Two-dimensional Potential Of Mean Force Research Articles

Distinguishing Weak and Strong Hydrogen Bonds in Liquid Water-A Potential of Mean Force-Based Approach.

The ability to form hydrogen bonds is one of the most important factors behind water's many anomalous properties. However, there is still no consensus on the hydrogen bond structure of liquid water, including the average number of hydrogen bonds in liquid water. We use molecular dynamics simulations of the polarizable iAMOEBA water model for investigating the hydrogen bond characteristics of liquid water over a wide range of temperatures and pressures. Geometric definitions of a hydrogen bond often use a rectangular region on the plane of hydrogen bond distances and angles. In this work, we find that an elliptical region is more appropriate for the identification of hydrogen bonds, based on statistically favorable molecular configurations. The two-dimensional potential of mean force (PMF) landscape along the hydrogen bond distance (O-H) and angle (O-H-O) is calculated for identifying the statistically favored molecular configurations, which is then used for defining hydrogen bond formation as well as the strength of a hydrogen bond. We further propose a new approach to characterize the hydrogen bonds as strong when the PMF is lower than -2 kT. Using this definition, a consistent explanation for the different average numbers of hydrogen bonds in water is obtained in agreement with the literature. Simulations are also performed with the rigid and nonpolarizable TIP4P/2005 water model. Both water models are qualitatively consistent in predicting the distribution of double-, single-, and non-donor configurations, in line with experimental data, while the iAMOEBA water model yields more quantitatively precise results, including a 10-15% double-donor fraction at 90 °C and 1 atm. The method is also demonstrated to be applicable to the recent, and more general, three-dimensional PMF-based definition of hydrogen bonds.

Consistency of geometrical definitions of hydrogen bonds based on the two-dimensional potential of mean force with respect to the time correlation in liquid water over a wide range of temperatures

We examine the temperature dependence of the hydrogen-bond (H-bond) dynamics in supercooled water through the molecular dynamics (MD) simulations using the TIP4P/2005 model. First, we investigate the two-dimensional (2D) potential of mean force (PMF) for the H-bond definition using a pair of distance and angle coordinates between two water molecules. Specifically, we utilize four combinations of the geometrical variables, R-β, r-α, r-γ, and r-ψ, where R and r are the intermolecular O-O and O-H distances, respectively. β and α represent the angles of O-OH and O-HO, respectively, while ψ and γ are angles introduced in terms of the intermolecular O-H vector and the HOH plane of the H-bond acceptor. The consistency among the four definitions of H-bond was then examined by identifying the saddle point on the 2D PMF and analyzing the time correlation function of H-bond. It was found over a wide range of temperatures from the ambient to supercooled that the H-bond definition does not affect the long-time H-bond correlation function and correspondingly, the H-bond lifetime τHB.

How do hydrogen bonds break in supercooled water?: Detecting pathways not going through saddle point of two-dimensional potential of mean force.

Supercooled water exhibits remarkably slow dynamics similar to the behavior observed for various glass-forming liquids. The local order of tetrahedral structures due to hydrogen-bonds (H-bonds) increases with decreasing temperature. Thus, it is important to clarify the temperature dependence of the H-bond breakage process. This was investigated here using molecular dynamics simulations of TIP4P supercooled water. The two-dimensional (2D) potential of mean force (PMF) is presented using combinations of intermolecular distance and angle between two water molecules. The saddle point of the 2D PMF suggests the presence of the transition state that distinguishes between H-bond and non H-bond states. However, we observed pathways not going through this saddle point particularly at supercooled states, which are due to translational rather than rotational motions of the molecules. We quantified the characteristic time scales of rotational and translational H-bond breakages. The time scale of the translational H-bond breakage shows a non-Arrhenius temperature dependence comparable to that of the H-bond lifetime. This time scale is relevant for the temperature dependence of the transmission coefficient based on the transition state theory. The translational H-bond breakage is also related to cage-jumps observed in glass-forming liquids, which mostly involve spatially correlated molecules. Our findings warrant further exploration of an appropriate free-energy surface or reaction coordinates beyond the geometrical variables of the water dimer to describe a possible saddle point related to collective jump motions.

Precise estimation of transfer free energies for ionic species between similar media.

Transfer properties and partition coefficients for individual ions are relevant in a variety of scientific and engineering contexts, such as predicting the effects of different electrolytes on biomacromolecules in a preferential interaction sense or predicting the distribution of heavy metal ions in soils, rivers, etc. Computer simulations allow free energies of transfer to be estimated by considering single ions explicitly. When the two media under consideration are similar to each other regarding ion solvation, the resultant free energies are small in absolute magnitude. In these cases, it is advisable to simulate the transfer process directly. Here, we demonstrate how this can be achieved using two-dimensional umbrella sampling in conjunction with canonical ensemble molecular dynamics simulations where two liquid media are in direct contact. By calculating full two-dimensional potentials of mean force, these simulations allow the estimation of single-ion transfer free energies by integrating this surface accordingly. We report statistical accuracies to highlight that very high precision is achieved and needed to make even just qualitative statements about the transfer process. We close by discussing implications of our results for the specific case considered: the transfer of polypeptide side chain analogs from water to aqueous denaturant solutions.

Ambient-Potential Composite Ewald Method for ab Initio Quantum Mechanical/Molecular Mechanical Molecular Dynamics Simulation.

A new approach for performing Particle Mesh Ewald in ab initio quantum mechanical/molecular mechanical (QM/MM) simulations with extended atomic orbital basis sets is presented. The new approach, the Ambient-Potential Composite Ewald (CEw) method, does not perform the QM/MM interaction with Mulliken charges nor electrostatically fit charges. Instead the nuclei and electron density interact directly with the MM environment, but in a manner that avoids the use of dense Fourier transform grids. By performing the electrostatics with the underlying QM density, the CEw method avoids self-consistent field instabilities that have been encountered with simple charge mapping procedures. Potential of mean force (PMF) profiles of the p-nitrophenyl phosphate dissociation reaction in explicit solvent are computed from PBE0/6-31G* QM/MM molecular dynamics simulations with various electrostatic protocols. The CEw profiles are shown to be stable with respect to real-space Ewald cutoff, whereas the PMFs computed from truncated and switched electrostatics produce artifacts. PBE0/6-311G**, AM1/d-PhoT, and DFTB2 QM/MM simulations are performed to generate two-dimensional PMF profiles of the phosphoryl transesterification reactions with ethoxide and phenoxide leaving groups. The semiempirical models incorrectly produce a concerted ethoxide mechanism, whereas PBE0 correctly produces a stepwise mechanism. The ab initio reaction barriers agree more closely to experiment than the semiempirical models. The failure of Mulliken-charge QM/MM-Ewald is analyzed.

Two-Dimensional Potentials of Mean Force of Nile Red in Intact and Damaged Model Bilayers. Application to Calculations of Fluorescence Spectra

Fluorescent dyes revolutionized and expanded our understanding of biological membranes. The interpretation of experimental fluorescence data in terms of membrane structure, however, requires detailed information about the molecular environment of the dyes. Nile red is a fluorescent molecule whose excitation and emission maxima depend on the polarity of the solvent. It is mainly used as a probe to study lipid microenvironments, for example in imaging the progression of damage to the myelin sheath in multiple sclerosis. In this study, we determine the position and orientation of Nile red in lipid bilayers by calculating two-dimensional Potential of Mean Force (2D-PMF) profiles in a defect-free 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) bilayer and in damaged bilayers containing two mixtures of the oxidized lipid 1-palmitoyl-2-(9'-oxo-nonanoyl)-sn-glycero-3-phosphocholine and POPC. From 2D-PMF simulations we obtain positions and orientations of Nile Red corresponding to the minimum on the binding free energy surface in three different membrane environments with increasing amounts of water, mimicking damage in biological tissue. Using representative snapshots from the simulations, we use combined quantum mechanical/molecular mechanical (QM/MM) models to calculate the emission spectrum of Nile red as a function of its local solvation environment. The results of QM and QM/MM computations are in qualitative agreement with the experimentally observed shift in fluorescence for the dye moving from aqueous solution to the more hydrophobic environment of the lipid interiors. The range of the conformation dependent values of the computed absorption-emission spectra and the lack of solvent relaxation effects in the QM/MM calculations made it challenging to delineate specific differences between the intact and damaged bilayers.

The importance of ensemble averaging in enzyme kinetics.

ConspectusThe active site of an enzyme is surrounded by a fluctuating environment of protein and solvent conformational states, and a realistic calculation of chemical reaction rates and kinetic isotope effects of enzyme-catalyzed reactions must take account of this environmental diversity. Ensemble-averaged variational transition state theory with multidimensional tunneling (EA-VTST/MT) was developed as a way to carry out such calculations. This theory incorporates ensemble averaging, quantized vibrational energies, energy, tunneling, and recrossing of transition state dividing surfaces in a systematic way. It has been applied successfully to a number of hydrogen-, proton-, and hydride-transfer reactions. The theory also exposes the set of effects that should be considered in reliable rate constants calculations.We first review the basic theory and the steps in the calculation. A key role is played by the generalized free energy of activation profile, which is obtained by quantizing the classical potential of mean force as a function of a reaction coordinate because the one-way flux through the transition state dividing surface can be written in terms of the generalized free energy of activation. A recrossing transmission coefficient accounts for the difference between the one-way flux through the chosen transition state dividing surface and the net flux, and a tunneling transmission coefficient converts classical motion along the reaction coordinate to quantum mechanical motion. The tunneling calculation is multidimensional, accounting for the change in vibrational frequencies along the tunneling path and shortening of the tunneling path with respect to the minimum energy path (MEP), as promoted by reaction-path curvature. The generalized free energy of activation and the transmission coefficients both involve averaging over an ensemble of reaction paths and conformations, and this includes the coupling of protein motions to the rearrangement of chemical bonds in a statistical mechanically correct way. The standard deviations of the transmissions coefficients provide information on the diversity of the distribution of reaction paths, barriers, and protein conformations along the members of an ensemble of reaction paths passing through the transition state.We first illustrate the theory by discussing the application to both wild-type and mutant Escherichia coli dihydrofolate reductase and hyperthermophilic Thermotoga maritima dihydrofolate reductase (DHFR); DHFR is of special interest because the protein conformational changes have been widely studied. Then we present shorter discussions of several other applications of EA-VTST/MT to transfer of protons, hydrogen atoms, and hydride ions and their deuterated analogs. Systems discussed include hydride transfer in alcohol dehydrogenase, xylose isomerase, and thymidylate synthase, proton transfer in methylamine dehydrogenase, hydrogen atom transfer in methylmalonyl-CoA mutase, and nucleophilic substitution in haloalkane dehalogenase and two-dimensional potentials of mean force for potentially coupled proton and hydride transfer in the β-oxidation of butyryl-coenzyme A catalyzed by short-chain acyl-CoA dehydrogenase and in the pyruvate to lactate transformation catalyzed by lactate dehydrogenase.

Origin of product selectivity in a prenyl transfer reaction from the same intermediate: exploration of multiple FtmPT1-catalyzed prenyl transfer pathways.

FtmPT1 is a fungal indole prenyltransferase that catalyzes the reaction of tryptophan derivatives with dimethylallyl pyrophosphate to form various biologically active compounds. Herein, we describe detailed studies of FtmPT1 catalysis involving dimethylallyl pyrophosphate and Brevianamide F following the native pathway (yielding Tryprostatin B) and an alternate pathway observed in the Gly115Thr mutant of FtmPT1 yielding a novel cyclized product. Importantly, these two products arise from the same intermediate state, meaning that a step other than the cleavage of the dimethylallyl pyrophosphate (DMAPP; C–O) bond is differentiating between the two product reaction channels. From detailed potential of mean force (PMF) and two-dimensional PMF analyses, we conclude that the rate-limiting step is the cleavage of the C–O bond in DMAPP, while the deprotonation/cyclization step determines the final product distribution. Hence, in the case of FtmPT1, the optimization of the necessary catalytic machinery guides the generation of the final product after formation of the intermediate carbocation.

Mechanistic insights into Mg2+-independent prenylation by CloQ from classical molecular mechanics and hybrid quantum mechanics/molecular mechanics molecular dynamics simulations.

Understanding the mechanism of prenyltransferases is important to the design of engineered proteins capable of synthesizing derivatives of naturally occurring therapeutic agents. CloQ is a Mg(2+)-independent aromatic prenyltransferase (APTase) that transfers a dimethylallyl group to 4-hydroxyphenylpyruvate in the biosynthetic pathway for clorobiocin. APTases consist of a common ABBA fold that defines a β-barrel containing the reaction cavity. Positively charged basic residues line the inside of the β-barrel of CloQ to activate the pyrophosphate leaving group to replace the function of the Mg(2+) cofactor in other APTases. Classical molecular dynamics simulations of CloQ, its E281G and F68S mutants, and the related NovQ were used to explore the binding of the 4-hydroxyphenylpyruvate (4HPP) and dimethylallyl diphosphate substrates in the reactive cavity and the role of various conserved residues. Hybrid quantum mechanics/molecular mechanics potential of mean force (PMF) calculations show that the effect of the replacement of the Mg(2+) cofactor with basic residues yields a similar activation barrier for prenylation to Mg(2+)-dependent APTases like NphB. The topology of the binding pocket for 4HPP is important for selective prenylation at the ortho position of the ring. Methylation at this position alters the conformation of the substrate for O-prenylation at the phenol group. Further, a two-dimensional PMF scan shows that a "reverse" prenylation product may be a possible target for protein engineering.

Medium effects on the 1,3-dipolar cycloaddition of pyridazinium dicyanomethanide with ethyl vinyl ketone in pure and mixed solvents from QM/MM simulations.

The 1,3-dipolar cycloaddition reaction between pyridazinium dicyanomethanide 1 and ethyl vinyl ketone (EVK) has been reported to be a concerted mechanism based on gas-phase ab initio calculations. Our current investigation of this 1,3-dipolar cycloaddition reaction in water, methanol, acetonitrile, H2O-CH3CN, and CH3OH-CH3CN mixtures using novel two-dimensional potentials of mean force (2-D PMF) calculations coupled to QM/MM simulations predicts an alternative free energy surface that supports a stepwise mechanism. The results for the kinetic effect are uniformly in close accord with experimental data and reflect a trigger point for the exponential rate rise in water-acetonitrile mixture. When methanol replaced water, the rate enhancements are more gradual, and there is no trigger point. Calculations in pure solvents and their mixtures at 25 °C and with pure water and acetonitrile at 37 °C indicate that the secondary bridging H-bonding from the first water molecules is necessary for the exponential rate enhancements, which is strong supported by the experimental results. This work provides new insight into solvent effects on 1,3-dipolar cycloaddition reaction.

An Explicit Consideration of Desolvation is Critical to Binding Free Energy Calculations of Charged Molecules at Ionic Surfaces.

Identifying factors that control the strength and specificity of interactions between peptides and nanoparticles is essential for understanding the potential beneficial and deleterious effects of nanoparticles on biological systems. Computer simulations are valuable in this context, although the reliability of such calculations depends on the force field and sampling algorithm, as well as how the binding constant and binding free energy are defined; the latter must be carefully defined with a clear connection to microscopic models based on statistical mechanics. Using the example of formate binding to the rutile titanium dioxide (TiO2) (110) surface, we demonstrate that a reliable description of the binding process requires an explicit consideration of changes in the solvation state of the binding site. Specifically, we carry out metadynamics simulations in which the solvent coordination number of the binding site, s, is introduced as a collective variable in addition to the vertical distance of the adsorbate to the surface (z). The resulting two-dimensional potential of mean force (2D-PMF) clearly shows that explicitly including the local desolvation of the binding site on the TiO2 surface strongly impacts the convergence and result of the binding free energy calculations. Projecting the 2D-PMF into a one-dimensional PMF along either z or s leads to large errors in the free energy barriers. Results from metadynamics simulations are quantitatively supported by independent alchemical free energy simulations, in which the solvation state of the binding site is also carefully considered by explicitly introducing water molecules to the binding site as the adsorbate is decoupled from the system. On the other hand, preliminary committor analysis for the approximate transition state ensemble constructed based on the 2D-PMF suggests that to properly describe the binding/unbinding kinetics, variables beyond s and z, such as those describing the hydrogen bonding pattern of the adsorbate and surface water, need to be included. We expect that the insights and computational methodologies established in this work will be generally applicable to the analysis of binding interactions between highly charged adsorbates and ionic surfaces in solution, such as those implicated in peptide/nanoparticle binding and biomineralization processes.

Insight into the phosphodiesterase mechanism from combined QM/MM free energy simulations.

Molecular dynamics simulations employing a combined quantum mechanical and molecular mechanical potential have been carried out to elucidate the reaction mechanism of the hydrolysis of a cyclic nucleotide cAMP substrate by phosphodiesterase 4B (PDE4B). PDE4B is a member of the PDE superfamily of enzymes that play crucial roles in cellular signal transduction. We have determined a two-dimensional potential of mean force (PMF) for the coupled phosphoryl bond cleavage and proton transfer through a general acid catalysis mechanism in PDE4B. The results indicate that the ring-opening process takes place through an S(N)2 reaction mechanism, followed by a proton transfer to stabilize the leaving group. The computed free energy of activation for the PDE4B-catalyzed cAMP hydrolysis is about 13 kcal·mol(-1) and an overall reaction free energy is about -17 kcal·mol(-1), both in accord with experimental results. In comparison with the uncatalyzed reaction in water, the enzyme PDE4B provides a strong stabilization of the transition state, lowering the free energy barrier by 14 kcal·mol(-1). We found that the proton transfer from the general acid residue His234 to the O3' oxyanion of the ribosyl leaving group lags behind the nucleophilic attack, resulting in a shallow minimum on the free energy surface. A key contributing factor to transition state stabilization is the elongation of the distance between the divalent metal ions Zn(2+) and Mg(2+) in the active site as the reaction proceeds from the Michaelis complex to the transition state.

Proton Transport in Triflic Acid Pentahydrate Studied via Ab Initio Path Integral Molecular Dynamics

Trifluoromethanesulfonic acid hydrates provide a well-defined system to study proton dissociation and transport in perfluorosulfonic acid membranes, typically used as the electrolyte in hydrogen fuel cells, in the limit of minimal water. The triflic acid pentahydrate crystal (CF(3)SO(3)H·5H(2)O) is sufficiently aqueous that it contains an extended three-dimensional water network. Despite it being extended, however, long-range proton transport along the network is structurally unfavorable and would require considerable rearrangement. Nevertheless, the triflic acid pentahydrate crystal system can provide a clear picture of the preferred locations of local protonic defects in the water network, which provides insights about related structures in the disordered, low-hydration environment of perfluorosulfonic acid membranes. Ab initio molecular dynamics simulations reveal that the proton defect is most likely to transfer to the closest water that has the expected presolvation and only contains water in its first solvation shell. Unlike the tetrahydrate of triflic acid (CF(3)SO(3)H·4H(2)O), there is no evidence of the proton preferentially transferring to a water molecule bridging two of the sulfonate groups. However, this could be an artifact of the crystal structure since the only such water molecule is separated from the proton by long O-O distances. Hydrogen bonding criteria, using the two-dimensional potential of mean force, are extracted. Radial distribution functions, free energy profiles, radii of gyration, and the root-mean-square displacement computed from ab initio path integral molecular dynamics simulations reveal that quantum effects do significantly extend the size of the protonic defect and increase the frequency of proton transfer events by nearly 15%. The calculated IR spectra confirm that the dominant protonic defect mostly exists as an Eigen cation but contains some Zundel ion characteristics. Chain lengths and ring sizes determined from the hydrogen bond network, counted using graph theory techniques, are only moderately sensitive to quantum effects. Deliberately introducing a structural defect into the native crystal yields a protonic defect with one hydrogen bond to a sulfonate group that was found to be metastable for at least 10 ps.

Protegrin‐1 orientation and physicochemical properties in membrane bilayers studied by potential of mean force calculations

Protegrin-1 (PG-1) belongs to the family of antimicrobial peptides. It interacts specifically with the membrane of a pathogen and kills the pathogen by releasing its cellular contents. To fully understand the energetics governing the orientation of PG-1 in different membrane environments and its effects on the physicochemical properties of the peptide and membrane bilayers, we have performed the potential of mean force (PMF) calculations as a function of its tilt angle at four distinct rotation angles in explicit membranes composed of either DLPC (1,2-dilauroylphosphatidylcholine) or POPC (1-palmitoyl-2-oleoylphosphatidylcholine) lipid molecules. The resulting PMFs in explicit lipid bilayers were then used to search for the optimal hydrophobic thickness of the EEF1/IMM1 implicit membrane model in which a two-dimensional PMF in the tilt and rotation space was calculated. The PMFs in explicit membrane systems clearly reveal that the energetically favorable tilt angle is affected by both the membrane hydrophobic thickness and the PG-1 rotation angle. Local thinning of the membrane around PG-1 is observed upon PG-1 tilting. The thinning is caused by both hydrophobic mismatch and arginine-lipid head group interactions. The two-dimensional PMF in the implicit membrane is in good accordance with those from the explicit membrane simulations. The ensemble-averaged Val16 (15)N and (13)CO chemical shifts weighted by the two-dimensional PMF agree fairly well with the experimental values, suggesting the importance of peptide dynamics in calculating such ensemble properties for direct comparison with experimental observables.

Protegrin-1 Orientation in Membrane Bilayers: Insights from Potential of Mean Force Calculations as A Function of Its Tilt and Rotation Angles

Protegrin-1 (PG-1) belongs to the family of antimicrobial peptides. It interacts specifically with the membrane of a pathogen and kills the pathogen by releasing its cellular contents. To fully understand the energetics governing the orientation of PG-1 in different membrane environments and its effects on the physicochemical properties of the peptide, we have calculated the potentials of mean force (PMF) of PG-1 as a function of its tilt angle in explicit membrane bilayers composed of either DLPC (1,2-dilauroylphosphatidylcholine) or POPC (1-palmitoyl-2-oleoylphosphatidylcholine) lipid molecules. The resulting PMFs in explicit lipid bilayers were then used to search for the optimal hydrophobic thickness of the implicit membrane, in which a two-dimensional PMF in the tilt and rotation space was calculated. The calculated PMFs in explicit membrane systems clearly reveal that the energetically favorable tilt angle is affected by both the membrane hydrophobic thickness and the PG-1 rotation angle. Local thinning of the membrane around PG-1 is observed upon PG-1 tilting. The thinning effect is caused by different arginines in regard to the rotation orientation of the peptide. The two-dimensional PMF calculated in implicit membrane at specified rotation angles is in good accordance with those from the explicit membrane simulations. The ensemble-averaged Val16 15N and 13CO chemical shifts calculated from the two-dimensional free energy distribution agree fairly well with the experimental values, suggesting the accuracy and reliability of the application of PMFs to understand important physicochemical properties of membrane peptides/proteins.

Proton Transport in Triflic Acid Hydrates Studied via Path Integral Car−Parrinello Molecular Dynamics

The mono-, di-, and tetrahydrates of trifluoromethanesulfonic acid, which contain characteristic H(3)O(+), H(5)O(2)(+), and H(9)O(4)(+) structures, provide model systems for understanding proton transport in materials with high perfluorosulfonic acid density such as perfluorosulfonic acid membranes commonly employed in hydrogen fuel cells. Ab initio molecular dynamics simulations indicate that protons in these solids are predisposed to transfer to the water most strongly bound to sulfonate groups via a Grotthuss-type mechanism, but quickly return to the most solvated defect structure either due to the lack of a nearby species to stabilize the new defect or a preference for the proton to be maximally hydrated. Path integral molecular dynamics of the mono- and dihydrate reveal significant quantum effects that facilitate proton transfer to the "presolvated" water or SO(3)(-) in the first solvation shell and increase the Zundel character of all the defects. These trends are quantified in free energy profiles for each bonding environment. Hydrogen bonding criteria for HOH-OH(2) and HOH-O(3)S are extracted from the two-dimensional potential of mean force. The quantum radial distribution function, radius of gyration, and root-mean-square displacement position correlation function show that the protonic charge is distributed over two or more water molecules. Metastable structural defects with one excess proton shared between two sulfonate groups and another Zundel or Eigen type cation defect are found for the mono- and dihydrate but not for the tetrahydrate crystal. Results for the tetrahydrate native crystal exhibit minor differences at 210 and 250 K. IR spectra are calculated for all native and stable defect structures. Graph theory techniques are used to characterize the chain lengths and ring sizes in the hydrogen bond network. Low conductivities when limited water is present may be attributable to trapping of protons between SO(3)(-) groups and the increased probability that protons transfer to waters bridging two different sulfonate groups.

Spectroscopic Properties of a Strongly Anharmonic Mannich Base N‐oxide

Car-Parrinello molecular dynamics simulations in vacuum and in the solid state are performed on a strongly anharmonic system, namely, 2-(N-diethylamino-N-oxymethyl)-4,6-dichlorophenol, to investigate its molecular and spectroscopic properties. The investigated compound contains two slightly different molecules in the crystal cell with very short intramolecular hydrogen bonds (of 2.400 and 2.423 A), as determined previously by neutron diffraction. The vibrational properties of the compound are studied on the basis of standard approaches, that is, Fourier transformation of the autocorrelation functions of the atomic velocities and dipole moments. Then, the trajectory obtained from ab initio molecular dynamics is sampled and the obtained snapshots are used to solve the vibrational Schrödinger equations and to calculate the O--H stretching envelope as a superposition of the 0-->1 transition. Using an envelope method, the a posteriori quantum effects are included in the O--H stretching. In addition, NMR spectra are calculated also using the obtained snapshots. One- and two-dimensional potentials of mean force (1D and 2D pmf) are derived to explain the details of the proton dynamics. The computational results are supported by NMR experimental data. In addition, the calculated results are compared with previously published X-ray, neutron diffraction, and spectroscopic descriptions. A detailed analysis of the bridged proton's dynamics is thus obtained. The application of 1D and 2D pmf in a system with a strong bridged-proton delocalization is also demonstrated.

Quantum Mechanical/Molecular Mechanical Simulation Study of the Mechanism of Hairpin Ribozyme Catalysis

The molecular mechanism of hairpin ribozyme catalysis is studied with molecular dynamics simulations using a combined quantum mechanical and molecular mechanical (QM/MM) potential with a recently developed semiempirical AM1/d-PhoT model for phosphoryl transfer reactions. Simulations are used to derive one- and two-dimensional potentials of mean force to examine specific reaction paths and assess the feasibility of proposed general acid and base mechanisms. Density-functional calculations of truncated active site models provide complementary insight to the simulation results. Key factors utilized by the hairpin ribozyme to enhance the rate of transphosphorylation are presented, and the roles of A38 and G8 as general acid and base catalysts are discussed. The computational results are consistent with available experimental data, provide support for a general acid/base mechanism played by functional groups on the nucleobases, and offer important insight into the ability of RNA to act as a catalyst without explicit participation by divalent metal ions.

First-Principle Molecular Dynamics Study of Selected Schiff and Mannich Bases: Application of Two-Dimensional Potential of Mean Force to Systems with Strong Intramolecular Hydrogen Bonds.

Car-Parrinello Molecular Dynamics simulations were performed for selected anharmonic systems, i.e., Schiff and Mannich base-type compounds, to investigate the vibrational properties associated with O-H stretching. All calculations were performed in the gas phase to compare them with available experimental data. First the vibrational properties of the two compounds were analyzed on the basis of well-established approaches: Fourier transformation of the autocorrelation function of both the atomic velocities and dipole moments. Then path integral molecular dynamics simulations were performed to demonstrate the influence of quantum effects on the proton's position in the hydrogen bridge. In addition, quantum effects were incorporated a posteriori into calculations of O-H stretching envelopes for the Schiff and Mannich bases. Proton potential snapshots were extracted from the ab initio molecular dynamics trajectory. Vibrational Schrödinger equations (one- and two-dimensional) were solved numerically for the snapshots, and the O-H stretching envelopes were calculated as a superposition of the 0→1 transitions. Subsequently, one- and two-dimensional potentials of mean force (1D and 2D pmf) were calculated for the proton stretching mode from the proton vibrational eigenfunctions and eigenvalues incorporating statistical sampling and nuclear quantum effects. The results show that the applied methodologies are in good agreement with experimental infrared spectra. Additionally, it is demonstrated that the 2D pmf method could be applied in systems with strong anharmonicity to describe the properties of the O-H stretching mode more accurately. Future applications of the 2D pmf technique include, in principle, large biomolecular systems treated within the QM/MM framework.

A New Solvent-Dependent Mechanism for a Triazolinedione Ene Reaction

The ene reaction between 4-phenyl-1,2,4-triazoline-3,5-dione (PTAD) and tetramethylethylene has been investigated using QM/MM calculations in water, methanol, DMSO, and acetonitrile. The effects of solvation on the mechanism and rates of reaction are elucidated using two-dimensional potentials of mean force (PMF) simulations utilizing free-energy perturbation theory and Monte Carlo statistical mechanics. A new mechanism is proposed where direct formation of an open dipolar intermediate following the addition of PTAD to the alkene is rate-limiting and the pathway toward ene product is significantly dependent on the reaction medium. In protic solvents, the open dipolar intermediate may proceed directly to the ene product or reversibly form an aziridinium imide (AI) intermediate that does not participate in the reaction. However, in aprotic solvents the open intermediate is short-lived (<10-11 s) and the ene product forms via the AI intermediate. The calculated free energies of activation are in close agreement with those derived from experiment, e.g., DeltaG of 14.9 kcal/mol compared to 15.0 kcal/mol in acetonitrile. Density functional theory calculations at the (U)B3LYP/6-311++G(2d,p) level using the CPCM continuum solvent model were also carried out and confirmed a zwitterionic, and not diradical, open intermediate present in the reaction. Only the QM/MM methodology was able to accurately reproduce the experimental rates and differentiate between the protic and aprotic solvents. Solute-solvent interaction energies, radial distribution functions, and charges are analyzed and show that the major factor dictating the changes in reaction path is hydrogen bond stabilization of the charge separations spanning 2 to 4 atoms in the intermediates and transition states.