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Analyzing large biological networks: protein-protein interactions example

Understanding the inner workings of the cell constitutes the foremast fundamental problem of modern biology. The information contained in large protein-protein interaction (PPI) networks is being exploited for understanding the cell and developing new drugs. Currently available PPI networks of model organisms, containing thousands of nodes (proteins) and tens of thousands of edges (interactions), are noisy and largely incomplete. PPI networks of higher organisms will be much larger. As these data sets grow, it is important that our models keep representing the data well, since the models can be used for data cleaning and experimental planning. 
The currently accepted scale-free model of PPI networks is based on global statistical properties of PPI networks. However, global measures are very weak, since qualitatively different graphs can have equal values in these measures. It is possible that the observed global proper ties of PPI networks are an artifact of noisy, high-throughput experimental techniques used to detect PPIs, as well as the incompleteness of the data. Fortunately, some parts of PPI networks have been extensively studied due to their importance for basic biological function and human disease. We expect the local structural properties of these highly studied portions of PPI networks to give a much better indication of the true structure of PPI networks. Therefore, we use a sensitive, local structure approach. 
We measure local structural properties of a PPI network by finding and counting all instances of 3-, 4-, and 5-node connected induced subgraphs, called graphlets. We compare the graphlet frequency distributions of the PPI and various model networks with the same number of nodes and edges as the PPI network. Using this measure of local network structure, we show that PPI networks are better modeled by geometric random graphs than by previously proposed models, including scale-free networks. In a geometric random graph, nodes correspond to uniformly randomly distributed points in a metric space; two nodes are adjacent in the graph if they are close enough in the metric space. We use this new model to develop efficient and scalable heuristic algorithms for estimating graphlet frequency distribution patterns in PPI and geometric random networks.