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

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

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

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

Computational Studies of Carbodiimide Rings

Computational studies of alicyclic carbodiimides (RNCNR) (rings five through twelve) at the MP2/6-31G­(d,p)//MP2/6-31G­(d,p) level of theory were conducted to locate the transition states between carbodiimides isomers. Transition states for rings six through twelve were found. The RNCNR dihedral angle is ∼0° for even-numbered rings, but deviates from 0° for rings seven, nine, eleven, and twelve. The even- and odd-numbered ring transition states have different symmetry point groups. C_s transition states (even rings) have an imaginary frequency mode that transforms as the asymmetric irreducible representation of the group. C₂ transition states (odd rings) have a corresponding mode that transforms as the totally symmetric representation. Intrinsic reaction coordinate analyses followed by energy minimization along the antisymmetric pathways led to enantiomeric pairs. The symmetric pathways give diastereomeric isomers. The five-membered ring carbodiimide is a stable structure, possibly isolable. A twelve-membered ring transition state was found only without applying symmetry constraints (C₁). Molecular mechanics and molecular dynamics studies of the seven-, eight-, and nine-membered rings gave additional structures, which were then minimized using ab initio methods. No structures beyond those found from the IRC analyses described were found. The potential for optical resolution of the seven-membered ring is discussed

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 (<i>J. Phys. Chem. B</i> <b>2007</b>, <i>111</i>, 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 <i>Escherichia coli</i> CLC chloride ion transport protein, in particular, the intracellular binding site S_int discovered by crystallography and one putative additional binding site S_add 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 <i>n</i>(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

Effect of follistatin on protein synthesis and activation of mTOR/p70S6K pathway in C2C12 cells treated with dexamethasone (DEX, 100 μM for 36 h).

<p>The changes in protein synthesis rate (A) and phospho-mTOR (Ser 2448) (B) and phospho-p70S6K (C) levels in C2C12 cells after treatment with DEX (100 μM) and follistatin (800 ng/ml) for 36 h. The values are presented as the means ± SEM (n = 6). ^a,b Means with different letters differ significantly (<i>P <</i> 0.05).</p

Immunofluorescence of injected ECTO-MSCs in nasal mucosa.

<p>MSCs were labeled with DAPI and nestin (A), indicating endogenous MSCs exist in nasal mucosa of mouse. CM-Dil staining as cell tracker shows the migration of injected MSCs to nasal mucosa via tail vein injection (C) compared to saline control (B) (scale bar = 200 μm).</p

Histological analysis of nasal mucosa.

<p>Control (A) and ECTO-MSC (B) groups had neglectable inflammatory eosinophils infiltration into the nasal mucosa. The extravasation of eosinophils was shown in mice sensitized by OVA (C). After MSCs injection, eosinophils were impressively reduced (D). Nasal mucosa sections were stained with hematoxylin and eosin with 200× magnification. Scale bar = 500 μm.</p