Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-18T10:11:48.442Z Has data issue: false hasContentIssue false
  • English
  • Français

Poisson-Boltzmann Calculations: van der Waals or Molecular Surface?

Published online by Cambridge University Press:  03 June 2015

Xiaodong Pang  and
Huan-Xiang Zhou
Xiaodong Pang
Affiliation:
State Key Laboratory of Surface Physics, Department of Physics, Fudan University, Shanghai 200433, China Department of Physics and Institute of Molecular Biophysics, Florida State University, Tallahassee, Florida 32306, USA
Huan-Xiang Zhou*
Affiliation:
Department of Physics and Institute of Molecular Biophysics, Florida State University, Tallahassee, Florida 32306, USA
*
*Corresponding author.Email:[email protected]
Get access

Abstract

The Poisson-Boltzmann equation is widely used for modeling the electro-statics of biomolecules, but the calculation results are sensitive to the choice of the boundary between the low solute dielectric and the high solvent dielectric. The default choice for the dielectric boundary has been the molecular surface, but the use of the van der Waals surface has also been advocated. Here we review recent studies in which the two choices are tested against experimental results and explicit-solvent calculations. The assignment of the solvent high dielectric constant to interstitial voids in the solute is often used as a criticism against the van der Waals surface. However, this assignment may not be as unrealistic as previously thought, since hydrogen exchange and other NMR experiments have firmly established that all interior parts of proteins are transiently accessible to the solvent.

Keywords

41.20.CvPoisson-Boltzmann calculationbiomolecular electrostaticsdielectric boundaryvan der Waals surfacemolecular surface
Type
Research Article
Information
Communications in Computational Physics , Volume 13 , Issue 1 , January 2013 , pp. 1 - 12
Copyright
Copyright © Global Science Press Limited 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Davis, M. E. and Mccammon, J. A., Electrostatics in biomolecular structure and dynamics, Chem Rev, 90 (1990), 509–521.CrossRefGoogle Scholar
[2]Sharp, K. A. and Honig, B., Electrostatic interactions in macromolecules – theory and applications, Annu Rev Biophys Biophys Chem, 19 (1990), 301–332.Google Scholar
[3]Kukic, P. and Nielsen, J. E., Electrostatics in proteins and protein-ligand complexes, Future Med Chem, 2 (2010), 647–666.Google Scholar
[4]Fogolari, F., Brigo, A. and Molinari, H., The Poisson-Boltzmann equation for biomolecular electrostatics: a tool for structural biology, J Mol Recognit, 15 (2002), 377–392.Google Scholar
[5]Lamm, G., The Poisson-Boltzmann Equation, Rev Comp Ch, 19 (2003), 147–365.Google Scholar
[6]Baker, N. A., Poisson-Boltzmann methods for biomolecular electrostatics, Method Enzymol, 383 (2004), 94–118.CrossRefGoogle ScholarPubMed
[7]Grochowski, P. and Trylska, J., Review: Continuum molecular electrostatics, salt effects, and counterion binding-a review of the Poisson-Boltzmann theory and its modifications, Biopolymers, 89 (2008), 93–113.Google Scholar
[8]Dong, F., Olsen, B. and Baker, N. A., Computational methods for biomolecular electrostatics, Method Cell Biol, 84 (2008), 843–870.Google Scholar
[9]Lu, B. Z., Zhou, Y. C., Holst, M. J. and McCammon, J. A., Recent progress in numerical methods for the Poisson-Boltzmann equation in biophysical applications, Commun Comput Phys, 3 (2008), 973–1009.Google Scholar
[10]Chen, J. H., Brooks, C. L. and Khandogin, J., Recent advances in implicit solvent-based methods for biomolecular simulations, Curr Opin Struc Biol, 18 (2008), 140–148.CrossRefGoogle ScholarPubMed
[11]Nina, M., Beglov, D. and Roux, B., Atomic radii for continuum electrostatics calculations based on molecular dynamics free energy simulations, J Phys Chem B, 101 (1997), 5239–5248.CrossRefGoogle Scholar
[12]Vijayakumar, M. and Zhou, H. X., Salt bridges stabilize the folded structure of barnase, J Phys Chem B, 105 (2001), 7334–7340.Google Scholar
[13]Dong, F. and Zhou, H. X., Electrostatic contributions to T4 lysozyme stability: Solvent-exposed charges versus semiburied salt bridges, Biophys J, 83 (2002), 1341–1347.CrossRefGoogle ScholarPubMed
[14]Dong, F., Vijayakumar, M. and Zhou, H. X., Comparison of calculation and experiment implicates significant electrostatic contributions to the binding stability of barnase and barstar, Biophys J, 85 (2003), 49–60.CrossRefGoogle Scholar
[15]Dong, F. and Zhou, H. X., Electrostatic contribution to the binding stability of protein-protein complexes, Proteins, 65 (2006), 87–102.Google Scholar
[16]Qin, S. B. and Zhou, H. X., Do electrostatic interactions destabilize protein-nucleic acid binding? Biopolymers, 86 (2007), 112–118.Google Scholar
[17]Swanson, J. M. J., Wagoner, J. A., Baker, N. A. and McCammon, J. A., Optimizing the Poisson dielectric boundary with explicit solvent forces and energies: Lessons learned with atom-centered dielectric functions, J Chem Theory Comput, 3 (2007), 170–183.Google Scholar
[18]Alsallaq, R. and Zhou, H. X., Electrostatic rate enhancement and transient complex of protein-protein association, Proteins, 71 (2008), 320–335.Google Scholar
[19]Tjong, H. and Zhou, H. X., On the dielectric boundary in Poisson-Boltzmann calculations, J Chem Theory Comput, 4 (2008), 507–514.CrossRefGoogle ScholarPubMed
[20]Jinnouchi, R. and Anderson, A. B., Electronic structure calculations of liquid-solid interfaces: Combination of density functional theory and modified Poisson-Boltzmann theory, Phys Rev B, 77 (2008).Google Scholar
[21]Chen, Z., Baker, N. A. and Wei, G. W., Differential geometry based solvation model I: Eulerian formulation, J Comput Phys, 229 (2010), 8231–8258.Google Scholar
[22]Zhou, H. X., Macromolecular electrostatic energy within the nonlinear Poisson-Boltzmann equation, J Chem Phys, 100 (1994), 3152–3262.CrossRefGoogle Scholar
[23]Baker, N. A., Sept, D., Joseph, S., Holst, M. J. and McCammon, J. A., Electrostatics of nanosystems: Application to microtubules and the ribosome, Proc Natl Acad Sci USA, 98 (2001), 10037–10041.Google Scholar
[24]Still, W. C., Tempczyk, A., Hawley, R. C. and Hendrickson, T., Semianalytical treatment of solvation for molecular mechanics and dynamics, J Am Chem Soc, 112 (1990), 6127–6129.Google Scholar
[25]Lee, M. S., Feig, M., Salsbury, F. R. and Brooks, C. L., New analytic approximation to the standard molecular volume definition and its application to generalized born calculations, J Comput Chem, 24 (2003), 1821–1821.Google Scholar
[26]Gallicchio, E. and Levy, R. M., AGBNP: An analytic implicit solvent model suitable for molecular dynamics simulations and high-resolution modeling, J Comput Chem, 25 (2004), 479499.Google Scholar
[27]Onufriev, A., Bashford, D. and Case, D. A., Exploring protein native states and large-scale conformational changes with a modified generalized born model, Proteins, 55 (2004), 383–394.CrossRefGoogle ScholarPubMed
[28]Tjong, H. and Zhou, H. X., GBr6: A parameterization-free, accurate, analytical generalized born method, J Phys Chem B, 111 (2007), 3055–3061.Google Scholar
[29]Richards, F. M., Areas, volumes, packing, and protein structure, Annu Rev Biophys Bioeng, 6 (1977), 151–176.Google Scholar
[30]Swanson, J. M. J., Mongan, J. and McCammon, J. A., Limitations of atom-centered dielectric functions in implicit solvent models, J Phys Chem B, 109 (2005), 14769–14772.Google Scholar
[31]Grant, J. A., Pickup, B. T. and Nicholls, A., A smooth permittivity function for Poisson-Boltzmann solvation methods, J Comput Chem, 22 (2001), 608–640.Google Scholar
[32]Im, W., Beglov, D. and Roux, B., Continuum solvation model: Computation of electrostatic forces from numerical solutions to the Poisson-Boltzmann equation, Comput Phys Commun, 111 (1998), 59–75.Google Scholar
[33]Honig, B., Sharp, K. and Yang, A.-S., Macroscopic models of aqueous solutions: Biological and chemical applications, J Phys Chem, 97 (1993), 1101–1109.Google Scholar
[34]Sheinerman, F. B., Norel, R. and Honig, B., Electrostatic aspects of protein-protein interactions, Curr Opin Struct Biol, 10 (2000), 153–159.Google Scholar
[35]Hendsch, Z. S. and Tidor, B., Do salt bridges stabilize proteins? A continuum electrostatic analysis, Protein Sci, 3 (1994), 211–226.CrossRefGoogle ScholarPubMed
[36]Cornell, W. D., Cieplak, P., Bayly, C. I., Gould, I. R., Merz, K. M., Ferguson, D. M., Spellmeyer, D. C., Fox, T., Caldwell, J. W. and Kollman, P. A., A second generation force field for the simulation of proteins, nucleic acids, and organic molecules, J Am Chem Soc, 117 (1995), 5179–5197.Google Scholar
[37]Bondi, A., van der Waals volumes and radii, J Phys Chem, 68 (1964), 441–451.Google Scholar
[38]Antosiewicz, J., Mccammon, J. A. and Gilson, M. K., Prediction of pH-dependent properties of proteins, J Mol Biol, 238 (1994), 415–436.Google Scholar
[39]Antosiewicz, J., McCammon, J. A. and Gilson, M. K., The determinants of pKas in proteins, Biochemistry, 35 (1996), 7819–7833.Google Scholar
[40]Caflisch, A. and Karplus, M., Acid and thermal denaturation of barnase investigated by molecular dynamics simulations, J Mol Biol, 252 (1995), 672–708.Google Scholar
[41]Schreiber, G., Haran, G. and Zhou, H. X., Fundamental aspects of protein-protein association kinetics, Chem Rev, 109 (2009), 839–860.Google Scholar
[42]Qin, S. B. and Zhou, H. X., Prediction of salt and mutational effects on the association rate of U1A protein and U1 small nuclear RNA stem/loop II, J Phys Chem B, 112 (2008), 5955–5960.Google Scholar
[43]Qin, S. and Zhou, H. X., Dissection of the high rate constant for the binding of a ribotoxin to the ribosome, Proc Natl Acad Sci USA, 106 (2009), 6974–6979.Google Scholar
[44]Pang, X., Qin, S. and Zhou, H. X., Rationalizing 5,000-fold differences in receptor-binding rate constants of four cytokines, Biophys J, 101 (2011), 1175–1183.Google Scholar
[45]Halle, B. 1999. Water in biological systems: the NMR picture. In Hydration Processes in Biology. Bellisent-Funel, M.-C., editor. IOS Press, Dordrecht, the Netherlands. 233–249.Google Scholar
[46]Woodward, C. K. and Hilton, B. D., Hydrogen exchange kinetics and internal motions in proteins and nucleic acids, Annu Rev Biophys Bioeng, 8 (1979), 99–127.Google Scholar
[47]Ghosh, D., Sawicki, M., Lala, P., Erman, M., Pangborn, W., Eyzaguirre, J., Gutierrez, R., Jorn-vall, H. and Thiel, D. J., Multiple conformations of catalytic serine and histidine in acetylxylan esterase at 0.90 Å, J Biol Chem, 276 (2001), 11159–11166.Google Scholar
[48]Lee, M. S. and Olson, M. A., Evaluation of Poisson solvation models using a hybrid explicit/implicit solvent method, J Phys Chem B, 109 (2005), 5223–5236.Google Scholar
[49]Aguilar, B., Shadrach, R. and Onufriev, A. V., Reducing the secondary structure bias in the generalized Born model via R6 effective radii, J Chem Theory Comput, 6 (2010), 3613–3630.Google Scholar
[50]Salari, R. and Chong, L. T., Desolvation costs of salt bridges across protein binding interfaces: Similarities and differences between implicit and explicit solvent models, J Phys Chem Lett, 1 (2010), 2844–2848.Google Scholar
[51]MacKerell, A. D., Bashford, D., Bellott, , Dunbrack, R. L., Evanseck, J. D., Field, M. J., Fischer, S., Gao, J., Guo, H., Ha, S., Joseph-McCarthy, D., Kuchnir, L., Kuczera, K., Lau, F. T. K., Mattos, C., Michnick, S., Ngo, T., Nguyen, D. T., Prodhom, B., Reiher, W. E., Roux, B., Schlenkrich, M., Smith, J. C., Stote, R., Straub, J., Watanabe, M., Wiorkiewicz-Kuczera, J., Yin, D. and Karplus, M., Allatom empirical potential for molecular modeling and dynamics studies of proteins, J Phys Chem B, 102 (1998), 3586–3616.CrossRefGoogle ScholarPubMed
[52]Roe, D. R., Okur, A., Wickstrom, L., Hornak, V. and Simmerling, C., Secondary structure bias in generalized Born solvent models: Comparison of conformational ensembles and free energy of solvent polarization from explicit and implicit solvation, J Phys Chem B, 111 (2007), 1846–1857.Google Scholar
[53]Kaminski, G. A., Friesner, R. A., Tirado-Rives, J. and Jorgensen, W. L., 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 (2001), 6474–6487.Google Scholar
[54]Yu, Z., Jacobson, M. P., Josovitz, J., Rapp, C. S. and Friesner, R. A., First-shell solvation of ion pairs: Correction of systematic errors in implicit solvent models, J Phys Chem B, 108 (2004), 6643–6654.Google Scholar
[55]Gallicchio, E., Paris, K. and Levy, R. M., The AGBNP2 implicit solvation model, J Chem Theory Comput, 5 (2009), 2544–2564.Google Scholar
[56]Fennell, C. J., Kehoe, C. W. and Dill, K. A., Modeling aqueous solvation with semi-explicit assembly, Proc Natl Acad Sci USA, 108 (2011), 3234–3239.Google Scholar