Proteins water relaxation

The temperature dependence of the MRD profile for the protein-water systems where the protein is magnetically a solid, is remarkably weak. The relaxation rate is proportional to IjT, which is consistent with Eq. (4) that was derived on the assumption that the relaxation process is a direct spin-phonon coupling rather than an indirect or Raman process. If it were a Raman process, there would be no magnetic field dependence of the relaxation rate therefore, the temperature dependence provides good evidence in support of the theoretical foundations of Eq. (6). 

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. ... 

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. 

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.

The simulation results from both isomer 1 and isomer 2 show that the observed solvation dynamics around the Trp7 site can arise from strongly coupled neighboring water and protein relaxation. Judging by the time dependence of their separate contributions to the total response, the Stokes shift over tens of picoseconds can apparently result from either surface water or protein conformational relaxation for isomers 1 and 2, respectively. To elucidate the origin of these observed time scales, we performed frozen protein and frozen water simulations. 

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. 

Polnaszek and Bryant (1984a,b) measured the frequency dependence of water proton relaxation for solutions of bovine serum albumin reacted with a nitroxide spin label (4.6 mol of nitroxide per mol of protein). The relaxation is dominated by interaction between water and the paramagnetic spin label. The data were best fit with a translational diffusion model, with the diffusion constant for the surface water in the immediate vicinity of the nitroxide being five times smaller than that for... 

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). 

To summarize, three conclusions transpire from the nanoscale thermodynamics results (a) The interfacial tension between protein and water is patchy and the result of both nanoscale confinement of interfacial water and local redshifts in dielectric relaxation (b) the poor hydration of polar groups (a curvature-dependent phenomenon) generates interfacial tension, a property previously attributed only to hydrophobic patches and (c) because of its higher occurrence at protein-water interfaces, the poorly hydrated dehydrons become collectively bigger contributors to the interfacial tension than the rarer nonpolar patches on the protein surface. 

Table 2. NMR studies of water relaxation in proteins and polysaccharide solutions.

Modem methods for study of metal-activated enzymes include NMR and ESR spectroscopy, water relaxation rates by pulsed NMR (PRR), atomic absorption, Mbssbauer, X-ray and neutron diffraction, high-resolution electron microscopy, UV/visible/IR spectroscopy, laser lanthanide pertubation methods, fluorescence, and equilibrium and kinetic binding techniques. Studies with Mg(II)-activated enzymes have been hampered by the lack of paramagnetic or optical properties that can be used to probe its environment, and the relative lack of sensitivity of other available methods initial velocity kinetics, changes in ORD/CD, fluorescence, or UV properties of the protein, atomic absorption assays for equilibrium binding, or competition with bound Mn(II) °. Recent developments in Mg and 0-NMR methodology have shown some promise to provide new insights . ... 

The most powerful technique for studying molecular motions in protein-water systems below 0°C is magnetic resonance. Dielectric relaxation measurements can be used, but these measurements are more suitable at higher temperatures in homogenous solutions (13). Recently, the frequency dependence of the mehcanical properties of biopolymers has been shown to yield considerable kinetic information (14). I will limit discussion to the salient results attainable from these techniques. 

The complete solutions of the coupled equations are given by Edzes and Samulski (Rf becomes kw and Rf/F becomes kn, in their notation) (T7). The water and protein proton relaxation curves... 

The aim of the present investigation is to study water dynamics in hydrated proteins while testing the cross relaxation model. According to equation 5, the temperature dependence of the observed water relaxation components could arise from changes in any of the three fundamental rate constants Riy, Rip. and Rf. Thus, extraction of R] from the observed R f and Rig in order to find its temperature dependence is necessary before a detailed interpretation in terms of water motion is attempted. 

Presently, the empirics is ahead of the theory the model mechanisms that we propose we have only been able to quantitate in one instance, that of the dependence of protein reorientational relaxation time on protein concentration. Nonetheless, we have been able to clarify the distinction between macroscopic and microscopic viscosity to measure protein-protein interactions within cells and to demonstrate magnetization transfer from protein protons to solvent protons all of this is consistent with the dynamics of water-protein interactions that we infer and have discussed. 

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