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 according 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 described in this paper are: Firstly, 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, namedgeneralized 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. Secondly, 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.

[1]  Eytan Domany,et al.  Protein fold recognition and dynamics in the space of contact maps , 1996, Proteins.

[2]  Klara Kedem,et al.  Finding the Consensus Shape for a Protein Family , 2002, SCG '02.

[3]  T. N. Bhat,et al.  The Protein Data Bank , 2000, Nucleic Acids Res..

[4]  Natalio Krasnogor,et al.  Measuring the similarity of protein structures by means of the universal similarity metric , 2004, Bioinform..

[5]  Natalio Krasnogor,et al.  Fuzzy Memes in Multimeme Algorithms: a Fuzzy-Evolutionary Hybrid , 2003 .

[6]  Natalio Krasnogor,et al.  Self Generating Metaheuristics in Bioinformatics: The Proteins Structure Comparison Case , 2004, Genetic Programming and Evolvable Machines.

[7]  Pierre Hansen,et al.  Variable neighborhood search: Principles and applications , 1998, Eur. J. Oper. Res..

[8]  Robert D. Carr,et al.  101 optimal PDB structure alignments: a branch-and-cut algorithm for the maximum contact map overlap problem , 2001, RECOMB.

[9]  Philip E Bourne,et al.  Structure comparison and alignment. , 2003, Methods of biochemical analysis.

[10]  Alberto Caprara,et al.  Structural alignment of large—size proteins via lagrangian relaxation , 2002, RECOMB '02.

[11]  K. Dill,et al.  Origins of structure in globular proteins. , 1990, Proceedings of the National Academy of Sciences of the United States of America.

[12]  Peter Willett,et al.  The use of graph theoretical methods for the comparison of the structures of biological macromolecules , 1995 .

[13]  R. Lathe.  Phd by thesis , 1988, Nature.

[14]  C. Sander,et al.  Antiparallel and parallel beta-strands differ in amino acid residue preferences. , 1979, Nature.

[15]  José L. Verdegay,et al.  A Fuzzy Valuation-Based Local Search Framework for Combinatorial Problems , 2002, Fuzzy Optim. Decis. Mak..

[16]  Irena Roterman-Konieczna,et al.  Search for structural similarity in proteins , 2003, Bioinform..

[17]  P. Koehl,et al.  Protein structure similarities. , 2001, Current opinion in structural biology.

[18]  Robert D. Carr,et al.  1001 Optimal PDB Structure Alignments: Integer Programming Methods for Finding the Maximum Contact Map Overlap , 2004, J. Comput. Biol..

[19]  Trevor J. Hastie,et al.  Regression Analysis of Multiple Protein Structures , 1998, J. Comput. Biol..

[20]  Roman A Laskowski,et al.  Structural quality assurance. , 2003, Methods of biochemical analysis.

[21]  Christos H. Papadimitriou,et al.  Algorithmic aspects of protein structure similarity , 1999, 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039).

[22]  Natalio Krasnogor,et al.  Studies on the theory and design space of memetic algorithms , 2002 .

[23]  Robert D. Carr,et al.  Alignment Of Protein Structures With A Memetic Evolutionary Algorithm , 2002, GECCO.

[24]  C. Sander,et al.  Protein structure comparison by alignment of distance matrices. , 1993, Journal of molecular biology.

[25]  Shneior Lifson,et al.  Antiparallel and parallel β-strands differ in amino acid residue preferences , 1979, Nature.

[26]  C Sander,et al.  Mapping the Protein Universe , 1996, Science.

[27]  Pierre Hansen,et al.  Variable Neighborhood Search , 2018, Handbook of Heuristics.

[28]  Natalio Krasnogor,et al.  Multimeme Algorithms Using Fuzzy Logic Based Memes For Protein Structure Prediction , 2005 .

[29]  Armando Blanco,et al.  Fuzzy Adaptive Neighborhood Search: Examples of Application , 2003 .

[30]  W. Taylor.  Protein structure comparison using iterated double dynamic programming , 2008, Protein science : a publication of the Protein Society.