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

The Poisson-Boltzmann equation is widely used for modeling the electrostatics 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.

[1]  Charles L Brooks,et al.  Recent advances in implicit solvent-based methods for biomolecular simulations. , 2008, Current opinion in structural biology.

[2]  Huan-Xiang Zhou,et al.  Prediction of salt and mutational effects on the association rate of U1A protein and U1 small nuclear RNA stem/loop II. , 2008, The journal of physical chemistry. B.

[3]  Michael K. Gilson,et al.  The determinants of pK(a)s in proteins , 1996 .

[4]  P. Kollman,et al.  A Second Generation Force Field for the Simulation of Proteins, Nucleic Acids, and Organic Molecules , 1995 .

[5]  Huan-Xiang Zhou,et al.  Dissection of the high rate constant for the binding of a ribotoxin to the ribosome , 2009, Proceedings of the National Academy of Sciences.

[6]  J Andrew McCammon,et al.  Limitations of atom-centered dielectric functions in implicit solvent models. , 2005, The journal of physical chemistry. B.

[8]  Nathan A. Baker,et al.  Differential geometry based solvation model I: Eulerian formulation , 2010, J. Comput. Phys..

[9]  Nathan A. Baker,et al.  Poisson-Boltzmann Methods for Biomolecular Electrostatics , 2004, Numerical Computer Methods, Part D.

[10]  Lauren Wickstrom,et al.  Secondary structure bias in generalized Born solvent models: comparison of conformational ensembles and free energy of solvent polarization from explicit and implicit solvation. , 2007, The journal of physical chemistry. B.

[11]  R. Friesner,et al.  Evaluation and Reparametrization of the OPLS-AA Force Field for Proteins via Comparison with Accurate Quantum Chemical Calculations on Peptides† , 2001 .

[12]  Alexander D. MacKerell,et al.  All-atom empirical potential for molecular modeling and dynamics studies of proteins. , 1998, The journal of physical chemistry. B.

[13]  Huan-Xiang Zhou,et al.  Macromolecular electrostatic energy within the nonlinear Poisson–Boltzmann equation , 1994 .

[14]  Nathan A. Baker,et al.  Optimizing the Poisson Dielectric Boundary with Explicit Solvent Forces and Energies:  Lessons Learned with Atom-Centered Dielectric Functions. , 2007, Journal of chemical theory and computation.

[15]  Alfred B. Anderson,et al.  Electronic structure calculations of liquid-solid interfaces: Combination of density functional theory and modified Poisson-Boltzmann theory , 2008 .

[16]  R. Norel,et al.  Electrostatic aspects of protein-protein interactions. , 2000, Current opinion in structural biology.

[17]  Mark A Olson,et al.  Evaluation of Poisson solvation models using a hybrid explicit/implicit solvent method. , 2005, The journal of physical chemistry. B.

[18]  P. Kollman,et al.  A Second Generation Force Field for the Simulation of Proteins, Nucleic Acids, and Organic Molecules J. Am. Chem. Soc. 1995, 117, 5179−5197 , 1996 .

[19]  Nathan A. Baker,et al.  Computational methods for biomolecular electrostatics. , 2008, Methods in cell biology.

[20]  Charles L. Brooks,et al.  New analytic approximation to the standard molecular volume definition and its application to generalized Born calculations , 2003, J. Comput. Chem..

[21]  J. A. McCammon,et al.  R EVIEW A RTICLE Recent Progress inNumericalMethods for the Poisson-Boltzmann Equation in Biophysical Applications , 2008 .

[22]  A Caflisch,et al.  Acid and thermal denaturation of barnase investigated by molecular dynamics simulations. , 1995, Journal of molecular biology.

[23]  Huan‐Xiang Zhou,et al.  Electrostatic rate enhancement and transient complex of protein–protein association , 2008, Proteins.

[24]  Huan-Xiang Zhou,et al.  Electrostatic contributions to T4 lysozyme stability: solvent-exposed charges versus semi-buried salt bridges. , 2002, Biophysical journal.

[25]  M. Gilson,et al.  Prediction of pH-dependent properties of proteins. , 1994, Journal of molecular biology.

[26]  W. C. Still,et al.  Semianalytical treatment of solvation for molecular mechanics and dynamics , 1990 .

[27]  Boris Aguilar,et al.  Reducing the Secondary Structure Bias in the Generalized Born Model via R6 Effective Radii , 2010 .

[28]  C. Woodward,et al.  Hydrogen exchange kinetics and internal motions in proteins and nucleic acids. , 1979, Annual review of biophysics and bioengineering.

[29]  Jens Erik Nielsen,et al.  Electrostatics in proteins and protein-ligand complexes. , 2010, Future medicinal chemistry.

[30]  Jaime Eyzaguirre,et al.  Multiple Conformations of Catalytic Serine and Histidine in Acetylxylan Esterase at 0.90 Å* , 2001, The Journal of Biological Chemistry.

[31]  Harianto Tjong,et al.  On the Dielectric Boundary in Poisson-Boltzmann Calculations. , 2008, Journal of chemical theory and computation.

[32]  Charles L. Brooks,et al.  Erratum: New Analytic Approximation to the Standard Molecular Volume Definition and Its Application to Generalized Born Calculations (Journal of Computational Chemistry (2003) 24:11 (1348-1356)) , 2003 .

[33]  G. Lamm,et al.  The Poisson–Boltzmann Equation , 2003 .

[34]  Huan-Xiang Zhou,et al.  Rationalizing 5000-fold differences in receptor-binding rate constants of four cytokines. , 2011, Biophysical journal.

[35]  K. Sharp,et al.  Electrostatic interactions in macromolecules: theory and applications. , 1990, Annual review of biophysics and biophysical chemistry.

[36]  Harianto Tjong,et al.  GBr(6): a parameterization-free, accurate, analytical generalized born method. , 2007, The journal of physical chemistry. B.

[37]  A. Brigo,et al.  The Poisson–Boltzmann equation for biomolecular electrostatics: a tool for structural biology , 2002, Journal of molecular recognition : JMR.

[38]  J. Andrew Grant,et al.  A smooth permittivity function for Poisson–Boltzmann solvation methods , 2001, J. Comput. Chem..

[39]  M. Gilson,et al.  The determinants of pKas in proteins. , 1996, Biochemistry.

[40]  Charles W. Kehoe,et al.  Modeling aqueous solvation with semi-explicit assembly , 2011, Proceedings of the National Academy of Sciences.

[41]  Huan-Xiang Zhou,et al.  Comparison of calculation and experiment implicates significant electrostatic contributions to the binding stability of barnase and barstar. , 2003, Biophysical journal.

[42]  Richard A. Friesner,et al.  First-Shell Solvation of Ion Pairs: Correction of Systematic Errors in Implicit Solvent Models† , 2004 .

[43]  J. Trylska,et al.  Continuum molecular electrostatics, salt effects, and counterion binding—A review of the Poisson–Boltzmann theory and its modifications , 2008, Biopolymers.

[44]  Reza Salari,et al.  Desolvation Costs of Salt Bridges across Protein Binding Interfaces: Similarities and Differences between Implicit and Explicit Solvent Models. , 2012, The journal of physical chemistry letters.

[45]  B. Tidor,et al.  Do salt bridges stabilize proteins? A continuum electrostatic analysis , 1994, Protein science : a publication of the Protein Society.

[46]  K. Sharp,et al.  Macroscopic models of aqueous solutions : biological and chemical applications , 1993 .

[47]  Ronald M. Levy,et al.  AGBNP: An analytic implicit solvent model suitable for molecular dynamics simulations and high‐resolution modeling , 2004, J. Comput. Chem..

[48]  F M Richards,et al.  Areas, volumes, packing and protein structure. , 1977, Annual review of biophysics and bioengineering.

[49]  Nathan A. Baker,et al.  Electrostatics of nanosystems: Application to microtubules and the ribosome , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[50]  D. Beglov,et al.  Atomic Radii for Continuum Electrostatics Calculations Based on Molecular Dynamics Free Energy Simulations , 1997 .

[51]  D. Case,et al.  Exploring protein native states and large‐scale conformational changes with a modified generalized born model , 2004, Proteins.

[52]  Huan-Xiang Zhou,et al.  Salt Bridges Stabilize the Folded Structure of Barnase , 2001 .

[53]  A. Bondi.  van der Waals Volumes and Radii , 1964 .

[54]  Huan-Xiang Zhou,et al.  Electrostatic contribution to the binding stability of protein–protein complexes , 2006, Proteins.

[55]  Malcolm E. Davis,et al.  Electrostatics in biomolecular structure and dynamics , 1990 .

[56]  Gideon Schreiber,et al.  Fundamental Aspects of Protein—Protein Association Kinetics , 2009 .

[57]  Emilio Gallicchio,et al.  The AGBNP2 Implicit Solvation Model. , 2009, Journal of chemical theory and computation.

[58]  W. Im,et al.  Continuum solvation model: Computation of electrostatic forces from numerical solutions to the Poisson-Boltzmann equation , 1998 .

[59]  Huan-Xiang Zhou,et al.  Do electrostatic interactions destabilize protein-nucleic acid binding? , 2007, Biopolymers.