The Function of Communities in Protein Interaction Networks at Multiple Scales

Background: If biology is modular then clusters, or communities, of proteins derived using only protein interaction network structure should define protein modules with similar biological roles. We investigate the link between biological modules and network communities in yeast and its relationship to the scale at which we probe the network. Results: Our results demonstrate that the functional homogeneity of communities depends on the scale selected, and that almost all proteins lie in a functionally homogeneous community at some scale. We judge functional homogeneity using a novel test and three independent characterizations of protein function, and find a high degree of overlap between these measures. We show that a high mean clustering coefficient of a community can be used to identify those that are functionally homogeneous. By tracing the community membership of a protein through multiple scales we demonstrate how our approach could be useful to biologists focusing on a particular protein. Conclusions: We show that there is no one scale of interest in the community structure of the yeast protein interaction network, but we can identify the range of resolution parameters that yield the most functionally coherent communities, and predict which communities are most likely to be functionally homogeneous.Comment: 26 pages, 6 figure

Post-processing partitions to identify domains of modularity optimization

We introduce the Convex Hull of Admissible Modularity Partitions (CHAMP) algorithm to prune and prioritize different network community structures identified across multiple runs of possibly various computational heuristics. Given a set of partitions, CHAMP identifies the domain of modularity optimization for each partition ---i.e., the parameter-space domain where it has the largest modularity relative to the input set---discarding partitions with empty domains to obtain the subset of partitions that are "admissible" candidate community structures that remain potentially optimal over indicated parameter domains. Importantly, CHAMP can be used for multi-dimensional parameter spaces, such as those for multilayer networks where one includes a resolution parameter and interlayer coupling. Using the results from CHAMP, a user can more appropriately select robust community structures by observing the sizes of domains of optimization and the pairwise comparisons between partitions in the admissible subset. We demonstrate the utility of CHAMP with several example networks. In these examples, CHAMP focuses attention onto pruned subsets of admissible partitions that are 20-to-1785 times smaller than the sets of unique partitions obtained by community detection heuristics that were input into CHAMP.Comment: http://www.mdpi.com/1999-4893/10/3/9

A Method Based on Total Variation for Network Modularity Optimization using the MBO Scheme

The study of network structure is pervasive in sociology, biology, computer science, and many other disciplines. One of the most important areas of network science is the algorithmic detection of cohesive groups of nodes called "communities". One popular approach to find communities is to maximize a quality function known as {\em modularity} to achieve some sort of optimal clustering of nodes. In this paper, we interpret the modularity function from a novel perspective: we reformulate modularity optimization as a minimization problem of an energy functional that consists of a total variation term and an $\ell_2$ balance term. By employing numerical techniques from image processing and $\ell_1$ compressive sensing -- such as convex splitting and the Merriman-Bence-Osher (MBO) scheme -- we develop a variational algorithm for the minimization problem. We present our computational results using both synthetic benchmark networks and real data.Comment: 23 page

Identification of a gene signature for discriminating metastatic from primary melanoma using a molecular interaction network approach

Understanding the biological factors that are characteristic of metastasis in melanoma remains a key approach to improving treatment. In this study, we seek to identify a gene signature of metastatic melanoma. We configured a new network-based computational pipeline, combined with a machine learning method, to mine publicly available transcriptomic data from melanoma patient samples. Our method is unbiased and scans a genome-wide protein-protein interaction network using a novel formulation for network scoring. Using this, we identify the most influential, differentially expressed nodes in metastatic as compared to primary melanoma. We evaluated the shortlisted genes by a machine learning method to rank them by their discriminatory capacities. From this, we identified a panel of 6 genes, ALDH1A1, HSP90AB1, KIT, KRT16, SPRR3 and TMEM45B whose expression values discriminated metastatic from primary melanoma (87% classification accuracy). In an independent transcriptomic data set derived from 703 primary melanomas, we showed that all six genes were significant in predicting melanoma specific survival (MSS) in a univariate analysis, which was also consistent with AJCC staging. Further, 3 of these genes, HSP90AB1, SPRR3 and KRT16 remained significant predictors of MSS in a joint analysis (HR = 2.3, P = 0.03) although, HSP90AB1 (HR = 1.9, P = 2 × 10−4) alone remained predictive after adjusting for clinical predictors