A fuzzy sets based generalization of contact maps for the overlap of protein structures

The comparison of protein structures is an important problem in bioinformatics. As a protein biological role is derived from its three dimensional native state, the comparison of a new protein structure (with unknown function) with other protein structures (with known biological activity) can shed light into the biological role of the former. Consequently, advances in the comparison (and clustering) of proteins accordingly to their three dimensional configurations might also have an impact on drug discovery and other biomedical research that relies on understanding the inter-relations between structure and function in proteins. The contributions on this paper are: First, we propose a generalization of the Maximum Contact Map Overlap Problem (MAX-CMO) by means of fuzzy sets and systems. The MAX-CMO is a model for protein structure comparison. In our new model, Generalized Maximum Fuzzy Contact Map Overlap (GMAX-FCMO), a contact map is defined by means of one (or more) fuzzy thresholds and one (or more) membership functions. The advantages and limitations of our new model are discussed. Second, we show how a fuzzy sets based metaheuristic can be used to compute protein similarities based on the new model. Finally, we compute the protein structure similarity of real-world proteins and show how our new model correctly measures their (di)similarity.