CoChat
Sign Up
Cited by 234Protein Structure and DynamicsAdvanced Chemical Physics StudiesAdvanced Physical and Chemical Molecular Interactions

Calculating the binding free energies of charged species based on explicit-solvent simulations employing lattice-sum methods: An accurate correction scheme for electrostatic finite-size effects

Open access
Rocklin, Gabriel J., Mobley, David L., Dill, Ken A., Hünenberger, Philippe H.·2013·The Journal of Chemical Physics
DOI 10.1063/1.4826261PMC PMC3838431
Open this paper in CoChat — free accountOpen PDF

Abstract

The calculation of a protein-ligand binding free energy based on molecular dynamics (MD) simulations generally relies on a thermodynamic cycle in which the ligand is alchemically inserted into the system, both in the solvated protein and free in solution. The corresponding ligand-insertion free energies are typically calculated in nanoscale computational boxes simulated under periodic boundary conditions and considering electrostatic interactions defined by a periodic lattice-sum. This is distinct from the ideal bulk situation of a system of macroscopic size simulated under non-periodic boundary conditions with Coulombic electrostatic interactions. This discrepancy results in finite-size effects, which affect primarily the charging component of the insertion free energy, are dependent on the box size, and can be large when the ligand bears a net charge, especially if the protein is charged as well. This article investigates finite-size effects on calculated charging free energies using as a test case the binding of the ligand 2-amino-5-methylthiazole (net charge +1 e) to a mutant form of yeast cytochrome c peroxidase in water. Considering different charge isoforms of the protein (net charges −5, 0, +3, or +9 e), either in the absence or the presence of neutralizing counter-ions, and sizes of the cubic computational box (edges ranging from 7.42 to 11.02 nm), the potentially large magnitude of finite-size effects on the raw charging free energies (up to 17.1 kJ mol−1) is demonstrated. Two correction schemes are then proposed to eliminate these effects, a numerical and an analytical one. Both schemes are based on a continuum-electrostatics analysis and require performing Poisson-Boltzmann (PB) calculations on the protein-ligand system. While the numerical scheme requires PB calculations under both non-periodic and periodic boundary conditions, the latter at the box size considered in the MD simulations, the analytical scheme only requires three non-periodic PB calculations for a given system, its dependence on the box size being analytical. The latter scheme also provides insight into the physical origin of the finite-size effects. These two schemes also encompass a correction for discrete solvent effects that persists even in the limit of infinite box sizes. Application of either scheme essentially eliminates the size dependence of the corrected charging free energies (maximal deviation of 1.5 kJ mol−1). Because it is simple to apply, the analytical correction scheme offers a general solution to the problem of finite-size effects in free-energy calculations involving charged solutes, as encountered in calculations concerning, e.g., protein-ligand binding, biomolecular association, residue mutation, pKa and redox potential estimation, substrate transformation, solvation, and solvent-solvent partitioning.

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1063/1.4826261

Cites

Statistics

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Cites

No references could be resolved yet.

Research works printed but not linked: 150

  1. M. K. Gilson, J. A. Given, B. L. Bush, and J. A. McCammon, "The statistical thermodynamic basis for computation of binding-affinities: A critical review," Biophys. J. 72, 1047-1069 (1997). · DOI
  2. S. Boresch, F. Tettinger, and M. Leitgeb, "Absolute binding free ener- gies: A quantitative approach for their calculation," J. Phys. Chem. B 107, 9535-9551 (2003). · DOI · Paper page
  3. J. M. J. Swanson, R. H. Henchman, and J. A. McCammon, "Revisiting free energy calculations: A theoretical connection to MM/PBSA and di- rect calculation of the association free energy," Biophys. J. 86, 67-74 (2004). · DOI
  4. J. Wang, Y. Deng, and B. Roux, "Absolute binding free energy calcula- tions using molecular dynamics simulations with restraining potentials," Biophys. J. 91, 2798-2814 (2006). · DOI
  5. Y. Deng and B. Roux, "Calculation of standard binding free energies: Aromatic molecules in the T4 lysozyme L99A mutant," J. Chem. Theory Comput. 2, 1255-1273 (2006). · DOI
  6. B. Roux, M. Nina, R. Pomès, and J. C. Smith, "Thermodynamic stability of water molecules in the Bacteriorhodopsin proton channel: A molec- ular dynamics free energy perturbation study," Biophys. J. 71, 670-681 (1996). · DOI
  7. J. Hermans and L. Wang, "Inclusion of loss of translational and rota- tional freedom in theoretical estimates of free energies of binding. Ap- plication to a complex of benzene and mutant T4 Lysozyme," J. Am. Chem. Soc. 119, 2707-2714 (1997). · DOI
  8. D. L. Beveridge and F. M. DiCapua, "Free energy via molecular simu- lation: Applications to chemical and biomolecular systems," Annu. Rev. Biophys. Biophys. Chem. 18, 431-492 (1989). · DOI
  9. W. F. van Gunsteren, and H. J. C. Berendsen, "Computer simulation of molecular dynamics: Methodology, applications and perspectives in chemistry," Angew. Chem. Int. Ed. 29, 992-1023 (1990). · DOI
  10. P. Kollman, "Free energy calculations: Applications to chemical and bio- chemical phenomena," Chem. Rev. 93, 2395-2417 (1993). · DOI
  11. M. Christen and W. F. van Gunsteren, "On searching in, sam- pling of, and dynamically moving through conformational space of biomolecular systems: A review," J. Comput. Chem. 29, 157-166 (2008). · DOI
  12. H. S. Hansen, X. Daura, and P. H. Hünenberger, "Enhanced conforma- tional sampling in molecular dynamics simulations of solvated peptides: Fragment-based local elevation umbrella sampling," J. Chem. Theory Comput. 6, 2598-2621 (2010). · DOI
  13. H. S. Hansen and P. H. Hünenberger, "Ball-and-stick local elevation umbrella sampling: Molecular simulations involving enhanced sam- pling within conformational or alchemical subspaces of low internal di- mensionalities, minimal irrelevant volume and problem-adapted geome- tries," J. Chem. Theory Comput. 6, 2622-2646 (2010). · DOI
  14. S. Boresch and M. Karplus, "The Jacobian factor in free energy simula- tions," J. Chem. Phys. 105, 5145-5154 (1996). · DOI
  15. W. K. den Otter and W. J. Briels, "The calculation of free-energy differ- ences by constrained molecular-dynamics simulations," J. Chem. Phys. 109, 4139-4146 (1998). · DOI
  16. J. Hermans, "Simple analysis of noise and hysteresis in (slow-growth) free energy simulations," J. Phys. Chem. 95, 9029-9032 (1991). · DOI
  17. R. H. Wood, "Estimation of errors in free energy calculations due to the lag between the Hamiltonian and the system configuration," J. Phys. Chem. 95, 4838-4842 (1991). · DOI
  18. T. C. Beutler, A. E. Mark, R. van Schaik, P. R. Gerber, and W. F. van Gunsteren, "Avoiding singularities and numerical instabilities in free en- ergy calculations based on molecular simulations," Chem. Phys. Lett. 222, 529-539 (1994). · DOI
  19. P. H. Hünenberger and J. A. McCammon, "Ewald artifacts in computer simulations of ionic solvation and ion-ion interaction: A continuum elec- trostatics study," J. Chem. Phys. 110, 1856-1872 (1999). · DOI
  20. M. A. Kastenholz and P. H. Hünenberger, "Influence of artificial peri- odicity and ionic strength in molecular dynamics simulations of charged biomolecules employing lattice-sum methods," J. Phys. Chem. B 108, 774-788 (2004). · DOI
  21. M. A. Kastenholz and P. H. Hünenberger, "Computation of methodology independent ionic solvation free energies from molecular simulations: I. The electrostatic potential in molecular liquids," J. Chem. Phys. 124, 124106-1-124106-27 (2006). · DOI
  22. M. A. Kastenholz and P. H. Hünenberger, "Computation of methodology independent ionic solvation free energies from molecular simulations: II. The hydration free energy of the sodium cation," J. Chem. Phys. 124, 224501-1-224501-20 (2006). · DOI
  23. M. M. Reif, V. Kräutler, M. A. Kastenholz, X. Daura, and P. H. Hünenberger, "Explicit-solvent molecular dynamics simulations of a reversibly-folding β-heptapeptide in methanol: Influence of the treat- ment of long-range electrostatic interactions," J. Phys. Chem. B 113, 3112-3128 (2009). · DOI
  24. P. H. Hünenberger, "Lattice-sum methods for computing electrostatic in- teractions in molecular simulations," in Simulation and Theory of Elec- trostatic Interactions in Solution: Computational Chemistry, Biophysics, and Aqueous Solution, edited by G. Hummer and L. R. Pratt (American Institute of Physics, New York, 1999), pp. 17-83.
  25. P. P. Ewald, "Die Berechnung optischer und elektrostatischer Gitterpo- tentiale," Ann. Phys. 369, 253-287 (1921). · DOI
  26. R. W. Hockney and J. W. Eastwood, Computer Simulation using Parti- cles (McGraw-Hill, New York, 1981).
  27. T. Darden, D. York, and L. Pedersen, "Particle mesh Ewald: An Nlog(N) method for Ewald sums in large systems," J. Chem. Phys. 98, 10089- 10092 (1993). · DOI
  28. U. Essmann, L. Perera, M. L. Berkowitz, T. Darden, H. Lee, and L. G. Pedersen, "A smooth particle mesh Ewald method," J. Chem. Phys. 103, 8577-8593 (1995). · DOI
  29. F. Figueirido, R. M. Levy, R. Zhou, and B. J. Berne, "Large scale simu- lation of macromolecules in solution: Combining the periodic fast mul- tipole method with multiple time step integrators," J. Phys. Chem. 106, 9835-9849 (1997). · DOI
  30. M. M. Reif and P. H. Hünenberger, "Computation of methodology- independent single-ion solvation properties from molecular simulations. III. Correction terms for the solvation free energies, enthalpies, en- tropies, heat capacities, volumes, compressibilities and expansivities of solvated ions," J. Chem. Phys. 134, 144103-1-144103-30 (2011). · DOI
  31. M. M. Reif and P. H. Hünenberger, "Computation of methodology- independent single-ion solvation properties from molecular simula- tions. IV. Optimized Lennard-Jones parameter sets for the alkali and halide ions in water," J. Chem. Phys. 134, 144104-1-144104-25 (2011). · DOI
  32. P. H. Hünenberger and M. M. Reif, Single-ion Solvation: Experimen- tal and Theoretical Approaches to Elusive Thermodynamic Quantities, 1st ed., Theoretical and Computational Chemistry Series Vol. 3 (Royal Society of Chemistry, London, 2011).
  33. B. Dahlgren, M. M. Reif, P. H. Hünenberger, and N. Hansen, "Calcu- lation of derivative thermodynamic hydration and aqueous partial mo- lar properties of ions based on atomistic simulations," J. Chem. Theory Comput. 8, 3542-3564 (2012). · DOI
  34. M. M. Reif, P. H. Hünenberger, and C. Oostenbrink, "New interaction parameters for charged amino acid side chains in the GROMOS force field," J. Chem. Theory Comput. 8, 3705-3723 (2012). · DOI
  35. M. M. Reif and C. Oostenbrink, "Net charge changes in the calculation of relative ligand-binding free energies via classical atomistic molecular dynamics simulations," J. Comput. Chem. (in press).
  36. H.-J. Woo and B. Roux, "Calculation of absolute protein-ligand binding free energy from computer simulations," Proc. Natl. Acad. Sci. U.S.A. 102, 6825-6830 (2005). · DOI · Paper page
  37. A. Y. Lau and B. Roux, "The hidden energetics of ligand binding and activation in a glutamate receptor," Nat. Struct. Biol. 18, 283-288 (2011) · DOI
  38. A. de Ruiter and C. Oostenbrink, "Protein-ligand binding from distance- field distances and Hamiltonian replica exchange simulations," J. Chem. Theory Comput. 9, 883892 (2013). · DOI
  39. S. B. Dixit and C. Chipot, "Can absolute free energies of associa- tion be estimated from molecular mechanical simulations? The biotin- streptavidin system revisited," J. Phys. Chem. A 105, 9795-9799 (2001). · DOI
  40. S. Donnini, A. E. Mark, A. H. Juffer, and A. Villa, "Incorporating the effect of ionic strength in free energy calculations using explicit ions," J. Comput. Chem. 26, 115122 (2005). · DOI
  41. R. Zhou, P. Das, and A. K. Royyuru, "Single mutation induced H3N2 hemagglutinin antibody neutralization: A free energy perturba- tion study," J. Phys. Chem. B 112, 15813-15820 (2008). · DOI
  42. B. R. Morgan and F. Massi, "Accurate estimates of free energy changes in charge mutations," J. Chem. Theory Comput. 6, 1884-1893 (2010). · DOI
  43. G. Hummer, L. R. Pratt, and A. E. Garcia, "Free energy of ionic hydra- tion," J. Phys. Chem. 100, 1206-1215 (1996). · DOI
  44. G. Hummer, L. R. Pratt, A. E. Garcia, B. J. Berne, and S. W. Rick, "Elec- trostatic potentials and free energies of solvation of polar and charged molecules," J. Phys. Chem. B 101, 3017-3020 (1997). · DOI
  45. G. Hummer, L. R. Pratt, and A. E. Garcia, "Ion sizes and finite-size corrections for ionic-solvation free energies," J. Chem. Phys. 107, 9275- 9277 (1997). · DOI
  46. R. J. Rosenfeld, A.-M. A. Hays, R. A. Musah, and D. B. Goodin, "Exci- sion of a proposed electron transfer pathway in cytochrome c peroxidase and its replacement by a ligand-binding channel," Protein Sci. 11, 1251- 1259 (2002). · DOI
  47. G. J. Rocklin, S. E. Boyce, M. Fischer, I. Fish, D. L. Mobley, B. K. Shoichet, and K. A. Dill, "Blind prediction of charged ligand binding affinities in a model binding site," J. Mol. Biol. (in press).
  48. J. Åqvist and T. Hansson, "On the validity of electrostatic linear response in polar solvents," J. Phys. Chem. 100, 9512-9521 (1996). · DOI
  49. T. Simonson, "Gaussian fluctuations and linear response in an electron transfer process," Proc. Natl. Acad. Sci. U.S.A. 99, 6544-6549 (2002). · DOI
  50. M. E. Davis, J. D. Madura, B. A. Luty, and J. A. McCammon, "Elec- trostatics and diffusion of molecules in solution: Simulations with the University of Houston Brownian dynamics program," Comput. Phys. Commun. 62, 187-197 (1991). · DOI
  51. J. D. Madura, J. M. Briggs, R. C. Wade, M. E. Davis, B. A. Luty, A. Ilin, J. Antosiewicz, M. K. Gilson, B. Bagheri, L. R. Scott, and J. A. McCam- mon, "Electrostatics and diffusion of molecules in solution: Simulations with the University of Houston Brownian Dynamics program," Comput. Phys. Commun. 91, 57-95 (1995). · DOI
  52. A. Nicholls and B. Honig, "A rapid finite-difference algorithm, utilizing successive over-relaxation to solve the Poisson-Boltzmann equation," J. Comput. Chem. 12, 435-445 (1991). · DOI
  53. N. A. Baker, D. Sept, S. Joseph, M. J. Holst, and J. A. McCammon, "Electrostatics of nanosystems: Application to microtubules and the ri- bosome," Proc. Natl. Acad. Sci. U.S.A. 98, 10037-10041 (2001). · DOI
  54. J. Chem. Phys. 139, 184103 (2013)
  55. N. Hansen, P. H. Hünenberger and W. F. van Gunsteren, "Efficient com- bination of environment change and alchemical perturbation within the enveloping distribution sampling (EDS) scheme: Twin-system EDS and application to the determination of octanol-water partition coefficients," J. Chem. Theory Comput. 9, 1334-1346 (2013). · DOI
  56. J. G. Kirkwood, "Statistical mechanics of fluid mixtures," J. Chem. Phys. 3, 300-313 (1935). · DOI · Paper page
  57. R. W. Zwanzig, "High-temperature equation of state by a perturbation method. I. Nonpolar gases," J. Chem. Phys. 22, 1420-1426 (1954). · DOI
  58. C. H. Bennet, "Efficient estimation of free energy differences from Monte Carlo data," J. Comput. Phys. 22, 245-268 (1976). · DOI
  59. M. R. Shirts and J. D. Chodera, "Statistically optimal analysis of sam- ples from multiple equilibrium states," J. Chem. Phys. 129, 124105-1- 124105-10 (2008). · DOI
  60. M. Christen, P. H. Hünenberger, D. Bakowies, R. Baron, R. Bürgi, D. P. Geerke, T. N. Heinz, M. A. Kastenholz, V. Kräutler, C. Oostenbrink, C. Peter, D. Trzesniak, and W. F. van Gunsteren, "The GROMOS soft- ware for biomolecular simulation: GROMOS05," J. Comput. Chem. 26, 1719-1751 (2005). · DOI
  61. B. Hess, C. Kutzner, D. van der Spoel, and E. Lindahl, "GROMACS 4: Algorithms for highly efficient, load-balanced, and scalable molecular simulation," J. Chem. Theory Comput. 4, 435-447 (2008). · DOI
  62. S. G. Brush, H. L. Sahlin, and E. Teller, "Monte Carlo study of a one- component plasma. I," J. Chem. Phys. 45, 2102-2118 (1966). · DOI
  63. G. Hummer and D. M. Soumpasis, "Correlations and free energies in restricted primitive model descriptions of electrolytes," J. Chem. Phys. 98, 581-591 (1993). · DOI
  64. G. Hummer, L. R. Pratt, and A. E. Garcia, "Hydration free energy of water," J. Phys. Chem. 99, 14188-14194 (1995). · DOI
  65. A. Redlack and J. Grindlay, "The electrostatic potential in a finite ionic crystal," Can. J. Phys. 50, 2815-2825 (1972). · DOI
  66. B. R. A. Nijboer and T. W. Ruijgrok, "On the energy per particle in three-and two-dimensional Wigner lattices," J. Stat. Phys. 53, 361-382 (1988). · DOI
  67. S. Bogusz, T. E. Cheatham, and B. R. Brooks, "Removal of pressure and free energy artifacts in charged periodic systems via net charge correc- tions to the Ewald potential," J. Chem. Phys. 108, 7070-7084 (1998). · DOI
  68. P. H. Hünenberger and J. A. McCammon, "Effect of artificial periodic- ity in simulations of biomolecules under Ewald boundary conditions: A continuum electrostatics study," Biophys. Chem. 78, 69-88 (1999). · DOI
  69. N. A. Baker, P. H. Hünenberger, and J. A. McCammon, "Polarization around an ion in a dielectric continuum with truncated electrostatic in- teractions," J. Chem. Phys. 110, 10679-10692 (1999). · DOI
  70. N. A. Baker, P. H. Hünenberger, and J. A. McCammon, "Erratum: "Po- larization around an ion in a dielectric continuum with truncated elec- trostatic interactions" [J. Chem. Phys. 110, 10679-10692 (1999)]," J. Chem. Phys. 113, 2510-2511 (2000). · DOI
  71. W. Weber, P. H. Hünenberger, and J. A. McCammon, "Molecular dy- namics simulations of a polyalanine octapeptide under Ewald boundary conditions: Influence of artificial periodicity on peptide conformation," J. Phys. Chem. B 104, 3668-3675 (2000). · DOI
  72. C. Peter, W. F. van Gunsteren, and P. H. Hünenberger, "Solving the Pois- son equation for solute-solvent systems using fast Fourier transforms," J. Chem. Phys. 116, 7434-7451 (2002). · DOI
  73. C. Peter, W. F. van Gunsteren, and P. H. Hünenberger, "A fast-Fourier- transform method to solve continuum-electrostatics problems with trun- cated electrostatic interactions: Algorithm and application to ionic sol- vation and ion-ion interaction," J. Chem. Phys. 119, 12205-12223 (2003). · DOI
  74. M. Bergdorf, C. Peter, and P. H. Hünenberger, "Influence of cutoff trun- cation and artificial periodicity of electrostatic interactions in molecu- lar simulations of solvated ions: A continuum electrostatics study," J. Chem. Phys. 119, 9129-9144 (2003). · DOI
  75. A. Warshel, P. K. Sharma, M. Kato, and W. W. Parson, "Modeling elec- trostatic effects in proteins," Biochim. Biophys. Acta 1764, 1647-1676 (2006). · DOI
  76. L. Li, C. Li, Z. Zhang, and E. Alexov, "On the dielectric "constant" of proteins: Smooth dielectric function for macromolecular modeling and its implementation in DelPhi," J. Chem. Theory Comput. 9, 2126-2136 (2013). · DOI
  77. J. Antosiewicz, J. M. Briggs, and J. A. McCammon, "Orientational steer- ing in enzyme-substrate association: Ionic strength dependence of hy- drodynamic torque effect," Eur. Biophys. J. 24, 137-141 (1996). · DOI
  78. F. Dong and H.-X. Zhou, "Electrostatic contribution to the binding sta- bility of protein-protein complexes," Proteins: Struct., Funct., Bioinf. 65, 87-102 (2006). · DOI
  79. S. Qin and H.-X. Zhou, "Do electrostatic interactions destabilize protein-nucleic acid binding?," Biopolymers 86, 112-118 (2007). · DOI
  80. P. Sloth and T. S. Sørensen, "Monte Carlo calculations of chemical po- tentials in ionic fluids by application of Widom's formula: Correction for finite-system effects," Chem. Phys. Lett. 173, 51-56 (1990). · DOI
  81. T. S. Sørensen, "Error in the Debye-Hückel approximation for dilute primitive model electrolytes with Bjerrum parameters of 2 and ca. 6.8 investigated by Monte Carlo methods," J. Chem. Soc., Faraday Trans. 87, 479-492 (1991). · DOI
  82. G. Hummer, "Electrostatic potential of a homogeneously charged square and cube in two and three dimensions," J. Electrostatics 36, 285-291 (1996). · DOI
  83. V. Hornak, R. Abel, A. Okur, B. Stockbine, A. Roitberg, and C. Sim- merling, "Comparison of multiple Amber force fields and development of improved protein backbone parameters," Proteins: Struct., Funct., Bioinf. 65, 712-725 (2006) · DOI
  84. W. L. Jorgensen, J. Chandrasekhar, J. D. Madura, R. W. Impey, and M. L. Klein, "Comparison of simple potential functions for simulating liquid water," J. Chem. Phys. 79, 926-935 (1983). · DOI
  85. S. E. Boyce, D. L. Mobley, G. J. Rocklin, A. P. Graves, K. A. Dill, and B. K. Stoichet, "Predicting ligand binding affinity with alchemical free energy methods in a polar model binding site," J. Mol. Biol. 394, 747- 763 (2009). · DOI
  86. W. F. van Gunsteren and H. J. C. Berendsen, "A leap-frog algorithm for stochastic dynamics," Mol. Simul. 1, 173-185 (1988). · DOI
  87. B. Hess, H. Bekker, H. J. C. Berendsen, and J. G. E. M. Fraaije, "LINCS: A linear constraint solver for molecular simulations," J. Comput. Chem. 18, 1463-1472 (1997). · DOI
  88. R. A. Musah, G. M. Jensen, S. W. Bunte, R. J. Rosenfeld, and D. B. Goodin, "Artificial protein cavities as specific ligand-binding templates: Characterization of an engineered heterocyclic cation-binding site that preserves the evolved specificity of the parent protein," J. Mol. Biol. 315, 845-857 (2002). · DOI
  89. E. G. Alexov and M. R. Gunner, "Incorporating protein conformational flexibility into the calculation of pH-dependent protein properties," Bio- phys. J. 74, 2075-2093 (1997). · DOI
  90. R. E. Georgescu, E. G. Alexov, and M. G. Gunner, "Combining confor- mational flexibility and continuum electrostatics for calculating pKas in proteins," Biophys. J. 83, 1731-1748 (2002). · DOI
  91. D. R. Lide, CRC Handbook of Chemistry and Physics, 83rd ed. (CRC Press, Boca Raton, FL, 2002).
  92. J. D. Chodera, W. C. Swope, J. W. Pitera, C. Seok, and K. A. Dill, "Use of the weighted histogram analysis method for the analysis of simulated and parallel tempering simulations," J. Chem. Theory Comput. 3, 26-41 (2007). · DOI
  93. J. Wang, Q. Cai, Y. Xiang, and R. Luo, "Reducing grid dependence in finite-difference Poisson-Boltzmann calculations," J. Chem. Theory Comput. 8, 2741-2751 (2012). · DOI
  94. P. Höchtl, S. Boresch, W. Bitmosky, and O. Steinhauser, "Rationaliza- tion of the dielectric properties of common three-site water models in terms of their force-field parameters," J. Chem. Phys. 109, 4927-4937 (1998). · DOI
  95. B. A. Luty, M. E. Davis, and J. A. McCammon, "Electrostatic energy calculations by a finite-difference method: Rapid calculation of charge- solvent interaction energies," J. Comput. Chem. 13, 768-771 (1992). · DOI
  96. R. B. Bruccoleri, J. Novotny, and M. E. Davis, "Finite differ- ence Poisson-Boltzmann electrostatic calculations: Increased accuracy achieved by harmonic dielectric smoothing and charge antialiasing," J. Comput. Chem. 18, 268-276 (1997). · DOI
  97. S. T. Kottmann, "Harmonic averaging of smooth permittivity functions in finite-difference Poisson-Boltzmann electrostatics," Theor. Chem. Acc. 119, 421-427 (2008). · DOI
  98. D.-S. Kim, C.-I. Won, and J. Bhak, "A proposal for the revision of molecular boundary typology," J. Biomol. Struct. Dyn. 28, 277-287 (2010). 100 · DOI
  99. F. Dong and H.-X. Zhou, "Electrostatic contributions to T4 lysozyme stability: Solvent-exposed charges versus semi-buried salt bridges," Bio- phys. J. 83, 1341-1347 (2002). · DOI
  100. H. Tjong and H. X. Zhou, "On the dielectric boundary in Poisson- Boltzmann calculations," J. Chem. Theory Comput. 4, 507-514 (2008). · DOI
  101. X. Pang and H.-X. Zhou, "Poisson-Boltzmann calculations: van der Waals or molecular surface," Commun. Comput. Phys. 13, 1-12 (2013). · DOI
  102. M. S. Lee and M. A. Olson, "Evaluation of Poisson solvation models using a hybrid explicit/implicit solvent method," J. Phys. Chem. B 109, 5223-5236 (2005). 104 · DOI
  103. J. M. J. Swanson, J. Mongan, and J. A. McCammon, "Limitations of atom-centered dielectric functions in implicit solvent models," J. Phys. Chem. B 109, 14769-14772 (2005). 105 · DOI
  104. J. Mongan, C. Simmerling, J. A. McCammon, D. A. Case, and A. Onufriev, "Generalized Born model with a simple, robust molecular vol- ume correction," J. Chem. Theory Comput. 3, 156-169 (2007). 106 · DOI
  105. H. Bekker, "Unification of box shapes in molecular simulations," J. Comput. Chem. 18, 1930-1942 (1997). · DOI
  106. H. C. Andersen, "Molecular dynamics simulations at constant pressure and/or temperature," J. Chem. Phys. 72, 2384-2393 (1980). · DOI
  107. M. Parrinello and A. Rahman, "Polymorphic transitions in single crys- tals: A new molecular dynamics method," J. Appl. Phys. 52, 7182-7190 (1981). 109 · DOI
  108. P. H. Hünenberger, "Calculation of the group-based pressure in molec- ular simulations. I. A general formulation including Ewald and particle- particle-particle-mesh electrostatics," J. Chem. Phys. 116, 6880-6897 (2002). 110 · DOI
  109. J. A. Barker and R. O. Watts, "Monte Carlo studies of the dielectric properties of water-like models," Mol. Phys. 26, 789-792 (1973). · DOI
  110. I. G. Tironi, R. Sperb, P. E. Smith, and W. F. van Gunsteren, "A gen- eralized reaction field method for molecular dynamics simulations," J. Chem. Phys. 102, 5451-5459 (1995). · DOI
  111. H. S. Ashbaugh and R. H. Wood, "Effects of long-range electrostatic po- tential truncation on the free energy of ionic hydration," J. Chem. Phys. 106, 8135-8139 (1997). 113 · DOI
  112. J. Åqvist and T. Hansson, "Analysis of electrostatic potential truncation schemes in simulations of polar solvents," J. Phys. Chem. B 102, 3837- 3840 (1998). 114 · DOI
  113. G. Hummer, L. R. Pratt, A. E. Garcia, S. Garde, B. J. Berne, and S. W. Rick, "Reply to comments on "Electrostatic potentials and free energies of solvation of polar and charged molecules," J. Phys. Chem. B 102, 3841-3843 (1998). · DOI
  114. H. S. Ashbaugh and R. H. Wood, "Reply to comment on "Electro- static potentials and free energies of solvation of polar and charged molecules," J. Phys. Chem. B 102, 3844-3845 (1998). 116 · DOI
  115. T. Darden, D. Pearlman, and L. G. Pedersen, "Ionic charging free en- ergies: Spherical versus periodic boundary conditions," J. Chem. Phys. 109, 10921-10935 (1998). · DOI
  116. S. Sakane, H. S. Ashbaugh, and R. H. Wood, "Continuum corrections to the polarization and thermodynamic properties of Ewald sum simula- tions for ions and ion pairs at infinite dilution," J. Phys. Chem. B 102, 5673-5682 (1998). 118 · DOI
  117. S. Garde, G. Hummer, and M. E. Paulaitis, "Free energy of hydration of a molecular ionic solute: Tetramethylammonium ion," J. Chem. Phys. 108, 1552-1561 (1998). · DOI
  118. Y. N. Vorobjev and J. Hermans, "A critical analysis of methods of calcu- lation of a potential in simulated polar liquids: Strong arguments in favor of "Molecule-based" summation and of vacuum boundary conditions in Ewald summations," J. Phys. Chem. B 103, 10234-10242 (1999). · DOI
  119. C. S. Babu, P.-K. Yang, and C. Lim, "On the charge and molecule based summations of solvent electrostatic potentials and the validity of elec- trostatic linear response in water," J. Biol. Phys. 28, 95-113 (2002). · DOI
  120. D. H. Herce, T. Darden, and C. Sagui, "Calculation of ionic charging free energies in simulation systems with atomic charges, dipoles, and quadrupoles," J. Chem. Phys. 119, 7621-7632 (2003). · DOI
  121. N. I. Christou, J. S. Whitehouse, D. Nicholson, and N. G. Parsonage, "Studies of high density water films by computer simulation," Mol. Phys. 55, 397-410 (1985). 123 · DOI
  122. G. Aloisi, R. Guidelli, R. A. Jackson, S. M. Clark, and P. Barnes, "The structure of water at a neutral interface," J. Electroanal. Chem 206, 131- 137 (1986). 124 · DOI
  123. E. N. Brodskaya, "The molecular dynamics simulation of water clus- ters," Mol. Phys. 62, 251-265 (1987) 125 · DOI
  124. M. A. Wilson, A. Pohorille, and L. R. Pratt, "Molecular dynamics of the water liquid-vapor interface," J. Phys. Chem. 91, 4873-4878 (1987). 126 · DOI
  125. M. Matsumoto and Y. Kataoka, "Study on liquid-vapor interface of wa- ter. I. Simulation results of thermodynamic properties and orientational structure," J. Chem. Phys. 88, 3233-3245 (1988). · DOI
  126. M. A. Wilson, A. Pohorille, and L. R. Pratt, "Surface potential of the water liquid-vapor interface," J. Chem. Phys. 88, 3281-3285 (1988). · DOI
  127. M. Matsumoto and Y. Kataoka, "Molecular orientation near liquid-vapor interface of methanol: Simulational study," J. Chem. Phys. 90, 2398- 2407 (1989). · DOI
  128. M. A. Wilson, A. Pohorille, and L. R. Pratt, "Comment on "Study on the liquid-vapor interface of water. I. Simulation results of thermodynamic properties and orientational structure," J. Chem. Phys. 90, 5211-5213 (1989). · DOI
  129. C. G. Barraclough, P. T. McTigue, and Y. L. Ng, "Surface potentials of water, methanol and water+methanol mixtures," J. Electroanal. Chem. 329, 9-24 (1992). · DOI
  130. A. Pohorille and M. A. Wilson, "Viewpoint 9-Molecular structure of aqueous interfaces," J. Mol. Struct.: THEOCHEM 284, 271-298 (1993). · DOI
  131. E. N. Brodskaya and V. V. Zakharov, "Computer simulation study of the surface polarization of pure polar liquids," J. Chem. Phys. 102, 4595- 4599 (1995). · DOI
  132. H. S. Ashbaugh, "Influence of potential truncation on anisotropic sys- tems," Mol. Phys. 97, 433-437 (1999). 135 · DOI
  133. P.-K. Yang and C. Lim, "Nonconvergence of the solute potential in an in- finite solvent and its implications in continuum models," J. Phys. Chem. B 106, 12093-12096 (2002). · DOI
  134. E. Harder and B. Roux, "On the origin of the electrostatic potential dif- ference at a liquid-vacuum interface," J. Chem. Phys. 129, 234706-1- 234706-9 (2008). · DOI
  135. S. M. Kathmann, W. K. I-Feng, and C. J. Mundy, "Electronic effects on the surface potential at the vapor-liquid interface of water," J. Am. Chem. Soc. 130, 16556-16561 (2008). · DOI
  136. K. Leung, S. B. Rempe, and O. A. von Lilienfeld, "Ab initio molecular dynamics calculations of ion hydration free energies," J. Chem. Phys. 130, 204507-1-204507-11 (2009). · DOI
  137. S. B. Rempe and K. Leung, "Response to Comment on "Ab initio molec- ular dynamics calculations of ion hydration free energies" [J. Chem. Phys. 133, 047103 (2010)]," J. Chem. Phys. 133, 047104-1-047104-2 (2010). 140 · DOI
  138. K. Leung, "Surface potential at the air-water interface computed using density functional theory," J. Phys. Chem. Lett. 1, 496-499 (2010). · DOI
  139. S. M. Kathmann, I.-F. W. Kuo, C. J. Mundy, and G. K. Schenter, "Un- derstanding the surface potential of water," J. Phys. Chem. B 115, 4369- 4377 (2011). · DOI
  140. M. N. Bannerman, R. Sargent, and L. Lue, "DynamO: A free O(N) gen- eral event-driven molecular dynamics simulator," J. Comput. Chem. 32, 3329-3338 (2011). · DOI
  141. Y. Shi and T. L. Beck, "Length scales and interfacial potentials in ion hydration," J. Chem. Phys. 139, 044504-1-044504-10 (2013) 144 · DOI
  142. T. L. Beck, "The influence of water interfacial potentials on ion hydra- tion in bulk water and near interfaces," Chem. Phys. Lett. 561-562, 1-13 (2013) 145 · DOI
  143. C. D. Wick, A. J. Lee, and S. W. Rick, "How intermolecular charge transfer influences the air-water interface," J. Chem. Phys. 137, 154701- 1-154701-9 (2012). · DOI
  144. L. Horváth, T. Beu, M. Manghi, and J. Palmeri, "The vapor-liquid inter- face potential of (multi)polar fluids and its influence on ion solvation," J. Chem. Phys. 138, 154702-1-154702-10 (2013). · DOI
  145. T. Fukushige, M. Taiji, J. Makino, T. Ebisuzaki, and D. Sugimoto, "A highly parallelized special-purpose computer for many-body simula- tions with an arbitrary central force: MD-GRAPE," Astrophys. J. 468, 51-61 (1996). · DOI
  146. D. E. Shaw, M. M. Deneroff, R. O. Dror, J. S. Kuskin, R. H. Larson, J. K. Salmon, C. Young, B. Batson, K. J. Bowers, J. C. Chao, M. P. Eastwood, J. Gagliardo, J. P. Grossman, C. R. Ho, D. J. Ierardi, I. Kolossváry, J. L. Klepeis, T. Layman, C. McLeavey, M. A. Moraes, R. Mueller, E. C. Priest, Y. Shan, J. Spengler, M. Theobald, B. Towles, and S. C. Wang, "Anton, a special-purpose ma- chine for molecular dynamics simulation," Commun. ACM 51, 91-97 (2008). · DOI
  147. Y. Ajima, S. Sumimoto, and T. Shimizu, "TOFU: A 6D mesh/torus in- terconnect for exascale computers," Computer 42, 36-40 (2009). · DOI
  148. M. J. Harvey and G. De Fabritiis, "An implementation of the smooth par- ticle mesh Ewald method on GPU hardware," J. Chem. Theory Comput. 5, 2371-2377 (2009). 151 · DOI
  149. D. J. Hardy, J. E. Stone, and K. Schulten, "Multilevel summation of electrostatic potentials using graphics processing units," Parallel Com- put. 35, 164-177 (2009). 152 · DOI
  150. R. Yokota, J. P. Bardhan, M. G. Knepley, L. A. Barba, and T. Hamada, "Biomolecular electrostatics using a fast multipole BEM on up to 512 GPUS and a billion unknowns," Comput. Phys. Commun. 182, 1271- 1283 (2011). 153 · DOI

Cited by

Sorted by citations

Authors
Rocklin, G. J., Mobley, D. L., Dill, K. A., & Hünenberger, P. H.
Affiliations
  • University of California, San Francisco (US)
  • LSU New Orleans (US)
  • Stony Brook University (US)
  • ETH Zurich (CH)
ORCID
Venue
The Journal of Chemical Physics
Publisher
AIP Publishing
Published
2013-11-08
Volume
139
Issue
18
Pages
184103-184103
ISSN
  • 0021-9606 (ISSN-L)
  • 1089-7690
DOI
10.1063/1.4826261
PMC
PMC3838431
OpenAlex
W1978393297
Cited by
234
References
0
Citations by year
2026: 15 · 2025: 13 · 2024: 21 · 2023: 15 · 2022: 28 · 2021: 21 · 2020: 25 · 2019: 8 · 2018: 31 · 2017: 21 · 2016: 15 · 2015: 4 · 2014: 14 · 2013: 3
FWCI
5.38
Type
journal article
Language
en
Open access
Locations
  • The Journal of Chemical Physics (publishedVersion)
  • Europe PMC (PubMed Central) (publishedVersion)
  • PubMed Central (publishedVersion)
  • PubMed (publishedVersion)
  • eScholarship (California Digital Library) (submittedVersion)
Funders
  • National Science Foundation (1003897)
  • U.S. Department of Defense
  • Louisiana Board of Regents (EPS-1003897)
  • Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (132739, 138020)
  • National Institutes of Health (1r15gm096257-01a1)
  • National Institute of General Medical Sciences (1R15GM096257-01A1, R15 GM096257)
Topics
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Protein Structure and Dynamics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Advanced Chemical Physics Studies
  • Physical Sciences › Chemistry › Physical and Theoretical Chemistry › Advanced Physical and Chemical Molecular Interactions
Keywords
protein-ligand binding free energy, finite-size effects, electrostatics, periodic boundary conditions, non-periodic boundary conditions, Poisson-Boltzmann equation, charged solutes, cytochrome c peroxidase, counterions, explicit solvent, continuum electrostatics
MeSH terms
Cytochrome-c Peroxidase, Ligands, Mutation, Saccharomyces cerevisiae, Solvents, Thermodynamics, Thiazoles, Water, Static Electricity, Molecular Dynamics Simulation

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review