Statistical Contact Potentials in Protein Coarse-Grained Modeling: From Pair to Multi-body Potentials
The basic concepts of coarse-graining protein structures led to the introduction of empirical statistical potentials in protein computations. We review the history of the development of statistical contact potentials in computational biology and discuss the common features and differences between various pair contact potentials. Potentials derived from the statistics of non-bonded contacts in protein structures from the Protein Data Bank (PDB) are compared with potentials developed for threading purposes based on the optimization of the selection of the native structures among decoys. The energy of transfer of amino acids from water to a protein environment is discussed in detail. We suggest that a next generation of statistical contact potentials should include the effects of residue packing in proteins to improve predictions of protein native three-dimensional structures. We review existing multi-body potentials that have been proposed in the literature, including our own recent four-body potentials. We show how these are related to amino acid substitution matrices.
KeywordsProtein Data Bank Protein Structure Prediction Contact Potential Delaunay Tessellation Contact Energy
We acknowledge the financial support provided by NIH grants 1R01GM073095-3, 1R01GM072014-5, and 1R01GM081680-2.
- Hendlich M, Lackner P, Weitckus S, Floechner H, Froschauer R, Gottsbachner K, Casari G, Sippl MJ (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 216:167–180PubMedCrossRefGoogle Scholar
- Hill TL (1960) Statistical mechanics. Addison-Wesley, Reading, MAGoogle Scholar
- Laurents DV, Huyghes-Despointes BMP, Bruix M, Thurlkill RL, Schell D, Newsom S, Grimsley GR, Shaw KL, Trevi S, Rico M, Briggs JM, Antosiewicz JM, Scholtz JM, Pace CN (2003) Charge–charge interactions are key determinants of the pK values of ionizable groups in ribonuclease Sa (pI = 3.5) and a basic variant (pI = 10.2). J Mol Biol 325:1077–1092PubMedCrossRefGoogle Scholar
- Li X, Liang J (2005a) Computational design of combinatorial peptide library for modulating protein–protein interactions. Pacific Symposium of Biocomputing 10:28–39Google Scholar
- Li X, Liang J (2007) Knowledge-based energy functions for computational studies of proteins. In: Xu Y, Xu D, Liang J (eds) Computational methods for protein structure prediction and modeling, 1st edn. Springer, New York, NY, pp 71–123Google Scholar
- Liwo A, Kazmierkiewicz R, Czaplewski C, Groth M, Oldziej S, Wawak RJ, Rackovsky S, Pincus MR, Scheraga HA (1998) United-residue force field for off-lattice protein-structure simulations: III. Origin of backbone hydrogen-bonding cooperativity in united-residue potentials. J Com Chem 19:259–276CrossRefGoogle Scholar
- Liwo A, Oldziej S, Pincus MR, Wawak RJ, Rackovsky S, Scheraga HA (1997a) A united-residue force field for off-lattice protein-structure simulations. 1. Functional forms and parameters of long-range side-chain interaction potentials from protein crystal data. J Com Chem 18:849–873CrossRefGoogle Scholar
- Liwo A, Pincus MR, Wawak RJ, Rackovsky S, Oldziej S, Scheraga HA (1997b) A united-residue force field for off-lattice protein-structure simulations. 2. Parameterization of short-range interactions and determination of weights of energy terms by Z-score optimization. J Com Chem 18:874–887CrossRefGoogle Scholar
- Pillardy J, Czaplewski C, Liwo A, Lee J, Ripoll DR, Kazmierkiewicz R, Oldziej S, Wedemeyer WJ, Gibson KD, Arnautova YA, Saunders J, Ye YJ, Scheraga HA (2001) Recent improvements in prediction of protein structure by global optimization of a potential energy function. Proc Nat Acad Sci USA 98:2329–2333PubMedCrossRefGoogle Scholar
- Skolnick J, Jaroszewski L, Kolinski A, Godzik A (1997) Derivation and testing of pair potentials for protein folding. When is the quasichemical approximation correct? Protein Sci 6:676–688Google Scholar
- Zheng W, Cho SJ, Vaisman II, Tropsha A (1997) A new approach to protein fold recognition based on Delaunay tessellation of protein structure. Pac Symp Biocomp 1997:486–497Google Scholar