Abstract
It is now possible to calculate the classical energy of a complex system such as a protein as a function of its coordinates. By making many such calculations for various coordinate values, one can explore multidimensional energy surfaces. These energy surfaces are the basis for molecular dynamics and Monte Carlo studies. Another important method for exploring these energy surfaces is to find configurations for which the energy is a minimum. By this, we mean finding a point in configuration space where all of the forces on the atoms are balanced. By simply minimizing the energy of a molecule, we can identify stable conformations. Perhaps more importantly, by adding external to the molecule in the form of restraints and constraints, a wide range of modeling strategies can be developed using minimization techniques as the foundation to answer specific questions. For example, by forcing specific atoms to overlap atoms in a template structure during a molecular geometry minimization, one can answer the question, “how much energy is required for one molecule to adopt the shape of another.” In this chapter, we discuss how minimization techniques are used in a variety of molecular strategies, focusing on the use of constraints and restraints to extend the scope and utility of traditional structure minimization.
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References
Abe, H., Braun, W., Noguti, T., and Go, N., 1984, Rapid calculation of firSt and second derivatives of conformational energy with respect to dihedral angles for proteins. General recurrent equations. Compo Chem. 8:239–247.
Baccanari, D. P., Daluge, S., and King, R. W., 1982. Inhibition of dihydrofolate reductase: Effect of reduced nicotinamide adenine dinucleotide phosphate on the selectivity and affinity of diaminobenzylpyrimidines. Biochemistry 21:5068–5075.
Baniak, E. L., Rivier, J. E., Struthers, R. S., Hagler, A. T., and Gierasch, L. M., 1987. Nuclear magnetic resonance analysis and conformational characterization of a cyclic decapeptide antagonist of gonadotropin-releasing hormone. Biochemistry 26: 2642–2656.
Berendsen. H. J. C., Postma, J. P. M., van Gunsteren, W. F., DiNola, A., and Haak, J. R., 1984. Molecular dynamics with coupling to an external bath, J. Chem. Phys. 81:3684–3690.
Braun, W., and Go, N., 1985. Calculation of protein conformations by proton-proton distance constraints: A new efficient algorithm. J. Mol. Biol. 186:611–626.
Brisson, A., and Unwin, P. N. T., 1985. Quaternary structure of the acetylcholine receptor, Nature 315:474–477.
Brooks, B. R., Bruccoleri, R. E., Olafson, B. D., States, D. J., Swaminathan,. S., and Karplus, M., 1983. CHARMM: A program for macromolecular energy, minimization, and dynamics calculations, J. Compo Chem. 4:187–217.
Brooks, C. L. III, Pettitt, B. M., and Karplus, M., 1985, Structural and energetic effects of truncating long ranged interactions in ionic and polar fluids, J. Chem. Phys. 83:5897–5908.
Chou, K. C., Nemethy, G., and Scheraga, H. A., 1983. Energetic approach to the packing of α-helices. 1. Equivalent helices, J. Phys. Chem. 87:2869–2881.
Clore, G. M., Bruenger, A. T., Karplus, M., and Gronenborn, A. M., 1986. Application of molecular dynamics with interproton distance restraints to three-dimensional protein structure determination. A model study of crambin, J. Mol. Biol. 191:523–551.
Crippen, G. M., 1977. A novel approach to calculation of conformation: distance geometry, J. Compo Phys. 24: 96–107.
Crippen, G. M., and Scheraga, H. A., 1969, Minimization of polypeptide energy. VIII. Application of the deflation technique to a dipeptide, Proc. Natl. Acad. Sci. U.S.A. 64:42–49.
Crippen, G. M., and Scheraga, H. A., 1971a, Minimization of polypeptide energy. X. A global search algorithm, Arch. Biochem. Biophys. 144:453–461.
Crippen, G. M., and Scheraga, H. A., 1971b, Minimization of polypeptide energy. XI. Method of gentlest ascent, Arch. Biochem. Biophys. 144:462–466.
Crippen, G. M., and Scheraga, H. A., 1973, Minimization of polypeptide energy. XII. Methods of partial energies and cubic subdivision, J. Comput. Phys. 12:491–497.
Dauber-Osguthorpe, P., Roberts, V. A., Osguthorpe, D. J., Wolff, J., Genest, M., and Hagler, A. T., 1988, Structure and energetics of ligand binding to proteins: E. coli dihydrofolate reductase-trimethoprim, a drug-receptor system, Proteins: Structure, Function and Genetics, 4: 31–47.
Dayringer, H. E., Tramontano, A., Sprang, S. R., and Retterick, R. J., 1986, Interactive program for visualization and modelling of proteins, nucleic acids, and small molecules, J. Mol. Graphics 6:82–87.
Eisenberg, D., 1984, Three-dimensional structure of membrane and surface proteins, Annu. Rev. Biochem. 53: 595–623.
Ermer, O., 1976, Calculation of molecular properties using force fields. Applications in organic chemistry, Structure Bonding 27:161–211.
Fine, R. M., Wang, H., Shenkin, P. S., Yarmush, D. L., and Levinthal, C., 1986, Predicting antibody hypervariable loop conformations II: Minimization and molecular dynamics studies of MCPC603 from many randomly generated loop conformations, Proteins 1:342–362.
Fletcher, R., 1980, Practical Methods of Optimization, Volume 1, John Wiley & Sons, New York.
Furois-Corbin, S., and Pullman, A., 1986, Theoretical study of the packing of α-helices by energy minimization: Effect of the length of the helices on the packing energy and on the optimal configuration of a pair, Chem. Phys. Lett. 123:305–310.
Gibson, K. D., and Scheraga, H. A., 1986, Predicted conformations for the immunodominant region of the circumsporozoite protein of the human malaria parasite Plasmodium falciparum, Proc. Natl. Acad. Sci. U.S.A. 83:5649–5653.
Gilson, M. K., Rashin, A., Fine, R., Honig, B., Kline, A. D., and Wüthrich, K., 1985, Secondary structure of the α-amylase polypeptide inhibitor tendamistat from Streptomyces tendae determined in solution by 1H nuclear magnetic resonance, J. Mol. Biol. 183:503–507.
Greer, J., 1985, Protein structure and function by comparative model building, Ann. N.Y. Acad. Sci. 439:44–63.
Hagler, A. T., 1985, Theoretical simulation of conformation, energetics, and dynamics of peptides, in: The Peptides, Volume 7 (V. J. Hruby and J. Meienhofer, eds.), Academic Press, New York, pp. 213–299.
Hagler, A. T., and Moult, J., 1978, Computer simulation of the solvent structure in biological macromolecules, Nature 272:222–226.
Hagler, A. T., Lifson, S., and Dauber, P., 1979a, Consistent force field studies of intermolecular forces in hydrogen bonded crystals. 2. A benchmark for the objective comparison of alternative force fields, J. Am. Chem. Soc. 101:5122–5130.
Hagler, A. T., Dauber, P., and Lifson, S., 1979b, Consistent force field studies of intermolecular forces in hydrogen bonded crystals. 3. The C=O···H-O hydrogen bond and the analysis of the energetics and packing of carboxylic acids, J. Am. Chem. Soc. 101:5131–5141.
Hagler, A. T., Stern, P. S., Sharon, R., Becker, J. M., and Naider, F., 1979c, Computer simulation of the conformational properties of oligopeptides: Comparison of theoretical methods and analysis of experimental results, J. Am. Chem. Soc. 101:6842–6852.
Hagler, A. T., Osguthorpe, D. J., Dauber-Osguthorpe, P., and Hempel, J. C., 1985, Dynamics and conformational energetics of a peptide hormone: Vasopressin, Science 227:1309–1315.
Harvey, S. C., and McCammon, J. A., 1982, Macromolecular conformational energy minimization: An algorithm varying pseudodihedral angles, Comput. Chem. 6:173–179.
Havel, T. F., and Wuthrich, K., 1984, A distance geometry program for determining the structures of small proteins and other macromolecules from nuclear magnetic resonance measurements of intramolecular 1H-1H proximities in solution, Bull. Math. Biol. 46:673–698.
Havel, T. F., Kuntz, I. D., and Crippen, G. M., 1983, The theory and practice of distance geometry, Bull. Math. Biol. 45:665–720.
Hwang, J. K., and Warshel, A., 1987, Semiquantitative calculations of catalytic free energies in genetically modified enzymes, Biochemistry 26:2669–2273.
Jones, T. A., 1982, FRODO: A graphics fitting program for macromolecules, in: Computational Crystallography (D. Sayre, ed.), Clarendon Press, London, p. 303.
Karfunkel, H. R., 1986, A fast algorithm for the interactive docking maneuver with flexible macromolecules and probes, J. Comput. Chem. 7:113–128.
Katz, L., and Levinthal, C., 1972, Interactive computer graphics and representation of complex biological structures, Annu. Rev. Biophys. Bioeng. 1:465–504.
Kirkwood, J. G., 1935, Statistical mechanics of fluid mixtures, J. Chem. Phys. 3:300–313.
Kitson, D. H., and Hagler, A. T., 1988, Theoretical studies of the structure and molecular dynamics of a peptide crystal, Biochemistry 27: 5246–5257.
Lifson, S., Hagler, A. T., and Dauber, P., 1979, Consistent force field studies of intermolecular forces in hydrogen bonded crystals. I. Carboxylic acids, amides, and the C=O···H-O hydrogen bonds, J. Am. Chem. Soc. 101:5111–5121.
Maple, J. R., Dinur, U., and Hagler, A. T., Derivation of forcefields for molecular mechanics and dynamics from ab initio energy surfaces, Proc. Natl. A cad. Sci. U.S.A. 85:5350–5354.
Matthews, D. A., Alden, R. A., Bolin, J. T., Freer, S. T., Hamlin, R., Xuong, N., Kraut, J., Poe, M., Williams, M., and Hoogsteen, K., 1977, Dihydrofolate reductase: X-ray structure of the binary complex with methotrexate, Science 197:452–455.
Mezei, M., and Beveridge, D., 1986, Free energy simulations. Ann. N.Y. Acad.Sci. 482: 1–23.
Moult, J., and James, M. N. G., 1986, An algorithm for determining the conformation of polypeptide segments in proteins by systematic search, Proteins 1:146–163.
Nilsson, L., and Karplus, M., 1986, Empirical energy functions for energy minimization and dynamics of nucleic acids, J. Comput. Chem. 7:591–616.
Noguti, T., and Go, N., 1983, A method of rapid calculation of a second derivative matrix of conformational energy for large molecules, J. Phys. Soc. (Jpn.) 52:3685–3690.
Pattabiraman, N., Levitt, M., Ferrin, T. E., and Langridge, R., 1985, Computer graphics in real-time docking with energy calculation and minimization, J. Comput. Chem. 6:432–436.
Poe, M., Hoogsteen, K., and Matthews, D. A., 1979, Proton magnetic resonance studies on E. coli dihydrofolate reductase, J. Biol. Chem. 254:8143–8152.
Press, W. H., Flannery, B. P., Teukolsky, S. A., and Vetterling, W. T., 1986, Numerical Recipes, The Art of Scientific Computing, Cambridge University Press, Cambridge.
Purisima, E. O., and Scheraga, H. A., 1986, An approach to the multiple-minima problem by relaxing dimensionality, Proc. Natl. Acad. Sci. U.S.A. 83:2782–2786.
Quirke, N., and Jacucci, G., 1982, Energy difference functions in Monte Carlo simulations: Application to (1) the calculation of free energy of liquid nitrogen, (2) the calculation of fluctuation in Monte Carlo averages, Mol. Phys. 45:823–838.
Rivier, J., Kupryszewski, G., Varga, J., Porter, J., Rivier, C., Perrin, M., Hagler, A., Struthers, S., and Corrigan, A., Design of potent cyclic gonadotropin releasing hormone antagonists, J. Med. Chem. 31: 677–682.
Roberts, V. A., Dauber-Osguthorpe, P., Osguthorpe, D. J., Levin, E., and Hagler, A. T., 1986, A comparison of the binding of the ligand trimethoprim to bacterial and vertebrate dihydrofolate reductases, Isr. J. Chem 27:198–210.
Singh, U. C., Brown, F. K., Bash, P. A., and Kollman, P. A., 1987, An approach to the application of free energy perturbation methods using molecular dynamics: Applications to the transformations of methanol to ethane, oxonium to ammonium, glycine to alanine, and alanine to phenylalanine in aqueous solution and to H3O+(H3O)3 NH4 + (H2O3) in the gas phase, J. Am. Chem. Soc. 109:1607–1614.
Stem, P. S., Chorev, M., Goodman, M., and Hagler, A. T., 1983, Computer simulation of the conformational properties of retro-inverso peptides. I. Empirical force field calculations of rigid and flexible geometries of N-acetylglycine-N′-methylamide, bis(acetamido)methane, and N,N ′-dimethylmalonamide and their corresponding Cα-methylated analogs, Biopolymers 22:1885–1900.
Straatsma, T. P., Berendsen, H. J. C., and Postma, J. P. M., 1986, Free energy of hydrophobic hydration: A molecular dynamics study of noble gases in water, J. Chem. Phys. 85:6720–6727.
Struthers, R. S., Rivier, J., and Hagler, A. T., 1984, Design of peptide analogs: Theoretical simulation of conformation, energetics, and dynamics, in: Coriformationally Directed Drug Design: Peptides and Nucleic Acids as Templates or Targets (J. A. Vida and M. Gordon, eds.), American Chemical Society, Washington, pp. 239–261, American Chemical Society, Washington.
Tembe, B. L., and McCammon, J. A., 1984, Ligand-receptor interactions, Comput. Chem. 8:281–283.
Van Gunsteren, W. F., and Karplus, M., 1980, A method for constrained energy minimization of macromolecules, J. Comput. Chem. 1:266–274.
Vasquez, M., and Scheraga, H. A., 1985, Use of buildup and energy-minimization procedures to compute low-energy structures of the backbone of enkephalin, Biopolymers 24:1437–1447.
Warme, P. K., and Scheraga, H. A., 1974, Refinement of the x-ray structure of lysozyme by complete energy minimization, Biochemistry 13:757–767.
Warshel, A., Sussman, F., and King, G., 1986, Free energy of charges in solvated proteins: Microscopic calculations using a reversible charging process, Biochemistry 25:8368–8372.
Warwicker, J., 1986, Continuum dielectric modelling of the protein-solvent system, and calculation of the long-range electrostatic field of the enzyme phosphoglycerate mutase, J. Theor. Biol. 121:199–210.
Warwicker, J., Ollis, D., Richards, F. M., and Steitz, T. A., 1985, Electrostatic field of the large fragment of Escherichia coli DNA polymerase I, J. Mol. Biol. 186:645–649.
Weiner, S. J., Kollman, P. A., Case, D. A., Singh, U. C., Ghio, C., Alagona, G., Profeta, S., Jr., and Weiner, P., 1984, A new force field for molecular mechanical simulation of nucleic acids and proteins, J. Am. Chem. Soc. 106:765–784.
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© 1989 Plenum Press, New York
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Mackay, D.H.J., Cross, A.J., Hagler, A.T. (1989). The Role of Energy Minimization in Simulation Strategies of Biomolecular Systems. In: Fasman, G.D. (eds) Prediction of Protein Structure and the Principles of Protein Conformation. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-1571-1_7
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DOI: https://doi.org/10.1007/978-1-4613-1571-1_7
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