Fitting a geometric graph to a proteinprotein interaction network
Higham, Desmond J. and Rasajski, Marija and Przulj, Natasa (2008) Fitting a geometric graph to a proteinprotein interaction network. Bioinformatics, 24 (8). pp. 10931099. ISSN 13674803

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Abstract
Finding a good network null model for proteinprotein 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 lowdimensional Euclidean space, under the premise that connectivity information corresponds to Euclidean proximity, as in geometricrandom 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 multidimensional 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 rewiring some links. Applying the algorithm to 19 publicly available PPI networks of various organisms indicated that: (a) geometric effects are present and (b) twodimensional Euclidean space is generally as effective as higher dimensional Euclidean space for explaining the connectivity. Testing on a highconfidence 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.
Item type:  Article 

ID code:  15054 
Keywords:  geometric graph, protein–protein interaction network, bioinformatics, mathematics, computational biology, Mathematics, Biology, Biochemistry, Computational Theory and Mathematics, Computational Mathematics, Molecular Biology, Statistics and Probability, Computer Science Applications 
Subjects:  Science > Mathematics Science > Natural history > Biology 
Department:  Faculty of Science > Mathematics and Statistics 
Depositing user:  Mrs Irene Spencer 
Date Deposited:  26 Jan 2010 15:09 
Last modified:  29 Apr 2016 22:17 
URI:  http://strathprints.strath.ac.uk/id/eprint/15054 