An improved fragment-based quantum mechanical method for calculation of electrostatic solvation energy of proteins.

An efficient approach that combines the electrostatically embedded generalized molecular fractionation with conjugate caps (EE-GMFCC) method with conductor-like polarizable continuum model (CPCM), termed EE-GMFCC-CPCM, is developed for ab initio calculation of the electrostatic solvation energy of proteins. Compared with the previous MFCC-CPCM study [Y. Mei, C. G. Ji, and J. Z. H. Zhang, J. Chem. Phys. 125, 094906 (2006)], quantum mechanical (QM) calculation is applied to deal with short-range non-neighboring interactions replacing the classical treatment. Numerical studies are carried out for proteins up to 3837 atoms at the HF/6-31G* level. As compared to standard full system CPCM calculations, EE-GMFCC-CPCM shows clear improvement over the MFCC-CPCM method for both the total electrostatic solvation energy and its components (the polarized solute-solvent reaction field energy and wavefunction distortion energy of the solute). For large proteins with 1000-4000 atoms, where the standard full system ab initio CPCM calculations are not affordable, the EE-GMFCC-CPCM gives larger relative wavefunction distortion energies and weaker relative electrostatic solvation energies for proteins, as compared to the corresponding energies calculated by the Divide-and-Conquer Poisson-Boltzmann (D&C-PB) method. Notwithstanding, a high correlation between EE-GMFCC-CPCM and D&C-PB is observed. This study demonstrates that the linear-scaling EE-GMFCC-CPCM approach is an accurate and also efficient method for the calculation of electrostatic solvation energy of proteins.

[1]  Yuto Komeiji,et al.  Change in a protein's electronic structure induced by an explicit solvent: An ab initio fragment molecular orbital study of ubiquitin , 2007, J. Comput. Chem..

[2]  K. Kitaura,et al.  Fragment molecular orbital method: an approximate computational method for large molecules , 1999 .

[3]  Paul G. Mezey,et al.  Ab Initio-Quality Electrostatic Potentials for Proteins: An Application of the ADMA Approach , 2002 .

[4]  Ye Mei,et al.  A new quantum method for electrostatic solvation energy of protein. , 2006, The Journal of chemical physics.

[5]  Jacopo Tomasi,et al.  Remarks on the use of the apparent surface charges (ASC) methods in solvation problems: Iterative versus matrix‐inversion procedures and the renormalization of the apparent charges , 1995, J. Comput. Chem..

[6]  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 .

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

[8]  H. Berendsen,et al.  Molecular dynamics with coupling to an external bath , 1984 .

[9]  Drug target interaction energies by the kernel energy method in aminoglycoside drugs and ribosomal A site RNA targets , 2007, Proceedings of the National Academy of Sciences.

[10]  P. Bandyopadhyay.  Assessment of Two Surface Monte Carlo (TSMC) method to find stationary points of (H2O)15 and (H2O)20 clusters , 2008 .

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

[12]  Xiao He,et al.  Electrostatically embedded generalized molecular fractionation with conjugate caps method for full quantum mechanical calculation of protein energy. , 2013, The journal of physical chemistry. A.

[13]  Kazuo Kitaura,et al.  Extending the power of quantum chemistry to large systems with the fragment molecular orbital method. , 2007, The journal of physical chemistry. A.

[14]  G. Hummer,et al.  Optimized molecular dynamics force fields applied to the helix-coil transition of polypeptides. , 2009, The journal of physical chemistry. B.

[15]  M. Parrinello,et al.  Sampling protein motion and solvent effect during ligand binding , 2012, Proceedings of the National Academy of Sciences.

[16]  Donald G Truhlar,et al.  Electrostatically Embedded Molecular Tailoring Approach and Validation for Peptides. , 2013, Journal of chemical theory and computation.

[17]  C. Cramer,et al.  Universal solvation model based on solute electron density and on a continuum model of the solvent defined by the bulk dielectric constant and atomic surface tensions. , 2009, The journal of physical chemistry. B.

[18]  Michael A Collins,et al.  Accuracy and efficiency of electronic energies from systematic molecular fragmentation. , 2006, The Journal of chemical physics.

[19]  Kaori Fukuzawa,et al.  Possibility of mutation prediction of influenza hemagglutinin by combination of hemadsorption experiment and quantum chemical calculation for antibody binding. , 2009, The journal of physical chemistry. B.

[20]  Paul G. Mezey,et al.  The Field-Adapted ADMA Approach: Introducing Point Charges , 2004 .

[21]  Spencer R Pruitt,et al.  Fragmentation methods: a route to accurate calculations on large systems. , 2012, Chemical reviews.

[22]  Holger Gohlke,et al.  The Amber biomolecular simulation programs , 2005, J. Comput. Chem..

[23]  Jacopo Tomasi,et al.  Molecular Interactions in Solution: An Overview of Methods Based on Continuous Distributions of the Solvent , 1994 .

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

[25]  Adrien Marchand,et al.  Mass spectrometry and ion mobility spectrometry of G-quadruplexes. A study of solvent effects on dimer formation and structural transitions in the telomeric DNA sequence d(TAGGGTTAGGGT). , 2012, Methods.

[26]  V. Barone,et al.  Quantum Calculation of Molecular Energies and Energy Gradients in Solution by a Conductor Solvent Model , 1998 .

[27]  Jan H. Jensen,et al.  Continuum solvation of large molecules described by QM/MM: a semi-iterative implementation of the PCM/EFP interface , 2003 .

[28]  Jacopo Tomasi,et al.  A new integral equation formalism for the polarizable continuum model: Theoretical background and applications to isotropic and anisotropic dielectrics , 1997 .

[29]  Shridhar R. Gadre,et al.  Ab initio quality one‐electron properties of large molecules: Development and testing of molecular tailoring approach , 2003, J. Comput. Chem..

[30]  P. Mezey,et al.  Evaluation of the field-adapted ADMA approach: absolute and relative energies of crambin and derivatives. , 2005, Physical chemistry chemical physics : PCCP.

[31]  Giovanni Scalmani,et al.  Energies, structures, and electronic properties of molecules in solution with the C‐PCM solvation model , 2003, J. Comput. Chem..

[32]  X. Chen,et al.  Molecular fractionation with conjugated caps density matrix with pairwise interaction correction for protein energy calculation. , 2006, The Journal of chemical physics.

[33]  M. Karplus,et al.  A Comprehensive Analytical Treatment of Continuum Electrostatics , 1996 .

[34]  Xiao He,et al.  A new method for direct calculation of total energy of protein. , 2005, The Journal of chemical physics.

[35]  V Ganesh,et al.  Molecular tailoring approach for geometry optimization of large molecules: energy evaluation and parallelization strategies. , 2006, The Journal of chemical physics.

[36]  C. Cramer,et al.  Implicit Solvation Models: Equilibria, Structure, Spectra, and Dynamics. , 1999, Chemical reviews.

[37]  Christian Silvio Pomelli,et al.  Recent Advances in the Description of Solvent Effects with the Polarizable Continuum Model , 1998 .

[38]  Heather Netzloff,et al.  Ab initio energies of nonconducting crystals by systematic fragmentation. , 2007, The Journal of chemical physics.

[39]  Wei Li,et al.  Generalized energy-based fragmentation approach for computing the ground-state energies and properties of large molecules. , 2007, The journal of physical chemistry. A.

[40]  John Z H Zhang,et al.  An efficient approach for ab initio energy calculation of biopolymers. , 2005, The Journal of chemical physics.

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

[42]  A. Imamura,et al.  Efficient and accurate calculations on the electronic structure of B-type poly(dG).poly(dC) DNA by elongation method: first step toward the understanding of the biological properties of aperiodic DNA. , 2007, The Journal of chemical physics.

[43]  Yun Xiang,et al.  Quantum study of mutational effect in binding of efavirenz to HIV‐1 RT , 2005, Proteins.

[44]  Kaori Fukuzawa,et al.  Fragment molecular orbital method: use of approximate electrostatic potential , 2002 .

[45]  Donald G Truhlar,et al.  Electrostatically Embedded Many-Body Correlation Energy, with Applications to the Calculation of Accurate Second-Order Møller-Plesset Perturbation Theory Energies for Large Water Clusters. , 2007, Journal of chemical theory and computation.

[46]  Yingkai Zhang,et al.  An efficient linear scaling method for ab initio calculation of electron density of proteins , 2004 .

[47]  Iñaki Tuñón,et al.  GEPOL: An improved description of molecular surfaces. III. A new algorithm for the computation of a solvent‐excluding surface , 1994, J. Comput. Chem..

[48]  Donald G Truhlar,et al.  Application of the Electrostatically Embedded Many-Body Expansion to Microsolvation of Ammonia in Water Clusters. , 2008, Journal of chemical theory and computation.

[49]  Shridhar R. Gadre,et al.  Tailoring approach for exploring electron densities and electrostatic potentials of molecular crystals , 2004 .

[50]  Xiao He,et al.  Quantum computational analysis for drug resistance of HIV‐1 reverse transcriptase to nevirapine through point mutations , 2005, Proteins.

[51]  Angel E Garcia,et al.  Simulation studies of protein folding/unfolding equilibrium under polar and nonpolar confinement. , 2011, Journal of the American Chemical Society.

[52]  Xiang Zhu,et al.  Effects of solvent on weak halogen bonds: Density functional theory calculations , 2012 .

[53]  M Scott Shell,et al.  Convergence and Heterogeneity in Peptide Folding with Replica Exchange Molecular Dynamics. , 2009, Journal of chemical theory and computation.

[54]  Nicholas J Mayhall,et al.  Many-Overlapping-Body (MOB) Expansion: A Generalized Many Body Expansion for Nondisjoint Monomers in Molecular Fragmentation Calculations of Covalent Molecules. , 2012, Journal of chemical theory and computation.

[55]  Xiao He,et al.  The generalized molecular fractionation with conjugate caps/molecular mechanics method for direct calculation of protein energy. , 2006, The Journal of chemical physics.

[56]  Martin Lepšík,et al.  Assessing the accuracy and performance of implicit solvent models for drug molecules: conformational ensemble approaches. , 2013, The journal of physical chemistry. B.

[57]  John Z. H. Zhang,et al.  Molecular fractionation with conjugate caps for full quantum mechanical calculation of protein-molecule interaction energy , 2003 .

[58]  Wei Li,et al.  An efficient fragment-based approach for predicting the ground-state energies and structures of large molecules. , 2005, Journal of the American Chemical Society.

[59]  Donald G Truhlar,et al.  Electrostatically Embedded Many-Body Expansion for Large Systems, with Applications to Water Clusters. , 2007, Journal of chemical theory and computation.

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

[61]  Ye Mei,et al.  Folding of a helix is critically stabilized by polarization of backbone hydrogen bonds: study in explicit water. , 2012, The journal of physical chemistry. B.

[62]  Ye Mei,et al.  Developing polarized protein-specific charges for protein dynamics: MD free energy calculation of pKa shifts for Asp26/Asp20 in thioredoxin. , 2008, Biophysical journal.

[63]  P. N. Day,et al.  A study of water clusters using the effective fragment potential and Monte Carlo simulated annealing , 2000 .

[64]  Hui Li,et al.  The polarizable continuum model (PCM) interfaced with the fragment molecular orbital method (FMO) , 2006, J. Comput. Chem..

[65]  Mark S Gordon,et al.  Systematic fragmentation method and the effective fragment potential: an efficient method for capturing molecular energies. , 2009, The journal of physical chemistry. A.

[66]  Richard Barrett,et al.  Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods , 1994, Other Titles in Applied Mathematics.

[67]  B. Honig,et al.  Accurate First Principles Calculation of Molecular Charge Distributions and Solvation Energies from Ab Initio Quantum Mechanics and Continuum Dielectric Theory , 1994 .

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

[69]  John M. Herbert,et al.  Polarizable Continuum Reaction-Field Solvation Models Affording Smooth Potential Energy Surfaces , 2010 .

[70]  John F. Ouyang,et al.  Combined Fragmentation Method: A Simple Method for Fragmentation of Large Molecules. , 2012, Journal of chemical theory and computation.

[71]  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 .

[72]  Kenneth M. Merz,et al.  Fully Quantum Mechanical Description of Proteins in Solution. Combining Linear Scaling Quantum Mechanical Methodologies with the Poisson−Boltzmann Equation , 1999 .

[73]  Michael A Collins,et al.  Approximate ab initio energies by systematic molecular fragmentation. , 2005, The Journal of chemical physics.

[74]  Jacopo Tomasi,et al.  A new definition of cavities for the computation of solvation free energies by the polarizable continuum model , 1997 .

[75]  B. Brooks,et al.  An analysis of the accuracy of Langevin and molecular dynamics algorithms , 1988 .

[76]  Shuhua Li,et al.  An efficient implementation of the generalized energy-based fragmentation approach for general large molecules. , 2010, The journal of physical chemistry. A.

[77]  Kazuo Kitaura,et al.  Role of the key mutation in the selective binding of avian and human influenza hemagglutinin to sialosides revealed by quantum-mechanical calculations. , 2010, Journal of the American Chemical Society.

[78]  Richard A. Friesner,et al.  Solvation Free Energies of Peptides: Comparison of Approximate Continuum Solvation Models with Accurate Solution of the Poisson−Boltzmann Equation , 1997 .

[79]  Kenneth M. Merz,et al.  Importance of dispersion and electron correlation in ab initio protein folding. , 2009, The journal of physical chemistry. B.

[80]  F. Javier Luque,et al.  Solvation in octanol: parametrization of the continuum MST model , 2001, J. Comput. Chem..

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

[82]  Kazuo Kitaura,et al.  Structural and interaction analysis of helical heparin oligosaccharides with the fragment molecular orbital method , 2009 .

[83]  K. Wiberg,et al.  Solvent Effects. 5. Influence of Cavity Shape, Truncation of Electrostatics, and Electron Correlation on ab Initio Reaction Field Calculations , 1996 .

[84]  Kenneth M Merz,et al.  Divide-and-Conquer Hartree-Fock Calculations on Proteins. , 2010, Journal of chemical theory and computation.

[85]  A. Klamt,et al.  COSMO : a new approach to dielectric screening in solvents with explicit expressions for the screening energy and its gradient , 1993 .

[86]  So Hirata,et al.  Second-order many-body perturbation study of ice Ih. , 2012, The Journal of chemical physics.