Water relaxation

The theoretical basis for the interpretation of water proton, deuterium and oxygen-17 relaxation in the dilute regime where water activities are close to 

Although water relaxation in the dilute regime is now set on a firm theoretical basis, this is not the case in the more concentrated, water-poor regime appropriate to most foods. In the following we will therefore focus mainly on the concentration dependence of the water relaxation, especially the oxygen-17 data, beginning with simple sugar solutions. 

Another problem is the use of the relationship aw — 1 — Vwap. Here Vw is the degree of hydration, ap is the NMR-derived protein activity and aw the water activity. This underived expression is analogous to a stoichiometric population expression but is inappropriate for activities whose relationships are determined by the Gibbs-Duhem equation. Despite these shortcomings the Kumosinski-Pessen theory has been extensively used in the food literature.37,38,40-43 

Here Cp is the concentration of protein molecules of charge Zp and Cs is the concentration of counterions of charge Zs (ZpCp + ZSCS = 0) e is the dielectric constant and h the shear viscosity of the solution at concentration Cp h0 is the pure solvent viscosity Dp and D6 are the diffusion coefficients of the protein and counterion at infinite dilution while 7 is the mean ionic activity coefficient. Both 7 and the relative visocity (h0/h) depend on protein concentration 

The concentration dependence of the shear viscosity can often be written, empirically, in the form34 

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It was determined, for example, that the surface tension of water relaxes to its equilibrium value with a relaxation time of 0.6 msec [104]. The oscillating jet method has been useful in studying the surface tension of surfactant solutions. Figure 11-21 illustrates the usual observation that at small times the jet appears to have the surface tension of pure water. The slowness in attaining the equilibrium value may partly be due to the times required for surfactant to diffuse to the surface and partly due to chemical rate processes at the interface. See Ref. 105 for similar studies with heptanoic acid and Ref. 106 for some anomalous effects. 

Hills, B.P., Ridge, C.E., and Brocklehurst, T. 1996b. NMR water relaxation, water activity, and bacterial survival in porous media. J. Sci. Food Agric. 71, 185-194. 

I have invited Professor Ivano Bertini (University of Florence, Italy), who is an expert in this field, to be the co-editor of this volume. Professor Bertini is a well-known inorganic chemist that has significantly contributed, both experimentally and theoretically, to the understanding of the relations between water relaxation and unpaired electron relaxation. On its turn, electron relaxation determines the high resolution NMR behavior of paramagnetic substances, a field in which he is quite active. 

After the partial exchange of the Na counter cations for Gd " ", the specific relaxivity (here defined as the measured water relaxation rate per gram of material) was measured at Larmor frequencies ranging from 0.01 to 30 MHz. The NMRD profiles obtained were compared with that obtained after complexing the encapsulated Gd(III) with DTPA. After correction for the differences in the Gd(III) content of the samples, the NMRD curves appeared to be superimposable. Based on this result, a... 

The volumetric power deposition calculated for bound water was appreciably greater—up to about five times—than that for free water the maximum difference occurs near the bound water relaxation frequency. This enhanced energy deposition is localized in the bound water shell and therefore may cause more damage than if it were distributed uniformly throughout the medium. But Dawkins et al. consider the enhancement of biological damage by localiza-... 

For example, Swift and Barr established the proton NMR data with 170 relaxation studies on frog skeletal muscles272. They also found that the water relaxation is enhanced in muscles in comparison with pure water272. Cooke and Wien273 observed on partially dried rabbit psoas fibers two phases of muscle water a small phase, less than 4—5% of the total water, which interacts strongly with the proteins and has short relaxation times and a major phase. .. with longer relaxation times a major fraction of the intracellular water exists in a less mobile form than water in a salt solution 273. ... 

Paramagnetic effects of metals such as those observed here with Gd + on the Ca +-ATPase can be used to determine distances, r, between the metal and pertinent nuclei or, if r is known, to determine g, the number of nuclei involved in the interaction with the metal (11). Thus, the water relaxation data described here can be used to determine the number of exchangeable water protons on Gd3+ at the two Ca + sites on the ATPase. As shown in Table II, the value of q appears to be distinctly different at the two Gd3+ sites. Calculations yield three exchangeable water protons on Gd3+ at site 1 and two exchangeable protons at site 2. 

Characteristic frequencies may be found from dielectric permittivity data or, even better, from conductivity data. The earlier data by Herrick et al. (6) suggest that there is no apparent difference between the relaxation frequency of tissue water and that of the pure liquid (7). However, these data extend only to 8.5 GHz, one-third the relaxation frequency of pure water at 37°C (25 GHz), so small discrepancies might not have been uncovered. We have recently completed measurements on muscle at 37°C and 1°C (where the pure water relaxation frequency is 9 GHz), up to 17 GHz. The dielectric properties of the tissue above 1 GHz show a Debye relaxation at the expected frequency of 9 GHz (8 ) (Figure 3). The static dielectric constant of tissue water as determined at 100 MHz compares with that of free water if allowance is made for the fraction occupied by biological macromolecules and their small amount of bound water (1, 9). 

At microwave frequencies the dielectric properties of tissues are dominated by the water relaxation centered near 20 GHz. The magnitude of this water dispersion in tissues is typically diminished by some 20 dielectric units due to the proteins which displace a corresponding volume of water. 

Assuming that the relaxation of a given proton is due to the paramagnetism of the lanthanide ions then for the elements other than gadolinium the Solomon-Bloembergen equations for the water relaxation rates, 1/Tj or 1/T2, reduce to... 

We can turn finally to the mono dipicolinate complexes. The same analysis as above shows that in solution the M(dipic) complexes are isostructural. The exact structure has been determined using shift and relaxation data as above, see Refs. 34—36. Knowledge of the relaxation data for both ligand and water protons and the known relaxation of the contribution to water relaxation from the outer sphere then permits calculation of the number of water molecules in M(dipic)(H20)n. We have shown that n = 6 for all the lanthanides. 

The relaxation dynamics (W7 in Fig. 38) is the response of the environment around Trp7 to its sudden shift in charge distribution from the ground state to the excited state. Under this perturbation, the response can result from both the surrounding water molecules and the protein. We separately calculated the linear-response correlation functions of indole-water, indole-protein, and the sum of the two. The results for isomer 1, relative to the time-zero values, are shown in Fig. 42a. The linear response correlation function is accumulated from a 6-ns interval indicated in Fig. 41a during which the protein was clearly in the isomer 1 substate. All three correlation functions show a significant ultrafast component 63% for the total response, 50% for indole-water, and nearly 100% for indole-protein. A fit to the total correlation function beyond the ultrafast inertial decrease requires two exponential decays 1.4 ps (3.6kJ/mol) and 23 ps (2.0kJ/mol). Despite the 6-ns simulation window for isomer 1, the 23-ps long component is not well determined on account of the noise apparent in the linear response correlation function (Fig. 42a) between 30 and 140 ps. The slow dynamics are mainly observed in the indole-water relaxation and the overall indole-protein interactions apparently make nearly no contributions to the slowest relaxation component. 

Figure 43. Solvation dynamics from MD simulations for isomer 2. (a) The linear-response calculated time-resolved Stokes shifts for indole-protein, indole-water, and their sum. (b) Direct nonequilibrium simulations of the time-resolved Stokes shifts for indole-water, indole-protein, and their sum. Note the lack of slow component in indole-water relaxation in both (a) and (b), which is opposite to isomer 1 in Fig. 42. Also shown is the indole-water (within 5 A of indole) with coupled long-time negative solvation, (c) Relaxation between indole-lys79 and indole-glu4. The interaction energy changes from these two residues nearly cancel each other, (d) The distance changes between the indole and two charged residues, but both residues move away from the indole ring.

MD simulations with either protein or water constrained at the instant of photoexcitation were performed for both isomer 1 and isomer 2. For isomer 1, because surface water relaxation dominates the slow component of the total Stokes shift, in Fig. 44a we show the result of simulations of isomer 1 with an ensemble of frozen protein configurations to examine the role of protein fluctuations. Clearly the long component of indole-water interactions disappears when the protein is constrained. This result shows that without protein fluctuations, indole-water relaxation over tens of picoseconds does not occur. Thus, although surface hydrating water molecules seem to drive the global solvation and, from the dynamics of the protein and water contributions, are apparently responsible for the slowest component of the solvation Stokes shift for isomer 1 (Fig. 42), local protein fluctuations are still required to facilitate this rearrangement process. When the protein is frozen, the ultrafast... 

Figure 44. Solvation dynamics from constrained MD simulations, (a) Comparison of indole-water relaxation with and without frozen protein structure for isomer 1. The slow component of the water response nearly disappears, which indicates that slow water relaxation needs protein fluctuations, (b) Comparison of indole—protein relaxation with and without frozen water for isomer 2. Similarly, the slow component of the indole—protein disappears, which indicates that the protein relaxation also requires water fluctuations.

The fact that the indole-water relaxation is still present under the frozen protein with nearly the same amplitude (compare the water contribution in Fig. 42b and 44a) is one indication that the water response is not qualitatively modified by freezing the protein. The rigid potential field of the frozen protein somewhat limits rearrangements of the local water networks, but the difference is quantitative, not qualitative. 

Figure 21.9. Correlation between distribution of water relaxation times (NMR) and perceived juiciness.

Caravan, P, Greenfield, M.T., Li, X., and Sherry, A.D. (2001) The Gd complex of a fatty acid analogue of DOTP binds to multiple albumin sites with variable water relaxivities. Inorganic Chemistry, 40, 6580-6587. 

Sloan et al. (1973) titrated glyceraldehyde-3-phosphate dehydrogenase with nicotinamide adenine dinucleotide (NAD) and observed an increase in water relaxation by about 25% over that from the protein alone. They interpreted this effect as an increase of at least 26 mol of hydration water per mol of protein. This conclusion contrasts with a volume contraction and decrease in preferential hydration observed through other measurements to be associated with binding of NAD (Durchschlag et al., 1971 Sloan and Velick, 1973). 

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