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Leveraging protein-protein interaction networks to identify groups of proteins and their common functionality is an important problem in bioinformatics. Systems-level analysis of protein-protein interactions is made possible through network science and modeling of high-throughput data. From these analyses, small protein complexes are traditionally represented graphically as complete graphs or dense clusters of nodes. However, there are certain graph theoretic properties that have not been extensively studied in PPI networks, especially as they pertain to cluster discovery, such as planarity. Planarity of graphs have been used to reflect the physical constraints of real-world systems outside of bioinformatics, in areas such as mapping and imaging. Here, we investigate the planarity property in network models of protein complexes. We hypothesize that complexes represented as PPI subgraphs will tend to be planar, reflecting the actual physical interface and limits of components in the complex. When testing the planarity of known complex subgraphs in S. cerevisiae and selected mammalian PPIs, we find that a majority of validated complexes possess this planar property. We discuss the biological motivation of planar versus nonplanar subgraphs, observing that planar subgraphs tend to have longer protein components. Functional classification of planar versus nonplanar complex subgraphs reveals differences in annotation of these groups relating to cellular component organization, structural molecule activity, catalytic activity, and nucleic acid binding. These results provide a new quantitative and biologically motivated measure of real protein complexes in the network model, important for the development of future complex-finding algorithms in PPIs. Accounting for this property paves the way to new means for discovering new protein complexes and uncovering the functionality of unknown or novel proteins. s 

We propose a novel method which we call the Probabilistic Infection Model (PIM). Instead of stochastically assigning exactly one state to each agent at a time, PIM tracks the likelihood of each agent being in a particular state. Thus, a particular agent can exist in multiple disease states concurrently. Our model gives an improved resolution of transitions between states, and allows for a more comprehensive view of outbreak dynamics at the individual level. Moreover, by using a probabilistic approach, our model gives a representative understanding of the overall trajectories of simulated outbreaks without the need for numerous (order of hundreds) of repeated Monte Carlo simulations. We simulate our model over a contact network constructed using registration data of university students. We model three diseases; measles and two strains of influenza. We compare the results obtained by PIM with those obtained by simulating stochastic SEIR models over the same the contact network. The results demonstrate that the PIM can successfully replicate the averaged results from numerous simulations of a stochastic model in a single deterministic simulation. Keywords: Computational epidemics, Outbreak simulation, SEIR model 

Analyzing large dynamic networks is an important problem with applications in a wide range of disciplines. A key operation is updating the network properties as its topology changes. In this paper we present graph sparsification as an efficient abstraction for updating the properties of dynamic networks. We demonstrate the applicability of graph sparsification in updating the connected components in random and scalefree networks on shared memory systems. Our results show that the updating is scalable (10X on 16 processors for larger networks). To the best of our knowledge this is the first parallel implementation of graph sparsification. Based on these initial results, we discuss how the current implementation can be further improved and how graph sparsification can be applied to updating other network properties.