Browsing by Subject "Free energy"

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    Conformational Changes in Two Inter-Helical Loops of Mhp1 Membrane Transporter
    (PLOS, 2015-07-17) Song, Hyun Deok; Zhu, Fangqiang; Department of Physics, School of Science
    Mhp1 is a bacterial secondary transporter with high-resolution crystal structures available for both the outward- and inward-facing conformations. Through molecular dynamics simulations of the ligand-free Mhp1 as well as analysis of its crystal structures, here we show that two inter-helical loops, respectively located at the extra- and intracellular ends of the “hash motif” in the protein, play important roles in the conformational transition. In the outward- and inward-facing states of the protein, the loops adopt different secondary structures, either wrapped to the end of an alpha-helix, or unwrapped to extended conformations. In equilibrium simulations of 100 ns with Mhp1 in explicit lipids and water, the loop conformations remain largely stable. In targeted molecular dynamics simulations with the protein structure driven from one state to the other, the loops exhibit resistance and only undergo abrupt changes when other parts of the protein already approach the target conformation. Free energy calculations on the isolated loops further confirm that the wrapping/unwrapping transitions are associated with substantial energetic barriers, and consist of multiple sequential steps involving the rotation of certain backbone torsion angles. Furthermore, in simulations with the loops driven from one state to the other, a large part of the protein follows the loops to the target conformation. Taken together, our simulations suggest that changes of the loop secondary structures would be among the slow degrees of freedom in the conformational transition of the entire protein. Incorporation of detailed loop structures into the reaction coordinate, therefore, should improve the convergence and relevance of the resulting conformational free energy.
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    Doubly Polarized QM/MM with Machine Learning Chaperone Polarizability
    (American Chemical Society, 2021) Kim, Bryant; Shao, Yihan; Pu, Jingzhi; Chemistry and Chemical Biology, School of Science
    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.