catalyzing auxin transport depending upon their molecular activity and subcellular localization in the root hair cell.Auxin plays a critical role in plant development and growth by forming local concentration gradients. Local auxin gradients, created by the polar cell-to-cell movement of auxin, are implicated in primary axis formation, root meristem patterning, lateral organ formation, and tropic movements of shoots and roots (for recent review, see Vanneste and Friml, 2009). The cell-to-cell movement of auxin is achieved by auxin influx and efflux transporters such as AUXIN-RESISTANT1 (AUX1)/LIKE-AUX1 for influx and PIN-FORMED (PIN) and the P-glycoprotein (PGP) of ABCB (ATP-binding cassette-type transporter subfamily B) for efflux. Since diffusive efflux of the natural auxin indole-3-acetic acid (IAA; pKa = 4.75) is not favorable and PINs are localized in the plasma membrane in a polar manner, PINs act as rate-limiting factors for cellular auxin efflux and polar auxin transport through the plant body. These PINs'' properties explain why representative physiological effects of auxin transport are associated with PINs.Auxin flows from young aerial parts all the way down to the root tip columella in which an auxin maximum is formed for root stem cell maintenance and moves up toward the root differentiation zone through root epidermal cells, where a part of it travels back to the root tip via cortical cells (Blilou et al., 2005). This directional auxin flow is supported by the polar localization of PINs: PIN1, PIN3, and PIN7 at the basal side of stele cells (Friml et al., 2002a, 2002b; Blilou et al., 2005), PIN4 at the basal side in root stem cells (Friml et al., 2002a), and PIN2 at the upper side of root epidermis and at the basal side of the root cortex (Luschnig et al., 1998; Müller et al., 1998). Another interesting aspect of PIN-mediated auxin transport is the dynamics in directionality of auxin flow due to environmental stimuli-directed changes of subcellular PIN polarity, as exemplified for PIN3, whose subcellular localization changes in response to the gravity vector (Friml et al., 2002b).An intriguing question is how different PIN proteins have different subcellular polarities, which might be attributable to PIN-specific molecular properties, cell-type-specific factors, or both. The different PIN subcellular polarities in different cell types seemingly indicate that cell-type-specific factors are involved in polarity. In the case of PIN1, however, both classes of factors appear to affect its subcellular localization because when expressed under the PIN2 promoter, PIN1 localizes to the upper or basal side of root epidermal cells, depending on the GFP insertion site of the protein (Wiśniewska et al., 2006). A recent study demonstrated that the polar targeting of PIN proteins is modulated by phosphorylation/dephosphorylation of the central hydrophilic loop of PINs, which is mediated by PINOID (PID; a Ser/Thr protein kinase)/PP2A phosphatase (Michniewicz et al., 2007). The central hydrophilic domain of PINs might provide the molecule-specific cue for PIN polarity, together with as yet unknown cell-specific factors. Different recycling behaviors of PINs, which show variable sensitivities to brefeldin A (BFA), also imply different molecular characters among PIN species. Most PIN1 proteins are internalized by BFA treatment, whereas considerable amounts of PIN2 remain in the plasma membrane in addition to internal accumulation after BFA treatment. Recycling and basal polar targeting of PIN1 is dependent on the BFA-sensitive guanine nucleotide exchange factor for adenosyl ribosylation factors (ARF GEFs), GNOM, which is the major target of BFA. In contrast, apical targeting and recycling of PIN2 is independent of GNOM and controlled by BFA-resistant ARF GEFs (Geldner et al., 2003; Kleine-Vehn and Friml, 2008).In contrast to their distinct subcellular localizations, the differential auxin-transporting activities of PINs remain to be studied. The divergent primary structures of PIN proteins are not only indicative of differential subcellular polarity, but also would represent their differential catalytic activities for auxin transport. The auxin efflux activities of Arabidopsis (Arabidopsis thaliana) PINs have been demonstrated using Arabidopsis and heterologous systems: PIN1 and PIN5 in Arabidopsis cells (Petrásek et al., 2006; Mravec et al., 2009); PIN2, PIN3, PIN4, PIN6, and PIN7 in tobacco (Nicotiana tabacum) Bright Yellow-2 (BY-2) cells (Lee and Cho, 2006; Petrásek et al., 2006; Mravec et al., 2008); PIN1, PIN2, PIN5, and PIN7 in yeast (Saccharomyces cerevisiae) cells (Petrásek et al., 2006; Blakeslee et al., 2007; Mravec et al., 2009; Yang and Murphy, 2009); and PIN1, PIN2, and PIN7 in HeLa cells (Petrásek et al., 2006; Blakeslee et al., 2007). Among the eight Arabidopsis PIN members, PIN1, PIN2, PIN3, PIN4, PIN6, and PIN7, which share a similar molecular structure in terms of the presence of a long central loop (hereafter called long-looped PINs; Fig. 1A; Supplemental Fig. S1), have been shown to catalyze auxin efflux at the cellular level. On the other hand, PIN5 and PIN8 possess a very short putative central loop (hereafter called short-looped PINs). Although PIN5 was recently shown to be localized in the endoplasmic reticulum (ER) and proposed to transport auxin metabolites into the ER lumen, its cellular function regarding its intracellular auxin-transporting activity has not been shown, and the auxin-transporting activity of PIN8 has yet to be demonstrated. In spite of the same transport directionality (auxin efflux) and similar molecular structures, the long-looped PINs exhibit sequence divergence not only in their central loop, but also in certain residues of the transmembrane domains. This structural divergence of long-looped PINs might be indicative of their differential auxin-transporting activities, which have not yet been quantitatively compared.Open in a separate windowFigure 1.Differential activities of PINs in the Arabidopsis root hair. A, Two distinctive PIN groups with different central hydrophilic loop sizes. Topology of PIN proteins was predicted by four different programs as described in Supplemental Figure S1. Numbers above indicate the number of transmembrane helices for each N- and C-terminal region, and numbers below indicate the number of amino acid residues of the central hydrophilic domain. B, Representative root images of control (Cont; Columbia-0) and root-hair-specific PIN-overexpressing (PINox; ProE7:PIN-GFP or ProE7:PIN [−]) plants. Bar = 100 μm for all. C, Root hair lengths of control and PINox plants. Six to 12 independent transgenic lines (average = 8.3), and 42 to 243 roots (average = 86.8) and 336 to 2,187 root hairs (average = 727.8) per construct, were observed for the estimation of root hair length. Data represent means ± se. The root hair lengths of PIN5ox lines were significantly longer than those of the control (P = 0.016 for PIN5ox; P < 0.0001 for PIN5-GFP1ox and PIN5-GFP2ox).To comparatively assess the cytological behaviors and molecular activities of different PIN members, it would be favorable to use a single assay system that provides a consistent cellular environment and enables quantitative estimation of PIN activity. In previous studies, we adopted the root hair single cell system to quantitatively assay auxin-transporting or regulatory activities of PINs, PGPs, AUX1, and PID (Lee and Cho, 2006; Cho et al., 2007a). Root hair growth is proportional to internal auxin levels in the root hair cell. Therefore, auxin efflux inhibits and auxin influx enhances root hair growth (Cho et al., 2007b; Lee and Cho, 2008). In addition, the use of a root-hair-specific promoter (Cho and Cosgrove, 2002; Kim et al., 2006) for expression of auxin transporters enables the transporters'' biological effect to be pinpointed to only the root hair cell, thus excluding probable non-cell-autonomous effects that could be caused by the general expression of auxin transporters.In this study, we expressed five long-looped PINs (PIN1, PIN2, PIN3, PIN4, and PIN7) and two short-looped PINs (PIN5 and PIN8) in root hair cells and compared their auxin-transporting activities and cytological dynamics. To directly measure the radiolabeled auxin-transporting activities of PIN5 and PIN8, we used an additional assay system, tobacco suspension cells. Our data revealed that PINs have differential molecular activities and pharmacological responses and that the short-looped and long-looped PINs have different subcellular localizations.     

The number of links to and from the starting node as a predictor of epidemic size in small-size directed networks

Much recent modelling is focusing on epidemics in large-scale complex networks. Whether or not findings of these investigations also apply to networks of small size is still an open question. This is an important gap for many biological applications, including the spread of the oomycete pathogen Phytophthora ramorum in networks of plant nurseries. We use numerical simulations of disease spread and establishment in directed networks of 100 individual nodes at four levels of connectivity. Factors governing epidemic spread are network structure (local, small-world, random, scale-free) and the probabilities of infection persistence in a node and of infection transmission between connected nodes. Epidemic final size at equilibrium varies widely depending on the starting node of infection, although the latter does not affect the threshold condition for spread. The number of links from (out-degree) but not the number of links to (in-degree) the starting node of the epidemic explains a substantial amount of variation in final epidemic size at equilibrium irrespective of the structure of the network. The proportion of variance in epidemic size explained by the out-degree of the starting node increases with the level of connectivity. Targeting highly connected nodes is thus likely to make disease control more effective also in case of small-size populations, a result of relevance not just for the horticultural trade, but for epidemiology in general.     

Mining Temporal Protein Complex Based on the Dynamic PIN Weighted with Connected Affinity and Gene Co-Expression

The identification of temporal protein complexes would make great contribution to our knowledge of the dynamic organization characteristics in protein interaction networks (PINs). Recent studies have focused on integrating gene expression data into static PIN to construct dynamic PIN which reveals the dynamic evolutionary procedure of protein interactions, but they fail in practice for recognizing the active time points of proteins with low or high expression levels. We construct a Time-Evolving PIN (TEPIN) with a novel method called Deviation Degree, which is designed to identify the active time points of proteins based on the deviation degree of their own expression values. Owing to the differences between protein interactions, moreover, we weight TEPIN with connected affinity and gene co-expression to quantify the degree of these interactions. To validate the efficiencies of our methods, ClusterONE, CAMSE and MCL algorithms are applied on the TEPIN, DPIN (a dynamic PIN constructed with state-of-the-art three-sigma method) and SPIN (the original static PIN) to detect temporal protein complexes. Each algorithm on our TEPIN outperforms that on other networks in terms of match degree, sensitivity, specificity, F-measure and function enrichment etc. In conclusion, our Deviation Degree method successfully eliminates the disadvantages which exist in the previous state-of-the-art dynamic PIN construction methods. Moreover, the biological nature of protein interactions can be well described in our weighted network. Weighted TEPIN is a useful approach for detecting temporal protein complexes and revealing the dynamic protein assembly process for cellular organization.