Cell Biochemistry and Biophysics

, Volume 46, Issue 2, pp 165–174 | Cite as

What is a desirable statistical energy functions for proteins and how can it be obtained?

  • Yaoqi Zhou
  • Hongyi Zhou
  • Chi Zhang
  • Song Liu


Can one obtain a physical energy function for proteins from statistical analysis of protein structures? A direct answer to this question is likely “no”. A less demanding question is whether one can produce a statistical energy function that has the desirable features of a physical-based energy function. Such a desirable energy function would be founded on a physical basis with few or no adjustable parameters, reproduce the known physical characters of amino acid residues, be mostly database independent and transferable, and, more importantly, reasonably accurate in various applications. In this review, we show how such a desirable energy function can be obtained via introducing a simple physical-based reference state called DRIRE (Distance-scaled, Finite, Ideal-gas Reference state).

Index Entries

knowledge-based potential hydrophobicity protein-ligand binding affinity database dependence 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    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. Comp. Chem. 4, 187–217.CrossRefGoogle Scholar
  2. 2.
    Weiner, S. J., Kollman, P., Nguyen, D., and Case, D. (1986) An all atom force field for simulations of proteins and nucleic acids. J. Comp. Chem. 7, 230–252.CrossRefGoogle Scholar
  3. 3.
    Jorgensen, W. L., Maxwell, D. S., and Tirado-Rives, J. (1996) Development and testing of the OPLS all-atom force field on conformational energetics and properties of organic liquids. J. Am. Chem. Soc. 118, 11225–11236.CrossRefGoogle Scholar
  4. 4.
    Scott, W. R. P., Hünenberger, P. H., Tironi, I. G., et al. (1999) The GROMOS biomolecular simulation program package. J. Phys. Chem. A 103, 3596–3607.CrossRefGoogle Scholar
  5. 5.
    Tanaka, S., and Scheraga, H. A. (1976) Medium- and longrange interaction parameters between amino acids for predicting three-dimensional structures of proteins. Macromolecules 9, 945–950.PubMedCrossRefGoogle Scholar
  6. 6.
    Ghosh, A., Rapp, C. S., and Friesner, R. A. (1998) Generalized Born model based on a surface integral formulation. J. Phys. Chem. B 102, 10983–10990.CrossRefGoogle Scholar
  7. 7.
    Lazaridis, T., and Karplus, M. (1999) Effective energy function for proteins in solution. Proteins 35, 133–152.PubMedCrossRefGoogle Scholar
  8. 8.
    Zhang, L. Y., Gallicchio, E., Friesner, R. A., and Levy, R. M. (2001) Solvent models for protein-ligand binding: Comparison of implicit solvent Poisson and surface generalized Born models with explicit solvent simulations. J. Comp. Chem. 22, 591–607.CrossRefGoogle Scholar
  9. 9.
    Dominy, B. N., and Brooks III, C. L. (2002) Identifying native-like protein structures using physics-based potentials. J. Comp. Chem. 23, 147–160.CrossRefGoogle Scholar
  10. 10.
    Lazaridis, T., and Karplus, M. (2000) Effective energy function for protein structure prediction. Curr. Opin. Struct. Biol. 10, 139–145.PubMedCrossRefGoogle Scholar
  11. 11.
    Gohlke, H., and Klebe, G. (2001) Statistical potentials and scoring functions applied to protein-ligand binding. Curr. Opin. Struct. Biol. 11, 231–235.PubMedCrossRefGoogle Scholar
  12. 12.
    Russ, W. P., and Ranganathan, R. (2002) Knowledge-based potential functions in protein design. Curr. Opin. Struct. Biol. 12, 447–452.PubMedCrossRefGoogle Scholar
  13. 13.
    Meller, J., and Elber, R. (2002) Protein recognition by sequence-to-structure fitness: Bridging efficiency and capacity of threading models. Adv. Chem. Phys. 120, 77–130.Google Scholar
  14. 14.
    N-V Buchete, J.S., and Thirumalai, D. (2004) Development of novel statistical potentials for protein fold recognition. Curr. Opin. Struct. Biol. 14, 225–232.CrossRefGoogle Scholar
  15. 15.
    Miyazawa, S., and Jernigan, R. L. (1985) Estimation of effective interresidue contact energies from protein crystal structures: quasi-chemical approximation. Macromole 18, 534–552.CrossRefGoogle Scholar
  16. 16.
    DeBolt, S. E., and Skolnick, J. (1996) Evaluation of atomic level mean force potentials via inverse folding and inverse refinement of protein structures: atomic burial position and pairwise non-bonded interactions. Protein Eng. 9, 637–655.PubMedCrossRefGoogle Scholar
  17. 17.
    Zhang, C., Vasmatzis, G., Cornette, J., and DeLisi, C. (1997) Determination of atomic desolvation energies from the structures of crystallized proteins. J. Mol. Biol. 267, 707–726.PubMedCrossRefGoogle Scholar
  18. 18.
    Skolnick, J., Kolinski, A., and Ortiz, A. (2000) Derivation of protein-specific pair potentials based on weak sequence fragment similarity. Proteins 38, 3–16.PubMedCrossRefGoogle Scholar
  19. 19.
    Sippl, M. J. (1993) Boltzmann's principle, knowledge-based mean fields and protein folding. An approach to the computational determination of protein structures. J. Comp. Aid. Mol. Design 7, 473–501.CrossRefGoogle Scholar
  20. 20.
    Melo, F., and Feytmans, E. (1998) Assessing protein structures using a non-local atomic interaction energy. J. Mol. Biol. 277, 1141–1152.PubMedCrossRefGoogle Scholar
  21. 21.
    Zhou, H., and Zhou, Y. (2004) Single-body knowledge-based energy score combined with sequence-profile and secondary structure information for fold recognition. Proteins 55, 1005–1013.PubMedCrossRefGoogle Scholar
  22. 22.
    Rooman, M. J., Kocher, J.-P. A., and Wodak, S. J. (1991) Prediction of protein backbone conformation based on seven structure assignments. Influence of local interactions. J. Mol. Biol. 211, 961–979.CrossRefGoogle Scholar
  23. 23.
    Rooman, M. J., Kocher, J.-P. A., and Wodak, S. J. (1992) Extracting information of folding from the amino acid sequence: accurate predictions for protein regions with preferred conformation in the absence of tertiary interactions. Biochemistry 31, 10226–10238.PubMedCrossRefGoogle Scholar
  24. 24.
    Kocher, J.-P. A., Rooman, M. J., and Wodak, S. J. (1994) Factors influencing the ability of knowledge-based potentials to identify native sequence-structure matches. J. Mol. Biol. 235, 1598–1613.PubMedCrossRefGoogle Scholar
  25. 25.
    Sippl, M. J. (1990) Calculation of conformational ensembles from potentials of mean force. An approach to the knowledge-based prediction of local structures in globular proteins. J. Mol. Biol. 213, 859–883.PubMedCrossRefGoogle Scholar
  26. 26.
    Hendlich, M., Lackner, P., Weitckus, S., et al. (1990) Identification of native protein folds amongst a large number of incorrect models. The calculation of low energy conformations from potentials of mean force. J. Mol. Biol. 216, 167–180.PubMedCrossRefGoogle Scholar
  27. 27.
    Tobi, D., and Elber, R. (2000) Distance-dependent, pair potential for protein folding: Results from linear optimization. Proteins 41, 40–46.PubMedCrossRefGoogle Scholar
  28. 28.
    Jones, D. T., Taylor, W. R., and Thornton, J. M. (1992) A new approach to protein fold recognition. Nature 358, 86–89.PubMedCrossRefGoogle Scholar
  29. 29.
    Samudrala, R., and Moult, J. (1998) An all-atom distance-dependent conditional probability discriminatory function for protein structure prediction. J. Mol. Biol. 275, 895–916.PubMedCrossRefGoogle Scholar
  30. 30.
    Lu, H., and Skolnick, J. (2001) A distance-dependent atomic knowledge-based potential for improved protein structure selection. Proteins 44, 223–232.PubMedCrossRefGoogle Scholar
  31. 31.
    Rojnuckarin, A., and Subramaniam, S. (1999) Knowledge-based interaction potentials for proteins. Proteins 36, 54–67.PubMedCrossRefGoogle Scholar
  32. 32.
    Hardin, C., Eastwood, M. P., Luthey-Schulten, Z., and Wolynes, P. G. (2000) Associative memory Hamiltonians for structure prediction without homology: alpha-helical proteins. Proc. Natl. Acad. Sci. USA 97, 14235–14240.PubMedCrossRefGoogle Scholar
  33. 33.
    Thomas, P. D., and Dill, K. A. (1996) Statistical potentials extracted from protein structures: how accurate are they? J. Mol. Biol. 257, 457–469.PubMedCrossRefGoogle Scholar
  34. 34.
    Lu, H., Lu, L., and Skolnick, J. (2003) Development of unified statistical potentials describing protein-protein interactions. Biophys. J. 84, 1895–1901.PubMedCrossRefGoogle Scholar
  35. 35.
    Glaser, F., Sternberg, D. M., Vakser, I., and Ben-Tal, N. (2001) Residue frequencies and pairing preferences at protein-protein interfaces. Proteins 43, 89–102.PubMedCrossRefGoogle Scholar
  36. 36.
    Ofran, Y., and Rost, B. (2003) Analyzing six types of protein-protein complexes. J. Mol. Biol. 325, 377–387.PubMedCrossRefGoogle Scholar
  37. 37.
    Furuichi, E., and Koehl, P. (1998) Influence of protein structure databases on the predictive power of statistical pair potentials. Proteins 31, 139–149.PubMedCrossRefGoogle Scholar
  38. 38.
    Moont, G., Gabb, H., and Sternberg, M. (1999) Use of pair potentials across protein interfaces in screening predicted docked complexes. Proteins 35, 364–373.PubMedCrossRefGoogle Scholar
  39. 39.
    Simons, K. T., Kooperberg, C., Huang, E., and Baker, D. (1997) Assembly of protein tertiary structures from fragments with similar local sequences using simulated annealing and Bayesian scoring functions. J. Mol. Biol. 268, 209–225.PubMedCrossRefGoogle Scholar
  40. 40.
    Eyrich, V. A., Standley, D. M., and Friesner, R. A. (2002) Ab initio protein structure prediction using a size-dependent tertiary folding potential. Adv. Chem. Phys. 120, 223–263.Google Scholar
  41. 41.
    Dehouck, Y., Gilis, D., and Rooman, M. (2004) Database-derived potentials dependent on protein size for in silico folding and design. Biophys. J. 87, 171–181.PubMedCrossRefGoogle Scholar
  42. 42.
    Jernigan, R. L., and Bahar, I. (1996) Structure-derived potentials and protein simulations. Curr. Opin. Struct. Biol. 6, 195–209.PubMedCrossRefGoogle Scholar
  43. 43.
    Moult, J. (1997) Comparison of database potentials and molecular mechanics force fields. Curr. Opin. Struct. Biol. 7, 194–199.PubMedCrossRefGoogle Scholar
  44. 44.
    Betancourt, M. R., and Thirumalai, D. (1999) Pair potentials for protein folding: choice of reference states and sensitivity of predicted native states to variations in the interaction schemes. Protein Sci. 8, 361–369.PubMedGoogle Scholar
  45. 45.
    Mitchell, J. B. O., Laskowski, R. A., Alex, A., and Thornton, J. M. (1999) BLEEP—potential of mean force describing protein-ligand interactions: I. generating potential. J. Comp. Chem. 20, 1165–1176.CrossRefGoogle Scholar
  46. 46.
    Vijayakumar, M., and Zhou, H.-X. (2000) Prediction of residue-residue pair frequencies in proteins. J. Phys. Chem. B 104, 9755–9764.CrossRefGoogle Scholar
  47. 47.
    McConkey, B. J., Sobolev, V., and Edelman, M. (2003) Discrimination of native protein structures using atom-atom contact scoring. Proc. Natl. Acad. Sci. USA 100, 3215–3220PubMedCrossRefGoogle Scholar
  48. 48.
    Friedman, H. L. A Course in Statistical Mechanics. Prentice-Hall, Inc., Englewood Cliffs, NJ, 1985.Google Scholar
  49. 49.
    Zhou, H., and Zhou, Y. (2002) Distance-scaled, finite idealgas reference state improves structure-derived potentials of mean force for structure selection and stability prediction. Protein Sci. 11, 2714–2726.PubMedCrossRefGoogle Scholar
  50. 50.
    Wang, G., and Dunbrack Jr., R. L. (2003) PISCES: a protein sequence culling server. Bioinformatics 19, 1589–1591.PubMedCrossRefGoogle Scholar
  51. 51.
    Privalov, P. L. (1979) Stability of proteins: Small globular proteins. Adv. Protein Chem. 33, 167–241.PubMedGoogle Scholar
  52. 52.
    Kauzmann, W. (1959) Some factors in the interpretation of protein denaturations. Adv. Protein Chem. 14, 1–63.PubMedGoogle Scholar
  53. 53.
    Dill, K. A. (1990) Dominant forces in protein folding. Biochemistry 29, 7133–7155.PubMedCrossRefGoogle Scholar
  54. 54.
    Zhou, H. & Zhou, Y. (2004) Quantifying the effect of burial of amino acid residues on protein stability. Proteins 54, 315–322.PubMedCrossRefGoogle Scholar
  55. 55.
    Sharp, K. A., Nicholls, A., Friedman, R., and Honig, B. (1991) Extracting hydrophobic free energies from experimental data: relationship to protein folding and theoretical models. Biochemistry 30, 9686–9697.PubMedCrossRefGoogle Scholar
  56. 56.
    Zhou, H., and Zhou, Y. (2002) The stability scale and atomic solvation parameters extracted from 1023 mutation experiments. Proteins 49, 483–492.PubMedCrossRefGoogle Scholar
  57. 57.
    Karplus, P. A. (1997) Hydrophobicity regained. Protein Sci. 6, 1302–1307.PubMedGoogle Scholar
  58. 58.
    Chan, H. S. Amino acid side-chain hydrophobicity. In Encyclopedia of Life Sciences. Nature Publishing Group, London, UK, 2001.Google Scholar
  59. 59.
    Zhang, C., Liu, S., Zhou, H., and Zhou, Y. (2004) The dependence of all-atom statistical potentials on training structural database. Biophys. J. 86, 3349–3358.PubMedCrossRefGoogle Scholar
  60. 60.
    Liu, S., Zhang, C., Zhou, H., and Zhou, Y. (2004) A physical reference state unifies the structure-derived potential of mean force for protein folding and binding. Proteins 56, 93–101.PubMedCrossRefGoogle Scholar
  61. 61.
    Zhang, C., Liu, S., Zhu, Q., and Zhou, Y. (2005) A knowledge-based energy function for protein-ligand, protein-protein and protein-DNA complexes. J. Med. Chem. 48, 2325–2335.PubMedCrossRefGoogle Scholar
  62. 62.
    Zhang, C., Liu, S., and Zhou, Y. (2004) Accurate and efficient loop selections using DFIRE-based all-atom statistical potential. Protein Sci. 13, 391–399.PubMedCrossRefGoogle Scholar
  63. 63.
    Zhang, C., Liu, S., Zhou, H., and Zhou, Y. (2004) An accurate residue-level pair potential of mean force for folding and binding based on the distance-scaled ideal-gas reference state. Protein Sci. 13, 400–411.PubMedCrossRefGoogle Scholar
  64. 64.
    de Armas, R. R., Diaz, H. G., Molina, R., and Uriarte, E. (2004) Markovian backbone negentropies: Molecular descriptors for protein research. I. Predicting protein stability in arc repressor mutants. Proteins 56, 715–723.CrossRefGoogle Scholar
  65. 65.
    Zhang, C., Liu, S., and Zhou, Y. (2005) Docking prediction using biological in-formation, ZDOCK sampling technique and clusterization guided by the DFIRE statistical energy function. (CAPRI Special Issue). Proteins 60, 314–318.PubMedCrossRefGoogle Scholar
  66. 66.
    Li, H., and Zhou, Y. (2005) Fold helical proteins by energy minimization in dihedral space and a DFIRE-based statistical energy fucntion. J. Bioinform. Comp. Biol. 3, 1151–1170.CrossRefGoogle Scholar
  67. 67.
    Dunker, A. K., Brown, C. J., and Obradovic, Z. (2002) Identification and functions of usefully disordered proteins. Adv. Protein Chem. 62, 25–49.PubMedCrossRefGoogle Scholar
  68. 68.
    Kolinski, A., Galazka, W., and Skolnick, J. (1996) On the origin of the cooperativity of protein folding: Implication from model simulations. Proteins 26, 271–287.PubMedCrossRefGoogle Scholar
  69. 69.
    Liwo, A., Oldziej, S., Pincus, M. R., Wawak, R. J., Rackovsky, S., and Scheraga, H. A. (1997) A united-residue force field for off-lattice protein-structure simulations. I. functional forms and parameters of long-range sidechain interaction potentials from protein crystal data. J. Comp. Chem. 18, 849–872.CrossRefGoogle Scholar
  70. 70.
    Gan, H. H., Tropsha, A., and Schlick, T. (2001) Lattice protein folding with two and four-body statistical potentials. Proteins 43, 161–174.PubMedCrossRefGoogle Scholar
  71. 71.
    Krishnamoorthy, B., and Tropsha, A. (2003) Development of a four-body statistical pseudo-potential to discriminate native from non-native protein conformations. Bioinformatics 19, 1540–1548.PubMedCrossRefGoogle Scholar
  72. 72.
    Ejtehadi, M. R., Avall, S. P., and Plotkin, S. S. (2004) Three-body interactions improve the prediction of rate and mechanism in protein folding models. Proc. Natl. Acad. Sci. USA 101, 15088–15093.PubMedCrossRefGoogle Scholar
  73. 73.
    Grishaev, A., and Bax, A. (2004) An empirical backbone-backbone hydrogen-bonding potential in proteins and its applications to NMR structure refinement and validation. J. Am. Chem. Soc. 126, 7281–7292.PubMedCrossRefGoogle Scholar
  74. 74.
    Kortemme, T., Morozov, A., and Baker, D. (2003) An orientation-dependent hydrogen bonding potential improves prediction of specificity and structure for proteins and protein-protein complexes. J. Mol. Biol. 326, 1239–1259.PubMedCrossRefGoogle Scholar
  75. 75.
    Buchete, N.-V., Straub, J. E., and Thirumalai, D. (2004) Orientational potentials extracted from protein structures improve native fold recognition. Protein Sci. 13, 862–874.PubMedCrossRefGoogle Scholar
  76. 76.
    Sternberg, M. J. E., Gabb, H. A., and Jackson, R. M. (1998) Predictive docking of protein-protein and protein-DNA complexes. Curr. Opin. Struct. Biol. 8, 250–256.PubMedCrossRefGoogle Scholar
  77. 77.
    Devos, D., Dokudovskaya, S., Alber, F., et al. (2004) Components of coated vesicles and nuclear pore complexes share a common molecular architecture. PLoS Biol. 2, 1–9.CrossRefGoogle Scholar
  78. 78.
    Grigoryan, G., and Keating, A. E. (2006) Structure-based prediction of bZIP partnering specificity. J. Mol. Biol. 355, 1125–1142.PubMedCrossRefGoogle Scholar

Copyright information

© Humana Press Inc. 2006

Authors and Affiliations

  1. 1.Howard Hughes Medical Institute Center for Single Molecule Biophysics, Department of Physiology and BiophysicsState University of New York at BuffaloBuffalo

Personalised recommendations