Free-energy function based on an all-atom model for proteins
Takashi Yoshidome
Institute of Advanced Energy, Kyoto University, Uji, Kyoto 611-0011, Japan
Search for more papers by this authorKoji Oda
Taisho Pharmaceutical Co., Ltd., Yoshino-cho, Kita-ku, Saitama 331-9530, Japan
Search for more papers by this authorYuichi Harano
Institute for Protein Research, Osaka University, 3-2 Yamadaoka, Suita, Osaka 565-0871, Japan
Search for more papers by this authorRoland Roth
Max-Planck-Institut für Metallforschung, Heisenbergstr. 3, D-70569 Stuttgart, Germany
ITAP, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
Search for more papers by this authorYuji Sugita
RIKEN Advanced Science Institute, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
Search for more papers by this authorMitsunori Ikeguchi
International Graduate School of Arts and Sciences, Yokohama City University, 1-7-29 Suehiro-cho, Tsurumi-ku, Yokohama 230-0045, Japan
Search for more papers by this authorCorresponding Author
Masahiro Kinoshita
Institute of Advanced Energy, Kyoto University, Uji, Kyoto 611-0011, Japan
Institute of Advanced Energy, Kyoto University, Uji, Kyoto 611-0011, Japan===Search for more papers by this authorTakashi Yoshidome
Institute of Advanced Energy, Kyoto University, Uji, Kyoto 611-0011, Japan
Search for more papers by this authorKoji Oda
Taisho Pharmaceutical Co., Ltd., Yoshino-cho, Kita-ku, Saitama 331-9530, Japan
Search for more papers by this authorYuichi Harano
Institute for Protein Research, Osaka University, 3-2 Yamadaoka, Suita, Osaka 565-0871, Japan
Search for more papers by this authorRoland Roth
Max-Planck-Institut für Metallforschung, Heisenbergstr. 3, D-70569 Stuttgart, Germany
ITAP, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
Search for more papers by this authorYuji Sugita
RIKEN Advanced Science Institute, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
Search for more papers by this authorMitsunori Ikeguchi
International Graduate School of Arts and Sciences, Yokohama City University, 1-7-29 Suehiro-cho, Tsurumi-ku, Yokohama 230-0045, Japan
Search for more papers by this authorCorresponding Author
Masahiro Kinoshita
Institute of Advanced Energy, Kyoto University, Uji, Kyoto 611-0011, Japan
Institute of Advanced Energy, Kyoto University, Uji, Kyoto 611-0011, Japan===Search for more papers by this authorAbstract
We have developed a free-energy function based on an all-atom model for proteins. It comprises two components, the hydration entropy (HE) and the total dehydration penalty (TDP). Upon a transition to a more compact structure, the number of accessible configurations arising from the translational displacement of water molecules in the system increases, leading to a water-entropy gain. To fully account for this effect, the HE is calculated using a statistical-mechanical theory applied to a molecular model for water. The TDP corresponds to the sum of the hydration energy and the protein intramolecular energy when a fully extended structure, which possesses the maximum number of hydrogen bonds with water molecules and no intramolecular hydrogen bonds, is chosen as the standard one. When a donor and an acceptor (e.g., N and O, respectively) are buried in the interior after the break of hydrogen bonds with water molecules, if they form an intramolecular hydrogen bond, no penalty is imposed. When a donor or an acceptor is buried with no intramolecular hydrogen bond formed, an energetic penalty is imposed. We examine all the donors and acceptors for backbone-backbone, backbone-side chain, and side chain-side chain intramolecular hydrogen bonds and calculate the TDP. Our free-energy function has been tested for three different decoy sets. It is better than any other physics-based or knowledge-based potential function in terms of the accuracy in discriminating the native fold from misfolded decoys and the achievement of high Z-scores. Proteins 2009. © 2009 Wiley-Liss, Inc.
REFERENCES
- 1 Dill KA,Ozkan SB,Shell MS,Weikl TR. The protein folding problem. Annu Rev Biophys 2008; 37: 289–316.
- 2 Yoda T,Sugita Y,Okamoto Y. Comparisons of force fields for proteins by generalized-ensemble simulations. Chem Phys Lett 2004; 386: 460–467.
- 3 Anfinsen CB. Principles that govern the folding of protein chains. Science 1973; 181: 223–230.
- 4 Lu M,Dousis AD,Ma J. OPUS-PSP: an orientation-dependent statistical all-atom potential derived from side-chain packing. J Mol Biol 2008; 376: 288–301.
- 5 Miyazawa S,Jernigan RL. How effective for fold recognition is a potential of mean force that includes relative orientations between contacting residues in proteins? J Chem Phys 2005; 122: 024901(1–18).
- 6 Zhang C,Liu S,Zhou H,Zhou Y. An accurate, residue-level, pair potential of mean force for folding and binding based on the distance-scaled, ideal-gas reference state. Protein Sci 2004; 13: 400–411.
- 7 Onizuka K,Noguchi T,Akiyama Y,Matsuda H. Using data compression for multidimensional distribution analysis. Control Intell Syst 2002; 17: 48–54.
- 8 Zhou H,Zhou Y. Distance-scaled, finite ideal-gas reference state improves structure-derived potentials of mean force for structure selection and stability prediction. Protein Sci 2002; 11: 2714–2726.
- 9 Toby D,Elber R. Distance-dependent, pair potential for protein folding: results from linear optimization. Proteins 2000; 41: 40–46.
- 10 Lee MC,Duan Y. Distinguish protein decoys by using a scoring function based on a new AMBER force field, short molecular dynamics simulations, and the generalized born solvent model. Proteins 2004; 55: 620–634.
- 11 Dominy BN,Brooks CLIII. Identifying native-like protein structures using physics-based potentials. J Comput Chem 2002; 23: 147–160.
- 12 Feig M,Brooks CL,III. Evaluating CASP4 predictions with physical energy functions. Proteins 2002; 49: 232–245.
- 13 Kinoshita M,Harano Y,Akiyama R. Changes in thermodynamic quantities upon contact of two solutes in solvent under isochoric and isobaric conditions. J Chem Phys 2006; 125: 244504(1–7).
- 14 Yoshidome T,Kinoshita M,Hirota S,Baden N,Terazima M. Thermodynamics of apoplastocyanin folding: comparison between experimental and theoretical results. J Chem Phys 2008; 128: 225104(1–9).
- 15 Harano Y,Kinoshita M. Large gain in translational entropy of water is a major driving force in protein folding. Chem Phys Lett 2004; 399: 342–348.
- 16 Harano Y,Kinoshita M. Translational-entropy gain of solvent upon protein folding. Biophys J 2005; 89: 2701–2710.
- 17 Harano Y,Roth R,Kinoshita M. On the energetics of protein folding in aqueous solution. Chem Phys Lett 2006; 432: 275–280.
- 18 Harano Y,Roth R,Sugita Y,Ikeguchi M,Kinoshita M. Physical basis for characterizing native structures of proteins. Chem Phys Lett 2007; 437: 112–116.
- 19 Harano Y,Kinoshita M. On the physics of pressure denaturation of proteins. J Phys Condens Matter 2006; 18: L107–L113.
- 20 Harano Y,Kinoshita M. Crucial importance of translational entropy of water in pressure denaturation of proteins. J Chem Phys 2006; 125: 024910(1–10).
- 21 Harano Y,Yoshidome T,Kinoshita M. Molecular mechanism of pressure denaturation of proteins. J Chem Phys 2008; 129: 145103(1–9).
- 22 Yoshidome T,Harano Y,Kinoshita M. Pressure effects on structures formed by the entropically driven self-assembly: illustration for denaturation of proteins. Phys Rev E 2009; 79: 011912(1–10).
- 23 Yoshidome T,Kinoshita M. Hydrophobicity at low temperatures and cold denaturation of a protein. Phys Rev E 2009; 79: 030509(1–4).
- 24 Amano K,Yoshidome T,Harano Y,Oda K,Kinoshita M. Theoretical analysis on thermal stability of a protein focused on the water entropy. Chem Phys Lett 2009; 474: 190–194.
- 25 Kauzmann W. Some factors in the interpretation of protein denaturation. Adv Protein Chem 1959; 14: 1–63.
- 26 Baden N,Hirota S,Takabe T,Funasaki N,Terazima M. Thermodynamical properties of reaction intermediates during apoplastocyanin folding in time domain. J Chem Phys 2007; 127: 175103(1–12).
- 27 Kinoshita M. Molecular origin of the hydrophobic effect: analysis using the angle-dependent integral equation theory. J Chem Phys 2008; 128: 024507(1–14).
- 28 Kusalik PG,Patey GN. On the molecular theory of aqueous electrolyte solutions. I. The solution of the RHNC approximation for models at finite concentration. J Chem Phys 1988; 88: 7715–7738.
- 29 Kusalik PG,Patey GN. The solution of the reference hypernettedchain approximation for water-like models. Mol Phys 1988; 65: 1105–1119.
- 30 König PM,Roth R,Mecke KR. Morphological thermodynamics of fluids: shape dependence of free energies. Phys Rev Lett 2004; 93: 160601(1–4).
- 31 Roth R,Harano Y,Kinoshita M. Morphometric approach to the solvation free energy of complex molecules. Phys Rev Lett 2006; 97: 078101(1–4).
- 32 Park B,Levitt M. Energy functions that discriminates X-ray and near native folds from well-constructed decoys. J Mol Biol 1996; 258: 367–392.
- 33 Berman HM,Westbrook J,Feng Z,Gilliland G,Bhat TN,Weissig H,Shindyalov IN,Bourne PE. The protein data bank. Nucleic Acids Res 2000; 28: 235–242.
- 34 Simons KT,Kooperberg C,Huang E,Baker D. Assembly of protein tertiary structures from fragments with similar local sequences using simulated annealing and bayesian scoring functions. J Mol Biol 1997; 268: 209–225.
- 35 Samudrala R,Levitt M. Decoys ‘R’ Us: a database of incorrect protein conformations to improve protein structure prediction. Protein Sci 2000; 9: 1399–1401.
- 36 MacKerell ADJr,Bashford D,Bellott M,Dunbrack RLJr,Evanseck JD,Field MJ,Fischer S,Gao J,Guo H,Ha S,Joseph-McCarthy D,Kuchnir L,Kuczera K,Lau FTK,Mattos C,Michnick S,Ngo T,Nguyen DT,Prodhom B,Reiher WEIII,Roux B,Schlenkrich M,Smith JC,Stote R,Straub J,Watanabe M,Wiorkiewicz-Kuczera J,Yin D,Karplus M. All-atom empirical potential for molecular modeling and dynamics studies of proteins. J Phys Chem B 1998; 102: 3586–3616.
- 37 MacKerell AD,Jr,Feig M,Brooks CL,III. Extending the treatment of backbone energetics in protein force fields: limitations of gas-phase quantum mechanics in reproducing protein conformational distributions in molecular dynamics simulations. J Comput Chem 2004; 25: 1400–1415.
- 38 Lee MS,Salsbury FRJr,Brooks CLIII. Novel generalized Born methods. J Chem Phys 2002; 116: 10606–10614.
- 39 Lee MS,Feig M,Salsbury FRJr,Brooks CLIII. New analytic approximation to the standard molecular volume definition and its application to generalized Born calculations. J Comput Chem 2003; 24: 1348–1356.
- 40 Chocholousšová J,Feig M. Balancing an accurate representation of the molecular surface in generalized born formalisms with integrator stability in molecular dynamics simulations. J Comput Chem 2006; 27: 719–729.
- 41 Feig M,Chocholousšová J,Tanizaki S. Extending the horizon: towards the efficient modeling of large biomolecular complexes in atomic detail. Theor Chem Acc 2006; 116: 194–205.
- 42 Kabsch W,Sander C. Dictionary of protein secondary structure: pattern recognition of hydrogen-bonded and geometrical features. Biopolymers 1983; 22: 2577–2637.
- 43 Smith PE. The alanine dipeptide free energy surface in solution. J Chem Phys 1999; 111: 5568–5579.
- 44 Mu Y,Kosov DS,Stock G. Conformational dynamics of trialanine in water. 2. Comparison of AMBER, CHARMM, GROMOS, and OPLS force fields to NMR and infrared experiments. J Phys Chem B 2003; 107: 5064–5073.
- 45 Cheung MS,Garcia AE,Onuchic JN. Protein folding mediated by solvation: water expulsion and formation of the hydrophobic core occur after the structural collapse. Proc Natl Acad Sci USA 2002; 99: 685–690.
- 46 Liu Z,Chan HS. Desolvation is a likely origin of robust enthalpic barriers to protein folding. J Mol Biol 2005; 349: 872–889.
- 47 Choudhury N,Pettitt BM. Enthalpy-entropy contributions to the potential of mean force of nanoscopic hydrophobic solutes. J Phys Chem B 2006; 110: 8459–8463.
- 48 MacCallum JL,Moghaddam MS,Chan HS,Tieleman DP. Hydrophobic association of α-helices, steric dewetting, and enthalpic barriers to protein folding. Proc Natl Acad Sci USA 2007; 104: 6206–6210.
- 49 Brooks BR,Bruccoleri RE,Olafson BD,States DJ,Swaminathan S,Karplus M. A program for macromolecular energy, minimization, and dynamics calculations. J Comput Chem 1983; 4: 187–217.
- 50 Feig M,Karanicolas J,Brooks CL,III. MMTSB tool set: enhanced sampling and multiscale modeling methods for applications in structural biology. J Mol Graph 2004; 22: 377–395.
- 51 Shenoy VS,Ichiye T. Influence of protein flexibility on the redox potential of rubredoxin: energy minimization studies. Proteins 1993; 17: 152–160.
- 52 Yelle RB,Park NS,Ichiye T. Molecular dynamics simulations of rubredoxin from clostridium pasteurianum: changes in structure and electrostatic potential during redox reactions. Proteins 1995; 22: 154–167.
- 53 Ponder JW,Richards FM. An efficient Newton-like method for molecular mechanics energy minimization of large molecules. J Comput Chem 1987; 8: 1016–1024.
- 54 Imai T,Harano Y,Kinoshita M,Kovalenko A,Hirata F. A theoretical analysis on hydration thermodynamics of proteins. J Chem Phys 2006; 125: 024911(1–7).
- 55 Lee B,Richards FM. The interpretation of protein structures: estimation of static accessibility. J Mol Biol 1971; 55: 379–400.
- 56 Connolly ML. Analytical molecular surface calculation. J Appl Crystallogr 1983; 16: 548–558.
- 57 Connolly ML. Computation of molecular volume. J Am Chem Soc 1985; 107: 1118–1124.
- 58 McDonald IK,Thornton JM. Satisfying hydrogen bonding potential in proteins. J Mol Biol 1994; 238: 777–793.
- 59 Sneddon SF,Tobias DJ,Brooks CL,III. Thermodynamics of amide hydrogen bond formation in polar and apolar solvents. J Mol Biol 1989; 209: 817–820.
- 60 Fleming PJ,Rose GD. Do all backbone polar groups in proteins form hydrogen bonds? Protein Sci 2005; 14: 1911–1917.
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