1932

Abstract

It would often be useful in computer simulations to use an implicit description of solvation effects, instead of explicitly representing the individual solvent molecules. Continuum dielectric models often work well in describing the thermodynamic aspects of aqueous solvation and can be very efficient compared to the explicit treatment of the solvent. Here, we review a particular class of so-called fast implicit solvent models, generalized Born (GB) models, which are widely used for molecular dynamics (MD) simulations of proteins and nucleic acids. These approaches model hydration effects and provide solvent-dependent forces with efficiencies comparable to molecular-mechanics calculations on the solute alone; as such, they can be incorporated into MD or other conformational searching strategies in a straightforward manner. The foundations of the GB model are reviewed, followed by examples of newer, emerging models and examples of important applications. We discuss their strengths and weaknesses, both for fidelity to the underlying continuum model and for the ability to replace explicit consideration of solvent molecules in macromolecular simulations.

Loading

Article metrics loading...

/content/journals/10.1146/annurev-biophys-052118-115325
2019-05-06
2024-03-29
Loading full text...

Full text loading...

/deliver/fulltext/biophys/48/1/annurev-biophys-052118-115325.html?itemId=/content/journals/10.1146/annurev-biophys-052118-115325&mimeType=html&fmt=ahah

Literature Cited

  1. 1.
    Aguilar B, Onufriev AV 2012. Efficient computation of the total solvation energy of small molecules via the R6 generalized Born model. J. Chem. Theory Comput. 8:2404–11
    [Google Scholar]
  2. 2.
    Aguilar B, Shadrach R, Onufriev AV 2010. Reducing the secondary structure bias in the generalized Born model via R6 effective radii. J. Chem. Theory Comput. 6:3613–30
    [Google Scholar]
  3. 3.
    Anandakrishnan R, Baker C, Izadi S, Onufriev AV 2013. Point charges optimally placed to represent the multipole expansion of charge distributions. PLOS ONE 8:e67715
    [Google Scholar]
  4. 4.
    Anandakrishnan R, Daga M, Onufriev AV 2011. An n log n generalized Born approximation. J. Chem. Theory Comput. 7:544–59
    [Google Scholar]
  5. 5.
    Anandakrishnan R, Drozdetski A, Walker RC, Onufriev AV 2015. Speed of conformational change: comparing explicit and implicit solvent molecular dynamics simulations. Biophys. J. 108:1153–64
    [Google Scholar]
  6. 6.
    Anandakrishnan R, Onufriev AV 2010. An N log N approximation based on the natural organization of biomolecules for speeding up the computation of long range interactions. J. Comput. Chem 31:691–706
    [Google Scholar]
  7. 7.
    Arthur EJ, Brooks CL III 2016. Parallelization and improvements of the generalized Born model with a simple sWitching function for modern graphics processors. J. Comput. Chem. 37:927–39
    [Google Scholar]
  8. 8.
    Baker NA, Bashford D, Case DA 2006. Implicit solvent electrostatics in biomolecular simulation. New Algorithms for Macromolecular Simulation B Leimkuhler, C Chipot, R Elber, A Laaksonen, A Mark et al.263–95 Berlin: Springer-Verlag
    [Google Scholar]
  9. 9.
    Bashford D, Case DA 2000. Generalized Born models of macromolecular solvation effects. Annu. Rev. Phys. Chem. 51:129–52
    [Google Scholar]
  10. 10.
    Bashford D, Karplus M 1990. pKa's of ionizable groups in proteins: atomic detail from a continuum electrostatic model. Biochemistry 29:10219–25
    [Google Scholar]
  11. 11.
    Bomble YJ, Case DA 2008. Multiscale modeling of nucleic acids: insights into DNA flexibility. Biopolymers 89:722–31
    [Google Scholar]
  12. 12.
    Born M 1920. Volumes and heats of hydration of ions. Z. Phys. 1:45–48
    [Google Scholar]
  13. 13.
    Brown RA, Case DA 2006. Second derivatives in generalized Born theory. J. Comput. Chem. 27:1662–75
    [Google Scholar]
  14. 14.
    Chen J, Brooks C 2008. Implicit modeling of nonpolar solvation for simulating protein folding and conformational transitions. Phys. Chem. Chem. Phys. 10:471–81
    [Google Scholar]
  15. 15.
    Chen J, Im W, Brooks C 2006. Balancing solvation and intramolecular interactions: toward a consistent generalized Born force field. J. Am. Chem. Soc. 128:3728–36
    [Google Scholar]
  16. 16.
    Chocholoušová J, Feig M 2006. Implicit solvent simulations of DNA and DNA–protein complexes: agreement with explicit solvent versus experiment. J. Phys. Chem. B 110:17240–51
    [Google Scholar]
  17. 17.
    Cramer CJ, Truhlar DG 2008. A universal approach to solvation modeling. Acc. Chem. Res. 41:760–68
    [Google Scholar]
  18. 18.
    Duan Y, Kollman PA 1998. Pathways to a protein folding intermediate observed in a 1-microsecond simulation in aqueous solution. Science 282:740–44
    [Google Scholar]
  19. 19.
    Dutagaci B, Feig M 2017. Determination of hydrophobic lengths of membrane proteins with the HDGB implicit membrane model. J. Chem. Inform. Model. 57:3032–42
    [Google Scholar]
  20. 20.
    Dutagaci B, Heo L, Feig M 2018. Structure refinement of membrane proteins via molecular dynamics simulations. Proteins 86:738–50
    [Google Scholar]
  21. 21.
    Dutagaci B, Sayadi M, Feig M 2017. Heterogeneous dielectric generalized Born model with a van der Waals term provides improved association energetics of membrane-embedded transmembrane helices. J. Comput. Chem. 38:1308–20
    [Google Scholar]
  22. 22.
    Eastman P, Pande V 2010. Efficient nonbonded interactions for molecular dynamics on a graphics processing unit. J. Comput. Chem. 31:1268–72
    [Google Scholar]
  23. 23.
    Erler J, Zhang R, Petridis L, Cheng X, Smith JC, Langowski J 2014. The role of histone tails in the nucleosome: a computational study. Biophys. J. 107:2902–13
    [Google Scholar]
  24. 24.
    Feig M, Im W, Brooks CL 2004. Implicit solvation based on generalized Born theory in different dielectric environments. J. Chem. Phys. 120:903–11
    [Google Scholar]
  25. 25.
    Felts AK, Gallicchio E, Chekmarev D, Paris KA, Friesner RA, Levy RM 2008. Prediction of protein loop conformations using the AGBNP implicit solvent model and torsion angle sampling. J. Chem. Theory Comput. 4:855–68
    [Google Scholar]
  26. 26.
    Fenley A, Killian B, Hnizdo V, Fedorowicz A, Sharp D, Gilson M 2014. Correlation as a determinant of configurational entropy in supramolecular and protein systems. J. Phys. Chem. B 118:6447–55
    [Google Scholar]
  27. 27.
    Forouzesh N, Izadi S, Onufriev AV 2017. Grid-based surface generalized Born model for calculation of electrostatic binding free energies. J. Chem. Inform. Model. 57:2505–13
    [Google Scholar]
  28. 28.
    Gallicchio E, Levy R 2004. AGBNP: an analytic implicit solvent model suitable for molecular dynamics simulations and high-resolution modeling. J. Comput. Chem. 25:479–99
    [Google Scholar]
  29. 29.
    Genheden S, Essex J 2015. A simple and transferable all-atom/coarse-grained hybrid model to study membrane processes. J. Chem. Theory Comput. 11:4749–59
    [Google Scholar]
  30. 30.
    Genheden S, Kongsted J, Soderhjelm P, Ryde U 2010. Nonpolar solvation free energies of protein–ligand complexes. J. Chem. Theory Comput. 6:3558–68
    [Google Scholar]
  31. 31.
    Genheden S, Mikulskis P, Hu L, Kongsted J, Soderhjelm P, Ryde U 2011. Accurate predictions of nonpolar solvation free energies require explicit consideration of binding-site hydration. J. Am. Chem. Soc. 133:13081–92
    [Google Scholar]
  32. 32.
    Ghosh A, Rapp C, Friesner R 1998. Generalized Born model based on a surface integral formulation. J. Phys. Chem. B 102:10983–90
    [Google Scholar]
  33. 33.
    Götz AW, Williamson MJ, Xu D, Poole D, Le Grand S, Walker RC 2012. Routine microsecond molecular dynamics simulations with AMBER on GPUs. 1. Generalized Born. J. Chem. Theory Comput. 8:1542–55
    [Google Scholar]
  34. 34.
    Grant J, Pickup B 1995. A Gaussian description of molecular shape. J. Phys. Chem. 99:3503–10
    [Google Scholar]
  35. 35.
    Grant J, Pickup B, Nicholls A 2001. A smooth permittivity function for Poisson–Boltzmann solvation methods. J. Comput. Chem. 22:608–41
    [Google Scholar]
  36. 36.
    Grant J, Pickup B, Sykes M, Kitchen C, Nicholls A 2007. A simple formula for dielectric polarisation energies: the Sheffield Solvation Model. Chem. Phys. Lett. 441:163–66
    [Google Scholar]
  37. 37.
    Grant J, Pickup B, Sykes M, Kitchen C, Nicholls A 2007. The Gaussian Generalized Born model: application to small molecules. Phys. Chem. Chem. Phys. 9:4913–22
    [Google Scholar]
  38. 38.
    Grycuk T 2003. Deficiency of the Coulomb-field approximation in the generalized Born model: an improved formula for Born radii evaluation. J. Chem. Phys. 119:4817–26
    [Google Scholar]
  39. 39.
    Havranek J, Harbury P 1999. Tanford–Kirkwood electrostatics for protein modeling. PNAS 96:11145
    [Google Scholar]
  40. 40.
    Hawkins G, Cramer C, Truhlar D 1995. Pairwise solute descreening of solute charges from a dielectric medium. Chem. Phys. Lett. 246:122–29
    [Google Scholar]
  41. 41.
    Hawkins G, Cramer C, Truhlar D 1996. Parametrized models of aqueous free energies of solvation based on pairwise descreening of solute atomic charges from a dielectric medium. J. Phys. Chem. 100:19824–39
    [Google Scholar]
  42. 42.
    Hoijtink GJ, de Boer E, van der Meij PH, Weijland WP 1956. Reduction potentials of various aromatic hydrocarbons and their univalent anions. Recl. Trav. Chim. Pays-Bas 75:487–503
    [Google Scholar]
  43. 43.
    Huang Y, Chen W, Wallace JA, Shen J 2016. All-Atom continuous constant pH molecular dynamics with particle mesh ewald and titratable water. J. Chem. Theory Comput. 12:5411–21
    [Google Scholar]
  44. 44.
    Im W, Lee M, Brooks CL III 2003. Generalized Born model with a simple smoothing function. J. Comput. Chem. 24:1691–702
    [Google Scholar]
  45. 45.
    Izadi S, Aguilar B, Onufriev AV 2015. Protein–ligand electrostatic binding free energies from explicit and implicit solvation. J. Chem. Theory Comput. 11:4450–59
    [Google Scholar]
  46. 46.
    Izadi S, Anandakrishnan R, Onufriev AV 2016. Implicit solvent model for million-atom atomistic simulations: Insights into the organization of 30-nm chromatin fiber. J. Chem. Theory Comput. 12:5946–59
    [Google Scholar]
  47. 47.
    Izadi S, Harris RC, Fenley MO, Onufriev AV 2018. Accuracy comparison of generalized Born models in the calculation of electrostatic binding free energies. J. Chem. Theory Comput. 14:1656–70
    [Google Scholar]
  48. 48.
    Izairi R, Kamberaj H 2017. Comparison study of polar and nonpolar contributions to solvation free energy. J. Chem. Inf. Model. 57:2539–53
    [Google Scholar]
  49. 49.
    Jackson J 1975. Classical Electrodynamics New York: Wiley and Sons
  50. 50.
    Jang S, Kim E, Shin S, Pak Y 2003. Ab initio folding of helix bundle proteins using molecular dynamics simulations. J. Am. Chem. Soc. 125:14841–46
    [Google Scholar]
  51. 51.
    Jayaram B, Liu Y, Beveridge D 1998. A modification of the generalized Born theory for improved estimates of solvation energies and pK shifts. J. Chem. Phys. 109:1465–71
    [Google Scholar]
  52. 52.
    Karplus M, Kushick J 1981. Method for estimating the configurational entropy of macromolecules. Macromolecules 14:325–32
    [Google Scholar]
  53. 53.
    Khandogin J, Raleigh D, Brooks C 2007. Folding intermediate in the villin headpiece domain arises from disruption of a N-terminal hydrogen-bonded network. J. Am. Chem. Soc. 129:3056–57
    [Google Scholar]
  54. 54.
    Kirkwood J 1934. Theory of solutions of molecules containing widely separated charges with special application to zwitterions. J. Chem. Phys. 2:351–61
    [Google Scholar]
  55. 55.
    Kirkwood J 1939. The dielectric polarization of polar liquids. J. Chem. Phys. 7:911–19
    [Google Scholar]
  56. 56.
    Klamt A, Schüürmann G 1993. COSMO: a new approach to dielectric screening in solvents with explicit expressions for the screening energy and its gradient. J. Chem. Soc. Perkin Trans. 2:799–805
    [Google Scholar]
  57. 57.
    Kollman P, Massova I, Reyes C, Kuhn B, Huo S et al. 2000. Calculating structures and free energies of complex molecules: combining molecular mechanics and continuum models. Accts. Chem. Res. 33:889–97
    [Google Scholar]
  58. 58.
    Labute P 2008. The generalized Born/volume integral implicit solvent model: estimation of the free energy of hydration using London dispersion instead of atomic surface area. J. Comput. Chem. 29:1693–98
    [Google Scholar]
  59. 59.
    Lange AW, Herbert JM 2012. Improving generalized Born models by exploiting connections to polarizable continuum models. I. An improved effective Coulomb operator. J. Chem. Theory Comput. 8:1999–2011
    [Google Scholar]
  60. 60.
    Lee MS, Feig M, Salsbury FR, Brooks CL 2003. New analytic approximation to the standard molecular volume definition and its application to generalized Born calculations. J. Comput. Chem. 24:1348–56
    [Google Scholar]
  61. 61.
    Lee MS, Olson M 2013. Comparison of volume and surface area nonpolar solvation free energy terms for implicit solvent simulations. J. Chem. Phys. 139:044119
    [Google Scholar]
  62. 62.
    Lee MS, Salsbury FR, Brooks CL 2002. Novel generalized Born methods. J. Chem. Phys. 116:10606–14
    [Google Scholar]
  63. 63.
    Lee MS, Salsbury FR, Brooks CL 2004. Constant-pH molecular dynamics using continuous titration coordinates. Proteins 56:738–52
    [Google Scholar]
  64. 64.
    Lei H, Duan Y 2007. Two-stage folding of HP-35 from ab initio simulations. J. Mol. Biol. 370:196–206
    [Google Scholar]
  65. 65.
    Levy R, Zhang L, Gallicchio E, Felts A 2003. On the nonpolar hydration free energy of proteins: surface area and continuum solvent models for the solute–solvent interaction energy. J. Am. Chem. Soc. 125:9523–30
    [Google Scholar]
  66. 66.
    Lindorff-Larsen K, Piana S, Dror RO, Shaw DE 2011. How fast-folding proteins fold. Science 334:517–20
    [Google Scholar]
  67. 67.
    Liu H, Duan Y 2008. Effects of posttranslational modifications on the structure and dynamics of histone H3 N-terminal peptide. Biophys. J. 94:4579–85
    [Google Scholar]
  68. 68.
    Lopes A, Alexandrov A, Bathelt C, Archontis G, Simonson T 2007. Computational sidechain placement and protein mutagenesis with implicit solvent models. Proteins 67:853–67
    [Google Scholar]
  69. 69.
    Marenich AV, Cramer CJ, Truhlar DG 2009. Universal solvation model based on the generalized Born approximation with asymmetric descreening. J. Chem. Theory Comput. 5:2447–64
    [Google Scholar]
  70. 70.
    McQuarrie D 1976. Statistical Mechanics New York: Harper and Row
  71. 71.
    Mirjalili V, Feig M 2015. Interactions of amino acid side-chain analogs within membrane environments. J. Phys. Chem. B 119:2877–85
    [Google Scholar]
  72. 72.
    Mongan J, Case DA 2005. Biomolecular simulations at constant pH. Curr. Opin. Struct. Biol. 15:157–63
    [Google Scholar]
  73. 73.
    Mongan J, Case DA, McCammon JA 2004. Constant pH molecular dynamics in generalized Born implicit solvent. J. Comput. Chem. 25:2038–48
    [Google Scholar]
  74. 74.
    Mongan J, Simmerling C, McCammon JA, Case DA, Onufriev A 2007. Generalized Born model with a simple, robust molecular volume correction. J. Chem. Theory Comput. 3:156–69
    [Google Scholar]
  75. 75.
    Mongan J, Svrcek-Seiler WA, Onufriev A 2007. Analysis of integral expressions for effective Born radii. J. Chem. Phys. 127:185101
    [Google Scholar]
  76. 76.
    Mukhopadhyay A, Aguilar BH, Tolokh IS, Onufriev AV 2014. Introducing charge hydration asymmetry into the generalized Born model. J. Chem. Theory Comput. 10:1788–94
    [Google Scholar]
  77. 77.
    Mukhopadhyay A, Fenley AT, Tolokh IS, Onufriev AV 2012. Charge hydration asymmetry: the basic principle and how to use it to test and improve water models. J. Phys. Chem. B 116:9776–83
    [Google Scholar]
  78. 78.
    Mukhopadhyay A, Tolokh IS, Onufriev AV 2015. Accurate evaluation of charge asymmetry in aqueous solvation. J. Phys. Chem. B 119:6092–100
    [Google Scholar]
  79. 79.
    Nguyen H, Maier J, Huang H, Perrone V, Simmerling C 2014. Folding simulations for proteins with diverse topologies are accessible in days with a physics-based force field and implicit solvent. J. Am. Chem. Soc. 136:13959–62
    [Google Scholar]
  80. 80.
    Nguyen H, Pérez A, Bermeo S, Simmerling C 2015. Refinement of generalized Born implicit solvation parameters for nucleic acids and their complexes with proteins. J. Chem. Theory Comput. 11:3714–28
    [Google Scholar]
  81. 81.
    Nguyen H, Roe DR, Simmerling C 2013. Improved generalized Born solvent model parameters for protein simulations. J. Chem. Theory Comput. 9:2020
    [Google Scholar]
  82. 82.
    Onufriev A 2010. Continuum electrostatics solvent modeling with the generalized Born model. Modeling Solvent Environments M Feig 127–65 Weinheim, Ger: Wiley. , 1st ed..
    [Google Scholar]
  83. 83.
    Onufriev AV, Aguilar B 2014. Accuracy of continuum electrostatic calculations based on three common dielectric boundary definitions. J. Theor. Comput. Chem. 13:1440006
    [Google Scholar]
  84. 84.
    Onufriev AV, Bashford D, Case DA 2000. Modification of the generalized Born model suitable for macromolecules. J. Phys. Chem. B 104:3712–20
    [Google Scholar]
  85. 85.
    Onufriev AV, Bashford D, Case DA 2004. Exploring protein native states and large-scale conformational changes with a modified generalized Born model. Proteins 55:383–94
    [Google Scholar]
  86. 86.
    Onufriev AV, Case DA, Bashford D 2002. Effective Born radii in the generalized Born approximation: the importance of being perfect. J. Comput. Chem. 23:1297–304
    [Google Scholar]
  87. 87.
    Onufriev AV, Izadi S 2018. Water models for biomolecular simulations. WIRES: Comput. Mol. Sci. 8:e1347
    [Google Scholar]
  88. 88.
    Onufriev AV, Sigalov G 2011. A strategy for reducing gross errors in the generalized Born models of implicit solvation. J. Chem. Phys. 134:164104–15
    [Google Scholar]
  89. 89.
    Robinson PJJ, Fairall L, Huynh VAT, Rhodes D 2006. Em measurements define the dimensions of the 30-nm chromatin fiber: evidence for a compact, interdigitated structure. PNAS 103:6506–11
    [Google Scholar]
  90. 90.
    Rubenstein AB, Blacklock K, Nguyen H, Case DA, Khare SD 2018. Systematic comparison of Amber and Rosetta energy functions for protein structure evaluation. J. Chem. Theory Comput. 14:6015–25
    [Google Scholar]
  91. 91.
    Ruscio JZ, Onufriev A 2006. A computational study of nucleosomal DNA flexibility. Biophys. J. 91:4121–32
    [Google Scholar]
  92. 92.
    Rychkov GN, Ilatovskiy AV, Nazarov IB, Shvetsov AV, Lebedev DV et al. 2017. Partially assembled nucleosome structures at atomic detail. Biopys. J. 112:460–72
    [Google Scholar]
  93. 93.
    Savin AV, Kikot IP, Mazo MA, Onufriev AV 2013. Two-phase stretching of molecular chains. PNAS 110:2816–21
    [Google Scholar]
  94. 94.
    Savin AV, Mazo MA, Kikot IP, Manevitch LI, Onufriev AV 2011. Heat conductivity of the DNA double helix. Phys. Rev. B 83:245406
    [Google Scholar]
  95. 95.
    Schaefer M, Froemmel C 1990. A precise analytical method for calculating the electrostatic energy of macromolecules in aqueous solution. J. Mol. Biol. 216:1045–66
    [Google Scholar]
  96. 96.
    Schnieders M, Ponder J 2007. Polarizable atomic multipole solutes in a generalized Kirkwood continuum. J. Chem. Theory Comput. 3:2083–97
    [Google Scholar]
  97. 97.
    Schutz C, Warshel A 2001. What are the dielectric “constants” of proteins and how to validate electrostatic models. ? Proteins 44:400–17
    [Google Scholar]
  98. 98.
    Sharp KA, Honig B 1990. Electrostatic interactions in macromolecules: theory and experiment. Annu. Rev. Biophys. Biophys. Chem. 19:301–32
    [Google Scholar]
  99. 99.
    Sigalov G, Fenley A, Onufriev A 2006. Analytical electrostatics for biomolecules: beyond the generalized Born approximation. J. Chem. Phys. 124:124902
    [Google Scholar]
  100. 100.
    Sigalov G, Scheffel P, Onufriev A 2005. Incorporating variable dielectric environments into the generalized Born model. J. Chem. Phys. 122:094511
    [Google Scholar]
  101. 101.
    Simmerling C, Strockbine B, Roitberg AE 2002. All-atom structure prediction and folding simulations of a stable protein. J. Am. Chem. Soc. 124:11258–59
    [Google Scholar]
  102. 102.
    Spassov VZ, Yan L, Szalma S 2002. Introducing an implicit membrane in generalized Born/solvent accessibility continuum solvent models. J. Phys. Chem. B 106:8726–38
    [Google Scholar]
  103. 103.
    Srinivasan J, Cheatham TE, Cieplak P, Kollman PA, Case DA 1998. Continuum solvent studies of the stability of DNA, RNA, and phosphoramidate–DNA helices. J. Am. Chem. Soc. 120:9401–9
    [Google Scholar]
  104. 104.
    Srinivasan J, Miller J, Kollman P, Case DA 1998. Continuum solvent studies of the stability of RNA hairpin loops and helices. J. Biomol. Struct. Dyn. 16:671–82
    [Google Scholar]
  105. 105.
    Still W, Tempczyk A, Hawley R, Hendrickson T 1990. Semianalytical treatment of solvation for molecular mechanics and dynamics. J. Am. Chem. Soc. 112:6127–29
    [Google Scholar]
  106. 106.
    Swails J, Roitberg A 2012. Enhancing conformation and protonation state sampling of hen egg white lysozyme using pH replica exchange molecular dynamics. J. Chem. Theory Comput. 8:4393–404
    [Google Scholar]
  107. 107.
    Swails J, York D, Roitberg A 2014. Constant pH replica exchange molecular dynamics in explicit solvent using discrete protonation states: implementation, testing, and validation. J. Chem. Theory Comput. 10:1341–52
    [Google Scholar]
  108. 108.
    Tan C, Tan Y, Luo R 2007. Implicit nonpolar solvent models. J. Phys. Chem. B 111:12263–74
    [Google Scholar]
  109. 109.
    Tanford C, Kirkwood J 1957. Theory of titration curves. I. General equations for impenetrable spheres. J. Am. Chem. Soc. 79:5333–39
    [Google Scholar]
  110. 110.
    Tanford C, Roxby R 1972. Interpretation of protein titration curves. Biochemistry 11:2192–98
    [Google Scholar]
  111. 111.
    Tanizaki S 2006. Molecular dynamics simulations of large integral membrane proteins with an implicit membrane model. J. Phys. Chem. B 110:548
    [Google Scholar]
  112. 112.
    Tanizaki S, Feig M 2005. A generalized Born formalism for heterogeneous dielectric environments: application to the implicit modeling of biological membranes. J. Chem. Phys. 122:124706
    [Google Scholar]
  113. 113.
    Tolokh IS, Thomas DG, Onufriev AV 2018. Explicit ions/implicit water generalized Born model for nucleic acids. J. Chem. Phys. 148:195101
    [Google Scholar]
  114. 114.
    Tomasi J, Mennucci B, Cammi R 2005. Quantum mechanical continuum solvation models. Chem. Rev. 105:2999–3094
    [Google Scholar]
  115. 115.
    Tsui V, Case DA 2000. Molecular dynamics simulations of nucleic acids using a generalized Born solvation model. J. Am. Chem. Soc. 122:2489–98
    [Google Scholar]
  116. 116.
    Ulmschneider M, Ulmschneider J, Sansom M, DiNola A 2007. A generalized Born implicit-membrane representation compared to experimental insertion free energies. Biophys. J. 92:2338–49
    [Google Scholar]
  117. 117.
    Wallace JA, Wang Y, Shi C, Pastoor KJ, Nguyen BL et al. 2011. Toward accurate prediction of pKa values for internal protein residues: the importance of conformational relaxation and desolvation energy. Proteins 79:3364–73
    [Google Scholar]
  118. 118.
    Wang C, Greene D, Xiao L, Qi R, Luo R 2018. Recent developments and applications of the MMPBSA method. Front. Mol. Biosci. 4:87
    [Google Scholar]
  119. 119.
    Weiser J, Shenkin P, Still W 1999. Approximate atomic surfaces from linear combinations of pairwise overlaps (LCPO). J. Comput. Chem. 20:217–30
    [Google Scholar]
  120. 120.
    Xu Z, Cai W 2011. Fast analytical methods for macroscopic electrostatic models in biomolecular simulations. SIAM Rev 53:683–723
    [Google Scholar]
  121. 121.
    Zhou B, Trinajstic N 2007. On the largest eigenvalue of the distance matrix of a connected graph. Chem. Phys. Lett. 447:384–87
    [Google Scholar]
  122. 122.
    Zhou H-X, Pang X 2018. Electrostatic interactions in protein structure, folding, binding, and condensation. Chem. Rev. 118:1691–741
    [Google Scholar]
/content/journals/10.1146/annurev-biophys-052118-115325
Loading
/content/journals/10.1146/annurev-biophys-052118-115325
Loading

Data & Media loading...

  • Article Type: Review Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error