NMR Quadrupole Relaxation of Xenon-131 in Water

Computing the frequency-dependent NMR relaxation of 1H nuclei in liquid water

We present a computational framework for reliably determining the frequency-dependent intermolecular and intramolecular nuclear magnetic resonance (NMR) dipole-dipole relaxation rates of spin 1/2 nuclei from Molecular Dynamics (MD) simulations. This approach avoids the alterations caused by the well-known finite-size effects of translational diffusion. Moreover, a procedure is derived to control and correct for effects caused by fixed distance-sampling cutoffs and periodic boundary conditions. By construction, this approach is capable of accurately predicting the correct low-frequency scaling behavior of the intermolecular NMR dipole-dipole relaxation rate and thus allows for the reliable calculation of the frequency-dependent relaxation rate over many orders of magnitude. Our approach is based on the utilization of the theory of Hwang and Freed for the intermolecular dipole-dipole correlation function and its corresponding spectral density [L.-P. Hwang and J. H. Freed, J. Chem. Phys. 63, 4017-4025 (1975)] and its combination with data from MD simulations. The deviations from the Hwang and Freed theory caused by periodic boundary conditions and sampling distance cutoffs are quantified by means of random walker Monte Carlo simulations. An expression based on the Hwang and Freed theory is also suggested for correcting those effects. As a proof of principle, our approach is demonstrated by computing the frequency-dependent intermolecular and intramolecular dipolar NMR relaxation rates of 1H nuclei in liquid water at 273 and 298 K based on the simulations of the TIP4P/2005 model. Our calculations are suggesting that the intermolecular contribution to the 1H NMR relaxation rate of the TIP4P/2005 model in the extreme narrowing limit has previously been substantially underestimated.

Dynamics of TMAO and urea in the hydration shell of the protein SNase

Using all-atom molecular dynamics simulations of aqueous solutions of the globular protein SNase, the dynamic behavior of water molecules and cosolvents (trimethylamine-N-oxide (TMAO) and urea) in the hydration shell of the protein was studied for different solvent compositions. TMAO is a potent protein-stabilizing osmolyte, whereas urea is known to destabilize proteins. For molecules that are initially located in successive narrow layers at a given distance from the protein, the mean displacements and the distribution of displacements for short time intervals are calculated. For molecules that are initially located in solvation shells of a given thickness around the protein, the characteristic residence times in these shells are determined to characterize the dynamic behavior of the solvent molecules as a function of the distance to the protein. A combined consideration of these characteristics allows to reveal additional features of the dynamics of the cosolvents. It is shown that TMAO molecules leave the nearest vicinity of the protein faster than urea molecules, despite the fact that the mobility of TMAO molecules, measured by their mean displacements, is lower than that of urea. Moreover, we show that the rate of release of TMAO molecules from the hydration shell is lower in ternary (TMAO + urea + H₂O) solvent mixtures than in the binary ones. This is consistent with a recent observation that the fraction of TMAO near the protein decreases in the presence of urea. From the analysis of the decay of the number of particles initially located in the region of the first peak of the distribution function of solvent molecules around the protein, we estimated that about 20 water molecules and 6-7 urea molecules stay near the protein for more than 1000 ps.

Chemical shift extremum of 129Xe(aq) reveals details of hydrophobic solvation

The ¹²⁹Xe chemical shift in an aqueous solution exhibits a non-monotonic temperature dependence, featuring a maximum at 311 K. This is in contrast to most liquids, where the monotonic decrease of the shift follows that of liquid density. In particular, the shift maximum in water occurs at a higher temperature than that of the maximum density. We replicate this behaviour qualitatively via a molecular dynamics simulation and computing the ¹²⁹Xe chemical shift for snapshots of the simulation trajectory. We also construct a semianalytical model, in which the Xe atom occupies a cavity constituted by a spherical water shell, consisting of an even distribution of solvent molecules. The temperature dependence of the shift is seen to result from a product of the decreasing local water density and an increasing term corresponding to the energetics of the Xe-H₂O collisions. The latter moves the chemical shift maximum up in temperature, as compared to the density maximum. In water, the computed temperature of the shift maximum is found to be sensitive to both the details of the binary chemical shift function and the coordination number. This work suggests that, material parameters allowing, the maximum should be exhibited by other liquids, too.

Mode-coupling study on the dynamics of hydrophobic hydration

The molecular motion of water in water-hydrophobic solute mixtures was investigated by the mode-coupling theory for molecular liquids based on the interaction-site description. When the model Lennard-Jones solute was mixed with water, both the translational and reorientational motions of solvent water become slower, in harmony with various experiments and molecular dynamics simulations. We compared the mechanism of the slowing down with that of the pressure dependence of the molecular motion of neat water [T. Yamaguchi, S.-H. Chong, and F. Hirata, J. Chem. Phys. 119, 1021 (2003)]. We found that the decrease in the solvent mobility caused by the solute can essentially be elucidated by the same mechanism: That is, the fluctuation of the number density of solvent due to the cavity formation by the solute strengthens the friction on the collective polarization through the dielectric friction mechanism: We also employed the solute molecule that is the same as solvent water except for the amount of partial charges, in order to alter the strength of the solute-solvent interaction continuously. The mobility of the solvent water was reduced both by the hydrophobic and strongly hydrophilic solutes, but it was enhanced in the intermediate case. Such a behavior was discussed in connection with the concept of positive and negative hydrations.

Molecular dynamics averaging of Xe chemical shifts in liquids

The Xe nuclear magnetic resonance chemical shift differences that afford the discrimination between various biological environments are of current interest for biosensor applications and medical diagnostic purposes. In many such environments the Xe signal appears close to that in water. We calculate average Xe chemical shifts (relative to the free Xe atom) in solution in eleven liquids: water, isobutane, perfluoro-isobutane, n-butane, n-pentane, neopentane, perfluoroneopentane, n-hexane, n-octane, n-perfluorooctane, and perfluorooctyl bromide. The latter is a liquid used for intravenous Xe delivery. We calculate quantum mechanically the Xe shielding response in Xe-molecule van der Waals complexes, from which calculations we develop Xe (atomic site) interpolating functions that reproduce the ab initio Xe shielding response in the complex. By assuming additivity, these Xe-site shielding functions can be used to calculate the shielding for any configuration of such molecules around Xe. The averaging over configurations is done via molecular dynamics (MD). The simulations were carried out using a MD technique that one of us had developed previously for the simulation of Henry's constants of gases dissolved in liquids. It is based on separating a gaseous compartment in the MD system from the solvent using a semipermeable membrane that is permeable only to the gas molecules. We reproduce the experimental trends in the Xe chemical shifts in n-alkanes with increasing number of carbons and the large chemical shift difference between Xe in water and in perfluorooctyl bromide. We also reproduce the trend for a given solvent of decreasing Xe chemical shift with increasing temperature. We predict chemical shift differences between Xe in alkanes vs their perfluoro counterparts.