Highly accurate biomolecular electrostatics in continuum dielectric environments

Implicit solvent models based on the Poisson‐Boltzmann (PB) equation are frequently used to describe the interactions of a biomolecule with its dielectric continuum environment. A novel, highly accurate Poisson‐Boltzmann solver is developed based on the matched interface and boundary (MIB) method, which rigorously enforces the continuity conditions of both the electrostatic potential and its flux at the molecular surface. The MIB based PB solver attains much better convergence rates as a function of mesh size compared to conventional finite difference and finite element based PB solvers. Consequently, highly accurate electrostatic potentials and solvation energies are obtained at coarse mesh sizes. In the context of biomolecular electrostatic calculations it is demonstrated that the MIB method generates substantially more accurate solutions of the PB equation than other established methods, thus providing a new level of reference values for such models. Initial results also indicate that the MIB method can significantly improve the quality of electrostatic surface potentials of biomolecules that are frequently used in the study of biomolecular interactions based on experimental structures. © 2007 Wiley Periodicals, Inc. J Comput Chem, 2008

[1]  Soonmin Jang,et al.  Molecular Dynamics Study of Peptides in Implicit Water: Ab Initio Folding of β-Hairpin, β-Sheet, and ββα-motif , 2002 .

[2]  R. Zauhar,et al.  A new method for computing the macromolecular electric potential. , 1985, Journal of molecular biology.

[3]  David Andelman,et al.  Electrostatic Properties of Membranes: The Poisson-Boltzmann Theory , 1995 .

[4]  Michael Feig,et al.  Molecular dynamics simulations of large integral membrane proteins with an implicit membrane model. , 2006, The journal of physical chemistry. B.

[5]  Michael J. Holst,et al.  Multigrid solution of the Poisson—Boltzmann equation , 1992, J. Comput. Chem..

[6]  R. LeVeque,et al.  A comparison of the extended finite element method with the immersed interface method for elliptic equations with discontinuous coefficients and singular sources , 2006 .

[7]  Michael J. Holst,et al.  Numerical solution of the nonlinear Poisson–Boltzmann equation: Developing more robust and efficient methods , 1995, J. Comput. Chem..

[8]  B. Berne,et al.  Can a continuum solvent model reproduce the free energy landscape of a β-hairpin folding in water? , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[9]  B. Roux,et al.  Implicit solvent models. , 1999, Biophysical chemistry.

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

[11]  Ariel Fernández,et al.  Continuum equations for dielectric response to macro-molecular assemblies at the nano scale , 2004 .

[12]  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.

[13]  J. Israelachvili.  Intermolecular and surface forces , 1985 .

[14]  C. Brooks,et al.  Recent advances in the development and application of implicit solvent models in biomolecule simulations. , 2004, Current opinion in structural biology.

[15]  B. Honig,et al.  Classical electrostatics in biology and chemistry. , 1995, Science.

[16]  Ivo Babuska,et al.  The finite element method for elliptic equations with discontinuous coefficients , 1970, Computing.

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

[18]  Eric J. Sorin,et al.  β-hairpin folding simulations in atomistic detail using an implicit solvent model1 , 2001 .

[19]  M. L. Connolly.  Analytical molecular surface calculation , 1983 .

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

[21]  Nathan A. Baker,et al.  Adaptive multilevel finite element solution of the Poisson–Boltzmann equation II. Refinement at solvent‐accessible surfaces in biomolecular systems , 2000 .

[22]  M. Karplus,et al.  CHARMM: A program for macromolecular energy, minimization, and dynamics calculations , 1983 .

[23]  Douglas A. Lauffenburger,et al.  NUMERICAL SOLUTION OF THE NONLINEAR POISSON-BOLTZMANN EQUATION FOR A MEMBRANE-ELECTROLYTE SYSTEM , 1994 .

[24]  Shan Zhao,et al.  High-order FDTD methods via derivative matching for Maxwell's equations with material interfaces , 2004 .

[25]  C. Peskin.  Numerical analysis of blood flow in the heart , 1977 .

[26]  K. Sharp,et al.  Calculating the electrostatic potential of molecules in solution: Method and error assessment , 1988 .

[27]  V. Mikhailova,et al.  Three-centered model of ultrafast photoinduced charge transfer: continuum dielectric approach. , 2006, The Journal of chemical physics.

[28]  Nathan A. Baker,et al.  Adaptive multilevel finite element solution of the Poisson–Boltzmann equation I. Algorithms and examples , 2000 .

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

[30]  Charles L. Brooks,et al.  Performance comparison of generalized born and Poisson methods in the calculation of electrostatic solvation energies for protein structures , 2004, J. Comput. Chem..

[31]  R. J. Hunter.  Foundations of Colloid Science , 1987 .

[32]  Richard A. Friesner,et al.  Numerical solution of the Poisson–Boltzmann equation using tetrahedral finite‐element meshes , 1997 .

[33]  Nathan A. Baker,et al.  Improving implicit solvent simulations: a Poisson-centric view. , 2005, Current opinion in structural biology.

[34]  Richard H. Henchman,et al.  Revisiting free energy calculations: a theoretical connection to MM/PBSA and direct calculation of the association free energy. , 2004, Biophysical journal.

[35]  Peijuan Zhu,et al.  Implementation and testing of stable, fast implicit solvation in molecular dynamics using the smooth‐permittivity finite difference Poisson–Boltzmann method , 2004, J. Comput. Chem..

[36]  Guo-Wei Wei,et al.  On the fictitious-domain and interpolation formulations of the matched interface and boundary (MIB) method , 2006, J. Comput. Phys..

[37]  Shan Zhao,et al.  High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources , 2006, J. Comput. Phys..

[38]  P. Kollman,et al.  Calculating structures and free energies of complex molecules: combining molecular mechanics and continuum models. , 2000, Accounts of chemical research.

[39]  H. Scheraga,et al.  A fast adaptive multigrid boundary element method for macromolecular electrostatic computations in a solvent , 1997 .

[40]  J. Kirkwood,et al.  Theory of Solutions of Molecules Containing Widely Separated Charges with Special Application to Zwitterions , 1934 .

[41]  Donald Bashford,et al.  Macroscopic electrostatic models for protonation states in proteins. , 2004, Frontiers in bioscience : a journal and virtual library.

[42]  M. Sanner,et al.  Reduced surface: an efficient way to compute molecular surfaces. , 1996, Biopolymers.

[43]  Gerhard Hummer,et al.  Simulation and Theory of Electrostatic Interactions in Solution: Computational Chemistry, Biophysics and Aqueous Solutions, Santa Fe, New Mexico, U. S. A., 23-25 June 1999 , 1999 .

[44]  B. Honig,et al.  Calculation of the total electrostatic energy of a macromolecular system: Solvation energies, binding energies, and conformational analysis , 1988, Proteins.

[45]  P. Strevens.  Iii , 1985 .

[46]  S. Osher,et al.  A Non-oscillatory Eulerian Approach to Interfaces in Multimaterial Flows (the Ghost Fluid Method) , 1999 .

[47]  J. Andrew McCammon,et al.  Solving the finite‐difference non‐linear Poisson–Boltzmann equation , 1992 .

[48]  Federico Fogolari,et al.  Protocol for MM/PBSA molecular dynamics simulations of proteins. , 2003, Biophysical journal.

[49]  Ray Luo,et al.  A Poisson–Boltzmann dynamics method with nonperiodic boundary condition , 2003 .