Molecular modeling of proteins and mathematical prediction of protein structure

SIAM Review

Volumn 39, Issue 3, 1997, Pages 407-460

  Neumaier, Arnold ^a  

^a UNIVERSITY OF VIENNA   (Austria)

Author keywords

Dynamic energy minimization; Harmonic approximation; Molecular dynamics simulations; Molecular mechanics; Multiple time scales; Protein folding; Stiffness, differential algebraic equation; Stochastic differential equations; Transition states

Indexed keywords

CONFORMATIONAL ENTROPY; PROTEIN FOLDING; STOCHASTIC DIFFERENTIAL EQUATIONS;

ALGORITHMS; APPROXIMATION THEORY; COMPUTER SIMULATION; CONFORMATIONS; DIFFERENTIAL EQUATIONS; MOLECULAR DYNAMICS; MOLECULAR STRUCTURE; OPTIMIZATION; PARAMETER ESTIMATION; PROBLEM SOLVING;

PROTEINS;

EID: 0031236591     PISSN: 00361445     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036144594278060     Document Type: Article

References (359)

1. R.A. ABAGYAN, Towards protein folding by global energy optimization, FEBS Letters, 325 (1993), pp. 17-22.
2. V.I. ABKEVICH, A.M. GUTIN, AND E.I. SHAKHNOVICH, Free energy landscapes for protein folding kinetics: Intermediates, traps, and multiple pathways in theory and lattice model simulations, J. Chem. Phys. 101 (1994), pp. 6052-6062.
3. M.P. ALLEN AND D.J. TILDESLEY, Computer Simulation of Liquids, Oxford Univ. Press, New York, 1990.
4. P. AMARA, J. MA, AND J.E. STRAUB, Global minimization on rugged energy landscapes, in Global Minimization of Nonconvex Energy Functions: Molecular Conformation and Protein Folding, P. M. Pardalos et al., eds., Amer. Math. Soc., Providence, RI, 1996, pp. 1-15.
5. I.P. ANDROULAKIS, C.D. MARANAS, AND C.A. FLOUDAS, Prediction of oligopeptide conformations via deterministic optimization, J. Global Optim., to appear.
6. F.A.L. ANET, Inflection points and chaotic behavior in searching the conformation space of cyclononane, J. Amer. Chem. Soc., 112 (1990), pp. 7172-7178.
7. N.L. ALLINGER, Y.H. YUH, AND J.-H. LII, Molecular mechanics. The MM3 force field for hydrocarbons, 1-3, J. Amer. Chem. Soc., 111 (1989), pp. 8551-8566, 8566-8575, 8576-8582.
8. A.W. APPEL, An efficient program for many-body simulation, SIAM J. Sci. Statist. Comput., 6 (1985), pp. 85-103.
9. A.C. ATKINSON. Developments in the design of experiments, Internat. Statist. Rev., 50 (1982), pp. 161-177.
10. C.L. ATWOOD, Optimal and efficient designes of experiments, Ann. Math. Statist., 40 (1969), pp. 1570-1602.
11. B.M. AXILROD AND E. TELLER, Interaction of the van der Wools' type between three atoms, J. Chem. Phys., 11 (1943), pp. 299-300.
12. L.M. BALBES, S.W. MASCARELLA, AND D.B. BOYD, A perspective of modern methods in computer-aided drug design, in Reviews in Computational Physics, Vol. V, K.B. Lipkowitz and D.B. Boyd, eds., VCH Publ., New York, 1994, pp 337-379.
13. R.E. BANK, R. BULIRSCH, H. GAJEWSKI, AND K. MERTEN, EDS., Mathematical Modelling and Simulation of Electrical Circuits and Semiconductor Devices, Birkhäuser, Basel, 1994.
14. E. BARTH, K. KUCZERA, B. LEIMKUHLER, AND R.D. SKEEL, Algorithms for constrained molecular dynamics, J. Comput. Chem., 16 (1995), pp. 1192-1209.
15. E. BARTH, M. MANDZIUK, AND T. SCHLICK, A separating framework for increasing the time step in molecular dynamics, in Computer Simulation of Biomolecular Systems: Theoretical and Experimental Applications, W. F. van Gunsteren et al., eds., ESCOM, Leiden, The Netherlands, 1997.
16. G.J. BARTON, Protein secondary structure prediction, Current Opinion in Structural Biology, 5 (1995), pp. 372-376.
17. A. BAUER AND A. BEYER, An improved pair potential to recognize native protein folds, Proteins: Struct. Funct. Gen., 18 (1994), pp. 254-261.
18. J. F. BAZAN, Structural design and molecular evolution of a cytokine receptor superfamily, Proc. Nat. Acad. Sci. USA, 87 (1990), pp. 6934-6938.
19. F.C. BERNSTEIN, T.F. KOETZLE, G.J.B. WILLIAMS, E. MEYER, M.D. BRYCE, J.R. ROGERS, O. KENNARD, T. SHIKANOUCHI, AND M. TASUMI, The protein data bank: A computer-based archival file for macromolecular structures, J. Mol. Biol., 112 (1977), pp. 535-542.
20. M. BILLETER, T.F. HAVEL, AND K. WÜTRICH, The ellipsoid algorithm as a method for the determination of polypeptide conformations from experimental distance constraints and energy minimization, J. Comput. Chem., 8 (1986), pp. 132-141.
21. M. BISHOP AND S. FRINKS. Error analysis in computer simulations, J. Chem. Phys., 87 (1987), pp. 3675-3676.
22. n, in Handbook of Numerical Analysis, P.G. Ciarlet and J.L. Lions, eds., North-Holland, Amsterdam, 1990, pp. 465-652.
23. A. BJÖRCK, Numerical Methods for Least Squares Problems, SIAM, Philadelphia, PA, 1996.
24. J.M. BLANEY AND J.S. DIXON, Distance geometry in molecular modeling, in Reviews in Computational Physics, Vol. V, K.B. Lipkowitz and D.B. Boyd, eds., VCH Publ., New York, 1994, pp. 299-335.
25. J.A. BOARD, J.W. CAUSEY, T.F. LEATHRUM JR., A. WINDEMUTH, AND K. SCHULTEN, Accelerated molecular dynamics simulation with the parallel fast multipole algorithm, Chem. Phys. Lett., 198 (1992), pp. 89-94.
26. B. BORŠTNIK, D. PUMPERNIK, D. JANEŽIČ, AND A. AŽMAN, Molecular dynamics studies of molecular interactions, in Molecular Interaction, H. Ratajczak and W.J. Orville-Thomas, eds., Wiley, New York, 1980.
27. G. BOSSIS, B. QUENTREC, AND J.P. BOON, Brownian dynamics and the fluctuation-dissipation theorem, Mol. Phys., 45 (1982), pp. 191-196.
28. J.P. BOWEN AND N.L. ALLINGER, Simplified models for understanding and predicting protein structure, in Reviews in Computational Chemistry, Vol. II, K.B. Lipkowitz and D.B. Boyd, eds., VCH Publ., New York, 1991, pp. 57-80.
29. J.U. BOWIE AND D. EISENBERG, Inverted protein structure prediction, Current Opinion in Structural Biology, 3 (1993), pp. 437-444.
30. C. BRANDEN AND J. TOOZE, Introduction To Protein Structure, Garland, New York, 1991.
31. K.E. BRENAN, S.L. CAMPBELL, AND L.R. PETZOLD, Numerical Solution of Initial Value Problems in Differential-Algebraic Equations, North-Holland, New York, 1989.
32. T. BRODMEIER AND E. PRETSCH, Application of genetic algorithms in molecular modeling. J. Comput. Chem., 15 (1994), pp. 588-595.
33. B.R. BROOKS, R. BRUCCOLERI, B. OLAFSON, D. STATES, S. SWAMINATHAN, AND M. KARPLUS, CHARMM: A program for macromolecular energy, minimization, and dynamics calculations, J. Comput. Chem., 4 (1983), pp. 187-217.
34. M.L. CONOLLY, Molecular surfaces: A review, Network Science, April 1996. (http.-//www. awod.com/netsci/Issues/Apr96/featurel.html)
35. C.L. BROOKS, M. KARPLUS, AND B.M. PETTITT, Proteins: A Theoretical Perspective of Dynamics, Structure, and Thermodynamics, Advances in Chem. Phys. 71, Wiley, New York, 1988.
36. A. BRÜNGER, C.B. BROOKS, AND M. KARPLUS, Stochastic boundary conditions for molecular dynamics simulations of ST2 water, Chem. Phys. Lett., 105 (1982). pp. 495-500.
37. A.T. BRÜNGER, J. KURIYAN, AND M. KARPLUS, Crystallographic R factor refinement by molecular dynamics, Science, 235 (1987), pp. 458-400.
38. U. BURKERT AND N.L. ALLINGER, Molecular Mechanics, Amer. Chem. Soc., Washington, D.C., 1982.
39. L.J. BUTUROVIĆ, T.F. SMITH, AND S. VAJDA, Finite-state and reduced-parameter representations of protein backbone conformations, J. Comput. Chem., 15 (1994), pp. 300-312.
40. R.H. BYRD, E. ESKOW, R.B. SCHNABEL, AND S.L. SMITH, Parallel global optimization: Numerical methods, dynamic scheduling methods, and applications to molecular configuration, in Parallel Computation, B. Ford and A. Fincham, eds., Oxford University Press, 1993, pp. 187-207.
41. R.H. BYRD, E. ESKOW, A. VAN DER HOEK, R.B. SCHNABEL, AND K.P.B. OLDENKAMP, A parallel global optimization method for method for solving molecular cluster and polymer conformation problems, in Proc. 7th SIAM Conference on Parellel Processing for Scientific Computing, SIAM, 1995, pp. 72-77.
42. R.H. BYRD, E. ESKOW, A. VAN DER HOEK, R.B. SCHNABEL, C.-S. SHAO, AND Z. ZOU, Global optimization methods for protein folding problems, in Global Minimization of Nonconvex Energy Functions: Molecular Conformation and Protein Folding, P. M. Pardalos et al., eds., Amer. Math. Soc., Providence, RI, 1996, pp. 29-39.
43. A. CAFLISCH AND M. KARPLUS, Molecular dynamics studies of protein and peptide folding and unfolding, in The Protein Folding Problem and Tetiary Structure Prediction, K. Merz et al., eds., Birkhäuser, Boston, 1994.
44. C.J. CAMACHO AND D. THIRUMALAI, Minimum energy compact structures of random sequences of heteropolymers, Phys. Rev. Lett., 71 (1993), pp. 2506-3808.
45. C.R. CANTOR AND P.R. SCHIMMEL, Biophysical Chemistry, Freeman, New York, 1980.
46. G. CASARI AND M.J. SIPPL, Structure-derived hydrophobic potential, J. Mol. Biol., 224 (1092). pp. 725-732.
47. H.F. CHAN AND K.A. DILL, Origins of stucture in globular proteins, Proc. Nat. Acad. Sci. USA, 87 (1990), pp. 6388-6392.
48. H.F. CHAN AND K.A. DILL, Polymer principles in protein structure and stability, Ann. Rev. Biophys. Chem., 20 (1991), pp. 447-490.
49. H.F. CHAN AND K.A. DILL, The protein folding problem, Physics Today, February 1993, pp. 24-32.
50. C. CHEN, Y. ZHU, J.A. KING, AND L.B. EVANS, A molecular thermodynamic approach to predict the secondery structure of homopolypeptides in aqueous systems, Biopolymers, 32 (1992), pp. 1375-1392.
51. G. CICCOTTI, D. FRENKEL, AND I.R. MCDONALD, Simulation of Liquids and Solids: Molecular Dynamics and Monte Carlo Methods in Statistical Mechanics, North-Holland, Amsterdam, 1987.
52. G. CICCOTTI AND J.P. RYCKAERT, On the derivation of the generalized Langevin equation for interacting Brownian particles, J. Stat. Phys., 26 (1981), pp. 73-82.
53. M. CLARK, R.D. CRAMER III, AND N. VAN OPDENBOSCH, Validation of the general purpose Tripos 5.2 force field. J. Comput. Chem., 10 (1989), pp. 982-1012.
54. T. CLARK, A Handbook of Computational Chemistry: A Practical Guide to Chemical Structure one Energy Calculations, Wiley-Intencience, New York, 1985.
55. F.E. COHEN, L.M. GREGORET, S.R. PRESNELL, AND I.D. KUNTZ, Theoretical approaches to protein structure prediction, in Protein Folding, L.M. Gierasch and J. King, eds., Amer. Assoc. Adv. Sci., Washington, 1990, pp. 251-258.
56. T. COLEMAN, D. SHALLOWAY, AND Z. WU, A parallel build-up algorithm for global energy minimizations of molecular clusters using effective energy simulated annealing, J. Global Optimization, 4 (1994), pp. 171-186.
57. J.H. CONWAY, T.D.S. DUFF, R.H. HARDIN, AND N.J.A. SLOANE, Minimal-energy clusters of hard spheres, Discr. Comput. Geom., 14 (1995), pp. 237-290.
58. W.D. CORNELL, P. CIEPLAK, C.I. BAYLY, I.R. GOULD, K.M. MERZ, D.M. FERGUSON, D.C. SPELLMEYER, T. Fox, J.W. CALDWELL, AND P.A. KOLLMANN, A second generation force field for the simulation of proteins, nucleic acids, and organic molecules, J. Amer. Chem. Soc., 117 (1995), pp. 5179-5197.
59. D.G. COVELL AND R.L. JERNIGAN, Conformations of folded proteins in restricted spaces, Biochemistry, 29 (1990), pp. 3287-3294.
60. C.J. CRAMER AND D.G. TRUHLAR, Continuum solvation models: Classical and quantum mechanical implementaions, in Reviews in Computational Chemistry, Vol. VI, K.B. Lipkowitz and D.B. Boyd, eds., VCH Pabl., New York, 1995, pp. 1-72.
61. I. P. CRAWFORD, T. NIERMANN, AND K. KIRSCHNER, Predictions of secondary structure Proteins: Struct., Funct. Genetics, 1 (1987), pp. 118-129.
62. T.E. CREIGHTON, Proteins, Structure and Molecular Principles, Freeman, New York, 1984.
63. T.E. CREIGHTON, Understanding protein folding pathways and mechanisms, in Protein Folding, L.M. Gierasch and J. King, eds., Amer. Assoc. Adv. Sci., Washington, 1990, pp. 157-170.
64. G.M. CRIPPEN, Chemical distance geometry: Current realization and future projection, J. Math. Chem., 6 (1991), pp. 307-324.
65. G.M. CRIPPEN, Distance Geometry and Conformational Calculations, Wiley, New York, 1981.
66. G.M. CRIPPEN AND T.F. HAVEL, Distance Geometry and Molecular Conformation, Wiley, New York, 1988.
67. G.M. CRIPPEN AND M.E. SNOW, 4 1.8 Å resolution potential function for protein folding, Biopolymers, 29 (1990), pp. 1479-1489.
68. P. CULOT, G. DIVE, V.H. NGUYEN, AND J.M. GHUYSEN, A quasi-Newton algorithm for first order saddle point location, Theor. Chim. Acta, 82 (1992), pp. 189-205.
69. V. DAGGETT AND M. LEVITT, Protein unfolding pathways explored through molecular dynamics simulatons, J. Mol. Biol., 232 (1993), pp. 600-619.
70. T. DARDEN, D. YORK, AND L. PEDERSEN, Particle mesh Ewald: An N · log(N) method for Ewald sums in large systems, J. Chem. Phys., 98 (1993), pp. 10089-10092.
71. P. DAUBER-OSGUTHORPB, AND D.J. OSGUTHORPE, Partitioning the motion in molecular dynamics simulations into characteristic modes of motion, J. Comput. Chem., 14 (1993), pp. 1259-1271.
72. P. DAUBER-OSGUTHORPE, V.A. ROBERTS, D.J. OSGUTHORPE, J. WOLFF, M. GENEST, AND A.T. HAGLER, Structure and energetics of ligand binding to proteins, Proteins: Struct. Funct. Gen., 4 (1988), pp. 31-17.
73. L. DAVIS, ED., Handbook of Genetic Algorithms, van Nostrand Reinhold, New York, 1991.
74. J.E. DENNIS AND R.B. SCHNABEL, Numerical methods for unconstrained optimization and nonlinear equations, Classics in Applied Math. 16, SIAM, Philadelphia, PA, 1996.
75. P. DERREUMAUX AND G. VERGOTEN, Influence of the spectroscopic potential energy function SPASIBA on molecular dynamics of proteins: Comparison with the AMBER potential, J. Mol. Struct., 286 (1993), pp. 55-64.
76. P. DERREUMAUX, G. ZHANG, T. SCHLICK, AND B. BROOKS, A truncated Newton minimizer adapted for CHARMM and biomolecular applications, J. Comput. Chem., 15 (1994), pp. 532-552.
77. J.M. DEUTCH AND I. OPPENHEIM, Molecular theory of Brownian motion for several particles, J. Chem. Phys., 54 (1971), pp. 3547-3555.
78. K.A. DILL, S. BROMBERG, K. YUE, K.M. FIEBIG, D.P. YEE, P.D. THOMAS, AND H.S. CHAN, Principles of protein folding - a perspective from simple exact models, Protein Science, 4 (1995), pp. 561-602.
79. K.A. DILL, A.T. PHILLIPS, AND J.B. ROSEN, Molecular structure prediction by global optimization, in Developments in Global Optimization, I.M. Botnze et al., eds., Kluwer, Dordrecht, 1997, pp. 217-234.
80. U. DINUR AND A.T. HAGLER, New approaches to empirical force fields, in Reviews in Computational Chemistry, Vol. II, K.B. Lipkowitz and D.B. Boyd, eds., VCH Publ., New York, 1991, pp. 99-164.
81. C.M. DOBSON, Unfolded proteins, compact states and molten globules, Current Opinion Struct. Biol., 2 (1992), pp. 6-12.
82. S. DOSANJH AND W.J. CAMP, Computational design of materials: Part II, SIAM News, May/June 1994, pp. 10-11.
83. N. DRAPER AND H. SMITH, Applied Regression Analysis, 2nd ed., Wiley, New York, 1981.
84. R.L. DUNBACK AND M. KARPLUS, Backbone-dependent rotamer library for proteins, Application to side-chain prediction, J. Mol. Biol., 230 (1993), pp. 543-574.
85. R.L. DUNBACK AND M. KARPLUS, Conformational analysis of the backbone-dependent rotamer preferences of protein sidechains, Struct. Biol., 1 (1994), pp. 334-340.
86. J.D. DUNITZ, H. ESER, M. BIXON, AND S. LIFSON, Die Strukturen der mittleren Ringverbindungen XII - XIII, Helvetica Chimica Acta, 50 (1967), pp. 1565-1572, 1572-1583.
87. Y. J. K. EDWARDS AND S.J. PERKINS, The protein fold of the von Willebrand factor type A is predicted to be similar to the open twisted beta-sheet flanked by alpha-helices found in human ras-p21, FEBS Letters 358 (1995), pp. 283-286.
88. J.E. EKSTEROWICZ AND K.N. HOUK, Transition state modeling with empirical force fields, Chem. Rev., 93 (1993), pp. 2439-2461.
89. R. ELBER AND M. KARPLUS, Multiple conformational states of proteins: A molecular dynamics analysis of myoglobin, Science, 235 (1987), pp. 318-321.
90. R.A. ENGH AND R. HUBER, Accurate bond and angle parameters for X-ray protein structure refinement, Acta Cryst., A47 (1991), pp. 392-400.
91. U. ESMANN, L. PERERA, M.L. BERKOWITZ, T. DARDEN, H. LEE, AND L.G. PEDERSEN, A smooth particle mesh Ewald method, J. Chem. Phys., 103 (1995), 8577-8593.
92. P. EWALD, Ann Phys., 64 (1921), pp. 253-287.
93. L. FARNELL, W.G. RICHARDS, AND C.R. GANELLIN, Calculation of conformational free energy of histamine, J. Theor. Biol., 43 (1974), pp. 389-392.
94. V.V. FEDOROV, Theory of optimal experiments, Acad. Press, London, 1972.
95. D.M. FERGUSON, A. MARSH, T. METZGER, D. GARRETT, AND K. KASTELLA, Conformational searches for the global minimum of protein models, J. Global Optim., 4 (1994), pp. 209-227.
96. J.S. FETROW AND S.H. BRYANT, New programs for protein tertiary structure prediction, Bio/tecnology, 11 (1993), pp. 479-484.
97. R. FLETCHER, Practical Methods of Optimization, Wiley, New York, 1987.
98. G. FOGARASI AND P. PULAY, Ab initio calculation of force fields one vibrational spectra, in Vibrational Spectra and Structure, Vol. 14, J.R. During, ed., Elsevier, Amsterdam, 1985, pp. 125-219.
99. S. FORTIER, I. CASTLEDEN, J. GLASGOW, D. CONKLIN, C. WALMSLEY, L. LEHERTE, AND F.A. ALLEN, Molecular scene analysis: The intergration of direct-method and artificial intelligence strategies for solving protein crystal structures, Acta Cryst., D49 (1993), pp. 168-178.
100. M.S. FRIEDRICHS, R.A. GOLDSTEIN, AND P.G. WOLYNES, Generalized protein tertiary structure recognition using associative memory Hamiltonians, J. Mol. Biol., 222 (1991), pp. 1013-1034.
101. H. FRÖHLICH, Theory of Dielectris, Clarendon Press, Oxford, 1958.
102. K. FUKUNAGA, Introduction to Statistical Pattern Recognition, 2nd ed., Academic Press, London, 1990.
103. C.W. GARDINER, Handbook of Stochastic Methods, Springer, Berlin, 1985.
104. J. GARNIER, Protein structure prediction, Biochime, 72 (1990), pp. 513-524.
105. D.L. GERLOFF, G. CHELVANAYAGAM, AND S.A. BENNER, A predicted consensus structure for the protein-kinase c2 homology (c2h) domain, the repeating unit of synaptotagmin, Proteins: Struct., Funct. Genetics, 22 (1995), pp. 299-310.
106. C. GIACOVAZZO, ED., Fundamendals of Crystallography, Oxford Univ. Press, Oxford, 1985.
107. J. GIBRAT, J. GARNIER, AND N. GO, Normal mode analysis of oligomeric proteins: Reduction of the memory requirements by consideration of rigid geometry and molecular symmetry, J. Comput. Chem., 15 (1994), pp. 820-837.
108. J. GIBRAT, J. GARNIER, AND B. ROBSON, Further developments of secondary structure predictions using information theory: New parameters and consideration of residue pairs, J. Mol. Biol., 198 (1987), pp. 425-443.
109. K.D. GIBSON AND H.A. SCHERAGA, Desicions in force field development. Reply to Kollman and Dill, J. Biomol. Struct. Dyn., 8 (1991), pp. 1109-1111.
110. L.M. GIERASCH AND J. KING, Protein Folding: Deciphering the Second Half of the Genetic Code, Amer. Assoc. Advancement Sci., Washington, 1990.
111. T.L. GILBERT, Soft-sphere model for closed-shell atoms and ions, J. Chem. Phys., 49 (1968), pp. 2640-2642.
112. P.E. GILL, W. MURRAY, AND M.H. WRIGHT, Practical Optimization, Acad. Press, London, 1981.
113. M.K. GILSON, K.A. SHARP, AND B.H. HONIG, Calculating the electrostatic potential of molecules in solution: Methods and error assessment, J. Comput. Chem., 9 (1987), pp. 327-335.
114. A. GODZIK, A. KOLINSKI, AND J. SKOLNICK, Topology fingerprint approach to the inverse folding problem, J. Mol. Biol., 227 (1992), pp. 227-238.
115. A. GODZIK, A. KOLINSKI, AND J. SKOLINCK, De novo and inverse folding predictions of protein structure and dynamics, J. Computer-Aided Mol. Des., 7 (1993). pp. 397-438.
116. A. GODZIK, A. KOLINSKI, AND J. SKOLNICK, Lattice represntations of globular proteins: How good are they?, J. Comput. Chem., 14 (1993), pp. 1194-1202.
117. R.A. GOLDSTEIN, Z.A. LUTHEY-SCHULTEN, AND P.G. WOLYNES, The Statistical Mechanical Basis of Sequence Alignment Algorithms for Protein Structure Recognition, manuscript, 1993.
118. N. GO AND H.A. SCHERAGA, Analysis of the contribution of internal vibrations to the statistical weights of equilibrium conformations of macromolecules, J. Chem. Phys., 51 (1969), pp. 4751-4767.
119. S.K. GRAY, D.W. NOID, AND B.G. SUMPTER, Symplectic integrators for large-scale molecular dynamics simulations: A comparison of several explicit methods, J. Chem. Phys., 101 (1994), pp. 4062-4072.
120. L. GREENGARD AND V. ROKHLIN, The rapid evaluation of potential fields in three dimensions, in Vortex Methods, C. Anderson and C. Greengaard, eds., Lecture Notes in Math., Springer, 1988, pp 121-141.
121. A. GREINER, W. STRITTMATTER, AND J. HONERKAMP, Numerical intergration of stochastic differential equations, J. Statist. Phys., 51 (1988). pp. 95-108.
122. T. GUND AND P. GUND, Three-dimensional molecular modeling by computer, in Molecular Structure and Energetics, J.F. Liebman and A. Greenberg, eds., 1987, pp. 319-340.
123. J. R. GUNN, A. MONGE, R.A. FRIESNER, AND MARSHALL, Hierarchical algorithm for computer modeling of protein tertiary structure: Folding of myoglobin to 6.2A resolution, J. Phys. Chem., 98 (1994), pp. 702-711.
124. Z. GUO, D. THIRUMALAI, AND J.D. HONEYCUTT, Folding kinetics of proteins: A model study, J. Chem. Phys., 97 (1992), pp. 525-535.
125. P. HÄNGGI, P. TALKNER, AND M. BORKOVEC, Reaction-rate theory: Fifty years after Kramers, Rev. Modern Phys., (1990), pp. 251-341.
126. A.T. HAGLER, D.J. OSGUTHORPE, P. DAUBER-OSGUTHORPE, AND J.C. HEMPEL, Dynamics and conformational energetics of a peptide hormone: Vasopressin, Science, 227 (1985), pp. 1309-1315.
127. E. HAIRER, C. LUBICH, AND M. ROCHE, The numerical solution of differential-algebraic systems by Runge-Kutta methods, Lecture Notes in Math. 1409, Springer, Berlin, 1989.
128. E. HAIRER, S.P. NORSETT, AND G. WANNER, Solving Ordinary Differential Equations I, 2nd rev ed., Springer, Berlin, 1993.
129. E. HAIRER AND G. WANNER, Solving Ordinary Differential Equations II, Springer, Berlin, 1991.
130. E. HANSEN, Global Optimization Using Internal Analysis, Dekker, New York, 1992.
131. M.-H HAO AND S.C. HARVEY, Analyzing the normal mode dynamics of macromolecules by the component synthesis method, Biopolymers, 32 (1992), pp. 1395-1405.
132. T. HEAD-GORDON AND F.H. STILLINGER, Predicting polypeptide and protein structures from amino acid sequence: Antlion method applied to melittin, Biopolymers, 33 (1993), pp. 293-303.
133. T. HEAD-GORDON, F.H. STILLINGER, AND J. ARRECIS, A strategy for finding classes of minima on a hypersurface: Implications for approaches to the protein folding problem, Proc. Nat. Acad. Sci. USA, 88 (1991), pp. 11076-11080.
134. T. HEAD-GORDON, F.H. STILLINGER, M.H. WRIGHT, AND D.M. GAY, Poly(L-alanine) as a universal reference material for understanding protein energies and structures, Proc. Nat. Acad. Sci. USA. 89 (1992), pp. 11513-11517.
135. M. HENDLICH, P. LACKNER, S. WEITCKUS, H. FLOECKNER, R. FROSCHAUER, K. GOTTSBACHER, G. CASARI, AND M. J. SIPPL, Identification of native protein folds amongst a large number of incorrect models, J. Mol. Biol., 216 (1990), pp. 167-180.
136. W.A. HENDRICKSON, Methods EncymoL, 115 (1985), pp. 252-270.
137. D.M. HIRST, A Computational Approach to Chemistry, Blackwell Sci. Publ., Oxford, 1990.
138. M.R. HOARE, Structure and dynamics of simple microclusters, Adv. Chem. Phys., 40 (1979), pp. 49-135.
139. M.R. HOARE AND J.A. MCINNES, Morphology and statistical statics of simple microclusters, Adv. Phys., 32 (1983), pp. 791-821.
140. U. HOBOHM, M. SCHARF, R. SCHNEIDER, AND C. SANDER, Selection of representative protein data sets, Protein Sci., 1 (1992), pp. 409-117.
141. C. HOHEISEL, Theoretical Treatment of Liquids and Liquid Mixtures, Elsevier, Amsterdam, 1993.
142. J. HOLLAND, Genetic algorithms and the optimal allocation of trials, SIAM J. Comput., 2 (1973), pp. 88-105.
143. L. HOLLEY AND M. KARPLUS, Protein secondary structure prediction with a neural network, Proc. Nat. Acad. Sci. USA. 86 (1989), pp. 152-156.
144. J. HONERKAMP, Stochastic Dynamical Systemes Concepts, Numerical Methods, Data Analysis, VCH Publishers, New York, 1994.
145. J.D. HONEYCUTT AND D. THIRUMALAI, The nature of folded states of globular proteins, Biopolymers, 32 (1992), pp. 695-709.
146. B. HONIG AND A. NICHOLLS, Clastical electrostatics in biology and chemistry, Science, 268 (1995), pp. 1144-1149.
147. A.J. HOPFINGER AND R.A. PEARLSTEIN, Molecular mechanics force-field parametriation procedures, J. Comput. Chem., 5 (1984), pp. 486-499.
148. Q.X. HUA, M. KOCHOYAN, AND M.A. WEISS, Structure and dynamics of despentapeptide-insulin in solution: The molten globule hypothesis, Proc Nat. Acad. Sci. USA, 89 (1992), pp. 2379-2383.
149. Q.X. HUA, J.E. LADBURY, AND M.A. WEISS, Dynamics of a monomeric insulin analogue: Testing the molten globule hypothesis, Biochemistry, 33 (1993), pp. 1433-1442.
150. A. INIESTA AND J.G. DB LA TORRE, A second-order algorithm for the Simulation of the Brownian dynamics of macromolecular models, J. Chem. Phys., 92 (1990), pp. 2015-3018.
151. G. IORI, E. MARINARI, AND G. PARISI, Heteropolymer folding en a APE-100 supercomputer, Int. J. Modern Physics C, 4 (1993), pp. 1333-1341.
152. A. IRBÄCK, C. PETERSON, AND F. POTTHAST, Identification of amino acid sequences with good folding properties, Phys. Rev. E, 55 (1997), p. 860.
153. A. IRBÄCK AND F. POTTHAST, studies of an off-lattice model for protein folding: Sequence dependence and improved sampling at finite temperature, J. Chem. Phys., 103 (1995), p. 10298
154. IUPAC-IUP COMMISSION ON BIOCHEMICAL NOMENCLATURE, Abbreviations and symbols for the description of the conformation of polypeptide chains, Biochemistry, 9 (1970), pp. 3471-3479.
155. R. JAENICKE, Protein folding: Local structures, domains, subunits, and assemblies, Biochemistry, 30 (1991), pp 3147-3161.
156. O. JARDETZKY AND A.N. LANE, Determination of the solution structure of proteins from NMR, in Physics of NMR Spectroscopy in Biology and Medicine, B. Maraviglia, ed., North-Holland, Amsterdam, 1988, pp. 367-301.
157. M.S. JOHNSON, N. SRINIVASAN, R. SOWDHAMINI, AND T.L. BLUNDELL, Knowledge-based protein modeling, Crit. Rev. Biochem. Mol. Biol., 29 (1994), pp. 1-68.
158. D. JONES AND J. THORNTON, Protem fold recognition, J. Comput. Aided Mol. Design, 7 (1903), pp. 439-456.
159. W. KABSCH, A discussion of the solution for the best rotation to relete two sets of vectors, Acta Cryst. A, 34 (1978), pp 827-828.
160. H.S. KANG, N.A. KUROCHKINA, AND B. LEE, Estimation and use of protein bacbone angle probelilities, J. Mol. Biol., 229 (1993), pp. 448-460.
161. I.G. KAPLAN, Theory of Molecular Interactions, Elsevier, Amsterdam, 1986.
162. M. KARPLUS, A. CAFLISH, A. ṠALI, AND E. SHAKNOVICH, Protein dynamics: From the native to the unfolded state and back again, in Proc. Int. Conf. Mol. Struct. Biol., Vienna, September 17-20, 1995, A.J. Kungl. et al., eds., Gesellschaft Österreichischer Chmiker, Wien, 1996, pp. 129-155.
163. H. KAWAI, T. KIKUCHI, AND Y. OKAMOTO, A prediction of tertiary structures of peptide by the Monte Carlo simulated annealing method, Protein Eng., 3 (1989), pp. 85-94.
164. T. KIHARA AND S. ICHIMARU, Intramolecular Forces, Wiley, Chishester, 1978.
165. S. KIRKPATRICK, C.D. GEDDAT, JR., AND M.P. VECCHI, Optimization by simulated annealing, Science, 230 (1983), pp. 671-680.
166. P.E. KLOEDEN AND E. PLATEN, Numerical Solution of Stochastic Differential Equations, Springer, Berlin, 1992.
167. P.E. KLOEDEN, E. PLATEN, AND H SCHURZ, Numerical Solution of SDE Through Computer Experiments, Springer, Berlin, 1994.
168. D. KNELLER, F. COHEN, AND R. LANGRIDGE, Improvements in protein secondary structure predictions by an enhanced neural network, J. Mol. Biol., 214 (1990), pp. 171-182.
169. H. KÖPPEN, The use of supercomputer in medical chemistry. Examples from peptide and protein projects, in Supercomputer and Chemistry, U. Harms, ed., Springer, Berlin, 1990, pp. 99-113.
170. A. KOLINSKI, A. GODZIK, AND J. SKOLNICK, A general method for the prediction of the three dimensional structure and folding pathway of globular proteins: Application to designed helical proteins, J. Chem. Phys., 98 (1993), pp. 7420-7433.
171. J. KOSTROWIKI, L. PIELA, B.J. CHERAYIL, AND H. SCHERAGA, Perfomance of the diffusion equation method in searches for optimum structures of clusters of Lennard-Jones atoms, J. Phys. Chem., 95 (1991), pp. 4113-4119.
172. J. KOSTROWICKI AND H.A. SCHERAGA, Application of the diffusion equation method for global optimization to oligopeptides, J. Phys. Chem., 96 (1992), pp. 7442-7449.
173. J. KOSTROWICKI AND H.A. SCHERAGA, Some approaches to the multiple-minima problem in protein folding, in Global Minimization of Nonconvex Energy Functions: Molecular Confomation and Protein Folding, P. M. Paradalos et al., Amer. Math. Soc., Providence, R1, 1996, pp. 123-132.
174. S. KRIMM, Spectra and structure of polypeptides, in Vibrational Spectra and Structure, Vol. 16, J.R. During, ed., Elsevier, Amsterdam, 1987, pp. 1-72.
175. B.M. LADANYI AND M.S. SKAF, Computer simulation of hydrogen-bonding liquids, Ann. Rev. Phys. Chem., 44 (1993), pp. 335-368.
176. M. LAMBERT AND H. SCHERAGA, Pattern recognition in the prediction of structure, I-III, J. Comput. Chem., 10 (1989), pp. 770-797; 798-816; 817-831.
177. E.S. LANDER AND M.S. WATERMAN, Calculating the Secrets of Life: Contributions of the Mathematical Sciences to Molecular Biology, National Academic Press, Washington, D.C., 1995.
178. R.H. LATHROP AND T.F. SMITH, Global optimum protein threading with gapped alignment and empirical pair score functions, J. Mol. Biol., 255 (1996), pp. 641-655.
179. A.R. LEACH, A survey of methods for searching the conformational space of small and mediumsized molecules, in Reviews in Computational Chemistry, Vol. II, K.B. Lopkowitz and D.B. Boyd, eds., VCH Publ., New York, 1991, pp. 1-55.
180. T. LEE, D.M. YORK, AND W. YANG, A new definition of atomic charges based on a variational principle for the electrostatic potential energy, J. Chem. Phys., 102 (1995), pp. 7549-7556.
181. C. LEE AND S. SUBBIAH, Prediction of protein side-chain conformation by packing optimization, J. Mol. Biol., 217 (1991), pp. 373-388.
182. S.L. LE GRAND AND K.M. MERZ JR., The application of the genetic algorithm to the minimization of potential energy functions, J. Global Optim., 3 (1993), pp. 49-66.
183. C. M.-R. LEMER, M.J. ROOMAN, AND S.J. WODAK, Protein structure perdiction by threading methods: Evaluation of current techniques, Proteins: Strict. Funct. Gen., 23 (1995), pp. 337-355.
184. P.E. LEOPOLD, M. MONTAL, AND J.N. ONUCHIC, Protein folding funnels: A kinetic approach to the sequence-structure relationship, Proc. Nat. Acad. Sci. USA, 89 (1992), pp. 8721-8725.
185. C. LEVINTHAL, Are there pathways to protein folding? J. Chem. Phys., 65 (1968), pp. 44-45.
186. M. LEVITT, C. SANDER, AND P.S. STERN, Protein normal-mode dynamics: Trypsin inhibitor, crambin, ribonuclease and lysozyme, J. Mol. Biol., 181 (1985), pp. 423-447.
187. R. M. LEVY, R.P. SHERIDAN, J.W. KEEPERS, G.S. DUBEY, S. SWAMINATHAN, AND M. KARPLUS, Molecular dynamics of myoglobin at 298° K. Biophys. J., 48 (1985), pp. 509-518.
188. Z. LI AND H.A. SCHERAGA, Monte Carlo approach to the multiple-minima problem in protein folding, Proc. Nat. Acad. Sci. USA, 84 (1987), pp. 15-29.
189. S. LIFSON, Potential energy functions for structural molecular biology, in Supramolecular Structure and Function, G. Pifat and J.N. Herak, eds., Plenum, New York, 1983, pp. 1-44.
190. K.B. LIPKOWITZ AND D.B. BOYD, Reviews in Computational Chemistry, Vol. I-VII, VCH Publ., New York, pp. 1990-1996, pp. 1-44.
191. J. MA AND J.E. STRAUB, Simulated annealing using the classical density distribution, J. Chem. Phys., 101 (1994), pp. 533-541.
192. R. MÄRZ, Numerical methods for differential-algebraic equations, in Acta Numerica 1992, A. Iserles, ed., Cambridge Univ. Press, Cambridge, 1992, pp. 141-198.
193. V.N. MAIOROV AND G.M. CRIPPEN, Contact potential that recognizes the correct folding of globular proteins, J. Mol. Biol., 227 (1992). pp. 876-888.
194. G.G. MAITLAND, M. RIGBY, E.B. SMITH, AND W.A. WAKEHAM, Intermolecular Forces. Their Origin and Determination, Clarendon Press, Oxford, 1981.
195. J.R. MAPLE, M.-J. HWANG, T.P. STOCKFISCH, U. DINUR, M. WALDMAN, C.S. EWING, AND A.T. HAGLER, Derivation of Class II Force Fields. I. Methodology and Quantum Force Field for the Alkyl Functional Group and Alkane Molecules. J. Comput. Chem., 15 (1994), pp. 162-182.
196. C.D. MARANAS AND C.A. FLOUDAS, A global optimization approach for Lennard- Jones microclusters. J. Chem. Phys., 97 (1992). pp. 7667-7678.
197. C.D. MARANAS AND C.A. FLOUDAS. Global minimum potential energy conformations of small molecules, J. Global Optim., 4 (1994), pp. 135-170.
198. C.D. MARANAS AND C.A. FLOUDAS, A deterministic global optimization approach for molecular structure determination. J. Chem. Phys., 100 (1994), pp. 1247-1261.
199. C.D. MARANAS, I.P. ANDROULAKIS, AND C.A. FLOUDAS, A deterministic global optimization approach for the protein folding problem, in Global Minimization of Nonconvex Energy Functions: Molecular Conformation and Protein Folding, P. M. Pardaloe et al., eds., Amer. Math. Soc., Providence, RI, 1996, pp. 133-150.
200. P. MATSTOMS, Sparse QR Factorization in MATLAB, ACM Trans. Math. Software, 20 (1994). pp. 136-150.
201. J.A. MCCAMMON AND S.C. HARVEY, Dynamics of Proteins and Nucleic Acids, Cambridge Univ. Press, Cambridge, 1997.
202. J.A. MCCAMMON AND M. KARPLUS, Simulation of protein dynamics, Ann. Rev. Phys. Chem., 31 (1980), pp. 29-45.
203. M.L. MCKES AND M. PAGE, Computing reaction pathways on molecular potential energy surfaces, in Reviews in Computational Physics, Vol. IV, K.B. Lipkowitz and D.B. Boyd, eds., VCH Publ., New York, 1993, pp. 337-379.
204. P.G. MEZEY, Potential Energy Hypersurfaces, Elsevier, Amsterdam, 1987.
205. S. MIYAZAWA AND R.L. JERNIGAN, A new subsitution matriz for protein sequence searches based on contact frequencies in protein structures, Protein Eng., 6 (1993), pp. 267-278.
206. A.D. MIRANKER AND C.M. DOBSON, Collapse and cooperativity in protein folding, Current Opinion Struct. Biol., 6 (1996), pp. 31-42.
207. S. MIYAMOTO AND P.A. KOLLMAN, SETTLE: An analytic version of the SHAKE end RATTLE algorithm for rigid water models, J. Comput. Chem., 13 (1992), pp. 952-962.
208. J. MOCKUS, Bayesian Approach to Global Optmization, Kluwer, Dordrecht, 1989.
209. F.A. MOMANY, R.F. MCGUIRE, A.W. BURGESS, AND H.A. SCHERAGA, Energy parameters in polypeptides, VIII, J. Phys. Chem., 79 (1975), pp. 2381-2381.
210. F.A. MOMANY, V.J. KLIMKOWSKI, AND L. SCHÄFER, On the use of conformationally dependent geometry trends from ab initio dipeptide studies to refine potentials for the empirical force field CHARMM, J. Comput Chem., 11 (1990), pp. 654-662.
211. F. MOMANY, R. MCGUIRE, A. BURGESS, AND H. SCHERAGA, Energy parameters in polypeptides VII, J. Phys. Chem., 79 (1975), pp. 2381-2381.
212. A. MONGE, R.A. FRIESNER, AND B. HONIG, An algorithm to generate low-resolution protein tertiary structures from knowledge of secondary structure, Proc Nat. Acad. Sci. USA, 91 (1994), pp. 5027-5029.
213. J.J. MORÉ AND Z. WU, Global continuation for distance geometry problems, SIAM J. Optim., 7 (1997), pp. 814-837.
214. J.J. MORÉ AND Z. WU, Smoothing techniques for macromolecular global optimization, in Nonlinear Optimization and Applications, G. DiPillo and F. Gianessi, eds., 1996, pp. 297-312.
215. B.T. NALL AND K.A. DILL, Conformations and Forces in Protein Folding, Amer. Asoc. Adv. Sci., Washington, 1991.
216. S.G. NASH, Preconditioning of truncated Newton methods, SIAM J. Sci. Statist. Comput., 6 (1985), pp. 599-616.
217. NATIONAL RESEARCH COUNCIL, Mathematical Challenges from Theoretical/Computational Chemistry, National Academy Press, Washington, D.C., 1995. (available via the World Wide Web. http://www.nas.edu)
218. G. NÉMETHY, K.D. GIBSON, K.A. PALMER, C.N. YOON, G. PATERLINI, A. ZAGARI, S. RUMSEY, AND H.A. SCHERAGA, Energy parameters in polypeptides. 10. Improved geometrical parameters and nonbonded interactions for use in the ECEPP/3 algorithm, with application to proline-containing peptides, J. Phys. Chem., 96 (1992), pp. 6472-6484.
219. G.L. NEMHAUSER AND L.A. WOLSEY, Integer programming, in Optimization, G.L. Nemhauser et al., eds., Handbooks in Operations Research and Management Science, Vol. 1, North-Holland, Amsterdam, 1989, pp. 447-527.
220. A. NEUMAIER, Interval Methods for Systems of Equations, Campridge Univ. Press, Cambridge, 1990.
221. A. NEUMAIER, Second-order sufficient optimality conditions for local and global nonlinear programming, J. Global Optim., 9 (1996), pp. 141-151.
222. A. NICHOLLS AND B. HONIG, A rapid finite difference algorithm, utilizing successive overrelazation to solve the Pisson-Boltzmann equation, J. Comput. Chem., 12 (1991), pp. 435-145.
223. J.A. NORTHBY, Stucture and binding of Lennard-Jones clusters: 13 ≤ N ≤ 147, J. Chem. Phys., 87 (1987), pp. 6166-6177.
224. J. NOVOTNŸ, R. BRUCCOLERI, AND M. KARPLUS, An analysis of incorrectly folded protein models, J. Mol. Biol., 177 (1984), pp. 787-818.
225. W.K. OLSON, How flexible is the furanose ring? An updated potential energy estimate, J. Amer. Chem. Soc., 104 (1982), pp. 278-286.
226. J.N. ONUCHIC, P.G. WOLYNES, Z. LUTHEY-SCHULTEN, AND N.D. SOCCI, Toward an outline of the topography of a realistic protein-folding funnel, Proc. Nat. Acad. Sci. USA, 92 (1995), pp. 3626-9630.
227. M. OOBATAKE AND G.M. CRIPPEN, Residue-residue potential function for conformational analysis of proteins, J. Phys. Chem., 85 (1981), pp. 1187-1197.
228. P.M. PARDALOS, D. SHALLOWAY, AND G. XUE, Optimization methods for computing global minima of nonconvex potential energy functions, J. Global Optim. 4 (1994), pp. 117-133.
229. P.M. PARDALOS, D. SHALLOWAY, AND G. XUE, EDS., Global Minimization of Nonconvex Energy Functions: Molecular Conformation and Protein Folding, Amer. Mat. Soc., Providence, RI, 1996.
230. B.N. PALETT, The Symmetric Eigenvalue Problem, Prentice-Hall, Englewood Cliffs, NJ, 1980.
231. R.W. PASTOR, Techniques and applications of Langevin dynamics simulations, in The molecular dynamics of liquid crustals, G.R. Luckhurst and C.A. Veracini, eds., Kluwer, Dordrecht, 1994, pp. 85-138.
232. R.W. PASTOR, B.R. BROOKS, AND A. SZABO, An analysis of the accuacy of Langevin and molecular dynamics algorithm, Mol. Phys., 65 (1988), pp. 1409-1419.
233. D.A. PEARLMAN AND P.A. KOLLMAN, Evaluating the assuptions underlying force field development and application using free energy coformational maps for nucleosides, J. Amer. Chem. Soc., 113 (1991), pp. 7167-7177.
234. G. PERROT, B. CHENG, K.D. GIBSON, J. VILA, K.A. PALMER, A. NAYEEM, B. MAIGRET, AND H.A. SCHERAGA, MSEED: A program for the analytic determination of accessible s uface areas and their derivatives, J. Comput. Chem., 13 (1992), pp. 1-11.
235. W.B. PERSON AND K. SZCEPANIAK, Calculated and experimental vibrational spectra and force fields for isolated pyrimidine bases, in Vibrational Spectra and Structure, Vol. 20, J.R. Durig, ed., Elsevier, Amsterdam, 1993, pp. 240-325.
236. C.S. PESKIN AND T. SCHLICK, Molecular dynamics by the backward-Euler method, Comm. Pure Appl. Math., 42 (1989), pp. 1001-1031.
237. A.T. PHILLIPS AND J.B. ROSEN, A quadratic assignment formulation of the molecular conformation problem, J. Global Optim., 4 (1994), pp. 229-241.
238. L. PIELA, J. KOSTROWICKI, AND H.A. SCHERAGA, The multiple-minima problem in the confomational analysis of molecules. Deformation of the protein energy hypersurface by the diffusion equation method, J. Phys. Chem., 93 (1989), pp. 3339-3346.
239. S.B. PRUSINER, The prion disease, Scientific American, January 1995, pp. 30-37.
240. F. PUKELSHEIM, On linear regression designs which maximize information, J. Statist. Plann. Inference, 4 (1980), pp. 339-364.
241. N. QIAN AND T. SEJNOWSKI, Predicting the secondary structure of globular proteins using neural network models, J. Mol. Biol., 202 (1988), pp. 865-884.
242. H. RABITZ, Systems sensitivity analysis at the molecular scale, Science, 246 (1989), pp. 221-226.
243. A.A. RABOW AND H.A. SCHERAGA, Lattice neural network minimization, J. Mol. Biol., 232 (1993), pp. 1157-1168.
244. S. RACKOVSKY, On the nature of the protein folding code, Proc. Nat. Acad. Sci. USA, 90 (1993), pp. 644-648.
245. S.E. RADFORD AND C. M. DOBSON, Insight into protein folding using physical techniques: Studies of lysozome and α-lactalbumin, Phil. Trans. R. Soc. Lond. B, 348 (1995), pp. 17-25.
246. C. RADIN AND L.S. SCHULMANN, Periodicity of classical ground states, Phys. Rev. Lett., 51 (1983), pp. 621-622.
247. G. RAMACHANDRAN AND T. SCHLICK, Beyond optimization: Simulating the dynamics of supercoiled DNA by a macroscopic mode, in Global Minimization of Nonconvex Energy nctions: Molecular Conformation and Protein Folding, P.M. Pardalos et al., eds., Amer Math. Soc., Providence, RI, 1996, pp. 215-231.
248. L. REGAN, S.P. Ho, Z. WASSERMAN, AND W.F. DE GRADO, Helical proteins. De novo designs, in Protein Folding, L.M. Gierasch and J. King, eds., Amer. Assoc. Adv. Sci., Washington, 1990, pp. 171-176.
249. W.G. RICHARDS, Calculation of conformational free energy of histamine, J. Theor. Biol., 43 (1974), p. 389.
250. T.J. RICHMOND, Solvent accessible surface area and excluded volume in proteins, J. Mol. Biol., 178 (1984), pp. 63-89.
251. F. RICHARDS. The protein folding problem, Scientific American, 264, (January 1991), pp. 54-63.
252. B. ROBSON AND J. GARNIER, Introduction to Proteins and Protein Engineering, Elsevier, New York, 1986.
253. G.D. ROSE AND T.P. CREAMER, Protein folding: Predicting predicting. Proteins: Struct., Funct. Gen., 19 (1994), pp. 1-3.
254. B. ROST AND C. SANDER, Prediction of protein secondary structure at better than 70% accuracy, J. Mol. Biol., 232 (1993), pp. 584-599.
255. I.K. ROTERMAN, M.H. LAMBERT, K.D. GIBSON, AND H.A. SCHERAGA, A comparison of the CHARMM AMBER and ECEPP potentials for peptides. II. φ - ψ maps for N-acetyl alanine N′-methyl amide: Comparisons, contrasts and simple experimental tests, J. Biomol. Struct. Dyn., 7 (1989), pp. 421-453.
256. R. B. RUSSELL AND M. J. E. STERNBERG, Protein structure prediction; How good are we?, Current Biology, 5 (1995), pp. 488-490.
257. J.P. RYCKAERT, C. CICCOTTI, AND H.J.C. BERENDSEN, Numerical integration of the cartesian equations of motion of a system with constraints: Molecular dynamics of n-alcanes, J. Comp. Phys., 23 (1977), pp. 327-341.
258. D.S. RYKUNOV, B.A. REVA, AND A.V. FINKELSTEIN, Accurate general method for lattice approximation of three-dimensional structure of a chain molecule, Proteins: Struct. Func. Gen., 22 (1995), pp. 100-109.
259. A. ŠALI, E. SHAKHNOVICH, AND M. KARPLUS, How does a protein fold?, Nature, 369 (1994), pp. 248-251.
260. A. ŠALI, E. SHAKHNOVICH, AND M. KARPLUS, Kinetics of protein folding. A lattice model study of the requirments for folding to the native state, J. Mol. Biol., 235 (1994), pp. 1614-1638.
261. A. ŠALI, E. SHAKHNOVICH, AND M. KARPLUS, Thermodynamics and kinetics of protein folding, in Global Minimization of Nonconvex Energy Functions: Molecular Conformation and Protein Folding, P. M. Pardalos et al., eds., Amer. Math. Soc., Providence, RI, 1996, pp. 199-213.
262. J.M. SANZ-SERNA, Symplectic integrators for Hamiltonian problems: An overviews, Acta Numerica, 1 (1992), pp. 243-286.
263. J.M. SANZ-SERNA AND M.P. CALVO, Numerical Hemiltonian Problems, Chapman and Hall, London, 1994.
264. M. SAUNDERS, K.N. HOUK, Y.-D. WU, W.C. STILL, M. LIPTON, G. CHANG, AND W.C. GUIDA, Conformations of cycloheptadecane. A comparison of methods for conformational searching. J. Amer. Chem. Soc., 112 (1990), pp. 1419-1427.
265. J.N. SCARSDALE, P. RAM, J.H. PRESTEGARD, AND R.K. YU, A molecular mechanics-NMR pseudoenergy approach to the solution conformation of glycolipids, J. Comput. Chem., 9 (1988), pp. 133-147.
266. S. SCHEINER, Calculating the properties of hydrogen bonds by ab initio methods, in Reviews in Computational Chemistry, Vol. II, K.B. Lipkowitz and D.B. Boyd, ed., VCH Publ., New York, 1991, pp. 165-218.
267. H.A. SCHERAGA, Predicting three-dimentional structures of oligopeptides, in Reviews in Computational Chemistry, Vol. III, K.B. Lipkowitz and D.B. Boyd, eds., VCH Publ., New York, 1992, pp. 73-142.
268. H.A. SCHERAGA, Treatment of Hydration in Conformational Energy Calculations on Polypeptides and Proteins, manuscript, 1994.
269. C.A. SCHIFFER, J.W. CALDWELL, P.A. KOLLMAN, AND R.M. STROUD, Protein structure prediction with a combined solvation free energy-molecular mechanics force field, Mol. Sim., 10 (1993), pp. 121-149.
270. T. SCHLICK, Modeling and Minimization Techniques for Predicting Three-Dimensional Structures of Large Biological Molecules, Ph.D. thesis, Courant Institute of Math. Sciences, New York, 1987.
271. T. SCHLICK, New approaches to potential energy minimization and molecular dynamics algorithms, Computers Chem., 15 (1991), pp 251-260.
272. T. SCHLICK, Optimization methods in computational chemistry, in Reviews in Computational Chemistry, Vol. III, K.B. Lipkowitz and D.B. Boyd, eds., VCH Publ., New York, 1992, pp. 1-71.
273. T. SCHLICK AND A. FOGELSON, TNPACK - A truncated Newton minimization package for large scale problems, ACM Trans. Math. Software, 18 (1992), pp. 46-70; 71-111.
274. T. SCHLICK AND W.K. OLSON, Supercoiled DNA energetics and dynamics by computer simulation, J. Mol. Biol., 223 (1992), pp. 1089-1119.
275. T. SCHLICK AND M. OVERTON, A powerful truncated Newton method for potential energy minimization, J. Comput. Chem., 8 (1987), pp. 1025-1039.
276. T. SCHLICK, C. PESKIN, S. BROYDE, AND M. OVERTON, An analysis of the structural and energetic properties of deoxyribose by potential energy methods, J. Comput. Chem., 8 (1987), pp. 1199-1224.
277. H. SCHREIBER AND O. STEINHAUSER, Taming cut-off induced artifacts in molecular dynamics studies of solvated polypeptides, J. Mol. Biol., 228 (1992), pp. 909-923.
278. H. SCHREIBER AND O. STEINHAUSER, Molecular dynamics studies of solvated polypeptides: Why the cut-off scheme does not work, Chem. Phys. 168 (1992), pp. 75-89.
279. H. SCHREIBER AND O. STEINHAUSER, Cutoff size does strongly influence molecular dynamics results on solvated polypeptides, Biochemsitry, 31 (1992), pp. 5856-5860.
280. H. SCHREIBER, O. STEINHAUSER, AND P. SCHUSTER, Parallel molecular dynamics of biomolecules, Parallel Computing, 18 (1992), pp. 557-573.
281. G.E. SCHULZ, A critical evaluation of methods for prediction of portein secondary structures, Ann. Rev. Biophys. Biophys. Chem., 17 (1988), pp. 1-21.
282. D. SHALLOWAY, Packet annealing: A deterministic method for global minimization. Application to molecular conformation, in Recent Advances in Global Optimization, C.A. Floudas and P.M. Pardalos, eds., Princeton Univ. Press, Princeton, 1992, pp. 433-477.
283. J. SHIMADA, H. KANEKO, AND T. TAKADA. Performance of fast multipole methods for calculating electrostatic interactions in biomacromolecular simulations, J. Comput. Chem., 15 (1994), pp. 28-43.
284. J.K. SHIN AND M.S. JHON, High directional Monte Carlo procedure coupled with the temperature heating and annealing method to obtain the global energy minimum structure of polypeptides and proteins, Biopolymers, 31 (1991), pp. 177-185.
285. S.D. SILVEY, Optimal Design, Chapman and Hall, London, 1980.
286. M.J. SIPPL, Boltzmann's principle, knowledge based mean fields and protein folding, J. Comp. Aided Mol. Design, 7 (1993), pp. 473-501.
287. M.J. SIPPL, Knowledge-based potentials for proteins, Curr. Opinion Str. Biol., 5 (1995), pp. 229-235.
288. M.J. SIPPL, M. HENDLICH, AND P. LACKNER, Assembly of polypeptide and protein backbone conformations from low energy ensembles of short fragments, Protein Sci., 1 (1982), pp. 625-640.
289. M.J. SIPPL, S. WEITCKUS, AND H. FLÖCKNER, In search of protein folds, in The Protein Folding Problem and Tertiary Structure Prediction, K. Merz and S. Legrand, eds., Birkhäuser, Boston, 1994, pp. 353-407.
290. M.J. SIPPL, S. WEITCKUS, AND H. FLÖCKNER, Fold recognition, in Modelling of Biomolecular Structures and Mechanisms, A. Pullman et al., eds., Kluwer, Dordrecht, 1995, pp. 107-118.
291. R.D. SKEEL, J. J. BIESIADECKI, AND D. OKUNBOR, Symplectic Integration for Macromolecular Dynamics, manuscript, 1994. (skeel@cs.uiuc.edu)
292. J. SKOLNICK AND A. KOLINSKI, Simulations of the folding of a globular protein, Science, 250 (1990), pp. 1121-1125.
293. J. SKOLNICK AND A. KOLINSKI, Monte Carlo Lattice Dynamics and the Prediction of Protein Folds, manuscript, 1996. (skolnick@scripps.edu)
294. J. SKOLNICK, A. KOLINSKI, C.L. BROOKS, A. GODZIK, AND A. REY, A method for predicting protein structure from sequence, Current Biology. 3 (1993), pp. 414-422.
295. Z. SLANINA, Does the global energy minimum always also mean the thermodynamically most stable structure?, J. Mol. Str., 206 (1990). pp. 143-151.
296. J.C. SLATER and J.G. KIRKWOOD, The van der Wools forces in gases, Phys. Rev., 37 (1931), pp. 682-697.
297. P.E. SMITH, B.M. PETTITT, AND M. KARPLUS. Stochastic dynamics simulations of the alanine dipeptide using a solvent-modified potential energy surface, J. Phys. Chem., 97 (1993), pp. 6907-6913.
298. P.E. SMITH AND B.M. PETTITT, Peptides in ionic solutions: A comparison of the Ewald and switching function techniques, J. Chem. Phys., 95 (1991), pp. 8430-8441.
299. K. SOBCZYK, Stochastic Differential Equations, Kluwer, Dordrecht, 1991.
300. K.V. SOMAN, A. KARIMI, AND D.A. CASE, Unfolding of an α-helix in water, Biopolymers, 31 (1991), pp. 1351-1361.
301. D.R. STAMPF, C.E. FELSER, AND J.L. SUSSMAN, PDBBrowse-A graphics interface to the Brookhaven Protein Data Bank, Nature. 374 (1995). pp. 572-574.
302. S. STEELE, E.R. LIPPINCOTT. AND J.T. VANDERSLICE, Comparative study of empirical internuclear potential functions. Rev. Mod. Phys., 34 (1962), pp. 239-251.
303. P.J. STEINBACH AND B.R. BROOKS, New spherical-cutoff methods for long-range forces in macromolecular simulation. J. Comput. Chem., 15 (1994), pp. 667-683.
304. F.H. STILUNGER, Theory and molecular models for water, Adv. Chem. Phys., 31 (1975), pp. 1-101.
305. F.H. STILLINGER, Role of potential-energy scaling in the low-temperature relaxation behavior of amorphous materials. Phys. Rev. B, 32 (1985). pp. 3134-3141.
306. F.H. STILLINGER, T. HEAD-GORDON, AND C.L. HIRSHFELD, Toy model for protein folding, Phys. Rev. E. 48 (1993), pp. 1469-1477.
307. F.H. STILLINGER AND T.A. WEBER, Nonlinear optimization amplified by hypersurface deformation. J. Statist. Phys., 52 (1988). pp. 1429-1445.
308. P. STOLORZ, A. LAPEDES, AND Y. XIA. Predicting protein secondary structure using neural nets and statistical methods. J. Mol. Biol., 225 (1992). pp. 363-377.
309. J.E. STRAUB. Optimization techniques with applications to proteins, in New Developments in Theoretical Studies of Proteins, R. Elber, ed., World Scientific, Singapore, 1996.
310. DE WITT L. SUMNERS, ED., New scientific applications of geometry and topology, in Proc. Symp. Appl. Math. 45, Amer. Math. Soc., Providence, RI, 1992.
311. S. SUN, Reduced representation model of protein structure prediction: Statistical potential and genetic algorithms, Protein Sci., 2 (1993), pp. 762-785.
312. S. SUN, Reduced representation approach to protein tertiary structure prediction: Statistical potential and simulated annealing, J. Theor. Biol., 172 (1995). pp. 13-32.
313. R. SUSNOV, R.B. NACHBAR, C. SCHUTT, AND H. RABITZ, Sensitivity of molecular structure to intramolecular potentials, J. Phys. Chem., 95 (1991), pp. 8886-8697.
314. O. TAPIA, Solvent effects on biomolecules and reactive systems. An overview of the theory and applications, in Computational Chemistry, S. Fraga, ed., Elsevier, New York, 1992, pp. 694-721
315. W.R. TAYLOR, ED., Patterns in Protein Sequence and Structure, Springer, New York, 1992.
316. O. TELEMEN AND B. JÖNSSON, Vectorizing a general purpose molecular dynamics simulation program, J. Comput. Chem., 7 (1986), pp. 58-68.
317. T.S. THACHER, A.T. HAGLER, AND H. RABITZ, Application of sensitivity analysis to the establishment of intermolecular potential functions, J. Amer. Chem. Soc., 113 (1991), pp. 2020-3033.
318. D.J. TOBIAS, J.E. MERTZ, AND C.L. BROOKS, Nanosecond time scale folding dynamics of a pentapetide in water, Biochemistry, 30 (1991). pp. 6054-6058.
319. A.E. TORDA AND W.F. VAN GUNSTEREN, Molecular modeling using nuclear magnettf -] resonance enta, in Reviews in Computational Chemistry, Vol. III, K.B. Lipkowitz and D.B. Boyd, eds., VCH Publ. New York, 1992, pp. 143-172.
320. J.M. TROTER AND F.E. COHEN. Simplifield models for uderstanding and predicting protein structure, in Reviews in Computational Chemistry, Vol. II, K.B. Lipkowitz and D.B. Boyd, eds., VCH Publ., New York, 1991, pp. 57-80.
321. M.E. TUCKERMAN AND B.J. BERNE, AND A. ROSSI, Molecular dynamics algorithms for multiple scales, J. Comput. Chem., 95 (1992), pp. 8362-8364.
322. M.E. TUCKERMAN, B.J. BERNE, AND A. ROSSI. Molecular dynamics algorithams for multiple time scales: Systems with disparate masses, J. Comput. Chem. 94 (1991), pp. 1465-1469.
323. P. TUFF́ERY, C. ETCHEBEST, S. HAZOUT, AND R. LAVERY, A critical comparison of research algorithms applied to the optimization of protein side-chain conformations, J. Comput. Chem., 14 (1993), pp. 790-798.
324. P. ULRICH, W. SCOTT, W.F. VAN GUNSTEREN, AND A. TORDA, Protein structure prediction force fields: Parametrization with quest Neutonian dynamics, Proteins, 27 (1997), pp. 367-384.
325. H. C. UREY AND C.A. BRADLEY, The vibrations of pentatonic tetrahedral molecules, Phys. Rev., 38 (1931), pp. 1969-1978.
326. S. VAJDA AND C. DELISI, Determining minium energy conformations of polypeptides by dynamic programming, Biopolymers, 29 (1990), pp. 1755-1772.
327. B. VAN DER GRAAF AND J.M.A. BAAS, The implementation of constraints in molecular me-chanics to explore potential energy surfaces, Rev. Trav. Chim. Pays-Bas, 99 (1980), p. 327.
328. A. VAN DER HOEK, Parallel Global Optimization of Proteins, Masters thesis, Erasmus Universiteit, Rotterdam, 1994.
329. W.F. VAN GUNSTEREN, Constrained dynamics of flexible molecules, Mol. Phys., 40 (1980), pp. 1015-1019
330. W.F. VAN GUNSTEREN, Computer simulation by molecular dynamics as a tool for modelling of molecular systems, Mol. Simul., 3 (1989), pp. 187-200.
331. W.F. VAN GUNSTEREN AND H.J.C. BERENDSEN, Algorithms for macromolecular dynamics and constrained dynamics, Mol. Phys., 34 (1977), pp. 1311-1327.
332. W.F. VAN GUNSTEREN AND H.J.C. BERENDSEN, Algorithms for Brownian dynamics, Mol. Phys., 45 (1982), pp. 637-647.
333. W-F. VAN GUNSTEREN, H.J.C. BERENDSEN, AND J.A.C. RULLMANN, Stochastic dynamics for molecules with constraints. Brownian dynamics of n-alcanes. Mol. Phys., 44 (1981), pp. 69-96.
334. N.G. VAN KAMPEN, Stochastic Processes in Physics and Chemistry, North-Holland, Amsterdam, 1981.
335. D.L. VEENSTRA, D.M. FERGUSON, AND P.A. KOLLMAN, How transferable are hydrogen parameters in molecular mechanics calculations?, J. Comput. Chem., 13 (1992), pp. 971-978.
336. G.A. VOTH AND E.V. O'GORMAN, An effective barrier model for describing quantum mechanical activated rate processes in condensed phases, J. Chem. Phys., 94 (1991), pp. 7342-7352.
337. L.L. WALSH, Navigating the Brookhaven Protein Data Bank, Cabos Communication, 10 (1994), pp. 551-557.
338. A. WARSHEL, Computer Modeling of Chemical Reactions in Enzymes and Solutions, Wiley-Interscience, New York, 1991.
339. M. WATANABE AND M. KARPLUS, Dynamics of molecules with internal degrees of freedom by multiple time-step methods, J. Chem. Phys., 99 (1993) pp. 8083-8074.
340. S.J. WEINER, P.A. KOLLMAN, D.A. CASE, U.C. SINGH, C. GHIO, G. ALAGONA, S. PROFETA, AND P. WEINER, A new force field for molecular mechanical simulation of nuclear acids and proteins, J. Amer. Chem. Soc., 106 (1984), pp. 765-784.
341. S.J. WEINER P.A. KOLLMAN, D.T. NGUYEN, AND D.A. CASE, An all atom force field for simulations of proteins and nuclear acids, J. Comput. Chem. 7 (1986), pp. 230-252.
342. L. WESSON AND D. EISENBERG, Atomic solvation parameters applied to molecular dynamics of proteins in solution, Protein Science, 1 (1992), pp. 227-235.
343. L.T. WILLE AND J. VENNIK, Computational complexity of the ground-state determination of atomic clusters, J. Phys. A. 18 (1985), pp. L419-422.
344. D. E. WILLIAMS, Net atomic charge and multipole models for theab initio molecular electric potential, in Reviews in Computational Chemistry, Vol. II, K.B. Lipkowitz and D.B. Boyd, eds., VCH Publ., New York, 1991, pp. 219-271.
345. S.J. WODAK AND M.J. ROOMAN, Generating and testing protein folds, Curr. Opinion Struct. Biol., 3 (1993) pp. 247-259.
346. P.G. WOLYNES, Spin glass ideas and the protein folding problem, in Spin Glasses and Biology, D.L. Stein, ed., World Scientific, New York, 1992, pp 225-259.
347. P.G. WOLYNES, J.N. ONUCHIC, AND D. THIRUMALAI, Navigating the folding routes, Science, 267 (1995), pp. 1619-1620.
348. Z. WU, The effective energy transformation scheme at a special continuation approach to global optimization with application to molecular conformation, SIAM J. Optim., 6 (1996), pp. 748-768.
349. G. XUE, Molecular conformation on the CM-5 6y parallel two-level simulated annealing, J. Global Optim., 4 (1994), pp. 187-208.
350. G. XUE, Improvements on the Northby algorithm for molecular conformation: Better solutions, J. Global Optim., 4 (1994), pp. 425-440.
351. G.L. XUE, A.J. ZALL, AND P.M. PARDALOS, Rapid evaluation of potential energy functions in molecular and protein conformations, in Global Minimization of Nonconvex Energy Functions: Molecular Conformation and Protein Folding, P. M. Pardalos et al., eds., Amer. Math. Soc., Providence, RI, 1996, pp. 237-249.
352. D.M. YORK, T.A. DARDEN, AND L.G. PEDERSEN, The effect of long-range electrostatic interactions in simulations of macromolecular crystals: A comparison of the Ewald and truncated list methods, J. Chem. Phys., 99 (1993), pp. 8345-8348.
353. D.M. YORK, A. WLODAWER, L.G. PEDERSEN, AND T.A. DARDEN, Atomic-level accuracy in simulations of large protein crystals, Proc. Nat. Acad. Sci. USA. 91 (1994). pp. 8715-8718.
354. T.Y. YOUNG AND K. FU, Handbook of Pattern Recognition and Image Processing, Academic Press, New York 1986.
355. K. YUE AND K.A. DILL, Inverse protein folding problem: Designing polymer sequences, Proc. Nat. Acad. Sci. USA, 89 (1992), pp. 4136-4167.
356. G. ZANOTTI, Protein crystallography, in Fundamentals of Crystallography, C. Giacovazzo, ed., Oxford Univ. Press, Oxford, 1992, pp. 535-597.
357. G. ZHANG AND T. SCHLICK, LIN: A new algorithm to simulate the dynamics of biomolecules by combining implicit-integration and normal mode techniques, J. Comput. Chem., 14 (1993), pp. 1212-1233.
358. G. ZHANG AND T. SCHLICK, The Langevin/implicit-Euler/normal-mode scheme (LIN) for molecular dynamics at large time steps, J. Chem. Phys., 101 (1994), pp. 4995-5012.
359. F. ZU-KANG AND M.J. SIPPL, Optimal superimposition of protein structures: Ambiguities and implications, Folding and Design, 1 (1996), pp. 123-132.