Specification of spatial relationships in directed graphs of cell signaling networks

Graph theory provides a useful and powerful tool for the analysis of cellular signaling networks. Intracellular components such as cytoplasmic signaling proteins, transcription factors and genes are connected by links, representing various types of chemical interactions that result in functional consequences. However, these graphs lack important information regarding the spatial distribution of cellular components. The ability of two cellular components to interact depends not only on their mutual chemical affinity but also on co-localization to the same subcellular region. Localization of components is often used as a regulatory mechanism to achieve specific effects in response to different receptor signals. Here we describe an approach for incorporating spatial distribution into graphs, and for the development of mixed graphs where links are specified by mutual chemical affinity as well as colocalization. We suggest that such mixed graphs will provide more accurate descriptions of functional cellular networks and their regulatory capabilities and aid in the development of large-scale predictive models of cellular behavior

Degree Ranking Using Local Information

Most real world dynamic networks are evolved very fast with time. It is not feasible to collect the entire network at any given time to study its characteristics. This creates the need to propose local algorithms to study various properties of the network. In the present work, we estimate degree rank of a node without having the entire network. The proposed methods are based on the power law degree distribution characteristic or sampling techniques. The proposed methods are simulated on synthetic networks, as well as on real world social networks. The efficiency of the proposed methods is evaluated using absolute and weighted error functions. Results show that the degree rank of a node can be estimated with high accuracy using only $1\%$ samples of the network size. The accuracy of the estimation decreases from high ranked to low ranked nodes. We further extend the proposed methods for random networks and validate their efficiency on synthetic random networks, that are generated using Erd\H{o}s-R\'{e}nyi model. Results show that the proposed methods can be efficiently used for random networks as well