Skip to main content

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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.

    Article  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • Brisson, A., and Unwin, P. N. T., 1985. Quaternary structure of the acetylcholine receptor, Nature 315:474–477.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  CAS  Google Scholar 

  • 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.

    Article  CAS  Google Scholar 

  • 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.

    Article  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • Crippen, G. M., 1977. A novel approach to calculation of conformation: distance geometry, J. Compo Phys. 24: 96–107.

    Article  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • Crippen, G. M., and Scheraga, H. A., 1971a, Minimization of polypeptide energy. X. A global search algorithm, Arch. Biochem. Biophys. 144:453–461.

    Article  PubMed  CAS  Google Scholar 

  • Crippen, G. M., and Scheraga, H. A., 1971b, Minimization of polypeptide energy. XI. Method of gentlest ascent, Arch. Biochem. Biophys. 144:462–466.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  CAS  Google Scholar 

  • 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.

    Article  CAS  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Eisenberg, D., 1984, Three-dimensional structure of membrane and surface proteins, Annu. Rev. Biochem. 53: 595–623.

    Article  PubMed  CAS  Google Scholar 

  • Ermer, O., 1976, Calculation of molecular properties using force fields. Applications in organic chemistry, Structure Bonding 27:161–211.

    CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • Fletcher, R., 1980, Practical Methods of Optimization, Volume 1, John Wiley & Sons, New York.

    Google Scholar 

  • 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.

    Article  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Greer, J., 1985, Protein structure and function by comparative model building, Ann. N.Y. Acad. Sci. 439:44–63.

    Article  CAS  Google Scholar 

  • 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.

    Google Scholar 

  • Hagler, A. T., and Moult, J., 1978, Computer simulation of the solvent structure in biological macromolecules, Nature 272:222–226.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  CAS  Google Scholar 

  • 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.

    Article  CAS  Google Scholar 

  • 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.

    Article  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • Harvey, S. C., and McCammon, J. A., 1982, Macromolecular conformational energy minimization: An algorithm varying pseudodihedral angles, Comput. Chem. 6:173–179.

    Article  CAS  Google Scholar 

  • 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.

    CAS  Google Scholar 

  • Havel, T. F., Kuntz, I. D., and Crippen, G. M., 1983, The theory and practice of distance geometry, Bull. Math. Biol. 45:665–720.

    Google Scholar 

  • Hwang, J. K., and Warshel, A., 1987, Semiquantitative calculations of catalytic free energies in genetically modified enzymes, Biochemistry 26:2669–2273.

    Article  PubMed  CAS  Google Scholar 

  • Jones, T. A., 1982, FRODO: A graphics fitting program for macromolecules, in: Computational Crystallography (D. Sayre, ed.), Clarendon Press, London, p. 303.

    Google Scholar 

  • Karfunkel, H. R., 1986, A fast algorithm for the interactive docking maneuver with flexible macromolecules and probes, J. Comput. Chem. 7:113–128.

    Article  CAS  Google Scholar 

  • Katz, L., and Levinthal, C., 1972, Interactive computer graphics and representation of complex biological structures, Annu. Rev. Biophys. Bioeng. 1:465–504.

    Article  PubMed  CAS  Google Scholar 

  • Kirkwood, J. G., 1935, Statistical mechanics of fluid mixtures, J. Chem. Phys. 3:300–313.

    Article  CAS  Google Scholar 

  • Kitson, D. H., and Hagler, A. T., 1988, Theoretical studies of the structure and molecular dynamics of a peptide crystal, Biochemistry 27: 5246–5257.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  CAS  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • Mezei, M., and Beveridge, D., 1986, Free energy simulations. Ann. N.Y. Acad.Sci. 482: 1–23.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • Nilsson, L., and Karplus, M., 1986, Empirical energy functions for energy minimization and dynamics of nucleic acids, J. Comput. Chem. 7:591–616.

    Article  CAS  Google Scholar 

  • 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.

    Article  CAS  Google Scholar 

  • 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.

    Article  CAS  Google Scholar 

  • Poe, M., Hoogsteen, K., and Matthews, D. A., 1979, Proton magnetic resonance studies on E. coli dihydrofolate reductase, J. Biol. Chem. 254:8143–8152.

    PubMed  CAS  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  CAS  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    CAS  Google Scholar 

  • 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.

    Article  CAS  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  CAS  Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • Tembe, B. L., and McCammon, J. A., 1984, Ligand-receptor interactions, Comput. Chem. 8:281–283.

    Article  CAS  Google Scholar 

  • Van Gunsteren, W. F., and Karplus, M., 1980, A method for constrained energy minimization of macromolecules, J. Comput. Chem. 1:266–274.

    Article  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • Warme, P. K., and Scheraga, H. A., 1974, Refinement of the x-ray structure of lysozyme by complete energy minimization, Biochemistry 13:757–767.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Plenum Press, New York

About this chapter

Cite this chapter

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

Download citation

  • DOI: https://doi.org/10.1007/978-1-4613-1571-1_7

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4612-8860-2

  • Online ISBN: 978-1-4613-1571-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics