Mathware & Soft Computing 16 (2009) 87-102 Fuzzy Contact Maps Overlap for Protein Comparison: the Roles of Fitness and Normalization and the relation with Crisp Contact Maps Juan R. Gonz´alez, David A. Pelta, Lluvia Morales Department of Computer Science and Artificial Intelligence, University of Granada, 18071 Granada, Spain e-mail: {jrgonzalez,dpelta}@decsai.ugr.es, lluviamorales@ugr.es Abstract The comparison of protein structures is an important problem in Bioinfor- matics, and Soft Computing techniques were recently introduced for achieving a better representation and, potentially, for getting better solving strategies. In this paper we propose new alternatives for measuring the cost in the Gen- eralized Maximum Fuzzy Contact Map Overlap problem, and we analyze the role of normalization when protein classification is performed. Moreover, we will also compare the optimization performance of the direct application of crisp contact maps over solving the problems through the fuzzy contact maps model. This extends our previous works where it was preliminarily shown that the resolution of the fuzzy model can sometimes lead to better crisp values than the ones obtained solving the crisp model directly. 1 INTRODUCTION A protein is a complex molecule composed by a linear arrangement of amino acids. Each amino acid is a multi-atom compound. Usually, only the “residue” part of these amino acids are considered when studying protein structures for comparison purposes. Thus a protein’s primary sequence is usually thought-of as composed of “residues”. Under specific physiological conditions, the linear arrangement of residues will fold and adopt a complex three dimensional shape. The shape thus adopted is called the native state (or tertiary structure) of the protein. In its native state, residues that are far away along the linear arrangement may come into proximity in three dimensional space in a fashion similar to what occurs with the extremes of a sheet of paper when used to produce complex origami shapes. The proximity relation between residues in a protein can be captured by a mathematical construct called a “contact map”. 87