Adaptive-partitioning QM/MM for molecular dynamics simulations: 4. Proton hopping in bulk water.

By reclassifying atoms as QM or MM on-the-fly, adaptive QM/MM dynamics simulations can utilize small QM subsystems whose locations and contents are continuously and automatically updated. Although adaptive QM/MM has been applied in studies of a variety of ions, dynamics simulations of a hydrated proton in bulk water remain a challenge. The difficulty arises from the need to transfer structural features (the covalent and hydrogen bonding networks) via the Grotthuss mechanism instead of the given proton. One must therefore identify an appropriate reference point from which the QM subsystem can be positioned that continuously follows the structural variations as the proton hops. To solve this problem, we propose a proton indicator that serves as the needed reference point. The location of the proton indicator varies smoothly from the hydronium oxygen in the resting (Eigen) state to the shared proton in the transition (Zundel) state. The algorithm is implemented in the framework of a modified permuted adaptive-partitioning QM/MM. As a proof of concept, we simulate an excess proton solvated in bulk water, where the QM subsystem is defined as a sphere of 4.0 Å radius centered at the proton indicator. We find that the use of the proton indicator prevents abrupt changes in the location and contents of the QM subsystem. The new method yields reasonably good agreement in the proton solvation structure and in the proton transfer dynamics with previously reported conventional QM/MM dynamics simulations that employed a much larger QM subsystem (a sphere of 12 Å radius). Also, the results do not change significantly with respect to variations in the time step size (0.1 or 0.5 fs), truncation of the many-body expansion of the potential (from fifth to second order), and absence/presence of thermostat. The proton indicator combined with the modified permuted adaptive-partitioning scheme thus appears to be a useful tool for studying proton transfer in solution.

Molecular dynamics simulations of ion solvation by flexible-boundary QM/MM: on-the-fly partial charge transfer between QM and MM subsystems.

The flexible-boundary (FB) quantum mechanical/molecular mechanical (QM/MM) scheme accounts for partial charge transfer between the QM and MM subsystems. Previous calculations have demonstrated excellent performance of FB-QM/MM in geometry optimizations. This article reports an implementation to extend FB-QM/MM to molecular dynamics simulations. To prevent atoms from getting unreasonably close, which can lead to polarization catastrophe, empirical correcting functions are introduced to provide additive penalty energies for the involved atom pairs and to improve the descriptions of the repulsive exchange forces in FB-QM/MM calculations. Test calculations are carried out for chloride, lithium, sodium, and ammonium ions solvated in water. Comparisons with conventional QM/MM calculations suggest that the FB treatment provides reasonably good results for the charge distributions of the atoms in the QM subsystems and for the solvation shell structural properties, albeit smaller QM subsystems have been used in the FB-QM/MM dynamics simulations.

Adaptive-Partitioning QM/MM Dynamics Simulations: 3. Solvent Molecules Entering and Leaving Protein Binding Sites.

The adaptive-partitioning (AP) schemes for combined quantum-mechanical/molecular-mechanical (QM/MM) calculations allow on-the-fly reclassifications of atoms and molecules as QM or MM in dynamics simulations. The permuted-AP (PAP) scheme (J. Phys. Chem. B 2007, 111, 2231) introduces a thin layer of buffer zone between the QM subsystem (also called active zone) and the MM subsystem (also known as the environmental zone) to provide a continuous and smooth transition and expresses the potential energy in a many-body expansion manner. The PAP scheme has been successfully applied to study small molecules solvated in bulk solvent. Here, we propose two modifications to the original PAP scheme to treat solvent molecules entering and leaving protein binding sites. First, the center of the active zone is placed at a pseudoatom in the binding site, whose position is not affected by the movements of ligand or residues in the binding site. Second, the extra forces due to the smoothing functions are deleted. The modified PAP scheme no longer describes a Hamiltonian system, but it satisfies the conservation of momentum. As a proof-of-concept experiment, the modified PAP scheme is applied to the simulations under the canonical ensemble for two binding sites of the Escherichia coli CLC chloride ion transport protein, in particular, the intracellular binding site Sint discovered by crystallography and one putative additional binding site Sadd suggested by molecular modeling. The exchange of water molecules between the binding sites and bulk solvent is monitored. For comparison, simulations are also carried out using the same model system and setup with only one exception: the extra forces due to the smoothing functions are retained. The simulations are benchmarked against conventional QM/MM simulations with large QM subsystems. The results demonstrate that the active zone centered at the pseudo atom is a reasonable and convenient representation of the binding site. Moreover, the transient extra forces are non-negligible and cause the QM water molecules to move out of the active zone. The modified PAP scheme, where the extra forces are excluded, avoids the artifact, providing a realistic description of the exchange of water molecules between the protein binding sites and bulk solvent.

Charge transfer and polarization for chloride ions bound in ClC transport proteins: natural bond orbital and energy decomposition analyses.

ClC transport proteins show a distinct "broken-helix" architecture, in which certain α-helices are oriented with their N-terminal ends pointed toward the binding sites where the chloride ions are held extensively by the backbone amide nitrogen atoms from the helices. To understand the effectiveness of such binding structures, we carried out natural bond orbital analysis and energy decomposition analysis employing truncated active-site model systems for the bound chloride ions along the translocation pore of the EcClC proteins. Our results indicated that the chloride ions are stabilized in such a binding environment by electrostatic, polarization, and charge-transfer interactions with the backbone and a few side chains. Up to ~25% of the formal charges of the chloride ions were found smeared out to the surroundings primarily via charge transfer from the chloride's lone pair n(Cl) orbitals to the protein's antibonding σ*(N-H) or σ*(O-H) orbitals; those σ* orbitals are localized at the polar N-H and O-H bonds in the chloride's first solvation shells formed by the backbone amide groups and the side chains of residues Ser107, Arg147, Glu148, and Tyr445. Polarizations by the chloride ions were dominated by the redistribution of charge densities among the π orbitals and lone pair orbitals of the protein atoms, in particular the atoms of the backbone peptide links and of the side chains of Arg147, Glu148, and Tyr445. The substantial amounts of electron density involved in charge transfer and in polarization were consistent with the large energetic contributions by the two processes revealed by the energy decomposition analysis. The significant polarization and charge-transfer effects may have impacts on the mechanisms and dynamics of the chloride transport by the ClC proteins.

Specific Reaction Path Hamiltonian for Proton Transfer in Water: Reparameterized Semiempirical Models.

The semiempirical MNDO-based AM1 and PM3 methods and the orthogonalization-corrected OM1, OM2, and OM3 models were reparameterized to improve their description of bulk water and of proton transfer in water. Reference data included the gas-phase geometries and energies of the water molecule, small water clusters, the hydronium ion, and small hydronium ion-water clusters, as well as the gas-phase potential energy surface for proton transfer between the two water molecules in a Zundel ion, all calculated at the MP2/aug-cc-pVTZ level of theory. Combined QM/MM molecular dynamics simulations were carried out for bulk water and for a proton solvated in water using large cluster models. Both the authentic and reparameterized semiempirical models were employed in the simulations. The reparameterization led to significantly better results in all cases. The new set of OM3 parameters gave the best overall results for the structural and dynamic properties of water and the hydrated proton, with a small but finite barrier of 0.1-0.2 kcal/mol in the potential of mean force for proton transfer, in agreement with ab initio path-integral molecular dynamics simulations. The reparameterized OM3 model is expected to be useful for efficient modeling of proton transfer in aqueous solution.

Adaptive-Partitioning Redistributed Charge and Dipole Schemes for QM/MM Dynamics Simulations: On-the-fly Relocation of Boundaries that Pass through Covalent Bonds.

Recently, Heyden, Lin, and Truhlar (J. Phys. Chem. B2007, 111, 2231-2241) formularized the adaptive-partitioning schemes for quantum mechanical and molecular mechanical (QM/MM) molecular dynamics simulations. The adaptive-partitioning schemes permit on-the-fly reclassification of atoms/groups as part of the QM or MM subsystems during dynamics simulations. Test simulations of argon atoms in a periodic box with dual-level MM potentials in the microcanonical ensemble demonstrated that the adaptive-partitioning schemes conserved energy and momentum, which is critical to ensure correct sampling of configuration spaces of desired ensembles. In this work, we reported the extension of the adaptive-partitioning schemes to deal with groups that are molecular fragments. The newly developed adaptive-partitioning redistributed charge scheme and adaptive-partitioning redistributed charge and dipole schemes allow on-the-fly relocation of the QM/MM boundaries that cut through covalent bonds during dynamics simulations. Test QM/MM simulations with a variety of QM levels of theory in the microcanonical ensembles demonstrated that the new schemes conserve energy and momentum.

Comparing the temperature-dependent conductance of the two structurally similar E. coli porins OmpC and OmpF.

The temperature-dependent ion conductance of OmpC, a major outer membrane channel of Escherichia coli, is predicted using all-atom molecular dynamics simulations and experimentally verified. To generalize previous results, OmpC is compared to its structural homolog OmpF at different KCl concentrations, pH values, and a broad temperature range. At low salt concentrations and up to room temperature, the molecular modeling predicts the experimental conductance accurately. At high salt concentrations above 1 M KCl and above room temperature, the simulations underestimate the conductance. Moreover, the temperature dependence of the channel conductance is different from that of the bulk, both in experiment and simulation, indicating a strong contribution of surface effects to the ion conductance. With respect to OmpC, subconductance levels can be observed in experiments only. Subconductance and gating levels can be clearly distinguished by their differences in conductance values and temperature-dependent behavior. With increasing temperature, the probability of a subconductance state to occur, increases, while the dwell time is decreased. The open probability, frequency, and dwell time of such states is largely pH- and KCl concentration-independent, while their amplitudes show a lower increase with increasing salt concentration than gating amplitudes. Voltage dependence of subconductance has been found to be negligible within the uncertainty of the measurements.

Understanding ion conductance on a molecular level: an all-atom modeling of the bacterial porin OmpF.

All-atom molecular dynamics simulations of the ion current through OmpF, the major porin in the outer membrane of Escherichia coli, were performed. Starting from the crystal structure, the all-atom modeling allows us to calculate a parameter-free ion conductance in semiquantitative agreement with experiment. Discrepancies between modeling and experiment occur, e.g., at salt concentrations above 1 M KCl or at high temperatures. At lower salt concentrations, the ions have separate pathways along the channel surface. The constriction zone in the channel contains, on one side, a series of positively charges (R42, R82, R132), and on the opposite side, two negatively charged residues (D113, E117). Mutations generated in the constriction zone by removing cationic residues enhance the otherwise small cation selectivity, whereas removing the anionic residues reverses the selectivity. Reduction of the negatively charged residues decreases the conductance by half, whereas cationic residues enhance the conductance. Experiments on mutants confirm the results of the molecular-level simulations.

Shaping femtosecond coherent anti-Stokes Raman spectra using optimal control theory.

Optimal control theory is used to tailor laser pulses which enhance a femtosecond time-resolved coherent anti-Stokes Raman scattering (fs-CARS) spectrum in a certain frequency range. For this aim the optimal control theory has to be applied to a target state distributed in time. Explicit control mechanisms are given for shaping either the Stokes or the probe pulse in the four-wave mixing process. A simple molecule for which highly accurate potential energy surfaces are available, namely molecular iodine, is used to test the procedure. This approach of controlling vibrational motion and delivering higher intensities to certain frequency ranges might also be important for the improvement of CARS microscopy.

Transport at the nanoscale: temperature dependence of ion conductance.

Temperature dependent ion conductance in nanopores is measured in a wide range of electrolyte concentrations and compared with molecular modeling. Single outer membrane protein F (OmpF) channels from E. coli are reconstituted into planar lipid bilayers. In qualitative agreement with the experimental data, applied-field molecular dynamics unraveled atomistic details of the ion transport. Comparing the temperature dependence of the channel conductance with that of the bulk conductivity in the range from 0 to 90 degrees C revealed that at low salt concentrations the transport is mainly driven along the pore surface. Increasing the salt concentration saturates the surface charge transport and induces ion transport in the center of the nanopore. The confinement of the nanopore then favors the formation of ion pairs. Stepping up the temperature reduces the life time of the ion pairs and increases the channel conductance more than expected from the bulk behavior.