Improved Indicator Algorithms for Tracking a Hydrated Proton as A Local Structural Defect in Grotthuss Diffusion in Aqueous Solutions.

Keeping track of a hydrated proton in dynamics simulations is important and nontrivial. Here, we report two revised algorithms for the proton indicator, a pseudo-atom whose position approximates the location of an excess proton diffusing via the Grotthuss mechanism in aqueous solution. The new methods describe the delocalized proton as a structural defect. Encouragingly, in test simulations of a hydrated proton in bulk water, the new algorithms substantially outperform the original scheme by significantly reducing large displacements in the indicator positions upon donor switch, yielding smoother trajectories that effectively track the movement of the solvated proton.

Adaptive-Partitioning Multilayer Dynamics Simulations: 1. On-the-Fly Switch between Two Quantum Levels of Theory.

We propose to generalize the previously developed two-layer permuted adaptive-partitioning quantum-mechanics/molecular-mechanics (QM/MM), which reclassifies atoms as QM or MM on-the-fly in dynamics simulations, to multilayer adaptive-partitioning algorithms that enable multiple levels of theory. In this work, we formulate two new algorithms that smoothly interpolate the energy between two QM (Q1 and Q2) levels of theory. The first "permuted adaptive-partitioning" scheme is based on the weighted many-body expansion of the potential, as in the adaptive-partitioning QM/MM. Unconventional and potentially more efficient, the second "interpolated adaptive-partitioning" method employs alchemical QM calculations with Q1/Q2-mixed basis sets, Fock matrices, and overlap matrices. To our knowledge, this is the first time that such alchemical calculations are performed in QM, although they are routinely done in MM. Test calculations on water-cluster models show that both new algorithms indeed yield smooth energy curves when water molecules shift between Q1 and Q2.

Riding elevators into and out of cells.

The mechanisms responsible for the trafficking of carboxylate ions across cell membranes are becoming clearer.

Tracking Proton Transfer through Titratable Amino Acid Side Chains in Adaptive QM/MM Simulations.

Ubiquitous throughout biological processes, proton transport usually occurs through the Grotthuss shuttling mechanism, where the hydrated proton exists as a charge or structural defect and is propagated quickly through a network of hydrogen bonds with minimal perturbation to the positions of the involved heavy atoms. The rapid reorganization of the bonding network and changing identity of the migrating proton can cause difficulties in molecular dynamics (MD) simulations. Previously, we formulated a proton indicator that tracks the proton as a structural defect for proton exchange between water molecules. In this work, we extend the proton indicator to treat proton transfer between water and amino acid side chains with titratable functional groups. Of particular interest are histidine, glutamate, and arginine, all of which have titratable groups featuring multiple protonation sites. Comparison with the modified center of excess charge (mCEC) suggests that the proton indicator and mCEC are both comparable in approximating the location of the proton. The location of the proton indicator was then used as the center of the QM subsystem in adaptive quantum-mechanical/molecular-mechanical (QM/MM) simulations of proton transport through a model channel along a path consisting of water and titratable amino acid side chains. In the adaptive QM/MM simulations, atoms were reclassified on the fly in a continuous and smooth manner as QM or MM depending on their distances from the proton indicator. Employing a small, mobile QM subsystem, the adaptive QM/MM simulations were found to be much more efficient than the conventional QM/MM simulations with a large QM subsystem that covered the entire pathway for proton relay.

Adaptive Partitioning QM/MM for Molecular Dynamics Simulations: 6. Proton Transport through a Biological Channel.

Adaptive quantum-mechanics/molecular-mechanics (QM/MM) dynamics simulations feature on-the-fly reclassification of atoms as QM or MM continuously and smoothly as trajectories are propagated. This allows one to use small, mobile QM subsystems, the contents of which are dynamically updated as needed. In this work, we report the first adaptive QM/MM simulations of H+ transfer through a biological channel, in particular, the protein EcCLC, a chloride channel (CLC) Cl-/H+ antiporter derived from E. coli. To this end, the H+ indicator previously formulated for approximating the location of an excess H+ in bulk water was extended to include Cl- ions and carboxyl groups as H+ donors/acceptors. Furthermore, when setting up buffer groups, a new "sushi-roll" scheme was employed to group multiple water molecules, ions, and titratable residues along the one-dimensional channel for adaptive partitions. Our simulations reveal that the H+ relay path, which consists of water molecules in the pore, a bound Cl- ion at the central binding site (Cl-cen) of the protein, and the external gating residue E148, exhibits certain mobility within the channel. A two-stage journey of H+ migration was observed: the H+ moves toward Cl-cen and is then shared between Cl-cen and nearby water molecules in the first stage and departs from Cl-cen via nearly concerted transfer to protonate E148 in the second stage. Most of the simulated trajectories show the bound Cl- ion in the channel to be transiently protonated, a possibility that was previously suggested by experiments and computations. Comparisons with conventional QM/MM simulations revealed that both adaptive and conventional treatments yield similar qualitative pictures. This work demonstrates the feasibility of adaptive QM/MM in the simulations of H+ migration through biological channels.

Adaptive QM/MM for Molecular Dynamics Simulations: 5. On the Energy-Conserved Permuted Adaptive-Partitioning Schemes.

In combined quantum-mechanical/molecular-mechanical (QM/MM) dynamics simulations, the adaptive-partitioning (AP) schemes reclassify atoms on-the-fly as QM or MM in a smooth manner. This yields a mobile QM subsystem with contents that are continuously updated as needed. Here, we tailor the Hamiltonian adaptive many-body correction (HAMBC) proposed by Boreboom et al. [J. Chem. Theory Comput.2016, 12, 3441] to the permuted AP (PAP) scheme. The treatments lead to the HAMBC-PAP method (HPAP), which both conserves energy and produces accurate solvation structures in the test of "water-in-water" model system.

Chloride Ion Transport by the E. coli CLC Cl-/H+ Antiporter: A Combined Quantum-Mechanical and Molecular-Mechanical Study.

We performed steered molecular dynamics (SMD) and umbrella sampling simulations of Cl- ion migration through the transmembrane domain of a prototypical E. coli CLC Cl-/H+ antiporter by employing combined quantum-mechanical (QM) and molecular-mechanical (MM) calculations. The SMD simulations revealed interesting conformational changes of the protein. While no large-amplitude motions of the protein were observed during pore opening, the side chain rotation of the protonated external gating residue Glu148 was found to be critical for full access of the channel entrance by Cl-. Moving the anion into the external binding site (Sext) induced small-amplitude shifting of the protein backbone at the N-terminal end of helix F. As Cl- traveled through the pore, rigid-body swinging motions of helix R separated it from helix D. Helix R returned to its original position once Cl- exited the channel. Population analysis based on polarized wavefunction from QM/MM calculations discovered significant (up to 20%) charge loss for Cl- along the ion translocation pathway inside the pore. The delocalized charge was redistributed onto the pore residues, especially the functional groups containing π bonds (e.g., the Tyr445 side chain), while the charges of the H atoms coordinating Cl- changed almost negligibly. Potentials of mean force computed from umbrella sampling at the QM/MM and MM levels both displayed barriers at the same locations near the pore entrance and exit. However, the QM/MM PMF showed higher barriers (~10 kcal/mol) than the MM PMF (~2 kcal/mol). Binding energy calculations indicated that the interactions between Cl- and certain pore residues were overestimated by the semi-empirical PM3 Hamiltonian and underestimated by the CHARMM36 force fields, both of which were employed in the umbrella sampling simulations. In particular, CHARMM36 underestimated binding interactions for the functional groups containing π bonds, missing the stabilizations of the Cl- ion due to electron delocalization. The results suggested that it is important to explore these quantum effects for accurate descriptions of the Cl- transport.

Restrained Proton Indicator in Combined Quantum-Mechanics/Molecular-Mechanics Dynamics Simulations of Proton Transfer through a Carbon Nanotube.

Recently, a collective variable "proton indicator" was purposed for tracking an excess proton solvated in bulk water in molecular dynamics simulations. In this work, we demonstrate the feasibility of utilizing the position of this proton indicator as a reaction coordinate to model an excess proton migrating through a hydrophobic carbon nanotube in combined quantum-mechanics/molecular-mechanics simulations. Our results indicate that applying a harmonic restraint to the proton indicator in the bulk solvent near the nanotube pore entrance leads to the recruitment of water molecules into the pore. This is consistent with an earlier study that employed a multistate empirical valence bond potential and a different representation (center of excess charge) of the proton. We attribute this water recruitment to the delocalized nature of the solvated proton, which prefers to be in high-dielectric bulk solvent. While water recruitment into the pore is considered an artifact in the present simulations (because of the artificially imposed restraint on the proton), if the proton were naturally restrained, it could assist in building water wires prior to proton transfer through the pore. The potential of mean force for a proton translocation through the water-filled pore was computed by umbrella sampling, where the bias potentials were applied to the proton indicator. The free energy curve and barrier heights agree reasonably with those in the literature. The results suggest that the proton indicator can be used as a reaction coordinate in simulations of proton transport in confined environments.