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Abstract

Multiscale simulation methods utilize microscopic information, such as atomic interactions, to infer macroscopic thermodynamic or kinetic properties. For example, free energy sampling connects dynamics with free energy curves, enabling the estimation of reaction rates and equilibrium constants, while coarse-graining methods pre-average interactions in finer-grain systems to build coarse-grained models, allowing longer simulations of larger systems. A key challenge of these multiscale methods is their reliance on accurate microscopic molecular dynamics statistics and the need for ergodic sampling of the phase space. Despite advances in computational power enabling unprecedented levels of brute force sampling, the curse of dimensionality dictates that such efforts become exponentially more difficult as system size increases. This limitation is particularly relevant for systems like membrane proteins, which are challenging to study due to the limited temporal and spatial resolution of experimental techniques, yet their biological significance necessitates a deeper understanding for the sake of drug discovery and bioengineering. This study first demonstrates the multiscale simulation of EmrE, a secondary active transporter that effluxes toxins from \emph{E. coli} using proton motive force. EmrE, a member of the Small Multidrug Resistant (SMR) transporter family, exhibits transport cycles that deviate significantly from the canonical alternating access model while preventing substrate leakage. Our simulations show that at higher pH levels, the C-terminal of EmrE acts as a secondary gate, controlling a water wire into the binding site. In the tail truncation mutant ∆107-EmrE, a hydrated water wire not previously observed in WT-EmrE is found. Further, we demonstrate that this gate allosterically controls a hydrophobic gate, preventing water wire formation. This secondary gating hypothesis is corroborated by high pH structural analysis of EmrE, revealing a hydrogen bonding network occluding the binding site. A 2D potential of mean force (PMF) analysis, using hydrogen bond formation and channel hydration as collective variables, shows that breaking this hydrogen bond leads to EmrE hydration, facilitating subsequent proton transport. While cleverly choosing collective variables can aid in sampling specific slow degrees of freedom, unbiased slow degrees of freedom are often abundant and difficult to identify. Coarse-graining is a well-known method for accelerating system dynamics and handling longer timescale sampling. We developed the Quantum Mechanics with Coarse-Grained Molecular Mechanics (QM/CG-MM) method to introduce reactivity into coarse-grained models, extending previous methodologies to account for electrostatic coupling in polar environments. Demonstrations with a chloride-methyl chloride SN2 reaction in acetone, a system sensitive to solvent polarity, show that the QM/CG-MM method accurately replicates the potential of mean force and reaction barriers compared to atomistic simulations. The method's generalizability is validated across multiple reactive systems, achieving consistent agreement with atomistic models and proportional sampling speed-up relative to the acceleration of solvent rotational dynamics in the CG system. This advancement highlights the potential of QM/CG-MM to provide accurate and computationally efficient simulations for complex chemical systems.

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