Magnetic cross-relaxation among protons in protein solutions

Abstract

The magnetic spin-lattice relaxation rates of solvent water nuclei are known to increase upon addition of diamagnetic solute protein. This enhancement of the relaxation rate is a function of magnetic field, and the orientational relaxation time of the protein molecules can be deduced from analysis of the field-dependent relaxation rates. Although the nature of the interactions that convey information about the dynamics of protein motion to the solvent molecules is not established, it is known that there is a contribution to the relaxation rates of solvent protons that plays no role in the relaxation of solvent deuterons and 17O nuclei. We show here that the additional interaction arises from a cross-relaxation process between solvent and solute protons. We introduce a heuristic three-parameter model in which protein protons and solvent protons are considered as two separate thermodynamic systems that interact across the protein-solvent interface. The three parameters are the intrinsic relaxation rates of each system and a cross-relaxation term. The sign of the latter term must always be positive, for all values of magnetic field, in order for magnetization energy to flow from the hotter to the cooler system. We find that the magnetic field-dependence of the cross-relaxation contribution is much like that of the remaining solvent proton relaxation, i.e., about the same as the deuteron relaxation field dependence. This finding is not compatible with the predictions of expressions for the cross-relaxation that have been used by other authors, but not applied to data over a wide range of magnetic field strength. The model predicts that the relaxation behavior of both the protein protons and the solvent protons is the sum of two exponentials, the relative contributions of which would vary with protein concentration and solvent isotopic composition in a fashion suggestive of the presence of two classes of protein protons, when there is in reality only one. This finding has immediate implications for the interpretation of published proton relaxation rates in complex systems such as tissues; these data should be reexamined with cross-relaxation taken into account.

Protein Hydration Dynamics in Aqueous Solution: A Comparison of Bovine Pancreatic Trypsin Inhibitor and Ubiquitin by Oxygen-17 Spin Relaxation Dispersion

“…The divergent pictures of protein hydration (especially its dynamic aspects) derived from spin relaxation studies can be largely blamed on three complicating factors. First, as is now generally recognized, the 1 H relaxation is dominated by cross-relaxation effects and therefore cannot be interpreted solely in terms of water dynamics (Edzes & Samulski, 1978;Koenig et al, 1978;Hills, 1992). Second, 1 H and 2 H relaxation both contain significant contributions from labile protein hydrogens that exchange with water Hills et al, 1989;Hills, 1992).…”

“…The 1 H dispersion is complicated by cross-relaxation between protein and water protons (Edzes & Samulski, 1978;Koenig et al, 1978;Hills, 1992), and both 1 H and 2 H relaxation are affected by hydrogen exchange between water and protein (Picullel & Halle, 1986;Hills et al, 1989;Hills, 1992;Denisov & Halle,1995).Eventhe 17 Orelaxationdispersion,which does not suffer from these complications, cannot, by itself, provide a unique, model-independent picture of protein hydration. In particular, it does not appear possible, solely on the basis of relaxation dispersion data, to determine both the number of perturbed water molecules and the degree of this perturbation (relative to bulk water).…”

Pulsed Z‐spectroscopic imaging of cross‐relaxation parameters in tissues for human MRI: Theory and clinical applications

“…The k and f parametric images were calculated by Eqs. [24] and [25]. The T 1 maps were computed using a pixel-by-pixel linear fitting to variable flip angle data in the coordinates {SI (␣)/sin ␣, SI (␣)/tan ␣} (22).…”

“…The processing scheme included the computation of P and Q maps using a twoparameter fit with fixed T 2 B ϭ 8.5 s for all pixels, the reconstruction of the T 1 map, and the calculation of f and k maps by Eqs. [24] and [25].…”

Mitochondrial membrane permeabilization produced by PTP, Bax and apoptosis: a 1H-NMR relaxation study

“…17 In this study, a new method of characterization of mitochondrial water was used, which takes into account the importance of magnetic crossrelaxation between protein protons and water protons, 18 based on the analysis of the temperature dependency of proton relaxation times of both bulk and structured water on a low-field (20 MHz) NMR spectrometer. This technique allows the characterization of the physical changes observed in the whole structured water fraction (the totality of water that does not freeze under the freezing point of bulk water) to be determined.…”