Coupling nonpolar and polar solvation free energies in implicit solvent models.

Recent studies on the solvation of atomistic and nanoscale solutes indicate that a strong coupling exists between the hydrophobic, dispersion, and electrostatic contributions to the solvation free energy, a facet not considered in current implicit solvent models. We suggest a theoretical formalism which accounts for coupling by minimizing the Gibbs free energy of the solvent with respect to a solvent volume exclusion function. The resulting differential equation is similar to the Laplace-Young equation for the geometrical description of capillary interfaces but is extended to microscopic scales by explicitly considering curvature corrections as well as dispersion and electrostatic contributions. Unlike existing implicit solvent approaches, the solvent accessible surface is an output of our model. The presented formalism is illustrated on spherically or cylindrically symmetrical systems of neutral or charged solutes on different length scales. The results are in agreement with computer simulations and, most importantly, demonstrate that our method captures the strong sensitivity of solvent expulsion and dewetting to the particular form of the solvent-solute interactions.

[1]  Mark S.P. Sansom,et al.  A Hydrophobic Gating Mechanism for Nanopores , 2001 .

[2]  T. Straatsma,et al.  THE MISSING TERM IN EFFECTIVE PAIR POTENTIALS , 1987 .

[3]  R. Levy,et al.  Enthalpy−Entropy and Cavity Decomposition of Alkane Hydration Free Energies: Numerical Results and Implications for Theories of Hydrophobic Solvation , 2000 .

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

[5]  Sergei Sukharev,et al.  Water dynamics and dewetting transitions in the small mechanosensitive channel MscS. , 2004, Biophysical journal.

[6]  M Gerstein,et al.  Packing at the protein-water interface. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[7]  R. Fox,et al.  Classical Electrodynamics, 3rd ed. , 1999 .

[8]  D. Chandler,et al.  The hydrophobic effect and the influence of solute-solvent attractions , 2002 .

[9]  García,et al.  Origin of Entropy Convergence in Hydrophobic Hydration and Protein Folding. , 1996, Physical review letters.

[10]  Anders Wallqvist,et al.  Computer Simulation of Hydrophobic Hydration Forces on Stacked Plates at Short Range , 1995 .

[11]  E. Kaler,et al.  Hydration and conformational equilibria of simple hydrophobic and amphiphilic solutes. , 1998, Biophysical journal.

[12]  A. Pohorille,et al.  An information theory model of hydrophobic interactions. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[13]  W. Helfrich,et al.  Bending energy of vesicle membranes: General expressions for the first, second, and third variation of the shape energy and applications to spheres and cylinders. , 1989, Physical review. A, General physics.

[14]  Rudolf Podgornik,et al.  Statistical thermodynamics of surfaces, interfaces, and membranes , 1995 .

[15]  Ruhong Zhou,et al.  Observation of a dewetting transition in the collapse of the melittin tetramer , 2005, Nature.

[16]  宁北芳,et al.  疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A , 2005 .

[17]  R. Evans,et al.  Wetting and drying at a curved substrate: long-ranged forces. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Ruhong Zhou,et al.  Hydrophobic Collapse in Multidomain Protein Folding , 2004, Science.

[19]  Dietmar Paschek.  Temperature dependence of the hydrophobic hydration and interaction of simple solutes: an examination of five popular water models. , 2004, The Journal of chemical physics.

[20]  Barry Honig,et al.  Calculating total electrostatic energies with the nonlinear Poisson-Boltzmann equation , 1990 .

[21]  B. Berne,et al.  Dewetting-induced collapse of hydrophobic particles , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[22]  Benoît Roux,et al.  Solvation of complex molecules in a polar liquid: An integral equation theory , 1996 .

[23]  J. Andrew McCammon,et al.  Computation of electrostatic forces on solvated molecules using the Poisson-Boltzmann equation , 1993 .

[24]  D. Henderson.  Fundamentals of Inhomogeneous Fluids , 1992 .

[25]  Phil Attard,et al.  BUBBLES, CAVITIES, AND THE LONG-RANGED ATTRACTION BETWEEN HYDROPHOBIC SURFACES , 1994 .

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

[27]  H. Reiss.  Scaled Particle Methods in the Statistical Thermodynamics of Fluids , 2007 .

[28]  Martin Zacharias,et al.  Continuum Solvent Modeling of Nonpolar Solvation: Improvement by Separating Surface Area Dependent Cavity and Dispersion Contributions , 2003 .

[29]  D. Chandler.  Interfaces and the driving force of hydrophobic assembly , 2005, Nature.

[30]  T. Frankel.  The Geometry of Physics , 1997 .

[31]  D. Case,et al.  Generalized born models of macromolecular solvation effects. , 2000, Annual review of physical chemistry.

[32]  W. Helfrich.  Elastic Properties of Lipid Bilayers: Theory and Possible Experiments , 1973, Zeitschrift fur Naturforschung. Teil C: Biochemie, Biophysik, Biologie, Virologie.

[33]  Samuel A. Safran,et al.  Statistical Thermodynamics Of Surfaces, Interfaces, And Membranes , 1994 .

[34]  Intermittent permeation of cylindrical nanopores by water. , 2002, Physical review letters.

[35]  J Dzubiella,et al.  Competition of hydrophobic and Coulombic interactions between nanosized solutes. , 2004, The Journal of chemical physics.

[36]  Gareth H. McKinley,et al.  Superhydrophobic Carbon Nanotube Forests , 2003 .

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

[38]  Electric field-controlled water permeation coupled to ion transport through a nanopore. , 2003, The Journal of chemical physics.

[39]  Emilio Gallicchio,et al.  On the nonpolar hydration free energy of proteins: surface area and continuum solvent models for the solute-solvent interaction energy. , 2003, Journal of the American Chemical Society.

[40]  G. Hummer,et al.  Electric field and temperature effects on water in the narrow nonpolar pores of carbon nanotubes. , 2004, The Journal of chemical physics.

[41]  Alex M. Andrew,et al.  Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science (2nd edition) , 2000 .

[42]  Marko Subasic,et al.  Level Set Methods and Fast Marching Methods , 2003 .

[43]  Gerhard Hummer,et al.  Ion sizes and finite-size corrections for ionic-solvation free energies , 1997 .

[44]  D. Chandler,et al.  Hydrophobicity at Small and Large Length Scales , 1999 .

[45]  Ariel Fernández,et al.  Keeping dry and crossing membranes , 2004, Nature Biotechnology.

[46]  William L. Jorgensen,et al.  Optimized intermolecular potential functions for liquid hydrocarbons , 1984 .

[47]  J. Hansen,et al.  Molecular dynamics investigation of water permeation through nanopores , 2003 .

[48]  R. Zwanzig,et al.  Fluctuation Theory of Surface Tension , 1972 .

[49]  Emilio Gallicchio,et al.  The non-polar solvent potential of mean force for the dimerization of alanine dipeptide: the role of solute-solvent van der Waals interactions. , 2004, Biophysical chemistry.

[50]  J. Hansen,et al.  Electric-field-controlled water and ion permeation of a hydrophobic nanopore. , 2005, The Journal of chemical physics.

[51]  B Montgomery Pettitt,et al.  On the mechanism of hydrophobic association of nanoscopic solutes. , 2005, Journal of the American Chemical Society.

[52]  Wetting of curved surfaces , 1997, cond-mat/9711033.

[53]  H. -. Kim,et al.  On the temperature and pressure dependences of cavities in the dielectric continuum picture. , 2005, The Journal of chemical physics.

[54]  R. Tolman.  The Effect of Droplet Size on Surface Tension , 1949 .

[55]  J. Hansen,et al.  Reduction of the hydrophobic attraction between charged solutes in water , 2003 .

[56]  D. A. Dunnett.  Classical Electrodynamics , 2020, Nature.

[57]  Frank H. Stillinger,et al.  Structure in aqueous solutions of nonpolar solutes from the standpoint of scaled-particle theory , 1973 .

[58]  Ronald M. Levy,et al.  The SGB/NP hydration free energy model based on the surface generalized born solvent reaction field and novel nonpolar hydration free energy estimators , 2002, J. Comput. Chem..

[59]  P. Attard.  Thermodynamic Analysis of Bridging Bubbles and a Quantitative Comparison with the Measured Hydrophobic Attraction , 2000 .

[60]  B. Berne,et al.  Drying and hydrophobic collapse of paraffin plates. , 2005, Journal of Physical Chemistry B.

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

[62]  S. C. Tucker,et al.  A Continuum Solvation Model Including Electrostriction: Application to the Anisole Hydrolysis Reaction in Supercritical Water , 1996 .

[63]  Peter J. Rossky,et al.  Surface topography dependence of biomolecular hydrophobic hydration , 1998, Nature.

[64]  G. Hummer,et al.  Water conduction through the hydrophobic channel of a carbon nanotube , 2001, Nature.

[65]  M L Connolly,et al.  The molecular surface package. , 1993, Journal of molecular graphics.

[66]  D. Chandler,et al.  Scaling of Hydrophobic Solvation Free Energies , 2001 .

[67]  H. Berendsen,et al.  A systematic study of water models for molecular simulation: Derivation of water models optimized for use with a reaction field , 1998 .

[68]  D. Tildesley,et al.  Molecular dynamics simulation of the orthobaric densities and surface tension of water , 1995 .

[69]  Gerhard Hummer,et al.  Free Energy of Ionic Hydration , 1996 .