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Item Machine Learning Facilitated Quantum Mechanic/Molecular Mechanic Free Energy Simulations(2023-08) Snyder, Ryan; Pu, Jingzhi; Naumann, Christoph; Webb, Ian; Deng, YongmingBridging the accuracy of ab initio (AI) QM/MM with the efficiency of semi-empirical (SE) QM/MM methods has long been a goal in computational chemistry. This dissertation presents four ∆-Machine learning schemes aimed at achieving this objective. Firstly, the incorporation of negative force observations into the Gaussian process regression (GPR) model, resulting in GPR with derivative observations, demonstrates the remarkable capability to attain high-quality potential energy surfaces, accurate Cartesian force descriptions, and reliable free energy profiles using a training set of just 80 points. Secondly, the adaptation of the sparse streaming GPR algorithm showcases the potential of memory retention from previous phasespace, enabling energy-only models to converge using simple descriptors while faithfully reproducing high-quality potential energy surfaces and accurate free energy profiles. Thirdly, the utilization of GPR with atomic environmental vectors as input features proves effective in enhancing both potential energy surface and free energy description. Furthermore, incorporating derivative information on solute atoms further improves the accuracy of force predictions on molecular mechanical (MM) atoms, addressing discrepancies arising from QM/MM interaction energies between the target and base levels of theory. Finally, a comprehensive comparison of three distinct GPR schemes, namely GAP, GPR with an average kernel, and GPR with a system-specific sum kernel, is conducted to evaluate the impact of permutational invariance and atomistic learning on the model’s quality. Additionally, this dissertation introduces the adaptation of the GAP method to be compatible with the sparse variational Gaussian processes scheme and the streaming sparse GPR scheme, enhancing their efficiency and applicability. Through these four ∆-Machine learning schemes, this dissertation makes significant contributions to the field of computational chemistry, advancing the quest for accurate potential energy surfaces, reliable force descriptions, and informative free energy profiles in QM/MM simulations.Item Mapping Free Energy Pathways for ATP Hydrolysis in the E. coli ABC Transporter HlyB by the String Method(MDPI, 2018-10-16) Zhou, Yan; Ojeda-May, Pedro; Nagaraju, Mulpuri; Kim, Bryant; Pu, Jingzhi; Chemistry and Chemical Biology, School of ScienceHlyB 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.Item Toward Determining ATPase Mechanism in ABC Transporters: Development of the Reaction Path–Force Matching QM/MM Method(Elsevier, 2016) Zhou, Y.; Ojeda-May, P.; Nagaraju, M.; Pu, J.; Department of Chemistry & Chemical Biology, School of ScienceAdenosine triphosphate (ATP)-binding cassette (ABC) transporters are ubiquitous ATP-dependent membrane proteins involved in translocations of a wide variety of substrates across cellular membranes. To understand the chemomechanical coupling mechanism as well as functional asymmetry in these systems, a quantitative description of how ABC transporters hydrolyze ATP is needed. Complementary to experimental approaches, computer simulations based on combined quantum mechanical and molecular mechanical (QM/MM) potentials have provided new insights into the catalytic mechanism in ABC transporters. Quantitatively reliable determination of the free energy requirement for enzymatic ATP hydrolysis, however, requires substantial statistical sampling on QM/MM potential. A case study shows that brute force sampling of ab initio QM/MM (AI/MM) potential energy surfaces is computationally impractical for enzyme simulations of ABC transporters. On the other hand, existing semiempirical QM/MM (SE/MM) methods, although affordable for free energy sampling, are unreliable for studying ATP hydrolysis. To close this gap, a multiscale QM/MM approach named reaction path-force matching (RP-FM) has been developed. In RP-FM, specific reaction parameters for a selected SE method are optimized against AI reference data along reaction paths by employing the force matching technique. The feasibility of the method is demonstrated for a proton transfer reaction in the gas phase and in solution. The RP-FM method may offer a general tool for simulating complex enzyme systems such as ABC transporters.