Solving large protein secondary structure classification problems by a nonlinear complementarity algorithm with {0,1} variables

Optimization Methods and Software

Volumn 22, Issue 1, 2007, Pages 25-49

  Cifarelli, C ^a   Patrizi, G ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

Complementarity Problems; Protein secondary structure classification; Protein sequences

Indexed keywords

ALGORITHMS; CLASSIFICATION (OF INFORMATION); CONVERGENCE OF NUMERICAL METHODS; NONLINEAR SYSTEMS; PROBLEM SOLVING; STATISTICAL METHODS;

COMPLEMENTARITY PROBLEMS; PROTEIN SECONDARY STRUCTURE CLASSIFICATION; PROTEIN SEQUENCES;

PROTEINS;

EID: 33845347886     PISSN: 10556788     EISSN: 10294937     Source Type: Journal    
DOI: 10.1080/10556780600881845     Document Type: Conference Paper

References (44)

1. Berman, H.M., Westbrook, J., Feng, Z., Gilarid, G., Bhat, T.N., Wessig, H., Shindyakov, I.N. and Bournel, P.E., 2000, The protein data bank. Nucleic Acids Research, 28, 235-242.
2. Jardine, N. and Sibson, R., 1971, Mathematical Taxonomy (New York: Wiley).
3. Silvestri, L. and Hill, J.R., 1964, Some problems on the taxonomic approach. In: V.H. Heywood and J. McNeill (Eds) Phonetic and Philogenic Classification, pp. 87-104 (London: Systematics Association).
4. Duda, R.O. and Hait, P.E., 1973, Pattern Recognition and Scene Analysis (New York: Wiley).
5. Watanabe, S., 1985, Pattern Recognition: Human and Mechanical (New York: Wiley).
6. Nieddu, L. and Patrizi, G. 2000, Formal properties of pattern recognition algorithms: A review. European Journal of Operational Research, 120, 459-495.
7. Young, T.Y. and Calvert, W., 1974, Classification, Estimation and Pattern Recognition (New York: Elsevier).
8. Devroye, L., Gyorfi, L. and Lugosi, G., 1996, A Probabilistic Theory of Pattern Recognition (Berlin: Springer-Verlag).
9. Patrizi, G., 1979, Optimal clustering properties. Ricerca Operativa, 10, 41-64.
10. Patrizi, G., 1991, The equivalence of an lcp to a parametric linear program with a scalar parameter. European Journal of Operational Research, 51, 367-386.
11. Di Giacomo, L., Argento, E. and Patrizi, G., 2004, Linear complementarity methods for the solution of combinatorial problems. Submitted for publication: Copy at http://banach.sta.uniromal.it/patrizi/.
12. Facchinei, F. and Pang, J.-S., 2003, Finite-Dimensional Variational Inequalities and Complementarity Problems (Berlin: Springer). (2 volumes).
13. Nagurney, A., 1993, Network Economics: A Variational Inequality Approach (Boston: Kluwer).
14. Hartman, P. and Stampacchia, G., 1966, On some non linear elliptical differential functional equations. Acta Mathematica, 115, 153-188.
15. Eaves, B.C., 1971, On the basic theorem of complementarity. Mathematical Programming, 1, 68-75.
16. Dieudonne, J., 1960, Fundaments d'Analyse, Vol. 1 (Paris: Gauthiers Villars).
17. Lemke, C.E., 1965, Bimatrix equilibrium points and mathematical programming, Management Science, 11, 123-128.
18. Vapnik, V.N., 1998, Learning Theory (New York: Wiley).
19. Rost, B. and Sander, C., 1993, Prediction of secondary structure at better than 70 percent accuracy. Journal of Molecular Biology, 232, 584-599.
20. Konjin, H.S., 1973, Statistical Theory of Sample Design and Analysis (Amsterdam: North Holland).
21. Rost, B., 1999, Twilight zone of protein sequence alignment. Protein Engineering, 12, 85-94.
22. Cuff, J.A. and Barton, G.J., 1999, Evaluation and improvement of multiple sequence methods for protein secondary structure prediction. Proteins: Structure, Functions and Genetics, 34, 508-519.
23. Sander, C. and Schneider, R., 1991, Database of homology-derived protein structures and structural meaning of sequence alignments. Proteins, 9, 56-68.
24. Kabsch, W. and Sander, C., 1983, Dictionary of protein secondary structure: pattern recognition of hydrogen-bonded and geometrical features. The Journal of Biopolymers, 22, 2577-2637.
25. Frishman, D. and Argos, P., 1995, Knowledge-based protein secondary structure assignment. Proteins: Structure Functions and Genetics, 23, 566-579.
26. Richards, P.M. and Kundrot, C.E., 1988, Identification of structural motifs from protein coordinate data: Secondary structure and first-level supersecondary structure. Proteins: Structure Functions and Genetics, 3, 71-84.
27. Altschul, S.F., Madden, T.L., Schaeffer, A.A., Zhang, J., Zhang, Z., Miller, W. and Lipman, D.J., 1997, Gapped blast and psi-blast: a new generation of protein database programs. Nucleic Acids Research, 25, 3389-3402.
28. Garnier, J., Osghutorpe, D.J. and Robson, B., 1978, Analysis of the accuracy and implications of simple methods for predicting the secondary structure of globular proteins. Journal of Molecular Biology, 120, 97-120.
29. Jones, D.T., 1999, Protein structure prediction based on position-specific scoring matrices. Journal of Molecular Biology, 292, 195-202.
30. King, R.D. and Stenberg, M.J.E., 1996, Identification and application of the concepts important for accurate and reliable protein secondary structure prediction. Protein Science, 5, 2298-2310.
31. Dodge, C., Schneider, R. and Sander, C., 1998, The hssp database of protein-structure-sequence alignments and family profile. Nucleic Acids Research, 26, 313-315.
32. Raghava, G.P.S., Searle, S.M.J., Audley, P.C., Barber, J.D. and Barton, G.J., 2003, Oxbench: a benchmark for evaluation of protein multiple sequence alignment accuracy. BMC Bioinfoimatics available from: http://www.biomedcentral. eom/1471-2105/4/47, 4, 1-23.
33. Boscott, P.E., Barton, G.J. and Richards, W.G., 1993, Secondary structure prediction for modeling homology. Protein Engineering, 6, 261-266.
34. Chatfield, C., 1995, Model uncertainty, data mining and statistical inference. Journal of the Royal Statistical Society Series A, 158, 419-466.
35. Cuff, J.A. and Barton, G.J., 2000, Application of multiple sequence alignment profiles to improve protein secondary structure prediction. Proteins: Structure, Functions and Genetics, 40, 502-511.
36. Przybylski, D., Rost, B., 2002, Alignments grow, secondary prediction improves. Proteins: Structure, Function, and Genetics, 46, 197-205.
37. Brenner, S.E., Clothia, C. and Hubbard, T.J.P., 1998, Assessing the sequence comparison methods with reliable structurally identified distant evolutionary relationships. Proceedings of the National Academy of Science, 95, 6073-6078.
38. Frishman, D. and Argos, P., 1996, Incorporation of non-local interactions in protein secondary structure prediction from the amino acid sequence. Protein Engineering, 9, 133-142.
39. Yi, T.M. and Lander, E.S., 1993, Protein secondary structure prediction usign nearest-neighbour methods. Journal of Molecular Biology, 225, 1049-1063.
40. Salamoi, A. and Soloyev, V., 1995, Prediction of protein secondary structure by combining nearest neighbour algorithms and multiple sequence alignments. Journal of Molecular Biology, 247, 11-15.
41. Zvelebil, M.J.J.M., Barton, G.J., Taylor, W.R. and Sternberg, M.J.E., 1987, Prediction of protein secondary structure and active sites using the alignment of homologous sequences. Journal of Molecular Biology, 195, 957-961.
42. Altschul, S.F. and Gish, W., 1996, Local alignment statistics. Methods in Enzymology, 266, 460-480.
43. Rost, B., Eyrich, V.A., Przybylski, D., Pazos, F., Valencia, A., Fiser, A., Marti-Renom, M., Sanchez, R. and Sali, A., 2000, Eva evaluation of automatic protein structure prediction services. Technical report, Columbia University Rockefeller University CNB Madrid; WWW url: http://BioInfo.PL/LiveBench/.
44. Rost, B., 2001, Review: protein secondary structure prediction continues to rise. Journal of Structural Biology, 134, 204-218.