Bridging semiempirical and ab initio QM/MM potentials by Gaussian process regression and its sparse variants for free energy simulation.

Free energy simulations that employ combined quantum mechanical and molecular mechanical (QM/MM) potentials at ab initio QM (AI) levels are computationally highly demanding. Here, we present a machine-learning-facilitated approach for obtaining AI/MM-quality free energy profiles at the cost of efficient semiempirical QM/MM (SE/MM) methods. Specifically, we use Gaussian process regression (GPR) to learn the potential energy corrections needed for an SE/MM level to match an AI/MM target along the minimum free energy path (MFEP). Force modification using gradients of the GPR potential allows us to improve configurational sampling and update the MFEP. To adaptively train our model, we further employ the sparse variational GP (SVGP) and streaming sparse GPR (SSGPR) methods, which efficiently incorporate previous sample information without significantly increasing the training data size. We applied the QM-(SS)GPR/MM method to the solution-phase SN2 Menshutkin reaction, NH3+CH3Cl→CH3NH3++Cl-, using AM1/MM and B3LYP/6-31+G(d,p)/MM as the base and target levels, respectively. For 4000 configurations sampled along the MFEP, the iteratively optimized AM1-SSGPR-4/MM model reduces the energy error in AM1/MM from 18.2 to 4.4 kcal/mol. Although not explicitly fitting forces, our method also reduces the key internal force errors from 25.5 to 11.1 kcal/mol/Å and from 30.2 to 10.3 kcal/mol/Å for the N-C and C-Cl bonds, respectively. Compared to the uncorrected simulations, the AM1-SSGPR-4/MM method lowers the predicted free energy barrier from 28.7 to 11.7 kcal/mol and decreases the reaction free energy from -12.4 to -41.9 kcal/mol, bringing these results into closer agreement with their AI/MM and experimental benchmarks.

Facilitating ab initio QM/MM free energy simulations by Gaussian process regression with derivative observations.

In combined quantum mechanical and molecular mechanical (QM/MM) free energy simulations, how to synthesize the accuracy of ab initio (AI) methods with the speed of semiempirical (SE) methods for a cost-effective QM treatment remains a long-standing challenge. In this work, we present a machine-learning-facilitated method for obtaining AI/MM-quality free energy profiles through efficient SE/MM simulations. In particular, we use Gaussian process regression (GPR) to learn the energy and force corrections needed for SE/MM to match with AI/MM results during molecular dynamics simulations. Force matching is enabled in our model by including energy derivatives into the observational targets through the extended-kernel formalism. We demonstrate the effectiveness of this method on the solution-phase SN2 Menshutkin reaction using AM1/MM and B3LYP/6-31+G(d,p)/MM as the base and target levels, respectively. Trained on only 80 configurations sampled along the minimum free energy path (MFEP), the resulting GPR model reduces the average energy error in AM1/MM from 18.2 to 5.8 kcal mol-1 for the 4000-sample testing set with the average force error on the QM atoms decreased from 14.6 to 3.7 kcal mol-1 Å-1. Free energy sampling with the GPR corrections applied (AM1-GPR/MM) produces a free energy barrier of 14.4 kcal mol-1 and a reaction free energy of -34.1 kcal mol-1, in closer agreement with the AI/MM benchmarks and experimental results.

Mapping Free Energy Pathways for ATP Hydrolysis in the E. coli ABC Transporter HlyB by the String Method.

HlyB functions as an adenosine triphosphate (ATP)-binding cassette (ABC) transporter that enables bacteria to secrete toxins at the expense of ATP hydrolysis. Our previous work, based on potential energy profiles from combined quantum mechanical and molecular mechanical (QM/MM) calculations, has suggested that the highly conserved H-loop His residue H662 in the nucleotide binding domain (NBD) of E. coli HlyB may catalyze the hydrolysis of ATP through proton relay. To further test this hypothesis when entropic contributions are taken into account, we obtained QM/MM minimum free energy paths (MFEPs) for the HlyB reaction, making use of the string method in collective variables. The free energy profiles along the MFEPs confirm the direct participation of H662 in catalysis. The MFEP simulations of HlyB also reveal an intimate coupling between the chemical steps and a local protein conformational change involving the signature-loop residue S607, which may serve a catalytic role similar to an Arg-finger motif in many ATPases and GTPases in stabilizing the phosphoryl-transfer transition state.

Doubly Polarized QM/MM with Machine Learning Chaperone Polarizability.

A major shortcoming of semiempirical (SE) molecular orbital methods is their severe underestimation of molecular polarizability compared with experimental and ab initio (AI) benchmark data. In a combined quantum mechanical and molecular mechanical (QM/MM) treatment of solution-phase reactions, solute described by SE methods therefore tends to generate inadequate electronic polarization response to solvent electric fields, which often leads to large errors in free energy profiles. To address this problem, here we present a hybrid framework that improves the response property of SE/MM methods through high-level molecular-polarizability fitting. Specifically, we place on QM atoms a set of corrective polarizabilities (referred to as chaperone polarizabilities), whose magnitudes are determined from machine learning (ML) to reproduce the condensed-phase AI molecular polarizability along the minimum free energy path. These chaperone polarizabilities are then used in a machinery similar to a polarizable force field calculation to compensate for the missing polarization energy in the conventional SE/MM simulations. Because QM atoms in this treatment host SE wave functions as well as classical polarizabilities, both polarized by MM electric fields, we name this method doubly polarized QM/MM (dp-QM/MM). We demonstrate the new method on the free energy simulations of the Menshutkin reaction in water. Using AM1/MM as a base method, we show that ML chaperones greatly reduce the error in the solute molecular polarizability from 6.78 to 0.03 Å3 with respect to the density functional theory benchmark. The chaperone correction leads to ∼10 kcal/mol of additional polarization energy in the product region, bringing the simulated free energy profiles to closer agreement with the experimental results. Furthermore, the solute-solvent radial distribution functions show that the chaperone polarizabilities modify the free energy profiles through enhanced solvation corrections when the system evolves from the charge-neutral reactant state to the charge-separated transition and product states. These results suggest that the dp-QM/MM method, enabled by ML chaperone polarizabilities, provides a very physical remedy for the underpolarization problem in SE/MM-based free energy simulations.

Reaction Path-Force Matching in Collective Variables: Determining Ab Initio QM/MM Free Energy Profiles by Fitting Mean Force.

First-principles determination of free energy profiles for condensed-phase chemical reactions is hampered by the daunting costs associated with configurational sampling on ab initio quantum mechanical/molecular mechanical (AI/MM) potential energy surfaces. Here, we report a new method that enables efficient AI/MM free energy simulations through mean force fitting. In this method, a free energy path in collective variables (CVs) is first determined on an efficient reactive aiding potential. Based on the configurations sampled along the free energy path, correcting forces to reproduce the AI/MM forces on the CVs are determined through force matching. The AI/MM free energy profile is then predicted from simulations on the aiding potential in conjunction with the correcting forces. Such cycles of correction-prediction are repeated until convergence is established. As the instantaneous forces on the CVs sampled in equilibrium ensembles along the free energy path are fitted, this procedure faithfully restores the target free energy profile by reproducing the free energy mean forces. Due to its close connection with the reaction path-force matching (RP-FM) framework recently introduced by us, we designate the new method as RP-FM in collective variables (RP-FM-CV). We demonstrate the effectiveness of this method on a type-II solution-phase SN2 reaction, NH3 + CH3Cl (the Menshutkin reaction), simulated with an explicit water solvent. To obtain the AI/MM free energy profiles, we employed the semiempirical AM1/MM Hamiltonian as the base level for determining the string minimum free energy pathway, along which the free energy mean forces are fitted to various target AI/MM levels using the Hartree-Fock (HF) theory, density functional theory (DFT), and the second-order Møller-Plesset perturbation (MP2) theory as the AI method. The forces on the bond-breaking and bond-forming CVs at both the base and target levels are obtained by force transformation from Cartesian to redundant internal coordinates under the Wilson B-matrix formalism, where the linearized FM is facilitated by the use of spline functions. For the Menshutkin reaction tested, our FM treatment greatly reduces the deviations on the CV forces, originally in the range of 12-33 to ∼2 kcal/mol/Å. Comparisons with the experimental and benchmark AI/MM results, tests of the new method under a variety of simulation protocols, and analyses of the solute-solvent radial distribution functions suggest that RP-FM-CV can be used as an efficient, accurate, and robust method for simulating solution-phase chemical reactions.

Perioperative complications after noncardiac surgery in patients with insertion of second-generation drug-eluting stents.

The perioperative outcomes of noncardiac surgery in patients who have received second-generation drug-eluting stents (DESs) have received limited study. We reviewed the medical records of 1,748 consecutive patients who received DES at our institution (1,789 procedures) from January 1, 2009, to July 1, 2012, to determine the outcomes of subsequent noncardiac surgery. During a median follow-up of 43 months, 221 patients underwent 345 noncardiac surgeries (138 low risk, 130 intermediate risk, and 77 high risk), of which 278 were in patients with previous second-generation DES implantation. The incidence of noncardiac surgery in patients with previous second-generation DES implantation was 4.5% at 1 year, 11.6% at 2 years, and 15.2% at 3 years. The mean time from stent implantation to surgery was 21±12.9 months. Mean age was 66±8 years, 99% were men, and 11% had a perioperative complication, including 5.8% major bleeding, 2.5% acute kidney injury, 2.2% major adverse cardiac event, and 1.4% stroke. Perioperative stent thrombosis occurred in 2 patients (0.7%, 95% confidence interval 0.2% to 2.6%): 1 patient had received a DES 14 months before surgery and had stent thrombosis on the day of surgery and the other had a DES implanted 21 months before surgery and developed stent thrombosis the day after surgery. In conclusion, the incidence of perioperative complications with noncardiac surgery after second-generation DES implantation was 11% and consisted mainly of bleeding (5.8%). The incidence of definite stent thrombosis was 0.7%.

Assessment of pain and analgesic use in African American cancer patients: factors related to adherence to analgesics.

This study describes pain experience, analgesic use and barriers to pain control in African American cancer patients (N = 116). The overall adherence rate of analgesics was 46%. Constipation and nausea were the most commonly cited side effects of analgesics. Eighty-seven percent of patients reported concern about addiction to analgesics. Patients who believed their doctor needed to focus on curing illness rather than on controlling pain tended to comply with analgesic prescriptions (r = 0.20, p < 0.05). Patients with concerns that analgesics may cause confusion were less likely to take any type of analgesics (r = -0.16, p < 0.05). The study confirms that a patient's perceived barriers influence their decision to take analgesics, and also suggests that African American cancer patients may benefit from education that prevents misconceptions about analgesic use.