Current Status of Protein Force Fields for Molecular Dynamics Simulations

  • Pedro E. M. Lopes
  • Olgun Guvench
  • Alexander D. MacKerellJr.
Part of the Methods in Molecular Biology book series (MIMB, volume 1215)


The current status of classical force fields for proteins is reviewed. These include additive force fields as well as the latest developments in the Drude and AMOEBA polarizable force fields. Parametrization strategies developed specifically for the Drude force field are described and compared with the additive CHARMM36 force field. Results from molecular simulations of proteins and small peptides are summarized to illustrate the performance of the Drude and AMOEBA force fields.

Key words

Force field Molecular dynamics Drude polarizable force field CHARMM AMOEBA AMBER GROMOS OPLS NAMD Electronic polarization 



Financial support from the NIH (GM072558) and computational support from the University of Maryland Computer-Aided Drug Design Center, and the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number OCI-1053575, are acknowledged.


  1. 1.
    MacKerell AD (2004) Empirical force fields for biological macromolecules: overview and issues. J Comput Chem 25(13):1584–1604PubMedGoogle Scholar
  2. 2.
    Stone AJ (2008) Intermolecular potentials. Science 321(5890):787–789PubMedGoogle Scholar
  3. 3.
    Freddolino PL, Harrison CB, Liu YX, Schulten K (2010) Challenges in protein-folding simulations. Nat Phys 6(10):751–758PubMedPubMedCentralGoogle Scholar
  4. 4.
    Warshel A, Kato M, Pisliakov AV (2007) Polarizable force fields: history, test cases, and prospects. J Chem Theory Comput 3(6):2034–2045Google Scholar
  5. 5.
    Lopes PEM, Roux B, MacKerell AD (2009) Molecular modeling and dynamics studies with explicit inclusion of electronic polarizability: theory and applications. Theor Chem Acc 124(1–2):11–28PubMedPubMedCentralGoogle Scholar
  6. 6.
    Zhu X, Lopes PEM, MacKerell AD (2012) Recent developments and applications of the CHARMM force fields. Wiley Interdiscip Rev Comput Mol Sci 2(1):167–185PubMedPubMedCentralGoogle Scholar
  7. 7.
    Guvench O, MacKerell AD (2008) Comparison of protein force fields for molecular dynamics simulations. In: Kukol A (ed) Molecular modeling of proteins. Humana Press, Totowa, NJ, pp 63–88Google Scholar
  8. 8.
    Lopes PEM, Harder E, Roux B, MacKerell AD (2009) Formalisms for the explicit inclusion of electronic polarizability in molecular modeling and dynamics studies. In: York DM, Lee T-S (eds) Multi-scale quantum models for biocatalysis. Springer, Netherlands, pp 219–257Google Scholar
  9. 9.
    Salomon-Ferrer R, Case DA, Walker RC (2013) An overview of the Amber biomolecular simulation package. Wiley Interdiscip Rev Comput Mol Sci 3(2):198–210Google Scholar
  10. 10.
    Beauchamp K, Lin Y-S, Das R, Pande V (2012) Are protein force fields getting better? A systematic benchmark on 524 diverse NMR measurements. J Chem Theory Comput 8(4):1409–1414PubMedPubMedCentralGoogle Scholar
  11. 11.
    Burkert U, Allinger N (1982) Molecular mechanics. American Chemical Society, Washington, DCGoogle Scholar
  12. 12.
    McCammon JA, Harvey SC (1987) Dynamics of proteins and nucleic acids. Cambridge University Press, New YorkGoogle Scholar
  13. 13.
    Leach AR (2001) Molecular modelling: principles and applications. Prentice Hall, Harlow, EnglandGoogle Scholar
  14. 14.
    Becker OM (2001) Computational biochemistry and biophysics. M. Dekker, New YorkGoogle Scholar
  15. 15.
    Rapaport DC (2004) The art of molecular dynamics simulation. Cambridge University Press, Cambridge, UKGoogle Scholar
  16. 16.
    Schlick T (2002) Molecular modeling and simulation: an interdisciplinary guide. Springer, New YorkGoogle Scholar
  17. 17.
    Satoh A. Introduction to practice of molecular simulation molecular dynamics, Monte Carlo, Brownian dynamics, Lattice Boltzmann, dissipative particle dynamics.
  18. 18.
    Brooks BR, Bruccoleri RE, Olafson BD, States DJ, Swaminathan S, Karplus M (1983) CHARMM: a program for macromolecular energy, minimization, and dynamics calculations. J Comput Chem 4(2):187–217Google Scholar
  19. 19.
    MacKerell AD, Bashford D, Bellott M, Dunbrack RL, Evanseck JD, Field MJ et al (1998) All-atom empirical potential for molecular modeling and dynamics studies of proteins. J Phys Chem B 102(18):3586–3616PubMedGoogle Scholar
  20. 20.
    Best RB, Zhu X, Shim J, Lopes PEM, Mittal J, Feig M et al (2012) Optimization of the additive CHARMM all-atom protein force field targeting improved sampling of the backbone ϕ, ψ and side-chain χ1 and χ2 dihedral angles. J Chem Theory Comput 8(9):3257–3273PubMedPubMedCentralGoogle Scholar
  21. 21.
    MacKerell AD, Wiorkiewicz-Kuczera J, Karplus M (1995) An all-atom empirical energy function for the simulation of nucleic acids. J Am Chem Soc 117(48):11946–11975Google Scholar
  22. 22.
    Foloppe N, MacKerell AD (2000) All-atom empirical force field for nucleic acids: I. Parameter optimization based on small molecule and condensed phase macromolecular target data. J Comput Chem 21(2):86–104Google Scholar
  23. 23.
    MacKerell AD, Banavali NK (2000) All-atom empirical force field for nucleic acids: II. Application to molecular dynamics simulations of DNA and RNA in solution. J Comput Chem 21(2):105–120Google Scholar
  24. 24.
    Feller SE, MacKerell AD (2000) An improved empirical potential energy function for molecular simulations of phospholipids. J Phys Chem B 104(31):7510–7515Google Scholar
  25. 25.
    Feller SE, Gawrisch K, MacKerell AD (2001) Polyunsaturated fatty acids in lipid bilayers: intrinsic and environmental contributions to their unique physical properties. J Am Chem Soc 124(2):318–326Google Scholar
  26. 26.
    Klauda JB, Venable RM, Freites JA, O’Connor JW, Tobias DJ, Mondragon-Ramirez C et al (2010) Update of the CHARMM all-atom additive force field for lipids: validation on six lipid types. J Phys Chem B 114(23):7830–7843PubMedPubMedCentralGoogle Scholar
  27. 27.
    Kuttel M, Brady JW, Naidoo KJ (2002) Carbohydrate solution simulations: producing a force field with experimentally consistent primary alcohol rotational frequencies and populations. J Comput Chem 23(13):1236–1243PubMedGoogle Scholar
  28. 28.
    Guvench O, Greene SN, Kamath G, Brady JW, Venable RM, Pastor RW et al (2008) Additive empirical force field for hexopyranose monosaccharides. J Comput Chem 29(15):2543–2564PubMedPubMedCentralGoogle Scholar
  29. 29.
    Hatcher ER, Guvench O, MacKerell AD (2009) CHARMM additive all-atom force field for acyclic polyalcohols, acyclic carbohydrates, and inositol. J Chem Theory Comput 5(5):1315–1327PubMedPubMedCentralGoogle Scholar
  30. 30.
    Guvench O, Hatcher E, Venable RM, Pastor RW, MacKerell AD (2009) CHARMM additive all-atom force field for glycosidic linkages between hexopyranoses. J Chem Theory Comput 5(9):2353–2370PubMedPubMedCentralGoogle Scholar
  31. 31.
    Vanommeslaeghe K, Hatcher E, Acharya C, Kundu S, Zhong S, Shim J et al (2010) CHARMM general force field: a force field for drug-like molecules compatible with the CHARMM all-atom additive biological force fields. J Comput Chem 31(4):671–690PubMedPubMedCentralGoogle Scholar
  32. 32.
    MacKerell AD, Feig M, Brooks CL (2004) 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 25(11):1400–1415PubMedGoogle Scholar
  33. 33.
    MacKerell AD, Feig M, Brooks CL (2004) Improved treatment of the protein backbone in empirical force fields. J Am Chem Soc 126(3):698–699PubMedGoogle Scholar
  34. 34.
    Freddolino PL, Schulten K (2009) Common structural transitions in explicit-solvent simulations of villin headpiece folding. Biophys J 97(8):2338–2347PubMedPubMedCentralGoogle Scholar
  35. 35.
    Freddolino PL, Liu F, Gruebele M, Schulten K (2008) Ten-microsecond molecular dynamics simulation of a fast-folding WW domain. Biophys J 94(10):L75–L77PubMedPubMedCentralGoogle Scholar
  36. 36.
    Freddolino PL, Park S, Roux B, Schulten K (2009) Force field bias in protein folding simulations. Biophys J 96(9):3772–3780PubMedPubMedCentralGoogle Scholar
  37. 37.
    Best R, Buchete N-V, Hummer G (2008) Are current molecular dynamics force fields too helical? Biophys J 95(1):L07–L09PubMedPubMedCentralGoogle Scholar
  38. 38.
    Best RB, Hummer G (2009) Optimized molecular dynamics force fields applied to the helix-coil transition of polypeptides. J Phys Chem B 113(26):9004–9015PubMedPubMedCentralGoogle Scholar
  39. 39.
    Best RB, Mittal J (2010) Balance between α and β structures in ab initio protein folding. J Phys Chem B 114(26):8790–8798PubMedGoogle Scholar
  40. 40.
    Mittal J, Best RB (2010) Tackling force-field bias in protein folding simulations: folding of villin HP35 and Pin WW domains in explicit water. Biophys J 99(3):L26–L28PubMedPubMedCentralGoogle Scholar
  41. 41.
    Shim J, Zhu X, Best RB, MacKerell AD (2013) Ala4-X-Ala4 as a model system for the optimization of the χ1 and χ2 amino acid side-chain dihedral empirical force field parameters. J Comput Chem 34(7):593–603PubMedPubMedCentralGoogle Scholar
  42. 42.
    Vorobyov IV, Anisimov VM, MacKerell AD (2005) Polarizable empirical force field for alkanes based on the classical drude oscillator model. J Phys Chem B 109(40):18988–18999PubMedGoogle Scholar
  43. 43.
    Mason PE, Neilson GW, Enderby JE, Saboungi ML, Dempsey CE, MacKerell AD et al (2004) The structure of aqueous guanidinium chloride solutions. J Am Chem Soc 126(37):11462–11470PubMedGoogle Scholar
  44. 44.
    Macias AT, MacKerell AD (2005) CH/pi interactions involving aromatic amino acids: refinement of the CHARMM tryptophan force field. J Comput Chem 26(14):1452–1463PubMedGoogle Scholar
  45. 45.
    Hornak V, Abel R, Okur A, Strockbine B, Roitberg A, Simmerling C (2006) Comparison of multiple Amber force fields and development of improved protein backbone parameters. Proteins 65(3):712–725PubMedGoogle Scholar
  46. 46.
    Lindorff-Larsen K, Piana S, Palmo K, Maragakis P, Klepeis J, Dror R et al (2010) Improved side-chain torsion potentials for the Amber ff99SB protein force field. Proteins 78(8):1950–1958PubMedPubMedCentralGoogle Scholar
  47. 47.
    Li D-W, Bruschweiler R (2011) NMR-based protein potentials. Angew Chem 122(38):6930–6932Google Scholar
  48. 48.
    Nerenberg P, Head-Gordon T (2011) Optimizing protein–solvent force fields to reproduce intrinsic conformational preferences of model peptides. J Chem Theory Comput 7(4):1220–1230Google Scholar
  49. 49.
    Perez A, Marchan I, Svozil D, Sponer J, Cheatham TE, Laughton CA et al (2007) Refinenement of the AMBER force field for nucleic acids: improving the description of alpha/gamma conformers. Biophys J 92(11):3817–3829PubMedPubMedCentralGoogle Scholar
  50. 50.
    Joung IS, Cheatham TE (2008) Determination of alkali and halide monovalent ion parameters for use in explicitly solvated biomolecular simulations. J Phys Chem B 112(30):9020–9041PubMedPubMedCentralGoogle Scholar
  51. 51.
    Joung IS, Cheatham TE (2009) Molecular dynamics simulations of the dynamic and energetic properties of alkali and halide ions using water-model-specific ion parameters. J Phys Chem B 113(40):13279–13290PubMedPubMedCentralGoogle Scholar
  52. 52.
    Banas P, Hollas D, Zgarbova M, Jurecka P, Orozco M, Cheatham TE III et al (2010) Performance of molecular mechanics force fields for RNA simulations: stability of UUCG and GNRA hairpins. J Chem Theory Comput 6(12):3836–3849Google Scholar
  53. 53.
    Zgarbova M, Otyepka M, Sponer J, Mladek A, Banas P, Cheatham TE III et al (2011) Refinement of the Cornell et al. Nucleic acids force field based on reference quantum chemical calculations of glycosidic torsion profiles. J Chem Theory Comput 7(9):2886–2902PubMedPubMedCentralGoogle Scholar
  54. 54.
    Kirschner KN, Woods RJ (2001) Solvent interactions determine carbohydrate conformation. Proc Natl Acad Sci U S A 98(19):10541–10545PubMedPubMedCentralGoogle Scholar
  55. 55.
    Woods RJ, Dwek RA, Edge CJ, Fraser-Reid B (1995) Molecular mechanical and molecular dynamic simulations of glycoproteins and oligosaccharides. 1. GLYCAM_93 parameter development. J Phys Chem 99(11):3832–3846Google Scholar
  56. 56.
    Kirschner KN, Yongye AB, Tschampel SM, González-Outeiriño J, Daniels CR, Foley BL et al (2008) GLYCAM06: a generalizable biomolecular force field. Carbohydrates. J Comput Chem 29(4):622–655PubMedGoogle Scholar
  57. 57.
    Skjevik ÃGA, Madej BD, Walker RC, Teigen K (2012) LIPID11: a modular framework for lipid simulations using Amber. J Phys Chem B 116(36):11124–11136PubMedPubMedCentralGoogle Scholar
  58. 58.
    Brooks BR, Brooks CL III, MacKerell AD Jr, Nilsson L, Petrella RJ, Roux B et al (2009) CHARMM: the biomolecular simulation program. J Comput Chem 30(10):1545–1614PubMedPubMedCentralGoogle Scholar
  59. 59.
    Jiang W, Hardy DJ, Phillips JC, Mackerell AD Jr, Schulten K, Roux B (2011) High-performance scalable molecular dynamics simulations of a polarizable force field based on classical Drude oscillators in NAMD. J Phys Chem Lett 2(2):87–92PubMedPubMedCentralGoogle Scholar
  60. 60.
    Boulanger E, Thiel W (2012) Solvent boundary potentials for hybrid QM/MM computations using classical drude oscillators: a fully polarizable model. J Chem Theory Comput 8:4527–4538Google Scholar
  61. 61.
    Eastman P, Friedrichs MS, Chodera JD, Radmer RJ, Bruns CM, Ku JP et al (2012) OpenMM 4: a reusable, extensible, hardware independent library for high performance molecular simulation. J Chem Theory Comput 8:461–469Google Scholar
  62. 62.
    Lamoureux G, Roux B (2003) Modelling induced polarizability with drude oscillators: theory and molecular dynamics simulation algorithm. J Chem Phys 119:5185–5197Google Scholar
  63. 63.
    Lamoureux G, MacKerell AD, Roux B (2003) A simple polarizable model of water based on classical Drude oscillators. J Chem Phys 119(10):5185–5197Google Scholar
  64. 64.
    Lamoureux G, Harder E, Vorobyov IV, Roux B, MacKerell AD (2006) A polarizable model of water for molecular dynamics simulations of biomolecules. Chem Phys Lett 418(1–3):245–249Google Scholar
  65. 65.
    Anisimov VM, Lamoureux G, Vorobyov IV, Huang N, Roux B, MacKerell AD (2005) Determination of electrostatic parameters for a polarizable force field based on the classical Drude oscillator. J Chem Theory Comput 1(1):153–168Google Scholar
  66. 66.
    Anisimov VM, Vorobyov IV, Lamoureux G, Noskov S, Roux B, MacKerell AD (2004) CHARMM all-atom polarizable force field parameter development for nucleic acids. Biophys J 86(1):415AGoogle Scholar
  67. 67.
    Anisimov VM, Vorobyov IV, Roux B, MacKerell AD (2007) Polarizable empirical force field for the primary and secondary alcohol series based on the classical drude model. J Chem Theory Comput 3(6):1927–1946PubMedPubMedCentralGoogle Scholar
  68. 68.
    Lopes PEM, Lamoureux G, Roux B, MacKerell AD (2007) Polarizable empirical force field for aromatic compounds based on the classical drude oscillator. J Phys Chem B 111(11):2873–2885PubMedPubMedCentralGoogle Scholar
  69. 69.
    Harder E, Anisimov VM, Whitfield TW, MacKerell AD, Roux B (2008) Understanding the dielectric properties of liquid amides from a polarizable force field. J Phys Chem B 112(11):3509–3521PubMedGoogle Scholar
  70. 70.
    Baker CM, MacKerell AD (2010) Polarizability rescaling and atom-based Thole scaling in the CHARMM Drude polarizable force field for ethers. J Mol Model 16(3):567–576PubMedPubMedCentralGoogle Scholar
  71. 71.
    Vorobyov I, Anisimov VM, Greene S, Venable RM, Moser A, Pastor RW et al (2007) Additive and classical drude polarizable force fields for linear and cyclic ethers. J Chem Theory Comput 3(3):1120–1133Google Scholar
  72. 72.
    Zhu X, MacKerell AD (2010) Polarizable empirical force field for sulfur-containing compounds based on the classical drude oscillator model. J Comput Chem 31(12):2330–2341PubMedPubMedCentralGoogle Scholar
  73. 73.
    Baker CM, Anisimov VM, MacKerell AD (2011) Development of CHARMM polarizable force field for nucleic acid bases based on the classical drude oscillator model. J Phys Chem B 115(3):580–596PubMedPubMedCentralGoogle Scholar
  74. 74.
    He X, Lopes PEM, MacKerell AD (2013) Polarizable empirical force field for acyclic polyalcohols based on the classical drude oscillator. Biopolymers 99(10):724–738PubMedPubMedCentralGoogle Scholar
  75. 75.
    Harder E, MacKerell AD, Roux B (2009) Many-body polarization effects and the membrane dipole potential. J Am Chem Soc 131(8):2760–2761PubMedPubMedCentralGoogle Scholar
  76. 76.
    Chowdhary J, Harder E, Lopes PEM, Huang L, MacKerell AD, Roux B (2013) A polarizable force field of dipalmitoylphosphatidylcholine based on the classical drude model for molecular dynamics simulations of lipids. J Phys Chem B 117(31):9142–9160PubMedPubMedCentralGoogle Scholar
  77. 77.
    Shi Y, Xia Z, Zhang JH, Best RB, Wu C, Ponder JW et al (2013) Polarizable atomic multipole-based AMOEBA force field for proteins. J Chem Theory Comput 9(9):4046–4063PubMedPubMedCentralGoogle Scholar
  78. 78.
    Dudek MJ, Ponder JW (1995) Accurate modeling of the intramolecular electrostatic energy of proteins. J Comput Chem 16(7):791–816Google Scholar
  79. 79.
    Thole B (1981) Molecular polarizabilities calculated with a modified dipole interaction. Chem Phys 59(3):341–350Google Scholar
  80. 80.
    Ren PY, Ponder JW (2003) Polarizable atomic multipole water model for molecular mechanics simulation. J Phys Chem B 107(24):5933–5947Google Scholar
  81. 81.
    Ren PY, Ponder JW (2004) Temperature and pressure dependence of the AMOEBA water model. J Phys Chem B 108(35):13427–13437Google Scholar
  82. 82.
    Grossfield A, Ren PY, Ponder JW (2003) Ion solvation thermodynamics from simulation with a polarizable force field. J Am Chem Soc 125(50):15671–15682PubMedGoogle Scholar
  83. 83.
    Ren P, Wu C, Ponder JW (2011) Polarizable atomic multipole-based molecular mechanics for organic molecules. J Chem Theory Comput 7(10):3143–3161PubMedPubMedCentralGoogle Scholar
  84. 84.
    Shi Y, Wu C, Ponder JW, Ren P (2011) Multipole electrostatics in hydration free energy calculations. J Comput Chem 32(5):967–977PubMedPubMedCentralGoogle Scholar
  85. 85.
    Ponder JW, Case DA (2003) Force fields for protein simulations, Protein simulations. Academic, San Diego, pp 27–85Google Scholar
  86. 86.
    Ponder JW, Wu C, Ren P, Pande VS, Chodera JD, Schnieders MJ et al (2010) Current status of the AMOEBA polarizable force field. J Phys Chem B 114(8):2549–2564PubMedPubMedCentralGoogle Scholar
  87. 87.
    Ren PY, Ponder JW (2002) Consistent treatment of inter- and intramolecular polarization in molecular mechanics calculations. J Comput Chem 23(16):1497–1506PubMedGoogle Scholar
  88. 88.
    Jorgensen WL, Tirado-Rives J (1988) The OPLS potential function for proteins. Energy minimizations for crystals of cyclic peptides and crambin. J Am Chem Soc 110:1657–1666Google Scholar
  89. 89.
    Singh UC, Kollman PA (1984) An approach to computing electrostatic charges for molecules. J Comput Chem 5(2):129–145Google Scholar
  90. 90.
    Chirlian LE, Francl MM (1987) Atomic charges derived from electrostatic potentials: a detailed study. J Comput Chem 8(6):894–905Google Scholar
  91. 91.
    Merz KM (1992) Analysis of a large data base of electrostatic potential derived atomic charges. J Comput Chem 13(6):749–767Google Scholar
  92. 92.
    Bayly CI, Cieplak P, Cornell WD, Kollman PA (1993) A well-behaved electrostatic potential based method using charge restraints for deriving atomic charges: the RESP model. J Phys Chem 97(40):10269–10280Google Scholar
  93. 93.
    Francl M, Carey C, Chirlian L, Gange D (1996) Charges fit to electrostatic potentials. II. Can atomic charges be unambiguously fit to electrostatic potentials? J Comput Chem 17(3):367–383Google Scholar
  94. 94.
    Lopes PEM, Lamoureux G, Mackerell AD (2009) Polarizable empirical force field for nitrogen-containing heteroaromatic compounds based on the classical Drude oscillator. J Comput Chem 30(12):1821–1838PubMedPubMedCentralGoogle Scholar
  95. 95.
    Harder E, Anisimov VM, Vorobyov IV, Lopes PEM, Noskov SY, MacKerell AD et al (2006) Atomic level anisotropy in the electrostatic modeling of lone pairs for a polarizable force field based on the classical Drude oscillator. J Chem Theory Comput 2(6):1587–1597Google Scholar
  96. 96.
    Miller KJ (1990) Additivity methods in molecular polarizability. J Am Chem Soc 112(23):8533–8542Google Scholar
  97. 97.
    Baker CM, MacKerell AD (2009) Polarizability rescaling and atom-based Thole scaling in the CHARMM Drude polarizable force field for ethers. J Mol Model 16(3):567–576PubMedPubMedCentralGoogle Scholar
  98. 98.
    Yu HA, Whitfield TW, Harder E, Lamoureux G, Vorobyov I, Anisimov VM et al (2010) Simulating monovalent and divalent ions in aqueous solution using a drude polarizable force field. J Chem Theory Comput 6(3):774–786PubMedPubMedCentralGoogle Scholar
  99. 99.
    Jorgensen WL, Madura JD, Swenson CJ (1984) Optimized intermolecular potential functions for liquid hydrocarbons. J Am Chem Soc 106(22):6638–6646Google Scholar
  100. 100.
    Jorgensen WL (1986) Optimized intermolecular potential functions for liquid alcohols. J Phys Chem 90(7):1276–1284Google Scholar
  101. 101.
    MacKerell AD (2001) Atomistic models and force fields. In: Becker O et al (eds) Computational biochemistry and biophysics. Marcel Dekker, Inc., New York, pp 7–38Google Scholar
  102. 102.
    Yin D, MacKerell AD (1996) Ab initio calculations on the use of helium and neon as probes of the van der Waals surfaces of molecules. J Phys Chem 100(7):2588–2596Google Scholar
  103. 103.
    Yin DX, MacKerell AD (1998) Combined ab initio empirical approach for optimization of Lennard-Jones parameters. J Comput Chem 19(3):334–348Google Scholar
  104. 104.
    Chen IJ, Yin D, MacKerell AD (2002) Combined ab initio/empirical approach for optimization of Lennard-Jones parameters for polar-neutral compounds. J Comput Chem 23(2):199–213PubMedGoogle Scholar
  105. 105.
    Baker CM, Lopes PEM, Zhu X, Roux B, MacKerell AD (2010) Accurate calculation of hydration free energies using pair-specific Lennard-Jones parameters in the CHARMM drude polarizable force field. J Chem Theory Comput 6(4):1181–1198PubMedPubMedCentralGoogle Scholar
  106. 106.
    Scott AP, Radom L (1996) Harmonic vibrational frequencies: an evaluation of Hartree-Fock, Møller-Plesset, quadratic configuration interaction, density functional theory, and semiempirical scale factors. J Phys Chem 100(41):16502–16513Google Scholar
  107. 107.
    Pulay P, Fogarasi G, Pang F, Boggs JE (1979) Systematic ab initio gradient calculation of molecular geometries, force constants, and dipole moment derivatives. J Am Chem Soc 101(10):2550–2560Google Scholar
  108. 108.
    Foloppe N, Hartmann B, Nilsson L, MacKerell AD (2002) Intrinsic conformational energetics associated with the glycosyl torsion in DNA: a quantum mechanical study. Biophys J 82(3):1554–1569PubMedPubMedCentralGoogle Scholar
  109. 109.
    Foloppe N, Nilsson L, MacKerell AD (2001) Ab initio conformational analysis of nucleic acid components: intrinsic energetic contributions to nucleic acid structure and dynamics. Biopolymers 61(1):61–76PubMedGoogle Scholar
  110. 110.
    Lin B, Lopes PEM, Roux B, MacKerell AD (2013) Kirkwood-Buff analysis of aqueous N-methylacetamide and acetamide solutions modeled by the CHARMM additive and Drude polarizable force fields. J Chem Phys 139(8):084509PubMedPubMedCentralGoogle Scholar
  111. 111.
    Halkier A, Helgaker T, Jørgensen P, Klopper W, Koch H, Olsen J et al (1998) Basis-set convergence in correlated calculations on Ne, N2, and H2O. Chem Phys Lett 286(3–4):243–252Google Scholar
  112. 112.
    Graf J, Nguyen PH, Stock G, Schwalbe H (2007) Structure and dynamics of the homologous series of alanine peptides: a joint molecular dynamics/NMR study. J Am Chem Soc 129(5):1179–1189PubMedGoogle Scholar
  113. 113.
    Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220(4598):671–680PubMedGoogle Scholar
  114. 114.
    Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E (1953) Equation of state calculations by fast computing machines. J Chem Phys 21(6):1087–1092Google Scholar
  115. 115.
    Shoemaker KR, Kim PS, York EJ, Stewart JM, Baldwin RL (1987) Tests of the helix dipole model for stabilization of α-helices. Nature 326(6113):563–567PubMedGoogle Scholar
  116. 116.
    Shoemaker KR, Kim PS, Brems DN, Marqusee S, York EJ, Chaiken IM et al (1985) Nature of the charged-group effect on the stability of the C-peptide helix. Proc Natl Acad Sci 82(8):2349–2353PubMedPubMedCentralGoogle Scholar
  117. 117.
    Padmanabhan S, Marqusee S, Ridgeway T, Laue TM, Baldwin RL (1990) Relative helix-forming tendencies of nonpolar amino acids. Nature 344(6263):268–270PubMedGoogle Scholar
  118. 118.
    Fukunishi H, Watanabe O, Takada S (2002) On the Hamiltonian replica exchange method for efficient sampling of biomolecular systems: application to protein structure prediction. J Chem Phys 116(20):9058–9067Google Scholar
  119. 119.
    Zhu X, Lopes PEM, Shim J, MacKerell AD (2012) Intrinsic energy landscapes of amino acid side-chains. J Chem Inf Model 52(6):1559–1572PubMedPubMedCentralGoogle Scholar
  120. 120.
    Lopes PEM, Huang J, Shim J, Luo Y, Hui L, Roux B et al (2013) Polarizable force field for peptides and proteins based on the classical drude oscillator. J Chem Theory Comput. doi: 10.1021/ct400781b PubMedGoogle Scholar
  121. 121.
    Hegefeld WA, Chen S-E, DeLeon KY, Kuczera K, Jas GS (2010) Helix formation in a pentapeptide: experiment and force-field dependent dynamics. J Phys Chem A 114(47):12391–12402PubMedGoogle Scholar
  122. 122.
    Best RB, Mittal J, Feig M, MacKerell AD (2012) Inclusion of many-body effects in the additive CHARMM protein CMAP potential results in enhanced cooperativity of α-helix and β-hairpin formation. Biophys J 103(5):1045–1051PubMedPubMedCentralGoogle Scholar
  123. 123.
    Lindorff-Larsen K, Maragakis P, Piana S, Eastwood MP, Dror RO, Shaw DE (2012) Systematic validation of protein force fields against experimental data. PLoS One 7(2):e32131PubMedPubMedCentralGoogle Scholar
  124. 124.
    Karplus M (1959) Contact electron-spin coupling of nuclear magnetic moments. J Chem Phys 30(1):11–15Google Scholar
  125. 125.
    Kaminski GA, Friesner RA, Tirado-Rives J, Jorgensen WL (2001) Evaluation and reparametrization of the OPLS-AA force field for proteins via comparison with accurate quantum chemical calculations on peptides. J Phys Chem B 105(28):6474–6487Google Scholar
  126. 126.
    Oostenbrink C, Villa A, Mark AE, Van Gunsteren WF (2004) A biomolecular force field based on the free enthalpy of hydration and solvation: the GROMOS force-field parameter sets 53A5 and 53A6. J Comput Chem 25(13):1656–1676PubMedGoogle Scholar
  127. 127.
    Blanco FJ, Rivas G, Serrano L (1994) A short linear peptide that folds into a native stable [beta]-hairpin in aqueous solution. Nat Struct Mol Biol 1(9):584–590Google Scholar
  128. 128.
    Muñoz V, Thompson PA, Hofrichter J, Eaton WA (1997) Folding dynamics and mechanism of β-hairpin formation. Nature 390(6656):196–199PubMedGoogle Scholar
  129. 129.
    Schuler B, Eaton WA (2008) Protein folding studied by single-molecule FRET. Curr Opin Struct Biol 18(1):16–26PubMedPubMedCentralGoogle Scholar
  130. 130.
    Jo S, Kim T, Iyer VG, Im W (2008) CHARMM-GUI: a web-based graphical user interface for CHARMM. J Comput Chem 29(11):1859–1865PubMedGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Pedro E. M. Lopes
    • 1
  • Olgun Guvench
    • 2
  • Alexander D. MacKerellJr.
    • 1
  1. 1.Department of Pharmaceutical Sciences, School of PharmacyUniversity of MarylandBaltimoreUSA
  2. 2.Department of Pharmaceutical Sciences, College of PharmacyUniversity of New EnglandPortlandUSA

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