Xiangyu Jia

Calculations of Solvation Free Energy through Energy Reweighting from Molecular Mechanics to Quantum Mechanics

In this work, the solvation free energies of 20 organic molecules from the 4th Statistical Assessment of the Modeling of Proteins and Ligands (SAMPL4) have been calculated. The sampling of phase space is carried out at a molecular mechanical level, and the associated free energy changes are estimated using the Bennett Acceptance Ratio (BAR). Then the quantum mechanical (QM) corrections are computed through the indirect Non-Boltzmann Bennetts acceptance ratio (NBB) or the thermodynamics perturbation (TP) method. We show that BAR+TP gives a minimum analytic variance for the calculated solvation free energy at the Gaussian limit and performs slightly better than NBB in practice. Furthermore, the expense of the QM calculations in TP is only half of that in NBB. We also show that defining the biasing potential as the difference of the solute-solvent interaction energy, instead of the total energy, can converge the calculated solvation free energies much faster but possibly to different values. Based on the experimental solvation free energies which have been published before, it is discovered in this study that BLYP yields better results than MP2 and some other later functionals such as B3LYP, M06-2X, and ωB97X-D.

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.

The F130L mutation in streptavidin reduces its binding affinity to biotin through electronic polarization effect

Recently, Baugh et al. discovered that a distal point mutation (F130L) in streptavidin causes no distinct variation to the structure of the binding pocket but a 1000‐fold reduction in biotin binding affinity. In this work, we carry out molecular dynamics simulations and apply an end‐state free energy method to calculate the binding free energies of biotin to wild type streptavidin and its F130L mutant. The absolute binding affinities based on AMBER charge are repulsive, and the mutation induced binding loss is underestimated. When using the polarized protein‐specific charge, the absolute binding affinities are significantly enhanced. In particular, both the absolute and relative binding affinities are in line with the experimental measurements. Further investigation indicates that polarization effect is indispensable in both the generation of structural ensembles and the calculation of interaction energies. This work verifies Baughs conjecture that electrostatic polarization effect plays an essential role in modulating the binding affinity of biotin to the streptavidin through F130L mutation.

Hybrid QM/MM study of FMO complex with polarized protein-specific charge

The Fenna-Matthews-Olson (FMO) light-harvesting complex is now one of the primary model systems for the study of excitation energy transfer (EET). However, the mechanism of the EET in this system is still controversial. In this work, molecular dynamics simulations and the electrostatic-embedding quantum-mechanics/molecular-mechanics single-point calculations have been employed to predict the energy transfer pathways utilizing the polarized protein-specific charge (PPC), which provides a more realistic description of Coulomb interaction potential in the protein than conventional mean-field charge scheme. The recently discovered eighth pigment has also been included in this study. Comparing with the conventional mean-field charges, more stable structures of FMO complex were found under PPC scheme during molecular dynamic simulation. Based on the electronic structure calculations, an exciton model was constructed to consider the couplings during excitation. The results show that pigments 3 and 4 dominate the lowest exciton levels whereas the highest exciton level are mainly constituted of pigments 1 and 6. This observation agrees well with the assumption based on the spatial distribution of the pigments. Moreover, the obtained spectral density in this study gives a reliable description of the diverse local environment embedding each pigment.

Accessing the applicability of polarized protein‐specific charge in linear interaction energy analysis

The reliability of the linear interaction energy (LIE) depends on the atomic charge model used to delineate the Coulomb interaction between the ligand and its environment. In this work, the polarized protein‐specific charge (PPC) implementing a recently proposed fitting scheme has been examined in the LIE calculations of the binding affinities for avidin and β‐secretase binding complexes. This charge fitting scheme, termed delta restrained electrostatic potential, bypasses the prevalent numerical difficulty of rank deficiency in electrostatic‐potential‐based charge fitting methods via a dual‐step fitting strategy. A remarkable consistency between the predicted binding affinities and the experimental measurement has been observed. This work serves as a direct evidence of PPCs applicability in rational drug design.

Assessing the accuracy of the general AMBER force field for 2,2,2-trifluoroethanol as solvent

The alcohol-based cosolvent 2,2,2-trifluoroethanol (TFE) has been used widely in protein science and engineering. Many experimental and computational studies of its impact on protein structure have been carried out, but consensus on the mechanism has not been reached. In the past decade, several molecular mechanical models have been proposed to model the structure and dynamics of TFE. However, further calibration is still necessary. In particular, its compatibility with protein force fields has not been well examined. The general AMBER force field (GAFF) has proved quite successful in modeling small organic molecules, and is compatible with contemporary AMBER force field. In this work, we assessed the accuracy of GAFF for the TFE molecule as a bulk solvent. Several properties, such as density, dipole moment, radial distribution function, etc., were calculated and compared with experimental data. The results show that GAFF plays fairly well in the description of bulk TFE, although there is still room for improvement.

Efficient Strategy for the Calculation of Solvation Free Energies in Water and Chloroform at the Quantum Mechanical/Molecular Mechanical Level

The partitioning of solute molecules between immiscible solvents with significantly different polarities is of great importance. The polarization between the solute and solvent molecules plays an essential role in determining the solubility of the solute, which makes computational studies utilizing molecular mechanics (MM) rather difficult. In contrast, quantum mechanics (QM) can provide more reliable predictions. In this work, the partition coefficients of the side chain analogs of some amino acids between water and chloroform were computed. The QM solvation free energies were calculated indirectly via a series of MM states using the multistate Bennett acceptance ratio (MBAR) and the MM-to-QM corrections were applied at the two endpoints using thermodynamic perturbation (TP). Previously, it has been shown (Jia et al. J. Chem. Theory Comput. 2016, 12, 499-511) that this method provides the minimal variance in the results without running QM simulations. However, if there is insufficient overlap in phase space between the MM and QM Hamiltonians, this method fails. In this work, we propose, for the first time, a quantity termed the reweighting entropy that serves as a metric for the reliability of the TP calculations. If the reweighting entropy is below a certain threshold (0.65 for the solvation free energy calculations in this work), this MM-to-QM correction should be avoided and two alternative methods can be employed by either introducing a semiempirical state or conducting nonequilibrium simulations. However, the results show that the QM methods are not guaranteed to yield better results than the MM methods. Further improvement of the QM methods are imperative, especially the treatment of the van der Waals and the electrostatic interactions between the QM region and the MM region in the first shell. We also propose a scheme for the calculation of the van der Waals parameters for the solute molecules in nonaqueous solvent, which improves the quality of the computed thermodynamic properties. Furthermore, the force field parameters for the sulfur-containing molecules are also optimized.

Folding simulation of Trp-cage utilizing a new AMBER compatible force field with coupled main chain torsions

A newly developed AMBER compatible force field with coupled backbone torsion potential terms (AMBER032D) is utilized in a folding simulation of a mini-protein Trp-cage. Through replica exchange and direct molecular dynamics (MD) simulations, a multi-step folding mechanism with a synergetic folding of the hydrophobic core (HPC) and the α-helix in the final stage is suggested. The native structure has the lowest free energy and the melting temperature predicted from the specific heat capacity Cv is only 12 K higher than the experimental measurement. This study, together with our previous study, shows that AMBER032D is an accurate force field that can be used for protein folding simulations.

Calculations of the absolute binding free energies for Ralstonia solanacearum lectins bound with methyl-α-L-fucoside at molecular mechanical and quantum mechanical/molecular mechanical levels

A method that can reliably predict protein–ligand binding free energies is essential for rational drug design. Much effort has been devoted to this field, but it remains challenging especially for flexible ligands. In this work, both a molecular mechanical (MM) method and a hybrid quantum mechanical/molecular mechanical (QM/MM) method have been applied in the study of the binding affinities of methyl-α-L-fucoside to Ralstonia solanacearum lectins. The free energy at the MM level was calculated using the double-decoupling method (DDM) and the free energy change at each step was calculated via a series of intermediate states using the Bennett acceptance ratio (BAR). The binding free energy agrees well with the experimental measurement, no matter whether the general AMBER force field or GLYCAM06j was applied to the ligand. Nonetheless, slow convergence for some intermediate states has been observed, which requires substantially longer simulations than were used in many other studies. The QM/MM free energy was calculated by thermodynamic perturbation (TP) from the MM states. This strategy has been shown to yield minimal variance for the calculated free energy without direct sampling at the QM/MM level in a previous study. However, after this MM-to-QM/MM correction, the agreement with the experimental value decreased. This study serves as an implication of the demand for substantially longer simulations for the alchemical process than those that were used in many other studies and for further improvement of QM/MM methods, especially the description of interactions between the QM and MM regions.

Efficient Computation of Free Energy Surfaces of Diels–Alder Reactions in Explicit Solvent at Ab Initio QM/MM Level

For Diels–Alder (DA) reactions in solution, an accurate and converged free energy (FE) surface at ab initio (ai) quantum mechanical/molecular mechanical (QM/MM) level is imperative for the understanding of reaction mechanism. However, this computation is still far too expensive. In a previous work, we proposed a new method termed MBAR+wTP, with which the computation of the ai FE profile can be accelerated by several orders of magnitude via a three-step procedure: (I) an umbrella sampling (US) using a semi-empirical (SE) QM/MM Hamiltonian is performed; (II) the FE profile is generated using the Multistate Bennett Acceptance Ratio (MBAR) analysis; and (III) a weighted Thermodynamic Perturbation (wTP) from the SE Hamiltonian to the ai Hamiltonian is performed to obtain the ai QM/MM FE profile using weight factors from the MBAR analysis. In this work, this method is extended to the calculations of two-dimensional FE surfaces of two Diels–Alder reactions of cyclopentadiene with either acrylonitrile or 1-4-naphthoquinone at ai QM/MM level. The accurate activation free energies at the ai QM/MM level, which are much closer to the experimental measurements than those calculated by other methods, indicate that this MBAR+wTP method can be applied in the studies of complex reactions in condensed phase with much-enhanced efficiency.