Global optimization in protein docking using clustering, underestimation and semidefinite programming

Optimization Methods and Software

Volumn 22, Issue 5, 2007, Pages 803-811

  Marcia, Roummel F ^a   Mitchell, Julie C ^a   Wright, Stephen J ^b  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

^b University of Wisconsin Madison   (United States)

Author keywords

Convex underestimation; Global optimization; Protein docking; Semidefinite programming

Indexed keywords

FUNCTION EVALUATION; LIGANDS; PARAMETER ESTIMATION; PROBLEM SOLVING; PROTEINS;

CONVEX UNDERESTIMATION; PROTEIN DOCKING; SEMIDEFINITE PROGRAMMING; SEMIDEFINITE PROGRAMMING (SDP);

GLOBAL OPTIMIZATION;

EID: 34548124821     PISSN: 10556788     EISSN: 10294937     Source Type: Journal    
DOI: 10.1080/00207170701203756     Document Type: Article

References (31)

1. Phillips, A., Rosen, J. and Walke, V., 1996, Molecular structure determination by convex global underestimation of ocal energy minima. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 23, (American Mathematical Society), pp. 181-198.
2. Dill, K.A., Phillips, A.T. and Rosen, J.B., 1997, CGU: an algorithm, for molecular structure prediction. In Large-Scale Optimization, with Applications, Pan III (Minneapolis, MN, 1995), IMA Mathematics and its Applications, Vol. 94 (New York: Springer), pp. 1-21.
3. Rosen, J.B., Dill, K.A. and Phillips, A.T., 1997, Protein structure and energy landscape dependence on sequence using a continuous energy function. Journal of Computation Biology, 4, 227-239.
4. Phillips, A.T., Rosen, J.B. and Dill, K.A., 2001, Convex global underestimation for molecular structure prediction. In: P.M. Pardalos et al. (Ed.) From Local to Global Optimization (Dordrecht, Netherlands: Kluwer Academic Publishers), pp. 1-18.
5. Rosen, J.B. and Marcia, R.F., 2004, Convex quadratic approximation. Computational Optimization and Applications, 28(2), 173-184.
6. Mitchell, J.C., Rosen, J.B., Phillips, A.T. and Ten Eyck, L.F., 1999, Coupled optimization in protein docking. In Proceedings of the Third Annual International Confermce on Computational Molecular Biology, ACM Press, 280-284.
7. Marcia, R.F., Mitchell, J.C. and Rosen, J.B., 2005, Iterative convex quadratic approximation for global optimization in protein docking. Computational Optimization and Applications, 32(3), 285-297.
8. Mangasarian, O.L., Rosen, J.B. and Thompson, M.E., 2005, Global minimization via piecewise-linear underestimation. Journal of Global, Optimization, 32(1), 1-9.
9. Mangasarian, O.L., Rosen, J.B. and Thompson, M.E., 2006, Convex kernel estimation of functions with multiple local minima. Computational Optimization and Applications, 34(1), 35-45.
10. Mangasarian, O.L., Rosen, J.B. and Thompson, M.E., 2006, Nonconvex piecewise-quadratic underestimation for global minimization. Journal of Global Optimization, 34(4), 475-488.
11. Barrodale, I., 1968, L1 approximation and the analysis of data. Applied Statistics, 17, 51-57.
12. Barrodale, I. and Roberts, F.D.K., 1973, An improved algorithm for discrete L1 linear approximation. SIAM Journal of Numerical Analysis, 10, 839-848.
13. Rosen, J.B., Park, H., Glick, J. and Zhang, L., 2000, Accurate solution, to overdetermined linear equations with errors using L1 norm minimization. Computational Optimization and Applications, 17(2-3), 329-341.
14. Nesterov, Y. and Nemirovskii, A., 1994, Interior-point polynomial algorithms in convex programming, volume 13 of SIAM Studies in Applied Mathematics (Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM)).
15. Vandenberghe, L. and Boyd, S., 1996, Semidefinite programming. SIAM Review, 38(1), 49-95.
16. Paschalidis, I.Ch., Shen, Y., Vajda, S. and Vakili, P., 2005, A. semi-definite programming-based underestimation method for global optimization in molecular docking. Proceedings of the 44th IEEE Conference on Decision and Control and the European Control Conference 2005, 3675-3680.
17. Bernstein, F.C, Koetzle, T.F., Williams, G.J.B., Meyer, E.F., Jr. Brice, M.D., Rogers, J.R., Kennard, O., Shimanouchi, O.T. and Tasumi, M., 1977, The Protein Data Bank: a computer-based archival file for macromolecular structures. Journal of Molecular Biology, 112, 535-542.
18. Hasel, W., Hendrikson, T.F. and Still, W.C., 1988, A rapid approximation to the solvent accessible surface areas of atoms. Tetrahedron Computational Method, 1, 103-16.
19. Schlick, T., 2002, Molecular Modeling and Simulation (New York: Springer-Verlag).
20. Bradley, P.S., Mangasarian, O.L. and Street, W.N., 1997, Clustering via concave minimization.. In: Michael C. Mozer, Michael I. Jordan and Thomas Petsche (Eds) Advances in Neural Information Processing Systems, Vol. 9 (The MIT Press), pp. 368.
21. Bennett, K.P. and Mangasarian, O.L., 1993, Bilinear separation, of two sets in n-space. Computational Optimization and Applications, 2(3), 207-227.
22. Comeau, S.R., Gatchell, D.W., Vajda, S. and Camacho, C.J., 2004, ClusPro: an automated docking and discrimination method for the prediction of protein, complexes. Bioinformatics, 20(1), 45-50.
23. Welch, M., Chinardet, N., Mourey, L., Birck, C. and Samama, J.P., 1998, Structure of the CheYbinding domain of histidine kinase CheA in complex with CheY. Nature Structual Biology, 5, 25-29.
24. Arold, S., Franken, P., Strub, M.P., Hoh, F., Benichou, S., Benarous, R. and Dumas, C., 1997, The crystal structure of HIV-1 Nef protein bound to the Fyn kinase SH3 domain suggests a role for this complex in altered T cell receptor signaling. Structure, 5, 1361-1372.
25. Tsunogae, Y., Tanaka, I., Yamane, T., Kikkawa, J., Ashida, T., Ishikawa, C., Watanabe, K., Nakamura, S. and Takahashi, K., 1986, Structure of the trypsin-binding domain of Bowman-Birk type protease inhibitor and its interaction with trypsin. Journal of Biochemistry Tokyo, 100, 1637-1646.
26. Buckle, A.M., Schreiber, G. and Fersht, A.R., 1994, Protein-protein recognition: crystal structural analysis of a barnase-barstar complex at 2.0-Å resolution. Biochemistry, 33, 8878-8889.
27. Marquait, M., Walter, J., Deisenhofer, J., Bode, W. and Huber, R., 1983, the geometry of the reactive site and the peptide groups in trypsin, trypsinogen, and its complexes with inhibitors. Acta Crystallography, Section B, 39, 480-490.
28. Tütüncü, R.H., Toh, K.C. and Todd, M.J., 2003, Solving semidefinite-quadratic-linear programs using SDPT3. Mathematical Programming serial B, 95(2), 189-217 (Computational semidefinite and second order cone programming: the state of the art).
29. Helmberg, C., Rendl, F., Vanderbei, R.J. and Wolkowicz, H., 1996, An interior-point method for semidefinite programming. SIAM Journal on Optimization, 6(2), 342-361.
30. Kojima, M., Shindoh, S. and Hara, S., 1997, Interior-point methods for the monotone semidefinite linear complementarity problem in symmetric matrices. SIAM Journal on Optimization, 7(1), 86-125.
31. Monteiro, R.D.C., 1997, Primal-dual path-following algorithms for semidefinite programming. SIAM Journal on Optimization, 7(3), 663-678.