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Despite recent advances in the development of machine learning potentials (MLPs) for biomolecular simulations, there has been limited effort on developing stable and accurate MLPs for enzymatic reactions. Here we report a protocol for performing machine-learning-assisted free energy simulation of solution-phase and enzyme reactions at the ab initio quantum-mechanical/molecular-mechanical (ai-QM/MM) level of accuracy. Within our protocol, the MLP is built to reproduce the ai-QM/MM energy and forces on both QM (reactive) and MM (solvent/enzyme) atoms. As an alternative strategy, a delta machine learning potential (ΔMLP) is trained to reproduce the differences between the ai-QM/MM and semiempirical (se) QM/MM energies and forces. To account for the effect of the condensed-phase environment in both MLP and ΔMLP, the DeePMD representation of a molecular system is extended to incorporate the external electrostatic potential and field on each QM atom. Using the Menshutkin and chorismate mutase reactions as examples, we show that the developed MLP and ΔMLP reproduce the ai-QM/MM energy and forces with errors that on average are less than 1.0 kcal/mol and 1.0 kcal mol-1 A-1, respectively, for representative configurations along the reaction pathway. For both reactions, MLP/ΔMLP-based simulations yielded free energy profiles that differed by less than 1.0 kcal/mol from the reference ai-QM/MM results at only a fraction of the computational cost.

Calculating binding free energies with quantum-mechanical (QM) methods is notoriously time-consuming. In this work, we studied whether such calculations can be accelerated by using nonequilibrium (NE) molecular dynamics simulations employing Jarzynski's equality. We studied the binding of nine cyclic carboxylate ligands to the octa-acid deep-cavity host from the SAMPL4 challenge with the reference potential approach. The binding free energies were first calculated at the molecular mechanics (MM) level with free energy perturbation using the generalized Amber force field with restrained electrostatic potential charges for the host and the ligands. Then the free energy corrections for going from the MM Hamiltonian to a hybrid QM/MM Hamiltonian were estimated by averaging over many short NE molecular dynamics simulations. In the QM/MM calculations, the ligand was described at the semiempirical PM6-DH+ level. We show that this approach yields MM → QM/MM free energy corrections that agree with those from other approaches within statistical uncertainties. The desired precision can be obtained by running a proper number of independent NE simulations. For the systems studied in this work, a total simulation length of 20 ps was appropriate for most of the ligands, and 36-324 simulations were necessary in order to reach a precision of 0.3 kJ/mol.

To gain better insight into how the fluctuating protein environment influences the site energy ordering of the chromophores in PE545 light-harvesting antenna system, we carried out quantum mechanics/molecular mechanics (QM/MM) calculations along the molecular dynamics (MD) trajectory. The Polarized Protein-Specific Charge (PPC) scheme was adopted in both the MD simulation and the QM/MM calculations for a more realistic description of the protein environment. The deduced site energy ladder calculated using ZINDO/S-CIS agrees well with the best model extracted from experiments by a simultaneous fit of the steady-state spectra and transient absorption spectra. Three combinations of charge schemes were compared to elucidate how the protein environment modulates the site energy of chromophores. The result indicates that the multiroles that the protein environment is playing, for instance, by fine-tuning of the conformation of chromophores or by specific pigment-protein interactions, are both crucial for site energy arrangement. Furthermore, we investigated the effects of individual environments and found that the polar residues and water molecules contribute most to the energy shifts.

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 Bennett's 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.

To elucidate the energy transfer mechanism of the PE545 light-harvesting complex, an exciton model is constructed with the full Hamiltonian obtained from structure-based calculations. The electronic couplings and spectral densities are evaluated on the basis of the site energies and transition dipole moments obtained from our recent Molecular Dynamics-Quantum Mechanical/Molecular Mechanical (MD-QM/MM) study [Tong et al., J. Phys. Chem. B 123, 2040-2049 (2019)]. The polarized protein-specific charge model is employed both in the MD simulation and in the QM/MM calculations to account for the environmental fluctuation of the protein scaffold. The energy transfer pathways are, thus, derived, which agree well with the phenomenological models based on the spatial organization of the chromophores and the experimental observations. Moreover, the simulated linear absorption spectra using the dissipaton equation of motion approach agree well with the experimental ones, and the resulting population dynamics indicates that an optimal energy transfer efficiency is reproduced.

For Diels&ndash, 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&ndash, 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.

A recently developed MESS-E-QM/MM method (multiple-environment single-system quantum mechanical molecular/mechanical calculations with a Roothaan-step extrapolation) is applied to the computation of hydration free energies for the blind SAMPL4 test set and for 12 small molecules. First, free energy simulations are performed with a classical molecular mechanics force field using fixed-geometry solute molecules and explicit TIP3P solvent, and then the non-Boltzmann-Bennett method is employed to compute the QM/MM correction (QM/MM-NBB) to the molecular mechanical hydration free energies. For the SAMPL4 set, MESS-E-QM/MM-NBB corrections to the hydration free energy can be obtained 2 or 3 orders of magnitude faster than fully converged QM/MM-NBB corrections, and, on average, the hydration free energies predicted with MESS-E-QM/MM-NBB fall within 0.10-0.20 kcal/mol of full-converged QM/MM-NBB results. Out of five density functionals (BLYP, B3LYP, PBE0, M06-2X, and ωB97X-D), the BLYP functional is found to be most compatible with the TIP3P solvent model and yields the most accurate hydration free energies against experimental values for solute molecules included in this study.

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.

In combined quantum mechanical/molecular mechanical (QM/MM) free energy calculations, it is often advantageous to have a frozen geometry for the quantum mechanical (QM) region. For such multiple-environment single-system (MESS) cases, two schemes are proposed here for estimating the polarization energy: the first scheme, termed MESS-E, involves a Roothaan step extrapolation of the self-consistent field (SCF) energy; whereas the other scheme, termed MESS-H, employs a Newton-Raphson correction using an approximate inverse electronic Hessian of the QM region (which is constructed only once). Both schemes are extremely efficient, because the expensive Fock updates and SCF iterations in standard QM/MM calculations are completely avoided at each configuration. They produce reasonably accurate QM/MM polarization energies: MESS-E can predict the polarization energy within 0.25 kcal/mol in terms of the mean signed error for two of our test cases, solvated methanol and solvated β-alanine, using the M06-2X or ωB97X-D functionals; MESS-H can reproduce the polarization energy within 0.2 kcal/mol for these two cases and for the oxyluciferin-luciferase complex, if the approximate inverse electronic Hessians are constructed with sufficient accuracy.

The correct representation of solute-water interactions is essential for the accurate simulation of most biological phenomena. Several highly accurate quantum methods are available to deal with solvation by using both implicit and explicit solvents. So far, however, most evaluations of those methods were based on a single conformation, which neglects solute entropy. Here, we present the first test of a novel approach to determine hydration free energies that uses molecular mechanics (MM) to sample phase space and quantum mechanics (QM) to evaluate the potential energies. Free energies are determined by using re-weighting with the Non-Boltzmann Bennett (NBB) method. In this context, the method is referred to as QM-NBB. Based on snapshots from MM sampling and accounting for their correct Boltzmann weight, it is possible to obtain hydration free energies that incorporate the effect of solute entropy. We evaluate the performance of several QM implicit solvent models, as well as explicit solvent QM/MM for the blind subset of the SAMPL4 hydration free energy challenge. While classical free energy simulations with molecular dynamics give root mean square deviations (RMSD) of 2.8 and 2.3 kcal/mol, the hybrid approach yields an improved RMSD of 1.6 kcal/mol. By selecting an appropriate functional and basis set, the RMSD can be reduced to 1 kcal/mol for calculations based on a single conformation. Results for a selected set of challenging molecules imply that this RMSD can be further reduced by using NBB to reweight MM trajectories with the SMD implicit solvent model.

Inspired by the idea of charge decomposition in calculation of the dipole preserving and polarization consistent charges (Zhang et al., J. Comput. Chem. 2011, 32, 2127), we have proposed a numerically stable restrained electrostatic potential (ESP)-based charge fitting method for protein. The atomic charge is composed of two parts. The dominant part is fixed to a predefined value (e.g., AMBER charge), and the residual part is to be determined by restrained fitting to residual ESP on grid points around the molecule. Nonuniform weighting factors as a function of the dominant charge are assigned to the atoms. Because the residual part is several folds to several orders smaller than the dominant part, the impact of ill-conditioning is alleviated. This charge fitting method can be used in quantum mechanical/molecular mechanical (QM/MM) simulations and similar studies, where QM calculated electronic properties are frequently mapped to partial atomic charges.

Avidin-biotin is one of the strongest protein-ligand binding systems, with broad applications in biomedical science. Here we report a quantum-based computational study to help elucidate the mechanism of binding avidin to biotin (BTN1) and its close analogue, 2'-iminobiotin (BTN2). Our study reveals that electronic polarization of protein plays a critical role in stabilizing the beta sheet (Thr113-Arg122) at the binding site and makes a substantial contribution to the free energy of avidin-biotin binding. The current finding is in contradiction to the previous notion that electrostatic interaction has no effect on or makes an unfavorable contribution to the free energy of avidin-biotin binding. Our calculations also show that the difference in binding free energy of avidin to BTN1 and BTN2 is almost entirely due to the contribution of electrostatic interaction resulting from polarization-induced stabilization of a hydrogen bond between avidin and BTN1. The current result provides strong evidence that protein polarization accounts for the electrostatic contribution to binding free energy that was missing in previous studies of avidin-biotin binding.

Molecular dynamics simulations of NMR backbone relaxation order parameters have been carried out to investigate the polarization effect on the protein's local structure and dynamics for five benchmark proteins (bovine pancreatic trypsin inhibitor, immunoglobulin-binding domain (B1) of streptococcal protein G, bovine apo-calbindin D9K, human interleukin-4 R88Q mutant, and hen egg white lysozyme). In order to isolate the polarization effect from other interaction effects, our study employed both the standard AMBER force field (AMBER03) and polarized protein-specific charges (PPCs) in the MD simulations. The simulated order parameters, employing both the standard nonpolarizable and polarized force fields, are directly compared with experimental data. Our results show that residue-specific order parameters at some specific loop and turn regions are significantly underestimated by the MD simulations using the standard AMBER force field, indicating hyperflexibility of these local structures. Detailed analysis of the structures and dynamic motions of individual residues reveals that the hyperflexibility of these local structures is largely related to the breaking or weakening of relevant hydrogen bonds. In contrast, the agreement with the experimental results is significantly improved and more stable local structures are observed in the MD simulations using the polarized force field. The comparison between theory and experiment provides convincing evidence that intraprotein hydrogen bonds in these regions are stabilized by electronic polarization, which is critical to the dynamical stability of these local structures in proteins.

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.

In order to carry out a detailed analysis of the molecular static polarizability, which is the response of the molecule to a uniform external electric field, the molecular polarizability was computed using the finite-difference method for 21 small molecules, using density functional theory. Within nine charge population schemes (Lowdin, Mulliken, Becke, Hirshfeld, CM5, Hirshfeld-I, NPA, CHELPG, MK-ESP) in common use, the charge fluctuation contribution is found to dominate the molecular polarizability, with its ratio ranging from 59.9% with the Hirshfeld or CM5 scheme to 96.2% with the Mulliken scheme. The Hirshfeld-I scheme is also used to compute the other contribution to the molecular polarizability coming from the induced atomic dipoles, and the atomic polarizabilities in eight small molecules and water pentamer are found to be highly anisotropic for most atoms. Overall, the results suggest that (a) more emphasis probably should be placed on the charge fluctuation terms in future polarizable force field development and (b) an anisotropic polarizability might be more suitable than an isotropic one in polarizable force fields based entirely or partially on the induced atomic dipoles.

The accuracy of force fields is of utmost importance in molecular modeling of proteins. Despite successful applications of force fields for about the past 30 years, some inherent flaws lying in force fields, such as biased secondary propensities and fixed atomic charges, have been observed in different aspects of biomolecular research; hence, a correction to current force fields is desirable. Because of the simplified functional form and the limited number of parameters for main chain torsion (MCT) in traditional force fields, it is not easy to propose an exquisite force field that is well-balanced among various conformations. Recently, AMBER-compatible force fields with coupled MCT term have been proposed, which show some improvement over AMBER03 and AMBER99SB force fields. In this work, further calibration of the torsional parameters has been conducted by changing the solvation model in quantum mechanical calculation and minimizing the deviation from the nuclear magnetic resonance experiments for some benchmark model systems and a folded protein. The results show that the revised force fields give excellent agreement with experiments in J coupling, chemical shifts, and secondary structure populations. In addition, the polarization effect is found to be crucial for the systems with ordered secondary structures.

Conspectus Electrostatic interaction plays a significant role in determining many properties of biomolecules, which exist and function in aqueous solution, a highly polar environment. For example, proteins are composed of amino acids with charged, polar, and nonpolar side chains and their specific electrostatic properties are fundamental to the structure and function of proteins. An important issue that arises in computational study of biomolecular interaction and dynamics based on classical force field is lack of polarization. Polarization is a phenomenon in which the charge distribution of an isolated molecule will be distorted when interacting with another molecule or presented in an external electric field. The distortion of charge distribution is intended to lower the overall energy of the molecular system, which is counter balanced by the increased internal energy of individual molecules due to the distorted charge distributions. The amount of the charge redistribution, which characterizes the polarizability of a molecule, is determined by the level of the charge distortion. Polarization is inherently quantum mechanical, and therefore classical force fields with fixed atomic charges are incapable of capturing this important effect. As a result, simulation studies based on popular force fields, AMBER, CHARMM, etc., lack the polarization effect, which is a widely known deficiency in most computational studies of biomolecules today. Many efforts have been devoted to remedy this deficiency, such as adding additional movable charge on the atom, allowing atomic charges to fluctuate, or including induced multipoles. Although various successes have been achieved and progress at various levels has been reported over the past decades, the issue of lacking polarization in force field based simulations is far from over. For example, some of these methods do not always give converged results, and other methods require huge computational cost. This Account reviews recent work on developing polarized and polarizable force fields based on fragment quantum mechanical calculations for proteins. The methods described here are based on quantum mechanical calculations of proteins in solution, but with a different level of rigor and different computational efficiency for the molecular dynamics applications. In the general approach, a fragment quantum mechanical calculation for protein with implicit solvation is carried out to derive a polarized protein-specific charge (PPC) for any given protein structure. The PPC correctly reflects the polarization state of the protein in a given conformation, and it can also be dynamically changed as the protein changes conformation in dynamics simulations. Another approach that is computationally more efficient is the effective polarizable bond method in which only polar bonds or groups can be polarized and their polarizabilities are predetermined from quantum mechanical calculations of these groups in external electric fields. Both methods can be employed for applications in various situations by taking advantage of their unique features.

Main chain torsions of alanine dipeptide are parameterized into coupled 2-dimensional Fourier expansions based on quantum mechanical (QM) calculations at M06 2X/aug-cc-pvtz//HF/6-31G** level. Solvation effect is considered by employing polarizable continuum model. Utilization of the M06 2X functional leads to precise potential energy surface that is comparable to or even better than MP2 level, but with much less computational demand. Parameterization of the 2D expansions is against the full main chain torsion space instead of just a few low energy conformations. This procedure is similar to that for the development of AMBER03 force field, except unique weighting factor was assigned to all the grid points. To avoid inconsistency between quantum mechanical calculations and molecular modeling, the model peptide is further optimized at molecular mechanics level with main chain dihedral angles fixed before the calculation of the conformational energy on molecular mechanical level at each grid point, during which generalized Born model is employed. Difference in solvation models at quantum mechanics and molecular mechanics levels makes this parameterization procedure less straightforward. All force field parameters other than main chain torsions are taken from existing AMBER force field. With this new main chain torsion terms, we have studied the main chain dihedral distributions of ALA dipeptide and pentapeptide in aqueous solution. The results demonstrate that 2D main chain torsion is effective in delineating the energy variation associated with rotations along main chain dihedrals. This work is an implication for the necessity of more accurate description of main chain torsions in the future development of ab initio force field and it also raises a challenge to the development of quantum mechanical methods, especially the quantum mechanical solvation models.

Solvent effect on protein conformation and folding mechanism of E6-associated protein (E6ap) peptide are investigated using a recently developed charge update scheme termed as adaptive hydrogen bond-specific charge (AHBC). On the basis of the close agreement between the calculated helix contents from AHBC simulations and experimental results, we observed based on the presented simulations that the two ends of the peptide may simultaneously take part in the formation of the helical structure at the early stage of folding and finally merge to form a helix with lowest backbone RMSD of about 0.9 Å in 40% 2,2,2-trifluoroethanol solution. However, in pure water, the folding may start at the center of the peptide sequence instead of at the two opposite ends. The analysis of the free energy landscape indicates that the solvent may determine the folding clusters of E6ap, which subsequently leads to the different final folded structure. The current study demonstrates new insight to the role of solvent in the determination of protein structure and folding dynamics. Published version

Structures and dynamics of a recently designed dizinc metalloprotein (DFsc) (J. Mol. Biol. 2003, 334, 1101) are studied by molecular dynamics simulation using a dynamically adapted polarized force field derived from fragment quantum calculation for protein in solvent. To properly describe the effect of charge transfer and polarization in the present approach, quantum chemistry calculation of the zinc-binding group is periodically performed (on-the-fly) to update the atomic charges of the zinc-binding group during the MD simulation. Comparison of the present result with those obtained from simulations under standard AMBER force field reveals that charge transfer and polarization are critical to maintaining the correct asymmetric metal coordination in the DFsc. Detailed analysis of the result also shows that dynamic fluctuation of the zinc-binding group facilitates solvent interaction with the zinc ions. In particular, the dynamic fluctuation of the zinc-zinc distance is shown to be an important feature of the catalytic function of the di-ion zinc-binding group. Our study demonstrates that the dynamically adapted polarization approach is computationally practical and can be used to study other metalloprotein systems.

Molecular dynamics (MD) simulation has been carried out to study dynamical stability of intra-protein hydrogen bonds based on two set of atomic charges, the standard AMBER charge and the polarized protein-specific charge (PPC). The latter is derived from quantum mechanical calculation for protein in solution using a recently developed molecular fractionation with conjugate caps-Poisson-Boltzmann (MFCC-PB) approach and therefore includes electronic polarization effect of the protein at native structure. MD simulations are performed for a number of benchmark proteins containing helix and/or beta sheet secondary structures. The computational result shows that occupancy percentage of hydrogen bonds averaged over simulation time, as well as the number of hydrogen bonds as a function of simulation time, is consistently higher under PPC than AMBER charge. In particular, some intra-protein hydrogen bonds are found broken during MD simulation using AMBER charge but they are stable using PPC. The breaking of some intra-protein hydrogen bonds in AMBER simulation is responsible for deformation or denaturing of some local structures of proteins during MD simulation. The current study provides strong evidence that hydrogen bonding is dynamically more stable using PPC than AMBER charge, highlighting the stabilizing effect of electronic polarization on protein structure.

Quantum chemistry calculations at the levels of MP2/cc-pVDZ and MP2/cc-PVTZ have been carried out to study residue-specific interactions at the hydrophobic p53-MDM2 binding interface. The result of the calculation, based on structures from nanosecond molecular dynamics simulation, revealed that (19)Phe, (22)Leu, and (23)Trp of p53 have the strongest binding interaction with MDM2 followed by (26)Leu and (27)Pro. The specific residues of MDM2 that have dominant binding interactions with p53 are specifically identified to be (51)Lys, (54)Leu, (62)Met, (67)Tyr, (72)Gln, (94)Lys, (96)His, and (100)Tyr. The p53-MDM2 binding interaction is dominated by van der Waals interaction and to a lesser degree by electrostatic interaction. The MP2 results are in generally good agreement with those from the force field calculation while the DFT/B3LYP calculation failed to give attractive interaction energies for certain residue-residue interactions due to the lack of dispersion energy.

Systematic study has been carried out to investigate the accuracy of mid-bond functions in describing pi-pi interactions in benzene dimer. Potential energy curves are calculated for the sandwich, T-shaped, and parallel-displaced configurations of benzene dimer by adding bond functions in MP2 (second-order Moller-Plesset perturbation theory) calculations with a wide range of split-valence and augmented, correlation-consistent basis sizes. At MP2 level, the largest basis set used with a bond function (denoted aug-cc-pVDZf-6s6p4d2f) differs by only approximately 0.1 kcal/mol relative to the result obtained from the standard aug-cc-pVQZ basis calculation (without the bond function). The calculated potential energy curves from the bond function basis aug-cc-pVDZf-6s6p4d2f and the larger standard basis aug-cc-pVTZ are in excellent agreement with each other for all three configurations. The number of bond function basis aug-cc-pVDZf-6s6p4d2f is 526 compared to 828 of aug-cc-pVTZ and 1512 of aug-cc-pVQZ. Current study shows that bond functions can be effectively employed to give accurate description of pi-pi interactions with the addition of only a minimal number of bond functions.

Molecular dynamics simulations followed by quantum mechanical calculation and Molecular Mechanics Poisson-Boltzmann Surface Area (MM-PBSA) analysis have been carried out to study binding of proline- and pyrazinone-based macrocyclic inhibitors (L86 and T76) to human α-thrombin. Detailed binding interaction energies between these inhibitors and individual protein fragments are calculated using DFT method based on a new quantum mechanical approach for computing protein-ligand interaction energy. The analysis of detailed interaction energies provides insight on the protein-ligand binding mechanism. Study shows that T76 and L86 bind to thrombin in a very similar “inhibition mode” except that T76 has relatively weaker binding interaction with Glu217. The analysis from quantum calculation of binding interaction is consistent with the MM-PBSA calculation of binding free energy, and the calculated free energies for L86/T76-thrombin binding agree well with the experimental data.

Quantum chemical calculation has been carried out to analyze binding interactions of nevirapine to HIV-1 reverse transcriptase (RT) and single point mutants Lys103 --Asn (K103N) and Tyr181--Cys (Y181C). In this study, the entire system of HIV-1 RT/nevirapine complex with over 15,000 atoms is explicitly treated by using a recently developed MFCC (molecular fractionation with conjugate caps) approach. Quantum calculation of protein-drug interaction energy is performed at Hartree-Fock and DFT levels. The RT-nevirapine interaction energies are computed at fixed geometries given by the crystal structures of the HIV-1 RT/nevirapine complexes from protein data bank (PDB). The present calculation provides a quantum mechanical interaction spectrum that explicitly shows interaction energies between nevirapine and individual amino-acid fragments of RT. Detailed interactions that are responsible for drug resistance of two major RT mutations are elucidated based on computational analysis in relation to the crystal structures of binding complexes. The present result provides a qualitative molecular understanding of HIV-1 RT drug resistance to nevirapine and gives useful guidance in designing improved inhibitors with better resistance to RT mutation.

Full quantum mechanical compu- tational study has been carried out to study binding of efavirenz (EFZ), a second generation FDA ap- proved nonnucleoside inhibitor, to HIV-1 reverse transcriptase (RT) and its K103N and Y181C mu- tants using the MFCC (molecular fractionation with conjugate caps) method. The binding interaction energies between EFZ and each protein fragment are calculated using a combination of HF/3-21G, B3LYP/6-31G* and MP2/6-31G* ab initio levels. The present computation shows that Efavirenz binds to HIV-1 RT predominantly through strong electro- static interaction with the Lys101 residue. The small loss of binding to K103N mutant by Efavirenz can be attributed to a slightly weakened attractive interac- tion between the drug and Lys101 due to a conforma- tional change of mutation. The small loss of binding to Y181C mutant by efavirenz can be attributed to the Glu698 residue moving closer to EFZ due to conformational change, which results in an in- crease of repulsive energy relative to the wild type (WT). The binding of efavirenz-derived DPC961 to HIV-1 RT is enhanced by an additional attractive interaction to residue Hid235 and reduced repul- sion to Glu698, resulting in an increase of binding energy by about 4 kcal/mol. Proteins 2005;59:489 - 495.

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.

We present a fully quantum mechanical calculation for binding interaction between HIV-1 protease (PR) and the water molecule W301 which bridges the flaps of the protease with the inhibitors of PR. The quantum calculation is made possible by applying a recently developed molecular fractionation with conjugate caps (MFCC) method which divides a protein molecule into capped amino acid-based fragments and their conjugate caps. These individual fragments are properly treated to preserve the chemical property of bonds that are cut. Ab initio methods at HF, B3LYP, and MP2 levels with a fixed basis set 6-31+G* have been employed in the present calculation. The MFCC calculation produces a quantum mechanical interaction "map" representing interactions between individual residues of PR and W301. This enables a detailed quantitative analysis on binding of W301 to specific residues of PR at quantum mechanical level.