Generalized Born and Explicit Solvent Models for Free Energy Calculations in Organic Solvents: Cyclodextrin Dimerization.

Evaluation of solvation (binding) free energies with implicit solvent models in different dielectric environments for biological simulations as well as high throughput ligand screening remain challenging endeavors. In order to address how well implicit solvent models approximate explicit ones we examined four generalized Born models (GB(Still), GB(HCT), GB(OBC)I, and GB(OBC)II) for determining the dimerization free energy (ΔG(0)) of β-cyclodextrin monomers in 17 implicit solvents with dielectric constants (D) ranging from 5 to 80 and compared the results to previous free energy calculations with explicit solvents ( Zhang et al. J. Phys. Chem. B 2012 , 116 , 12684 - 12693 ). The comparison indicates that neglecting the environmental dependence of Born radii appears acceptable for such calculations involving cyclodextrin and that the GB(Still) and GB(OBC)I models yield a reasonable estimation of ΔG(0), although the details of binding are quite different from explicit solvents. Large discrepancies between implicit and explicit solvent models occur in high-dielectric media with strong hydrogen bond (HB) interruption properties. ΔG(0) with the GB models is shown to correlate strongly to 2(D-1)/(2D+1) (R(2) ∼ 0.90) in line with the Onsager reaction field ( Onsager J. Am. Chem. Soc. 1936 , 58 , 1486 - 1493 ) but to be very sensitive to D (D < 10) as well. Both high-dielectric environments where hydrogen bonds are of interest and low-dielectric media such as protein binding pockets and membrane interiors therefore need to be considered with caution in GB-based calculations. Finally, a literature analysis of Gibbs energy of solvation of small molecules in organic liquids shows that the Onsager relation does not hold for real molecules since the correlation between ΔG(0) and 2(D-1)/(2D+1) is low for most solutes. Interestingly, explicit solvent calculations of the solvation free energy ( Zhang et al. J. Chem. Inf. Model . 2015 , 55 , 1192 - 1201 ) reproduce the weak experimental correlations with 2(D-1)/(2D+1) very well.

[1]  R. Bell,et al.  The electrostatic energy of dipole molecules in different media , 1931 .

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

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

[4]  S. Genheden,et al.  The MM/PBSA and MM/GBSA methods to estimate ligand-binding affinities , 2015, Expert opinion on drug discovery.

[5]  Franca Fraternali,et al.  Design and application of implicit solvent models in biomolecular simulations , 2014, Current opinion in structural biology.

[6]  István Horváth,et al.  Mobility-based prediction of hydration structures of protein surfaces , 2015, Bioinform..

[7]  C. Cézard,et al.  Molecular dynamics studies of native and substituted cyclodextrins in different media: 1. Charge derivation and force field performances. , 2011, Physical chemistry chemical physics : PCCP.

[8]  Christian Kramer,et al.  Improving Docking Results via Reranking of Ensembles of Ligand Poses in Multiple X-ray Protein Conformations with MM-GBSA , 2014, J. Chem. Inf. Model..

[9]  Haiyang Zhang,et al.  Quantification of Solvent Contribution to the Stability of Noncovalent Complexes. , 2013, Journal of chemical theory and computation.

[10]  T. Darden,et al.  A smooth particle mesh Ewald method , 1995 .

[11]  Peter M. Kasson,et al.  GROMACS 4.5: a high-throughput and highly parallel open source molecular simulation toolkit , 2013, Bioinform..

[12]  R. Swendsen,et al.  THE weighted histogram analysis method for free‐energy calculations on biomolecules. I. The method , 1992 .

[13]  A. Warshel,et al.  What are the dielectric “constants” of proteins and how to validate electrostatic models? , 2001, Proteins.

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

[15]  W. L. Jorgensen,et al.  Prediction of Properties from Simulations: Free Energies of Solvation in Hexadecane, Octanol, and Water , 2000 .

[16]  Guangying Chen,et al.  Crystal Structures of β‐Cyclodextrin Inclusion Complexes with 7‐Hydroxycoumarin and 4‐Hydroxycoumarin and Substituent Effects on Inclusion Geometry , 2011 .

[17]  Gregory D. Hawkins,et al.  Pairwise solute descreening of solute charges from a dielectric medium , 1995 .

[18]  Niu Huang,et al.  Physics-Based Scoring of Protein-Ligand Complexes: Enrichment of Known Inhibitors in Large-Scale Virtual Screening , 2006, J. Chem. Inf. Model..

[19]  Jurriaan Huskens,et al.  Beta-cyclodextrin host-guest complexes probed under thermodynamic equilibrium: thermodynamics and AFM force spectroscopy. , 2004, Journal of the American Chemical Society.

[20]  Michele Vendruscolo,et al.  Role of Intermolecular Forces in Defining Material Properties of Protein Nanofibrils , 2007, Science.

[21]  Michael Feig,et al.  Implicit solvation based on generalized Born theory in different dielectric environments. , 2004, The Journal of chemical physics.

[22]  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..

[23]  B. Lee,et al.  The interpretation of protein structures: estimation of static accessibility. , 1971, Journal of molecular biology.

[24]  Haiyang Zhang,et al.  Molecular recognition in different environments: β-cyclodextrin dimer formation in organic solvents. , 2012, The journal of physical chemistry. B.

[25]  Samuel Genheden,et al.  Comparison of MM/GBSA calculations based on explicit and implicit solvent simulations. , 2013, Physical chemistry chemical physics : PCCP.

[26]  Julien Michel,et al.  Protein-ligand binding affinity predictions by implicit solvent simulations: a tool for lead optimization? , 2006, Journal of medicinal chemistry.

[27]  D. Case,et al.  Theory and applications of the generalized born solvation model in macromolecular simulations , 2000, Biopolymers.

[28]  J. Andrew McCammon,et al.  Identification of Protein–Ligand Binding Sites by the Level-Set Variational Implicit-Solvent Approach , 2015, Journal of chemical theory and computation.

[29]  Samuel Genheden,et al.  Effect of explicit water molecules on ligand-binding affinities calculated with the MM/GBSA approach , 2014, Journal of Molecular Modeling.

[30]  Bert L. de Groot,et al.  g_wham—A Free Weighted Histogram Analysis Implementation Including Robust Error and Autocorrelation Estimates , 2010 .

[31]  L. Onsager.  Electric Moments of Molecules in Liquids , 1936 .

[32]  Z. Fan,et al.  Encapsulation of quinine by beta-cyclodextrin: excellent model for mimicking enzyme-substrate interactions. , 2006, The Journal of organic chemistry.

[33]  Solvation of a spherical cavity in simple liquids: interpolating between the limits. , 2009, The journal of physical chemistry. B.

[34]  Jin Zhang,et al.  Force Field Benchmark of Organic Liquids. 2. Gibbs Energy of Solvation , 2015, J. Chem. Inf. Model..

[35]  Thomas Gaillard,et al.  Evaluation of DNA Force Fields in Implicit Solvation. , 2011, Journal of chemical theory and computation.

[36]  Emil Alexov,et al.  Rapid grid‐based construction of the molecular surface and the use of induced surface charge to calculate reaction field energies: Applications to the molecular systems and geometric objects , 2002, J. Comput. Chem..

[37]  Giovanni Scalmani,et al.  Continuous surface charge polarizable continuum models of solvation. I. General formalism. , 2010, The Journal of chemical physics.

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

[39]  E. Lattman,et al.  High apparent dielectric constants in the interior of a protein reflect water penetration. , 2000, Biophysical journal.

[40]  Wim E Hennink,et al.  Cyclodextrin-based polymeric materials: synthesis, properties, and pharmaceutical/biomedical applications. , 2009, Biomacromolecules.

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

[42]  Barry Honig,et al.  Comparative study of generalized Born models: protein dynamics. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[43]  B. Hess.  Determining the shear viscosity of model liquids from molecular dynamics simulations , 2002 .

[44]  Charles L. Brooks,et al.  Surveying implicit solvent models for estimating small molecule absolute hydration free energies , 2011, J. Comput. Chem..

[45]  M. Parrinello,et al.  Canonical sampling through velocity rescaling. , 2007, The Journal of chemical physics.

[46]  He Huang,et al.  Folding Simulations for Proteins with Diverse Topologies Are Accessible in Days with a Physics-Based Force Field and Implicit Solvent , 2014, Journal of the American Chemical Society.

[47]  R. Zhou.  Free energy landscape of protein folding in water: Explicit vs. implicit solvent , 2003, Proteins.

[48]  Gerrit Groenhof,et al.  GROMACS: Fast, flexible, and free , 2005, J. Comput. Chem..

[49]  J. Tomasi,et al.  Quantum mechanical continuum solvation models. , 2005, Chemical reviews.

[50]  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.

[51]  H. Nymeyer,et al.  Simulation of the folding equilibrium of α-helical peptides: A comparison of the generalized Born approximation with explicit solvent , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[52]  Xiaohua Zhang,et al.  Toward Fully Automated High Performance Computing Drug Discovery: A Massively Parallel Virtual Screening Pipeline for Docking and Molecular Mechanics/Generalized Born Surface Area Rescoring to Improve Enrichment , 2014, J. Chem. Inf. Model..

[53]  Eric J. Sorin,et al.  Simulations of the role of water in the protein-folding mechanism. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[54]  Xiaoqin Zou,et al.  Electrostatics of ligand binding: parametrization of the generalized Born model and comparison with the Poisson-Boltzmann approach. , 2006, The journal of physical chemistry. B.

[55]  Gregory D. Hawkins,et al.  Parametrized Models of Aqueous Free Energies of Solvation Based on Pairwise Descreening of Solute Atomic Charges from a Dielectric Medium , 1996 .

[56]  Jeremy C. Smith,et al.  Can the calculation of ligand binding free energies be improved with continuum solvent electrostatics and an ideal‐gas entropy correction? , 2002, J. Comput. Chem..

[57]  Carlos Simmerling,et al.  Improved Generalized Born Solvent Model Parameters for Protein Simulations. , 2013, Journal of chemical theory and computation.

[58]  Carsten Kutzner,et al.  GROMACS 4:  Algorithms for Highly Efficient, Load-Balanced, and Scalable Molecular Simulation. , 2008, Journal of chemical theory and computation.

[59]  K. Sharp,et al.  Potential energy functions for protein design. , 2007, Current opinion in structural biology.

[60]  Christophe Chipot,et al.  Molecular dynamics study of the inclusion of cholesterol into cyclodextrins. , 2006, The journal of physical chemistry. B.

[61]  V. Pande,et al.  Absolute comparison of simulated and experimental protein-folding dynamics , 2002, Nature.

[62]  P. Koehl.  Electrostatics calculations: latest methodological advances. , 2006, Current opinion in structural biology.

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

[64]  T. Darden,et al.  Particle mesh Ewald: An N⋅log(N) method for Ewald sums in large systems , 1993 .

[65]  W. C. Still,et al.  The GB/SA Continuum Model for Solvation. A Fast Analytical Method for the Calculation of Approximate Born Radii , 1997 .

[66]  M. Karplus,et al.  Solution conformations and thermodynamics of structured peptides: molecular dynamics simulation with an implicit solvation model. , 1998, Journal of molecular biology.

[67]  M. Jacobson,et al.  Molecular mechanics methods for predicting protein-ligand binding. , 2006, Physical chemistry chemical physics : PCCP.

[68]  Martin Karplus,et al.  A Smooth Solvation Potential Based on the Conductor-Like Screening Model , 1999 .

[69]  Carl Caleman,et al.  Thermodynamics of hydronium and hydroxide surface solvation. , 2014 .

[70]  M. Feig,et al.  A generalized Born formalism for heterogeneous dielectric environments: application to the implicit modeling of biological membranes. , 2005, The Journal of chemical physics.

[71]  M. Zacharias,et al.  Evaluation of Generalized Born Model Accuracy for Absolute Binding Free Energy Calculations. , 2014, The journal of physical chemistry. B.

[72]  Erik Lindahl,et al.  A high‐performance parallel‐generalized born implementation enabled by tabulated interaction rescaling , 2010, J. Comput. Chem..