Energetics and dynamics in MbCN: CN--vibrational relaxation from molecular dynamics simulations

The dynamics of the cyanide anion bound to sperm-whale myoglobin is investigated using atomistic simulations. With density-functional theory, a 2D potential energy surface for the cyanide-heme complex is calculated. Two deep minima with a stabilization energy of approximately 50 kcal/mol corresponding to two different binding orientations (Fe-CN and Fe-NC) of the ligand are found. The Fe-CN conformation is favored over Fe-NC by several kcal/mol. Mixed quantum mechanics/molecular mechanics calculations show that the binding orientation affects the bond strength of the ligand, with a significantly different bond length and a 25 cm-1 shift in the fundamental CN-frequency. For the molecular dynamics (MD) simulations, a 3-center fluctuating charge model for the Fe-CN unit is developed that captures polarization and ligand-metal charge transfer. Stability arguments based on the energetics around the active site and the CN- frequency shifts suggest that the Fe-CN conformation with epsilon-protonation of His epsilon 64 are most likely, which is in agreement with experiment. Both equilibrium and nonequilibrium MD simulations are carried out to investigate the relaxation time scale and possible relaxation pathways in bound MbCN. The nonequilibrium MD simulations with a vibrationally excited ligand reveal that vibrational relaxation takes place on a time scale of hundreds of picoseconds within the active site. This finding supports the hypothesis that the experimentally observed relaxation rate (3.6 ps) reflects the repopulation of the electronic ground state.     

Atomistic molecular dynamics simulations of model C(36) fullerite

We report atomistic molecular dynamics investigations of a model C(36) fullerite in which the fullerene molecules are modeled as rigid cages over which the carbon atoms occupy fixed interaction sites, distributed in space according to the experimentally known atomic positions in the molecule. Carbon sites belonging to different molecules are assumed to interact via a 12-6 Lennard-Jones-type potential; the parameters of the latter are employed in the framework of a molecular dynamics fitting procedure, through which the ambient condition physical quantities characterizing the hcp structure of solid C(36) are eventually reproduced. We discuss applications of the adopted modelization to the C(36) phases in a temperature range spanning from 300 to 1500 K, and compare the obtained results to the available data for C(36) and other fullerenes, and to the predictions of the well known Girifalco central potential modelization of interactions in fullerenes, as applied to the C(36) case.     

The NMR structure of [Xd(C2)]4 investigated by molecular dynamics simulations

The i‐motif tetrameric structure is built up from two parallel duplexes intercalated in a head‐to‐tail orientation, and held together by hemiprotonated cytosine pairs. Two topologies exist for the i‐motif structure, one with outermost 3′ extremities and the other with outermost 5′ extremities, called the 3′E and 5′E topology, respectively. Since the comparison of sugar and phosphate group interactions between the two topologies is independent of the length of the intercalation motif, the relative stability of the 3′E and 5′E topologies therefore should not depend on this length. Nevertheless, it has been shown that the 3′E topology of the [d(C2)]4 is much more stable than the 5′E topology, and that the former is the only species observed in solution. In order to understand the reason for this atypical behavior, the NMR structure of the [Xd(C2)]4 was determined and analyzed by molecular dynamics simulations. In the NMR structure, the width of the narrow groove is slightly smaller than in previously determined i‐motif structures, which supports the importance of phosphodiester backbone interactions in the structure stability. The simulations show that the stacking of cytosines, essential for the i‐motif stability, is produced by a similar and non‐negative twisting of the phosphodiester backbones. The twisting is induced by an interaction between the backbones; the [Xd(C2)]4 in 5′E topology, exhibiting very limited interaction between the phosphodiester backbones, is thus unstable. Copyright © 2002 John Wiley & Sons, Ltd.     

Interaction of water with the model ionic liquid [bmim][BF4]: molecular dynamics simulations and comparison with NMR data

We report on molecular dynamics simulations of the ionic liquid [bmim][BF 4] and its mixtures with water, from zero up to 0.5 mol fraction of water. All of the simulations are carried out with two published force fields. The results are compared with each other and with published as well as new NMR data on the same mixtures, whenever possible. We perform extensive analyses of structural quantities, such as pair correlation functions, nearest-neighbor analysis and size distribution of the water clusters formed at higher concentrations. We show that the water clusters are formed almost exclusively by linear chains of hydrogen-bonded molecules. There is a nanoscale structuring of the mixtures but no macroscopic phase separation among the components, in agreement with experiment. Roughly, we identify two solvation regimes. At low water content, the ions are selectively coordinated by individual water molecules, but their ionic network is largely unperturbed. At high water content, the ionic network is somewhat disrupted or swollen in a nonspecific way by the water clusters.     

NMR relaxation and relaxivity parameters of MRI probes revealed by optimal wavelet signal compression of molecular dynamics simulations

The MRI contrast agents (CAs) have been routinely used for detecting tumors at early stages. Currently, the most used CAs in MRI are gadolinium (Gd³⁺) complexes. However, these CAs can be toxic to the body. Thus, this work proposes Ni²⁺ complexes ([Ni(ACAC)₂(H₂O)₂], [Ni(TEA)]²⁺) as promising CAs. For the theoretical prediction, molecular dynamics simulations were carried out and the conformations were selected by the optimal wavelet signal compression algorithm method. The T₁ and T₂ values were obtained directly by means of the spectral density. Our findings showed that the Ni²⁺ complexes can be promising CAs in MRI.     

Nonadiabatic molecular dynamics simulations of correlated electrons in solution. 1. Full configuration interaction (CI) excited-state relaxation dynamics of hydrated dielectrons

The hydrated dielectron is composed of two excess electrons dissolved in liquid water that occupy a single cavity; in both its singlet and triplet spin states there is a significant exchange interaction so the two electrons cannot be considered to be independent. In this paper and the following paper,we present the results of mixed quantum/classical molecular dynamics simulations of the nonadiabatic relaxation dynamics of photoexcited hydrated dielectrons, where we use full configuration interaction (CI) to solve for the two-electron wave function at every simulation time step. To the best of our knowledge, this represents the first systematic treatment of excited-state solvation dynamics where the multiple-electron problem is solved exactly. The simulations show that the effects of exchange and correlation contribute significantly to the relaxation dynamics. For example, spin-singlet dielectrons relax to the ground state on a time scale similar to that of single electrons excited at the same energy, but spin-triplet dielectrons relax much faster. The difference in relaxation dynamics is caused by exchange and correlation: The Pauli exclusion principle imposes very different electronic structure when the electrons' spins are singlet paired than when they are triplet paired, altering the available nonadiabatic relaxation pathways. In addition, we monitor how electronic correlation changes dynamically during nonadiabatic relaxation and show that solvent dynamics cause electron correlation to evolve quite differently for singlet and triplet dielectrons. Despite such differences, our calculations show that both spin states are stable to excited-state dissociation, but that the excited-state stability has different origins for the two spin states. For singlet dielectrons, the stability depends on whether the solvent structure can rearrange to create a second cavity before the ground state is reached. For triplet dielectrons, in contrast, electronic correlation ensures that the two electrons do not dissociate, even if the dielectron is artificially kept from reaching the ground state. In addition, both singlet and triplet dielectrons change shape dramatically during relaxation, so that linear response fails to describe the solvation dynamics for either spin state. In the following paper (Larsen, R. E.; Schwartz, B. J. J. Phys. Chem. B 2006, 110, 9692), we use these simulations to calculate the pump-probe spectroscopic signal expected for photoexcited hydrated dielectrons and to predict an experiment to observe hydrated dielectrons directly.     

Dielectric relaxation and molecular motion in poly(vinylidene fluoride)

The dielectric properties of poly(vinylidene fluoride) have been studied in the frequency range 10 Hz to 100 kHz at temperatures between ?196 and 150°C. Three dielectric relaxations were observed: the α relaxation occurred near 130°C, the β near 0°C, and the γ near ?30°C at 100 kHz. In the α relaxation the magnitude of loss peak and the relaxation times increased not only with increasing lamellar thickness, but also with decrease of crystal defects in the crystalline regions. In the light of the above results, the α relaxation was attributed to the molecular motion in the crystalline regions which was related to the lamellar thickness and crystal defects in the crystalline phase. In the β relaxation, the magnitude of the loss peak increased with the amount of amorphous material. The relaxation times were independent of the crystal structure and the degree of crystallinity, but increased slightly with orientation of the molecular chains by drawing. The β relaxation was ascribed to the micro-Brownian motions of main chains in the amorphous regions. The Arrhenius plots were of the so-called WLF type, and the “freezing point” of the molecular motion was about ?80°C. The Cole-Cole distribution parameter of the relaxation time α increased almost linearly with decreasing temperature in the temperature range of the experiment. The γ relaxation was attributed to local molecular motions in the amorphous regions.     

Rotational dynamics in supercooled water from nuclear spin relaxation and molecular simulations

Structural dynamics in liquid water slow down dramatically in the supercooled regime. To shed further light on the origin of this super-Arrhenius temperature dependence, we report high-precision (17)O and (2)H NMR relaxation data for H(2)O and D(2)O, respectively, down to 37 K below the equilibrium freezing point. With the aid of molecular dynamics (MD) simulations, we provide a detailed analysis of the rotational motions probed by the NMR experiments. The NMR-derived rotational correlation time τ(R) is the integral of a time correlation function (TCF) that, after a subpicosecond librational decay, can be described as a sum of two exponentials. Using a coarse-graining algorithm to map the MD trajectory on a continuous-time random walk (CTRW) in angular space, we show that the slowest TCF component can be attributed to large-angle molecular jumps. The mean jump angle is ～48° at all temperatures and the waiting time distribution is non-exponential, implying dynamical heterogeneity. We have previously used an analogous CTRW model to analyze quasielastic neutron scattering data from supercooled water. Although the translational and rotational waiting times are of similar magnitude, most translational jumps are not synchronized with a rotational jump of the same molecule. The rotational waiting time has a stronger temperature dependence than the translation one, consistent with the strong increase of the experimentally derived product τ(R)?D(T) at low temperatures. The present CTRW jump model is related to, but differs in essential ways from the extended jump model proposed by Laage and co-workers. Our analysis traces the super-Arrhenius temperature dependence of τ(R) to the rotational waiting time. We present arguments against interpreting this temperature dependence in terms of mode-coupling theory or in terms of mixture models of water structure.     

Microsecond time-scale conformational exchange in proteins: using long molecular dynamics trajectory to simulate NMR relaxation dispersion data

With the advent of ultra-long MD simulations it becomes possible to model microsecond time-scale protein dynamics and, in particular, the exchange broadening effects (R(ex)) as probed by NMR relaxation dispersion measurements. This new approach allows one to identify the exchanging species, including the elusive "excited states". It further helps to map out the exchange network, which is potentially far more complex than the commonly assumed 2- or 3-site schemes. Under fast exchange conditions, this method can be useful for separating the populations of exchanging species from their respective chemical shift differences, thus paving the way for structural analyses. In this study, recent millisecond-long MD trajectory of protein BPTI (Shaw et al. Science 2010, 330, 341) is employed to simulate the time variation of amide (15)N chemical shifts. The results are used to predict the exchange broadening of (15)N lines and, more generally, the outcome of the relaxation dispersion measurements using Carr-Purcell-Meiboom-Gill sequence. The simulated R(ex) effect stems from the fast (~10-100 μs) isomerization of the C14-C38 disulfide bond, in agreement with the prior experimental findings (Grey et al. J. Am. Chem. Soc. 2003, 125, 14324).     

Solvation dynamics in protein environments: comparison of fluorescence upconversion measurements of coumarin 153 in monomeric hemeproteins with molecular dynamics simulations

The complexes of the fluorescence probe coumarin 153 with apomyoglobin and apoleghemoglobin are used as model systems to study solvation dynamics in proteins. Time-resolved Stokes shift experiments are compared with molecular dynamics simulations, and very good agreement is obtained. The solvation of the coumarin probe is very rapid with approximately 60% occurring within 300 fs and is attributed to interactions with water (or possibly to the protein itself). Differences in the solvation relaxation (or correlation) function C(t) for the two proteins are attributed to differences in their hemepockets.     

Structure of gramicidin a in a lipid bilayer environment determined using molecular dynamics simulations and solid-state NMR data

Two different high-resolution structures recently have been proposed for the membrane-spanning gramicidin A channel: one based on solid-state NMR experiments in oriented phospholipid bilayers (Ketchem, R. R.; Roux, B.; Cross, T. A. Structure 1997, 5, 1655-1669; Protein Data Bank, PDB:1MAG); and one based on two-dimensional NMR in detergent micelles (Townsley, L. E.; Tucker, W. A.; Sham, S.; Hinton, J. F. Biochemistry 2001, 40, 11676-11686; PDB:1JNO). Despite overall agreement, the two structures differ in peptide backbone pitch and the orientation of several side chains; in particular that of the Trp at position 9. Given the importance of the peptide backbone and Trp side chains for ion permeation, we undertook an investigation of the two structures using molecular dynamics simulation with an explicit lipid bilayer membrane, similar to the system used for the solid-state NMR experiments. Based on 0.1 micros of simulation, both backbone structures converge to a structure with 6.25 residues per turn, in agreement with X-ray scattering, and broad agreement with SS backbone NMR observables. The side chain of Trp 9 is mobile, more so than Trp 11, 13, and 15, and undergoes spontaneous transitions between the orientations in 1JNO and 1MAG. Based on empirical fitting to the NMR results, and umbrella sampling calculations, we conclude that Trp 9 spends 80% of the time in the 1JNO orientation and 20% in the 1MAG orientation. These results underscore the utility of molecular dynamics simulations in the analysis and interpretation of structural information from solid-state NMR.     

13C NMR relaxation study of molecular motions in tetraphenyltin and tetra(p-tolyl)tin in solution

The Woessner approach is applied to the 13C relaxation data for tetraphenyltin (1) and tetra(p-tolyl)tin (2) in CDCl3 solution over the temperature range 5-42 degrees C to obtain correlation times for rotational motions and hence the activation barriers. Quantum mechanical computations were carried out to obtain the rotational energy barriers for comparison. For 2 the relaxation data indicate (1) slower ring rotation than in 1, (2) highly hindered internal rotation of the methyl group. IR and chemical shift data support the hypothesis of hyperconjugation of the methyl correlated with interaction between the pi-electrons and the 5d orbitals of tin in the (p-tolyl)Sn moiety to account for the hindrances to the rotations of the ring and the methyl. The activation barrier for the tolyl group rotation is found to be much higher than that for the phenyl rotation. However, the Woessner approach yields an anomalously high barrier for the methyl rotation. An explanation based on correlated rotations of the tolyl ring and the methyl is offered.     

Backbone dynamics of proteins studied by two-dimensional heteronuclear NMR spectroscopy and molecular dynamics simulations

To investigate the backbone dynamics of proteins ¹⁵N longitudinal and transverse relaxation experiments combined with {¹H, ¹⁵N{ NOE measurements together with molecular dynamics simulations were carried out using ribonuclease T₁ and the complex of ribonuclease T₁ with 2′GMP as a model protein. The intensity decay of individual amide cross peaks in a series of (¹H, ¹⁵N)HSQC spectra with appropriate relaxation periods was fitted to a single exponential by using a simplex algorithm in order to obtain ¹⁵N T₁ and T₂ relaxation times. The relaxation times were analyzed in terms of the “model-free” approach introduced by Lipari and Szabo. In addition, a nanosecond molecular dynamics (MD ) simulation of ribonuclease T₁ and its 2′GMP complex in water was carried out. The angular reorientations of the backbone amide groups were classified with several coordinate frames following a transformation of NH vector trajectories. In this study, NH librations and backbone dihedral angle fluctuations were distinguished. The NH bond librations were found to be similar for all amides as characterized by correlation times of librational motions in a subpicosecond scale. The angular amplitudes of these motions were found to be about 10°–12° for out-of-plane displacements and 3°–5° for the in-plane displacement. The contributions from the much slower backbone dihedral angle fluctuations strongly depend on the secondary structure. The dependence of the amplitude of local motion on the residue location in the backbone is in good agreement with the results of NMR relaxation measurements and the X-ray data. The protein dynamics is characterized by a highly restricted local motion of those parts of the backbone with defined secondary structure as well as by a high flexibility in loop regions. Comparison of the MD and NMR data of the free liganded enzyme ribonuclease T₁ clearly indicates a restriction of the mobility within certain regions of the backbone upon inhibitor binding. © 1996 John Wiley & Sons, Inc.     

Nuclear magnetic relaxation and molecular motion in poly(vinylidine fluoride)

Pulsed NMR T₁, T₂, and T_1ρ measurements are reported for poly(vinylidine fluoride) (PVF₂). The results demonstrate clearly the presence of four relaxation processes, three amorphous and one crystalline. The α relaxation is undoubtedly a crystalline one, while β and γ are both amorphous, in agreement with earlier conclusions from dielectric and dynamic mechanical measurements. The fourth relaxation (β′) observed initially in the mechanical measurements of Kakutani, but undetected in dielectric experiments, has been confirmed in our results and the process is described by an activation energy of 15.1 kcl/mole. Motion of folds on the surface of crystal lamellae is deemed to be the responsible mechanism for the β′ relaxation. Two models have been considered in the interpretation of the α process; rotation of crystalline chains in the vicinity of defects and rotational oscillation of restricted amplitude of all crystalline chains about the main chain axes. Rotation of amorphous chains is a possible mechanism for the γ process while motions of a general nature are responsible for the β relaxation. Our experimental results again indicate that spin diffusion plays an important role in the overall NMR response of the polymer.     

First-principles molecular dynamics evaluation of thermal effects on the NMR (1)J(Li,C) spin-spin coupling

Car-Parrinello (CP) molecular dynamics were applied to sample conformations of various models of organolithium aggregates which are chosen to estimate (1)J(Li,C) NMR coupling constants. The results show that the deviations from the values computed using static (optimized) geometries are small provided no large-amplitude motions occur within the timescale of the simulations. In the case of the vinyllithium dimer, for which rotation of the vinyl chain is observed, this approach allows analysis of the various contributions to the experimentally measured constants. For the trisolvated methyllithium monomer, partial decoordination of solvating dimethyl ether is observed and results in a significant shift of (1)J(Li,C). All these results highlight that a varied physicochemical machinery is hidden behind general empirical formulas, such as the Bauer-Winchester-Schleyer rule used experimentally.     

Rotational dynamics of benzene and water in an ionic liquid explored via molecular dynamics simulations and NMR T1 measurements

The rotational dynamics of benzene and water in the ionic liquid (IL) 1-butyl-3-methylimidazolium chloride are studied using molecular dynamics (MD) simulation and NMR T(1) measurements. MD trajectories based on an effective potential are used to calculate the (2)H NMR relaxation time, T(1) via Fourier transform of the relevant rotational time correlation function, C(2R)(t). To compensate for the lack of polarization in the standard fixed-charge modeling of the IL, an effective ionic charge, which is smaller than the elementary charge is employed. The simulation results are in closest agreement with NMR experiments with respect to the temperature and Larmor frequency dependencies of T(1) when an effective charge of ±0.5e is used for the anion and the cation, respectively. The computed C(2R)(t) of both solutes shows a bi-modal nature, comprised of an initial non-diffusive ps relaxation plus a long-time ns tail extending to the diffusive regime. Due to the latter component, the solute dynamics is not under the motional narrowing condition with respect to the prevalent Larmor frequency. It is shown that the diffusive tail of the C(2R)(t) is most important to understand frequency and temperature dependencies of T(1) in ILs. On the other hand, the effect of the initial ps relaxation is an increase of T(1) by a constant factor. This is equivalent to an "effective" reduction of the quadrupolar coupling constant (QCC). Thus, in the NMR T(1) analysis, the rotational time correlation function can be modeled analytically in the form of aexp (-t/τ) (Lipari-Szabo model), where the constant a, the Lipari-Szabo factor, contains the integrated contribution of the short-time relaxation and τ represents the relaxation time of the exponential (diffusive) tail. The Debye model is a special case of the Lipari-Szabo model with a = 1, and turns out to be inappropriate to represent benzene and water dynamics in ILs since a is as small as 0.1. The use of the Debye model would result in an underestimation of the QCC by a factor of 2-3 as a compensation for the neglect of the Lipari-Szabo factor.     

Comparison of aqueous molecular dynamics with NMR relaxation and residual dipolar couplings favors internal motion in a mannose oligosaccharide.

An investigation has been performed to assess how aqueous dynamical simulations of flexible molecules can be compared against NMR data. The methodology compares state-of-the-art NMR data (residual dipolar coupling, NOESY, and (13)C relaxation) to molecular dynamics simulations in water over several nanoseconds. In contrast to many previous applications of residual dipolar coupling in structure investigations of biomolecules, the approach described here uses molecular dynamics simulations to provide a dynamic representation of the molecule. A mannose pentasaccharide, alpha-D-Manp-(1-->3)-alpha-D-Manp-(1-->3)-alpha-D-Manp-(1-->3)-alpha-D-Manp-(1-->2)-D-Manp, was chosen as the model compound for this study. The presence of alpha-linked mannan is common to many glycopeptides, and therefore an understanding of the structure and the dynamics of this molecule is of both chemical and biological importance. This paper sets out to address the following questions. (1) Are the single structures which have been used to interpret residual dipolar couplings a useful representation of this molecule? (2) If dynamic flexibility is included in a representation of the molecule, can relaxation and residual dipolar coupling data then be simultaneously satisfied? (3) Do aqueous molecular dynamics simulations provide a reasonable representation of the dynamics present in the molecule and its interaction with water? In summary, two aqueous molecular dynamics simulations, each of 20 ns, were computed. They were started from two distant conformations and both converged to one flexible ensemble. The measured residual dipolar couplings were in agreement with predictions made by averaging the whole ensemble and from a specific single structure selected from the ensemble. However, the inclusion of internal motion was necessary to rationalize the relaxation data. Therefore, it is proposed that although residual dipolar couplings can be interpreted as a single-structure, this may not be a correct interpretation of molecular conformation in light of other experimental data. Second, the methodology described here shows that the ensembles from aqueous molecular dynamics can be effectively tested against experimental data sets. In the simulation, significant conformational motion was observed at each of the linkages, and no evidence for intramolecular hydrogen bonds at either alpha(1-->2) or alpha(1-->3) linkages was found. This is in contrast to simulations of other linkages, such as beta(1-->4), which are often predicted to maintain intramolecular hydrogen bonds and are coincidentally predicted to have less conformational freedom in solution.     

Computing the (1)H NMR spectrum of a bulk ionic liquid from snapshots of car-parrinello molecular dynamics simulations.

We have investigated the performance of several computational protocols in predicting the NMR spectrum of a molecular ion in a complex liquid phase such as an ionic liquid. To do this, we computed the proton NMR chemical shifts of the 1-ethyl-3-methylimidazolium cation [emim](+) in [emim][Cl]. Environmental effects on the imidazolium ring proton chemical shifts are quite significant and must be taken into account explicitly. Calculations performed on the isolated imidazolium cation as well as on the [emim][Cl] ion pair grossly fail to reproduce the correct spacing between proton signals. In contrast, calculations performed on clusters extracted from the trajectory of a Car-Parrinello molecular dynamics simulation yield very good results.     

Molecular motion and 1H NMR relaxation of aqueous poly(N-isopropylacrylamide) solution under high pressure

In order to obtain useful information about the molecular motion and structure of poly(N-isopropylacrylamide) (PNiPAM) in aqueous solution, proton spin-lattice relaxation times, proton spin-spin relaxation times, and volume changes were measured at pressures from 1 to 400 kg/cm² as a function of temperature. We found that the molecular motion and the structure of water and PNiPAM in PNiPAM/water solution transitionally change at gelation temperature (31°C). The effect of pressure on such transitional changes is studied. It is suggested that application of pressure to the system prevents the gelation.