Journal of Global Optimization

, Volume 11, Issue 1, pp 1–34 | Cite as

Prediction of Oligopeptide Conformations via Deterministic Global Optimization

  • I.P. Androulakis
  • C.D. Maranas
  • C.A. Floudas
Article

Abstract

A deterministic global optimization method is described for identifying the global minimum potential energy conformation of oligopeptides. The ECEPP/3 detailed potential energy model is utilized for describing the energetics of the atomic interactions posed in the space of the peptide dihedral angles. Based on previous work on the microcluster and molecular structure determination [21, 22, 23, 24], a procedure for deriving convex lower bounding functions for the total potential energy function is developed. A procedure that allows the exclusion of domains of the (ø, ψ) space based on the analysis of experimentally determined native protein structures is presented. The reduced disjoint sub-domains are appropriately combined thus defining the starting regions for the search. The proposed approach provides valuable information on (i) the global minimum potential energy conformation, (ii) upper and lower bounds of the global minimum energy structure and (iii) low energy conformers close to the global minimum one. The proposed approach is illustrated with Ac-Ala4-Pro-NHMe, Met-enkephalin, Leu-enkephalin, and Decaglycine.

Protein folding deterministic global optimization 

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References

  1. [1]
    C. Adjiman, I.P. Androulakis, C.D Maranas, and C.A. Floudas, A Global Optimization Method, αBB, for Process Design. Comp. and Chem. Eng., 20:S419–S424, 1996.Google Scholar
  2. [2]
    C. Adjiman and C.A. Floudas, Rigorous Convex Underestimators for General Twice-Differentiable Problems. J. Global Opt., 9:23–40, 1996.Google Scholar
  3. [3]
    N.L. Allinger, Conformational Analysis. MM2 A Hydrocarbon Force Field Utilizing V 1 and V 2 Tortional Terms. J. Am. Chem. Soc., 99:8127–8134, 1977.Google Scholar
  4. [4]
    N.L. Allinger, Y.H. Yuh, and J.-H. Lii, Molecular Mechanics. The MM3 Force Field for Hydrocarbons. J. Am. Chem. Soc., 111:8551–8582, 1989.Google Scholar
  5. [5]
    I.P. Androulakis, C.D. Maranas and C.A. Floudas, αBB: A Global Optimization Method for General Constrained Nonconvex Problems. J. Global Opt., 7:337–363, 1995.Google Scholar
  6. [6]
    I.P. Androulakis, C.D. Maranas, and C.A. Floudas, αBB: A Global Optimization Method for General Constrained Nonconvex Problems. Paper presented at the AIChE Annual Meeting, Miami, FL, 1995.Google Scholar
  7. [7]
    I.P. Androulakis, C.D. Maranas, and C.A. Floudas, Distributed Branch and Bound Algorithms for Global Optimization. Paper presented at the AIChE Annual Meeting, Miami, FL, 1995.Google Scholar
  8. [8]
    C.B. Anfinsen, E. Haber, M. Sela, and F.H. White, The Kinetics of Formation of Native Ribonuclease During Oxidation of the Reduced Polypeptide Chain. J. Proc. Nat. Acad. Sci. U.S.A., 47:1309–1314, 1961.Google Scholar
  9. [9]
    F.C. Bernstein, T.F. Koetzle, G.J.B. Williams, E.F. Meyer Jr, M.D. Brice, J.R. Rodgers, O. Kennard, T. Shimanouchi, and M. Tasumi, he Protein Data Bank: A Computer-Based Archival File for Macromolecular Structures. J. Mol. Biol., 12:535–542, 1977.Google Scholar
  10. [10]
    B. Brooks, R. Bruccoleri, B. Olafson, D. States, S. Swaminathan, and M. Karplus, CHARM: A Program for Macromolecular Energy, Minimization, and Dynamics Calculations. J. Comp., Chem., 4:187–217, 1983.Google Scholar
  11. [11]
    T.E. Creighton, Proteins: Structures and Molecular Properties, W.H. Freeman and Company, New York, 1993.Google Scholar
  12. [12]
    P. Dauber-Osguthorpe, V.A. Roberts, D.J. Osguthorpe, J. Wolff, M. Genest and A.T. Hagler, Structure and Energetics of Ligand Bindings to Peptides: Escherichia coli Dihydrofolate Reductase-Trimethoprim, A Drug Receptor System. Proteins: Struct. Funct. Genet., 4:31–47, 1988.Google Scholar
  13. [13]
    B. Freyberg and W.J. Braun, Efficient Search for All Low Energy Conformations of Polypeptides by Monte Carlo Methods. J. Comp. Chem., 12:1065–1076, 1991.Google Scholar
  14. [14]
    L. Glasser and H.A. Scheraga, Calculations on Crystall Packing of a Flexible Molecule, Leu-Enkephalin. J. Mol. Biol., 199:513–524, 1988.Google Scholar
  15. [15]
    U.H. Hansmann and Y. Okamoto, Prediction of Peptide Conformation my Multicanonical Algorithm: New Approach to the Multiple-Minima Problem. J. Comp. Chem., 14:1333–1338, 1993.Google Scholar
  16. [16]
    A.J. Hopfinger, Conformational Properties of Macromolecules. Academic Press, New York, NY, 1973.Google Scholar
  17. [17]
    J. Kostrowicki and H.A. Scheraga, Application of the Diffusion Equation Method for Global Optimization to Oligopeptides. J. Phys. Chem., 96:7442–7449, 1992.Google Scholar
  18. [18]
    M.H. Lambert and H.A. Scheraga, Payttern Recognition in the Prediction of Protein Structure I. Tripeptide Conformational Probabilities Calculated from the Amino Acid Sequence. J. Comp. Chem., 6:770–797, 1989.Google Scholar
  19. [19]
    M. Levitt, Protein Folding by Restrained Energy Minimization and Molecular Dynamics. J. Mol. Biol., 170:723–764, 1983.Google Scholar
  20. [20]
    Z. Li and H.A. Scheraga, Structure and Free Energy of Complex Thermodynamic Systems. J. Mol. Struct. (Theochem.), 179:333–352, 1988.Google Scholar
  21. [21]
    C.D. Maranas and C.A. Floudas, A Global Optimization Approach for Lennard-Jones Microclusters. J. Chem. Phys., 97:7667–7678, 1992.Google Scholar
  22. [22]
    C.D. Maranas and C.A. Floudas, Global Optimization for Molecular Conformation Problems. Ann. Oper. Res., 42:85–117, 1993.Google Scholar
  23. [23]
    C.D. Maranas and C.A. Floudas, Global Minimum Potential Energy Conformations of Small Molecules. J. Global Opt., 4:135–170, 1994.Google Scholar
  24. [24]
    C.D. Maranas and C.A. Floudas, A Deterministic Global Optimization Approach for Molecular Structure Determination. J. Chem. Phys., 100:1247–1261, 1994.Google Scholar
  25. [25]
    C.D. Maranas, I.P. Androulakis, and C.A. Floudas, A Deterministic Global Optimization Approach for the Protein Folding Problem, Global Optimization of Nonconvex Energy Functions: Molecular Conformation and Protein Folding. P.M. Pardalos, D. Shaloway, and G. Xue (Eds.). DIMACS Series in Discrete Mathematics and Theoretical Computer Science, American Mathematical Society, 23:133–150, 1996.Google Scholar
  26. [26]
    B.A. Murtagh and M.A. Saunders, MINOS5.0 Users Guide. Systems Optimization Laboratory, Dept. of Operations Research, Stanford University, CA., 1983.Google Scholar
  27. [27]
    F.A. Momany, L.M. Carruthers, R.F. McGuire, and H.A. Scheraga, Intermolecular Potentials from Crystal Data. III.. Determination of Empirical Potentials and Applications to the Packing Configurations and Lattice Energies in Crystals of Hydrocarbons, Carboxylic Acids, and Amides. J. Phys. Chem., 78:1595–1620, 1974.Google Scholar
  28. [28]
    F.A. Momany, L.M. Carruthers, and H.A. Scheraga, Intermolecular Potentials from Crystal Structures. III. Application of Empirical Potentials to the Packing Configurations and Lattice Energies in Crystals of Amino Acids. J. Phys. Chem., 78:1621–1630, 1974.Google Scholar
  29. [29]
    F.A. Momany, R.F. McGuire, A.W. Burgess, and H.A. Scheraga, Energy Parameters in Polypeptiudes. VII Geometric Parameters, Patial Atomic Charges, Nonbonded Interactions, Hydrogen Bond Interactions, and Intrinsic Torsional Potentials for the Naturally Occurring Amino Acids. J. Phys. Chem., 79:2361–2381, 1975.Google Scholar
  30. [30]
    L.B. Moralles, R. Garduno-Juarez, and D. Romero, Applications of Simulated Annealling to the Multiple-Minima Problem in Small Peptides. J. Biomol. Struct. Dynamics, 8:721–735, 1991.Google Scholar
  31. [31]
    L.B. Moralles, R. Garduno-Juarez, and D. Romero, The Multiple-Minima Problem in Small Peptides Revisited. The Threshold Accepting Approach. J. Biomol. Struct. Dynamics, 9:951–957, 1992.Google Scholar
  32. [32]
    A. Nayeem, J. Vila, and H.A. Scheraga, A Comparative Study of the Simulated-Annealilng and Monte Carlo-with-Minimization Approaches to the Minimum-Energy Structures of Polypetides: Met-Enkephalin. J. Comp. Chem., 12:594–605, 1991.Google Scholar
  33. [33]
    G. Némethy, M.S. Pottle, and H.A. Scheraga, Energy Parameters in Polypeptides. 9. Updating of Geometrical Parameters, Nonbonbed Interaction, and Hydrogen Bond Interactions for the Naturally Occuring Amino Acids. J. Phys. Chem., 89:1883–1887, 1983.Google Scholar
  34. [34]
    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 Nonbounded Interactions for Use in the ECEPP/3 Algorithms, with Applications to Proline-Containing Peptides. J. Phys. Chem., 96:6472–6484, 1992.Google Scholar
  35. [35]
    A. Neumaier, Molecular Modeling of Proteins: The Mathematical Prediction of Protein Structure. SIAM Review, submitted for publication, 1995.Google Scholar
  36. [36]
    K.A. Olszewiski, L. Piela, and H.A. Scheraga, Mean Field Theory as a Tool for Intramolecular Coformational Optimization. Tests on Terminally-Blocked Alanine and Met enkeplhalin. J. Phys. Chem., 96:4672–4676, 1992.Google Scholar
  37. [37]
    P.M. Pardalos, D. Shalloway, and G. Xue (Eds.), Global Minimization of Nonconvex Energy Functions: Molecular Conformation and Protein Folding, DIMACS series in Discrete Mathematics and Theoretical Computer Science, 23, Providence, RI, American Mathematical Society, 1996.Google Scholar
  38. [38]
    D.R. Ripoll and H.A. Scheraga, On the Multiple-Minima Problem in the Conformational Analysis of Polypeptides. II An Electrostatically Driven Monte Carlo Method — Tests of Poly(L-Alanine). Biopolymers, 27:1283–1303, 1988.Google Scholar
  39. [39]
    D.R. Ripoll and H.A. Scheraga, The Multiple Minima Problem in the Conformational Analysis of Polypeptides. III. An Electrostatically Driven Monte Carlo Method — Tests on Enkephalin. J. Protein Chem., 8:263–287, 1989.Google Scholar
  40. [40]
    D.R. Ripoll, M. Vásquez, and H.A. Scheraga, The Electrostatically Driven Monte Carlo Method: Application to conformational Analysis of Decaglycine. Biopolymers, 31:319–330, 1991.Google Scholar
  41. [41]
    H.A. Scheraga, Reviews in Computational Chemistry. VCH Publishers, New York, NY, 1992.Google Scholar
  42. [42]
    J. Shin and M. Jhon, High Directional Monte Carlo Procedure Coupled with the Temperature and Annealing Method to Obtain the Global Energy Minimum Structure of Polypeptides and Proteins. Biopolymers, 31:177–185, 1991.Google Scholar
  43. [43]
    B.L. Sibanda and J.M. Thorton, β-Hairpin families in globular proteins. Nature, 316:170–174, 1985.Google Scholar
  44. [44]
    W.F. van Gunsteren and H.J.C. Berendsen, GROMOS. Groningen Molecular Simulation, Groningen, The Netherlands, 1987.Google Scholar
  45. [45]
    M. Vásquez and H.A. Scheraga, Use of Buildup and Energy-Minimization Procedures to Compute Low-Energy Structures of the Backbone of Enkephalin. Macromolecules, 16:1043–1049, 1983.Google Scholar
  46. [46]
    M. Vásquez, G. Némethy, and H.A. Scheraga, Conformation Energy Calculations on Polypeptides and Proteins. Chem. Rev., 94:2183–2239, 1994.Google Scholar
  47. [47]
    S. Weiner, P. Kollmann, D.A. Case, U.C. Singh., C. Ghio, G. Alagona, S. Profeta and P. Weiner, A New Force Field for Molecular mechanical Simulation of Nucleic Acids and Proteins. J. Am. Chem. Soc., 106:765–784, 1984.Google Scholar
  48. [48]
    S. Weiner, P. Kollmann, D. Nguyen, and D. Case, An All Atom Force Field for Simulations of Proteins and Nucleic Acids. J. Comp. Chem., 7:230–252, 1986.Google Scholar

Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • I.P. Androulakis
    • 1
  • C.D. Maranas
    • 2
  • C.A. Floudas
    • 3
  1. 1.Corporate Research Science LaboratoriesExxon Research and Engineering CompanyAnnandale
  2. 2.Department of Chemical EngineeringThe Pennsylvania State UniversityUniversity Park
  3. 3.Department of Chemical EngineeringPrinceton UniversityPrinceton

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