Modules identification in protein structures: the topological and geometrical solutions.

The identification of modules in protein structures has major relevance in structural biology, with consequences in protein stability and functional classification, adding new perspectives in drug design. In this work, we present the comparison between a topological (spectral clustering) and a geometrical (k-means) approach to module identification, in the frame of a multiscale analysis of the protein architecture principles. The global consistency of an adjacency matrix based technique (spectral clustering) and a method based on full rank geometrical information (k-means) give a proof-of-concept of the relevance of protein contact networks in structure determination. The peculiar "small-world" character of protein contact graphs is established as well, pointing to average shortest path as a mesoscopic crucial variable to maximize the efficiency of within-molecule signal transmission. The specific nature of protein architecture indicates topological approach as the most proper one to highlight protein functional domains, and two new representations linking sequence and topological role of aminoacids are demonstrated to be of use for protein structural analysis. Here we present a case study regarding azurin, a small copper protein implied in the Pseudomonas aeruginosa respiratory chain. Its pocket molecular shape and its electron transfer function have challenged the method, highlighting its potentiality to catch jointly the structure and function features of protein structures through their decomposition into modules.