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Papers by Demian Riccardi

The Journal of Physical Chemistry B, Jun 1, 2004

The importance of accurately treating van der Waals interactions between the quantum mechanical (... more The importance of accurately treating van der Waals interactions between the quantum mechanical (QM) and molecular mechanical (MM) atoms in hybrid QM/MM simulations has been investigated systematically. First, a set of van der Waals (vdW) parameters was optimized for an approximate density functional method, the self-consistent charge-tight binding density functional (SCC-DFTB) approach, based on small hydrogenbonding clusters. The sensitivity of condensed phase observables to the SCC-DFTB vdW parameters was then quantitatively investigated by SCC-DFTB/MM simulations of several model systems using the optimized set and two sets of extreme vdW parameters selected from the CHARMM22 forcefield. The model systems include a model FAD molecule in solution and a solvated enediolate, and the properties studied include the radial distribution functions of water molecules around the solute (model FAD and enediolate), the reduction potential of the model FAD and the potential of mean force for an intramolecular proton transfer in the enediolate. Although there are noticeable differences between parameter sets for gas-phase clusters and solvent structures around the solute, thermodynamic quantities in the condensed phase (e.g., reduction potential and potential of mean force) were found to be less sensitive to the numerical values of vdW parameters. The differences between SCC-DFTB/MM results with the three vdW parameter sets for SCC-DFTB atoms were explained in terms of the effects of the parameter set on solvation. The current study has made it clear that efforts in improving the reliability of QM/MM methods for energetical properties in the condensed phase should focus on components other than van der Waals interactions between QM and MM atoms.

Biochemistry Usa, Mar 1, 2008

Combined quantum mechanical/molecular mechanical (QM/MM) simulations are carried out to analyze f... more Combined quantum mechanical/molecular mechanical (QM/MM) simulations are carried out to analyze factors that dictate the proton transfer in carbonic anhydrase II (CAII), an enzyme that has been used as a prototypical example of long-range proton transfers in biomolecules. In contrast to the long-held conjecture in the experimental literature, the computed potentials of mean force (PMF) suggest that the proton transfer in CAII is not very sensitive to the orientation of the acceptor group (His 64) and, therefore, the number of water molecules that bridge the donor (zinc-water) and acceptor groups. Perturbative analysis indicates that a series of polar and charged residues close to the transfer pathways make the dominant contribution to the barrier and exothermicity of the proton transfer reaction, thus supporting the proposal from previous studies of Warshel and co-workers using a somewhat simpler QM/MM model that electrostatic interactions play a major role in the proton transfer in CAII. The PMF results are in striking contrast to previous analysis using the same QM/MM method but an ensemble of minimum energy path (MEP) calculations, which found a steep dependence of the barrier height on the number of bridging water molecules. Analysis of the configurations sampled in the PMF and MEP simulations suggests that this difference arises because the PMF simulations sample a largely stepwise mechanism while the local MEP calculations artificially favored concerted transfers due to the specific protocol used to generate the initial configurations. Therefore, this study presents a compelling argument for carrying out proper conformational sampling in the study of long-range proton transfers. Finally, we illustrate that Phi analysis, which has been widely used in protein folding studies, can potentially generate new mechanistic information for long-range proton transfers regarding the sequence of events. The results of the perturbation analysis and the Phi analysis provide opportunities for experimentally testing the mechanistic proposals from this study and our recent work in which a stepwise "proton hole" transfer pathway has been proposed.

J Phys Chem B, 2005

The accuracy of biological simulations depends, in large part, on the treatment of electrostatics... more The accuracy of biological simulations depends, in large part, on the treatment of electrostatics. Due to the availability of accurate experimental values, calculation of pK a provides stringent evaluation of computational methods. The generalized solvent boundary potential (GSBP) and Ewald summation electrostatic treatments were recently implemented for combined quantum mechanical and molecular mechanics (QM/MM) simulations by our group. These approaches were tested by calculating pK a shifts due to differences in electronic structure and electrostatic environment; the shifts were determined for a series of small molecules in solution, using various electrostatic treatments, and two residues (His 31, Lys 102) in the M102K T4-lysozyme mutant with large pK a shifts, using the GSBP approach. The calculations utilized a free energy perturbation scheme with the QM/MM potential function involving the self-consistent charge density functional tight binding (SCC-DFTB) and CHARMM as the QM and MM methods, respectively. The study of small molecules demonstrated that inconsistent electrostatic models produced results that were difficult to correct in a robust manner; by contrast, extended electrostatics, GSBP, and Ewald simulations produced consistent results once a bulk solvation contribution was carefully chosen. In addition to the electrostatic treatment, the pK a shifts were also sensitive to the level of the QM method and the scheme of treating QM/MM Coulombic interactions; however, simple perturbative corrections based on SCC-DFTB/CHARMM trajectories and higher level single point energy calculations were found to give satisfactory results. Combining all factors gave a root-mean-square difference of 0.7 pK a units for the relative pK a values of the small molecules compared to experiment. For the residues in the lysozyme, an accurate pK a shift was obtained for His 31 with multiple nanosecond simulations. For Lys 102, however, the pK a shift was estimated to be too large, even after more than 10 nanosecond simulations for each λ window; the difficulty was due to the significant, but slow, reorganization of the protein and water structure when Lys 102 was protonated. The simulations support that Lys 102 is deprotonated in the X-ray structure and the protein is highly destabilized when this residue is protonated.

Implicit dielectric solvent models have been developed in an effort to funnel computational resou... more Implicit dielectric solvent models have been developed in an effort to funnel computational resources to the solvated molecules of interest. More recently, the quasi-chemical theory developed by L. R. Pratt and S. Rempe provided a systematic way of including the most important solvent contributions to calculations of the chemical potential for the solute. The present work applies this theory to

J Phys Chem a, 2002

Quasi-chemical theory and electronic structure results on inner-sphere H(H 2 O) n + clusters are ... more Quasi-chemical theory and electronic structure results on inner-sphere H(H 2 O) n + clusters are used to discuss the absolute hydration free energy of H + (aq). It is noted that this quantity is not thermodynamically measurable, and this leads to some relative misalignment of available tables of absolute hydration free energies of ions in water. The simplest quasi-chemical model produces a reasonable quantitative result in the range of -256 to -251 kcal/mol. The primitive concepts on which the model is based naturally identify the Zundel cation H 5 O 2 + as the principal chemical structure contributing to this hydration free energy. The specific participation of an Eigen cation H 9 O 4 + is not required in this model because the definition of that structure depends on outer-sphere arrangements, and a crude dielectric continuum model is here used for outer-sphere contributions.

Science China Chemistry, 2011

ABSTRACT Implicit dielectric solvent models have been developed in an effort to funnel computatio... more ABSTRACT Implicit dielectric solvent models have been developed in an effort to funnel computational resources to the solvated molecules of interest. More recently, the quasi-chemical theory developed by L. R. Pratt and S. Rempe provided a systematic way of including the most important solvent contributions to calculations of the chemical potential for the solute. The present work applies this theory to aqueous proton solvation. Hydronium and zundel are the most important clusters to consider since the oxygens are within the first solvation shell. The gas phase Gibbs free energies for these species are calculated using Gaussian98 including normal mode zero point energy. The effect of using anharmonic vibrational energies from Diffusion Monte Carlo calculations is investigated. From the free energies and the dielectric solvation chemical potential of protonated water clusters, the solvation free energy of a proton is obtained. These results are useful in understanding the inherent geometry of aqueous proton solvation.

The Journal of Physical Chemistry B, 2005

The accuracy of biological simulations depends, in large part, on the treatment of electrostatics... more The accuracy of biological simulations depends, in large part, on the treatment of electrostatics. Due to the availability of accurate experimental values, calculation of pK a provides stringent evaluation of computational methods. The generalized solvent boundary potential (GSBP) and Ewald summation electrostatic treatments were recently implemented for combined quantum mechanical and molecular mechanics (QM/MM) simulations by our group. These approaches were tested by calculating pK a shifts due to differences in electronic structure and electrostatic environment; the shifts were determined for a series of small molecules in solution, using various electrostatic treatments, and two residues (His 31, Lys 102) in the M102K T4-lysozyme mutant with large pK a shifts, using the GSBP approach. The calculations utilized a free energy perturbation scheme with the QM/MM potential function involving the self-consistent charge density functional tight binding (SCC-DFTB) and CHARMM as the QM and MM methods, respectively. The study of small molecules demonstrated that inconsistent electrostatic models produced results that were difficult to correct in a robust manner; by contrast, extended electrostatics, GSBP, and Ewald simulations produced consistent results once a bulk solvation contribution was carefully chosen. In addition to the electrostatic treatment, the pK a shifts were also sensitive to the level of the QM method and the scheme of treating QM/MM Coulombic interactions; however, simple perturbative corrections based on SCC-DFTB/CHARMM trajectories and higher level single point energy calculations were found to give satisfactory results. Combining all factors gave a root-mean-square difference of 0.7 pK a units for the relative pK a values of the small molecules compared to experiment. For the residues in the lysozyme, an accurate pK a shift was obtained for His 31 with multiple nanosecond simulations. For Lys 102, however, the pK a shift was estimated to be too large, even after more than 10 nanosecond simulations for each λ window; the difficulty was due to the significant, but slow, reorganization of the protein and water structure when Lys 102 was protonated. The simulations support that Lys 102 is deprotonated in the X-ray structure and the protein is highly destabilized when this residue is protonated.

The Journal of Physical Chemistry B, 2004

The importance of accurately treating van der Waals interactions between the quantum mechanical (... more The importance of accurately treating van der Waals interactions between the quantum mechanical (QM) and molecular mechanical (MM) atoms in hybrid QM/MM simulations has been investigated systematically. First, a set of van der Waals (vdW) parameters was optimized for an approximate density functional method, the self-consistent charge-tight binding density functional (SCC-DFTB) approach, based on small hydrogenbonding clusters. The sensitivity of condensed phase observables to the SCC-DFTB vdW parameters was then quantitatively investigated by SCC-DFTB/MM simulations of several model systems using the optimized set and two sets of extreme vdW parameters selected from the CHARMM22 forcefield. The model systems include a model FAD molecule in solution and a solvated enediolate, and the properties studied include the radial distribution functions of water molecules around the solute (model FAD and enediolate), the reduction potential of the model FAD and the potential of mean force for an intramolecular proton transfer in the enediolate. Although there are noticeable differences between parameter sets for gas-phase clusters and solvent structures around the solute, thermodynamic quantities in the condensed phase (e.g., reduction potential and potential of mean force) were found to be less sensitive to the numerical values of vdW parameters. The differences between SCC-DFTB/MM results with the three vdW parameter sets for SCC-DFTB atoms were explained in terms of the effects of the parameter set on solvation. The current study has made it clear that efforts in improving the reliability of QM/MM methods for energetical properties in the condensed phase should focus on components other than van der Waals interactions between QM and MM atoms.

The Journal of Physical Chemistry A, 2002

Quasi-chemical theory and electronic structure results on inner-sphere H(H 2 O) n + clusters are ... more Quasi-chemical theory and electronic structure results on inner-sphere H(H 2 O) n + clusters are used to discuss the absolute hydration free energy of H + (aq). It is noted that this quantity is not thermodynamically measurable, and this leads to some relative misalignment of available tables of absolute hydration free energies of ions in water. The simplest quasi-chemical model produces a reasonable quantitative result in the range of -256 to -251 kcal/mol. The primitive concepts on which the model is based naturally identify the Zundel cation H 5 O 2 + as the principal chemical structure contributing to this hydration free energy. The specific participation of an Eigen cation H 9 O 4 + is not required in this model because the definition of that structure depends on outer-sphere arrangements, and a crude dielectric continuum model is here used for outer-sphere contributions.

The Journal of Physical Chemistry A, 2007

To quantitatively explore the applicability of the Generalized Solvent Boundary Potential (GSBP) ... more To quantitatively explore the applicability of the Generalized Solvent Boundary Potential (GSBP) based QM/MM approach as a "multi-scale" framework for studying chemical reactions in biomolecules, the structural and energetic properties of the Human Carbonic Anhydrase II (CAII) are analyzed and compared to those from periodic boundary condition (PBC) simulations and available experimental data. Although the atomic fluctuations from GSBP based simulations are consistently lower compared to those from PBC simulations or crystallographic data, the fluctuations and internal coordinate distributions for residues in the proximity of the active site as well as diffusion constants of active-site water molecules are fairly well described by GSBP simulations.

Physical Chemistry Chemical Physics, 2005

Benchmark calculations of proton affinities and gas-phase basicities of molecules most relevant t... more Benchmark calculations of proton affinities and gas-phase basicities of molecules most relevant to biological phosphoryl transfer reactions are presented and compared with available experimental results. The accuracy of proton affinity and gas-phase basicity results obtained from several multi-level model chemistries (CBS-QB3, G3B3, and G3MP2B3) and density-functional quantum models (PBE0, B1B95, and B3LYP) are assessed and compared. From these data, a set of empirical bond enthalpy, entropy, and free energy corrections are introduced that considerably improve the accuracy and predictive capability of the methods. These corrections are applied to the prediction of proton affinity and gas-phase basicity values of important biological phosphates and phosphoranes for which experimental data does not currently exist. Comparison is made with results from semiempirical quantum models that are commonly employed in hybrid quantum mechanical/molecular mechanical simulations. Data suggest that the design of improved semiempirical quantum models with increased accuracy for relative proton affinity values is necessary to obtain quantitative accuracy for phosphoryl transfer reactions in solution, enzymes, and ribozymes.

The Journal of Chemical Physics, 2005

Biophysical Journal, 2010

In this study, the variance-covariance matrix of protein motions is used to compare several elast... more In this study, the variance-covariance matrix of protein motions is used to compare several elastic network models within the theoretical framework of X-ray scattering from crystals. A set of 33 ultra-high resolution structures is used to characterize the average scaling behavior of the vibrational density of states and make comparisons between experimental and theoretical temperature factors. Detailed investigations of the vibrational density of states, correlations, and predicted diffuse X-ray scatter are carried out for crystalline Staphylococcal nuclease; correlations and diffuse X-ray scatter are also compared to predictions from the TLS (translation, libration, screw) model and a liquidlike dynamics model. We show that elastic network models developed to best predict temperature factors without regard for the crystal environment have relatively strong long-range interactions that yield very short-ranged atom-atom correlations. Further, we find that the the low-frequency modes dominate the variance-covariance matrix only for those models with a physically reasonable vibrational density of states, and the fraction of modes required to converge the correlations is higher than that typically used for elastic network model studies. The practical implications are explored using computed diffuse X-ray scatter, which can be measured experimentally.

Biophysical Journal, 2009

Normal mode analysis using elastic network models has grown popular for probing the low-frequency... more Normal mode analysis using elastic network models has grown popular for probing the low-frequency collective dynamics of proteins and other biomolecular assemblies. In most previous studies, these models were validated by comparing calculated atomic fluctuations for isolated proteins with experimental temperature factors determined in the crystalline state, although there were also hints that including crystal contacts in the calculations has an impact on the comparison. In this study, a set of 83 ultra high resolution crystal structures with experimentally determined anisotropic displacement parameters (ADPs) is used to evaluate several C α -based elastic network models that either ignore or treat the crystal environment in different ways; the latter include using periodic boundary conditions defined with respect to the asymmetric unit or the primitive unit cell as well as using the Born-von Kármán boundary condition that accounts for lattice vibrations. For all elastic network models, treating the crystal environment leads to better agreement with experimental ADPs with the Born-von Kármán boundary condition giving the best agreement. Atomic correlations over the entire protein are clearly affected by the presence of the crystal contacts and fairly sensitive to the way that the crystal environment is treated. These observations highlight the importance of properly treating the protein system in an environment consistent with experiment when either evaluating approximate protein models or using approximate dynamic models in structural refinment type of applications. Finally, investigation of the scaling behaviors of the cumulative density of states and the heat capacity indicates that there are still gaps between simplified elastic models and all-atom models for proteins.

Biochemistry, 2008

Combined quantum mechanical/molecular mechanical (QM/MM) simulations are carried out to analyze f... more Combined quantum mechanical/molecular mechanical (QM/MM) simulations are carried out to analyze factors that dictate the proton transfer in carbonic anhydrase II (CAII), an enzyme that has been used as a prototypical example of long-range proton transfers in biomolecules. In contrast to the long-held conjecture in the experimental literature, the computed potentials of mean force (PMF) suggest that the proton transfer in CAII is not very sensitive to the orientation of the acceptor group (His 64) and, therefore, the number of water molecules that bridge the donor (zinc-water) and acceptor groups. Perturbative analysis indicates that a series of polar and charged residues close to the transfer pathways make the dominant contribution to the barrier and exothermicity of the proton transfer reaction, thus supporting the proposal from previous studies of Warshel and co-workers using a somewhat simpler QM/MM model that electrostatic interactions play a major role in the proton transfer in CAII. The PMF results are in striking contrast to previous analysis using the same QM/MM method but an ensemble of minimum energy path (MEP) calculations, which found a steep dependence of the barrier height on the number of bridging water molecules. Analysis of the configurations sampled in the PMF and MEP simulations suggests that this difference arises because the PMF simulations sample a largely stepwise mechanism while the local MEP calculations artificially favored concerted transfers due to the specific protocol used to generate the initial configurations. Therefore, this study presents a compelling argument for carrying out proper conformational sampling in the study of long-range proton transfers. Finally, we illustrate that Phi analysis, which has been widely used in protein folding studies, can potentially generate new mechanistic information for long-range proton transfers regarding the sequence of events. The results of the perturbation analysis and the Phi analysis provide opportunities for experimentally testing the mechanistic proposals from this study and our recent work in which a stepwise "proton hole" transfer pathway has been proposed.

Biochimica et Biophysica Acta (BBA) - Proteins and Proteomics, 2010

Recent QM/MM analyses of proton transfer function of human carbonic anhydrase II (CAII) are brief... more Recent QM/MM analyses of proton transfer function of human carbonic anhydrase II (CAII) are briefly reviewed. The topics include a preliminary analysis of nuclear quadrupole coupling constant calculations for the zinc ion and more detailed analyses of microscopic pK(a) of the zinc-bound water and free energy profile for the proton transfer. From a methodological perspective, our results emphasize that performing sufficient sampling is essential to the calculation of all these quantities, which reflects the well solvated nature of CAII active site. From a mechanistic perspective, our analyses highlight the importance of electrostatics in shaping the energetics and kinetics of proton transfer in CAII for its function. We argue that once the pK(a) for the zinc-bound water is modulated to be in the proper range (approximately 7.0), proton transfer through a relatively well solvated cavity towards/from the protein surface (His64) does not require any major acceleration. Therefore, although structural details like the length of the water wire between the donor and acceptor groups still may make a non-negligible contribution, our computational results and the framework of analysis suggest that the significance of such "fine-tuning" is likely secondary to the modulation of pK(a) of the zinc-bound water. We encourage further experimental analysis with mutation of (charged) residues not in the immediate neighborhood of the zinc ion to quantitatively test this electrostatics based framework; in particular, Phi analysis based on these mutations may shed further light into the relative importance of the classical Grotthus mechanism and the "proton hole" pathway that we have proposed recently for CAII.

The Journal of Physical Chemistry B, Jun 1, 2004

The importance of accurately treating van der Waals interactions between the quantum mechanical (... more The importance of accurately treating van der Waals interactions between the quantum mechanical (QM) and molecular mechanical (MM) atoms in hybrid QM/MM simulations has been investigated systematically. First, a set of van der Waals (vdW) parameters was optimized for an approximate density functional method, the self-consistent charge-tight binding density functional (SCC-DFTB) approach, based on small hydrogenbonding clusters. The sensitivity of condensed phase observables to the SCC-DFTB vdW parameters was then quantitatively investigated by SCC-DFTB/MM simulations of several model systems using the optimized set and two sets of extreme vdW parameters selected from the CHARMM22 forcefield. The model systems include a model FAD molecule in solution and a solvated enediolate, and the properties studied include the radial distribution functions of water molecules around the solute (model FAD and enediolate), the reduction potential of the model FAD and the potential of mean force for an intramolecular proton transfer in the enediolate. Although there are noticeable differences between parameter sets for gas-phase clusters and solvent structures around the solute, thermodynamic quantities in the condensed phase (e.g., reduction potential and potential of mean force) were found to be less sensitive to the numerical values of vdW parameters. The differences between SCC-DFTB/MM results with the three vdW parameter sets for SCC-DFTB atoms were explained in terms of the effects of the parameter set on solvation. The current study has made it clear that efforts in improving the reliability of QM/MM methods for energetical properties in the condensed phase should focus on components other than van der Waals interactions between QM and MM atoms.

Biochemistry Usa, Mar 1, 2008

Combined quantum mechanical/molecular mechanical (QM/MM) simulations are carried out to analyze f... more Combined quantum mechanical/molecular mechanical (QM/MM) simulations are carried out to analyze factors that dictate the proton transfer in carbonic anhydrase II (CAII), an enzyme that has been used as a prototypical example of long-range proton transfers in biomolecules. In contrast to the long-held conjecture in the experimental literature, the computed potentials of mean force (PMF) suggest that the proton transfer in CAII is not very sensitive to the orientation of the acceptor group (His 64) and, therefore, the number of water molecules that bridge the donor (zinc-water) and acceptor groups. Perturbative analysis indicates that a series of polar and charged residues close to the transfer pathways make the dominant contribution to the barrier and exothermicity of the proton transfer reaction, thus supporting the proposal from previous studies of Warshel and co-workers using a somewhat simpler QM/MM model that electrostatic interactions play a major role in the proton transfer in CAII. The PMF results are in striking contrast to previous analysis using the same QM/MM method but an ensemble of minimum energy path (MEP) calculations, which found a steep dependence of the barrier height on the number of bridging water molecules. Analysis of the configurations sampled in the PMF and MEP simulations suggests that this difference arises because the PMF simulations sample a largely stepwise mechanism while the local MEP calculations artificially favored concerted transfers due to the specific protocol used to generate the initial configurations. Therefore, this study presents a compelling argument for carrying out proper conformational sampling in the study of long-range proton transfers. Finally, we illustrate that Phi analysis, which has been widely used in protein folding studies, can potentially generate new mechanistic information for long-range proton transfers regarding the sequence of events. The results of the perturbation analysis and the Phi analysis provide opportunities for experimentally testing the mechanistic proposals from this study and our recent work in which a stepwise "proton hole" transfer pathway has been proposed.

J Phys Chem B, 2005

The accuracy of biological simulations depends, in large part, on the treatment of electrostatics... more The accuracy of biological simulations depends, in large part, on the treatment of electrostatics. Due to the availability of accurate experimental values, calculation of pK a provides stringent evaluation of computational methods. The generalized solvent boundary potential (GSBP) and Ewald summation electrostatic treatments were recently implemented for combined quantum mechanical and molecular mechanics (QM/MM) simulations by our group. These approaches were tested by calculating pK a shifts due to differences in electronic structure and electrostatic environment; the shifts were determined for a series of small molecules in solution, using various electrostatic treatments, and two residues (His 31, Lys 102) in the M102K T4-lysozyme mutant with large pK a shifts, using the GSBP approach. The calculations utilized a free energy perturbation scheme with the QM/MM potential function involving the self-consistent charge density functional tight binding (SCC-DFTB) and CHARMM as the QM and MM methods, respectively. The study of small molecules demonstrated that inconsistent electrostatic models produced results that were difficult to correct in a robust manner; by contrast, extended electrostatics, GSBP, and Ewald simulations produced consistent results once a bulk solvation contribution was carefully chosen. In addition to the electrostatic treatment, the pK a shifts were also sensitive to the level of the QM method and the scheme of treating QM/MM Coulombic interactions; however, simple perturbative corrections based on SCC-DFTB/CHARMM trajectories and higher level single point energy calculations were found to give satisfactory results. Combining all factors gave a root-mean-square difference of 0.7 pK a units for the relative pK a values of the small molecules compared to experiment. For the residues in the lysozyme, an accurate pK a shift was obtained for His 31 with multiple nanosecond simulations. For Lys 102, however, the pK a shift was estimated to be too large, even after more than 10 nanosecond simulations for each λ window; the difficulty was due to the significant, but slow, reorganization of the protein and water structure when Lys 102 was protonated. The simulations support that Lys 102 is deprotonated in the X-ray structure and the protein is highly destabilized when this residue is protonated.

Implicit dielectric solvent models have been developed in an effort to funnel computational resou... more Implicit dielectric solvent models have been developed in an effort to funnel computational resources to the solvated molecules of interest. More recently, the quasi-chemical theory developed by L. R. Pratt and S. Rempe provided a systematic way of including the most important solvent contributions to calculations of the chemical potential for the solute. The present work applies this theory to

J Phys Chem a, 2002

Quasi-chemical theory and electronic structure results on inner-sphere H(H 2 O) n + clusters are ... more Quasi-chemical theory and electronic structure results on inner-sphere H(H 2 O) n + clusters are used to discuss the absolute hydration free energy of H + (aq). It is noted that this quantity is not thermodynamically measurable, and this leads to some relative misalignment of available tables of absolute hydration free energies of ions in water. The simplest quasi-chemical model produces a reasonable quantitative result in the range of -256 to -251 kcal/mol. The primitive concepts on which the model is based naturally identify the Zundel cation H 5 O 2 + as the principal chemical structure contributing to this hydration free energy. The specific participation of an Eigen cation H 9 O 4 + is not required in this model because the definition of that structure depends on outer-sphere arrangements, and a crude dielectric continuum model is here used for outer-sphere contributions.

Science China Chemistry, 2011

ABSTRACT Implicit dielectric solvent models have been developed in an effort to funnel computatio... more ABSTRACT Implicit dielectric solvent models have been developed in an effort to funnel computational resources to the solvated molecules of interest. More recently, the quasi-chemical theory developed by L. R. Pratt and S. Rempe provided a systematic way of including the most important solvent contributions to calculations of the chemical potential for the solute. The present work applies this theory to aqueous proton solvation. Hydronium and zundel are the most important clusters to consider since the oxygens are within the first solvation shell. The gas phase Gibbs free energies for these species are calculated using Gaussian98 including normal mode zero point energy. The effect of using anharmonic vibrational energies from Diffusion Monte Carlo calculations is investigated. From the free energies and the dielectric solvation chemical potential of protonated water clusters, the solvation free energy of a proton is obtained. These results are useful in understanding the inherent geometry of aqueous proton solvation.

The Journal of Physical Chemistry B, 2005

The accuracy of biological simulations depends, in large part, on the treatment of electrostatics... more The accuracy of biological simulations depends, in large part, on the treatment of electrostatics. Due to the availability of accurate experimental values, calculation of pK a provides stringent evaluation of computational methods. The generalized solvent boundary potential (GSBP) and Ewald summation electrostatic treatments were recently implemented for combined quantum mechanical and molecular mechanics (QM/MM) simulations by our group. These approaches were tested by calculating pK a shifts due to differences in electronic structure and electrostatic environment; the shifts were determined for a series of small molecules in solution, using various electrostatic treatments, and two residues (His 31, Lys 102) in the M102K T4-lysozyme mutant with large pK a shifts, using the GSBP approach. The calculations utilized a free energy perturbation scheme with the QM/MM potential function involving the self-consistent charge density functional tight binding (SCC-DFTB) and CHARMM as the QM and MM methods, respectively. The study of small molecules demonstrated that inconsistent electrostatic models produced results that were difficult to correct in a robust manner; by contrast, extended electrostatics, GSBP, and Ewald simulations produced consistent results once a bulk solvation contribution was carefully chosen. In addition to the electrostatic treatment, the pK a shifts were also sensitive to the level of the QM method and the scheme of treating QM/MM Coulombic interactions; however, simple perturbative corrections based on SCC-DFTB/CHARMM trajectories and higher level single point energy calculations were found to give satisfactory results. Combining all factors gave a root-mean-square difference of 0.7 pK a units for the relative pK a values of the small molecules compared to experiment. For the residues in the lysozyme, an accurate pK a shift was obtained for His 31 with multiple nanosecond simulations. For Lys 102, however, the pK a shift was estimated to be too large, even after more than 10 nanosecond simulations for each λ window; the difficulty was due to the significant, but slow, reorganization of the protein and water structure when Lys 102 was protonated. The simulations support that Lys 102 is deprotonated in the X-ray structure and the protein is highly destabilized when this residue is protonated.

The Journal of Physical Chemistry B, 2004

The importance of accurately treating van der Waals interactions between the quantum mechanical (... more The importance of accurately treating van der Waals interactions between the quantum mechanical (QM) and molecular mechanical (MM) atoms in hybrid QM/MM simulations has been investigated systematically. First, a set of van der Waals (vdW) parameters was optimized for an approximate density functional method, the self-consistent charge-tight binding density functional (SCC-DFTB) approach, based on small hydrogenbonding clusters. The sensitivity of condensed phase observables to the SCC-DFTB vdW parameters was then quantitatively investigated by SCC-DFTB/MM simulations of several model systems using the optimized set and two sets of extreme vdW parameters selected from the CHARMM22 forcefield. The model systems include a model FAD molecule in solution and a solvated enediolate, and the properties studied include the radial distribution functions of water molecules around the solute (model FAD and enediolate), the reduction potential of the model FAD and the potential of mean force for an intramolecular proton transfer in the enediolate. Although there are noticeable differences between parameter sets for gas-phase clusters and solvent structures around the solute, thermodynamic quantities in the condensed phase (e.g., reduction potential and potential of mean force) were found to be less sensitive to the numerical values of vdW parameters. The differences between SCC-DFTB/MM results with the three vdW parameter sets for SCC-DFTB atoms were explained in terms of the effects of the parameter set on solvation. The current study has made it clear that efforts in improving the reliability of QM/MM methods for energetical properties in the condensed phase should focus on components other than van der Waals interactions between QM and MM atoms.

The Journal of Physical Chemistry A, 2002

Quasi-chemical theory and electronic structure results on inner-sphere H(H 2 O) n + clusters are ... more Quasi-chemical theory and electronic structure results on inner-sphere H(H 2 O) n + clusters are used to discuss the absolute hydration free energy of H + (aq). It is noted that this quantity is not thermodynamically measurable, and this leads to some relative misalignment of available tables of absolute hydration free energies of ions in water. The simplest quasi-chemical model produces a reasonable quantitative result in the range of -256 to -251 kcal/mol. The primitive concepts on which the model is based naturally identify the Zundel cation H 5 O 2 + as the principal chemical structure contributing to this hydration free energy. The specific participation of an Eigen cation H 9 O 4 + is not required in this model because the definition of that structure depends on outer-sphere arrangements, and a crude dielectric continuum model is here used for outer-sphere contributions.

The Journal of Physical Chemistry A, 2007

To quantitatively explore the applicability of the Generalized Solvent Boundary Potential (GSBP) ... more To quantitatively explore the applicability of the Generalized Solvent Boundary Potential (GSBP) based QM/MM approach as a "multi-scale" framework for studying chemical reactions in biomolecules, the structural and energetic properties of the Human Carbonic Anhydrase II (CAII) are analyzed and compared to those from periodic boundary condition (PBC) simulations and available experimental data. Although the atomic fluctuations from GSBP based simulations are consistently lower compared to those from PBC simulations or crystallographic data, the fluctuations and internal coordinate distributions for residues in the proximity of the active site as well as diffusion constants of active-site water molecules are fairly well described by GSBP simulations.

Physical Chemistry Chemical Physics, 2005

Benchmark calculations of proton affinities and gas-phase basicities of molecules most relevant t... more Benchmark calculations of proton affinities and gas-phase basicities of molecules most relevant to biological phosphoryl transfer reactions are presented and compared with available experimental results. The accuracy of proton affinity and gas-phase basicity results obtained from several multi-level model chemistries (CBS-QB3, G3B3, and G3MP2B3) and density-functional quantum models (PBE0, B1B95, and B3LYP) are assessed and compared. From these data, a set of empirical bond enthalpy, entropy, and free energy corrections are introduced that considerably improve the accuracy and predictive capability of the methods. These corrections are applied to the prediction of proton affinity and gas-phase basicity values of important biological phosphates and phosphoranes for which experimental data does not currently exist. Comparison is made with results from semiempirical quantum models that are commonly employed in hybrid quantum mechanical/molecular mechanical simulations. Data suggest that the design of improved semiempirical quantum models with increased accuracy for relative proton affinity values is necessary to obtain quantitative accuracy for phosphoryl transfer reactions in solution, enzymes, and ribozymes.

The Journal of Chemical Physics, 2005

Biophysical Journal, 2010

In this study, the variance-covariance matrix of protein motions is used to compare several elast... more In this study, the variance-covariance matrix of protein motions is used to compare several elastic network models within the theoretical framework of X-ray scattering from crystals. A set of 33 ultra-high resolution structures is used to characterize the average scaling behavior of the vibrational density of states and make comparisons between experimental and theoretical temperature factors. Detailed investigations of the vibrational density of states, correlations, and predicted diffuse X-ray scatter are carried out for crystalline Staphylococcal nuclease; correlations and diffuse X-ray scatter are also compared to predictions from the TLS (translation, libration, screw) model and a liquidlike dynamics model. We show that elastic network models developed to best predict temperature factors without regard for the crystal environment have relatively strong long-range interactions that yield very short-ranged atom-atom correlations. Further, we find that the the low-frequency modes dominate the variance-covariance matrix only for those models with a physically reasonable vibrational density of states, and the fraction of modes required to converge the correlations is higher than that typically used for elastic network model studies. The practical implications are explored using computed diffuse X-ray scatter, which can be measured experimentally.

Biophysical Journal, 2009

Normal mode analysis using elastic network models has grown popular for probing the low-frequency... more Normal mode analysis using elastic network models has grown popular for probing the low-frequency collective dynamics of proteins and other biomolecular assemblies. In most previous studies, these models were validated by comparing calculated atomic fluctuations for isolated proteins with experimental temperature factors determined in the crystalline state, although there were also hints that including crystal contacts in the calculations has an impact on the comparison. In this study, a set of 83 ultra high resolution crystal structures with experimentally determined anisotropic displacement parameters (ADPs) is used to evaluate several C α -based elastic network models that either ignore or treat the crystal environment in different ways; the latter include using periodic boundary conditions defined with respect to the asymmetric unit or the primitive unit cell as well as using the Born-von Kármán boundary condition that accounts for lattice vibrations. For all elastic network models, treating the crystal environment leads to better agreement with experimental ADPs with the Born-von Kármán boundary condition giving the best agreement. Atomic correlations over the entire protein are clearly affected by the presence of the crystal contacts and fairly sensitive to the way that the crystal environment is treated. These observations highlight the importance of properly treating the protein system in an environment consistent with experiment when either evaluating approximate protein models or using approximate dynamic models in structural refinment type of applications. Finally, investigation of the scaling behaviors of the cumulative density of states and the heat capacity indicates that there are still gaps between simplified elastic models and all-atom models for proteins.

Biochemistry, 2008

Combined quantum mechanical/molecular mechanical (QM/MM) simulations are carried out to analyze f... more Combined quantum mechanical/molecular mechanical (QM/MM) simulations are carried out to analyze factors that dictate the proton transfer in carbonic anhydrase II (CAII), an enzyme that has been used as a prototypical example of long-range proton transfers in biomolecules. In contrast to the long-held conjecture in the experimental literature, the computed potentials of mean force (PMF) suggest that the proton transfer in CAII is not very sensitive to the orientation of the acceptor group (His 64) and, therefore, the number of water molecules that bridge the donor (zinc-water) and acceptor groups. Perturbative analysis indicates that a series of polar and charged residues close to the transfer pathways make the dominant contribution to the barrier and exothermicity of the proton transfer reaction, thus supporting the proposal from previous studies of Warshel and co-workers using a somewhat simpler QM/MM model that electrostatic interactions play a major role in the proton transfer in CAII. The PMF results are in striking contrast to previous analysis using the same QM/MM method but an ensemble of minimum energy path (MEP) calculations, which found a steep dependence of the barrier height on the number of bridging water molecules. Analysis of the configurations sampled in the PMF and MEP simulations suggests that this difference arises because the PMF simulations sample a largely stepwise mechanism while the local MEP calculations artificially favored concerted transfers due to the specific protocol used to generate the initial configurations. Therefore, this study presents a compelling argument for carrying out proper conformational sampling in the study of long-range proton transfers. Finally, we illustrate that Phi analysis, which has been widely used in protein folding studies, can potentially generate new mechanistic information for long-range proton transfers regarding the sequence of events. The results of the perturbation analysis and the Phi analysis provide opportunities for experimentally testing the mechanistic proposals from this study and our recent work in which a stepwise "proton hole" transfer pathway has been proposed.

Biochimica et Biophysica Acta (BBA) - Proteins and Proteomics, 2010

Recent QM/MM analyses of proton transfer function of human carbonic anhydrase II (CAII) are brief... more Recent QM/MM analyses of proton transfer function of human carbonic anhydrase II (CAII) are briefly reviewed. The topics include a preliminary analysis of nuclear quadrupole coupling constant calculations for the zinc ion and more detailed analyses of microscopic pK(a) of the zinc-bound water and free energy profile for the proton transfer. From a methodological perspective, our results emphasize that performing sufficient sampling is essential to the calculation of all these quantities, which reflects the well solvated nature of CAII active site. From a mechanistic perspective, our analyses highlight the importance of electrostatics in shaping the energetics and kinetics of proton transfer in CAII for its function. We argue that once the pK(a) for the zinc-bound water is modulated to be in the proper range (approximately 7.0), proton transfer through a relatively well solvated cavity towards/from the protein surface (His64) does not require any major acceleration. Therefore, although structural details like the length of the water wire between the donor and acceptor groups still may make a non-negligible contribution, our computational results and the framework of analysis suggest that the significance of such "fine-tuning" is likely secondary to the modulation of pK(a) of the zinc-bound water. We encourage further experimental analysis with mutation of (charged) residues not in the immediate neighborhood of the zinc ion to quantitatively test this electrostatics based framework; in particular, Phi analysis based on these mutations may shed further light into the relative importance of the classical Grotthus mechanism and the "proton hole" pathway that we have proposed recently for CAII.