ESR correlation times of 2,2,6,6-tetramethyl piperidone-N-oxyl (Tempone) in solutions of hemoglobin A and hemoglobin S.

Correlation times for the tumbling motion of the spin probe 2,2,6,6,-tetramethyl piperidone-N-oxyl (Tempone) were obtained in the presence of different concentrations of oxyhemoglobin A, oxyhemoglobin S, and deoxyhemoglobin S and compared to the viscosity of non-gelling hemoglobin solutions. Reorientational motion (or tumbling) of Tempone in gelled solutions of deoxyhemoglobin S is as great as that in non-gelled hemoglobins of the same total concentration. It is concluded that the gel does not exclusively partition Tempone into an aqueous phase of lower solute concentration after gel formation. The gel at room temperature is a highly mobile and dynamic structure on the microscopic level.     

Demonstration of lag phase in the sol-gel transformation of deoxygenated S hemoglobin without temperature alteration.

1). During the sol to gel transformation of deoxygenated sickle hemoglobin, a time-dependent process preceding gel formation (lag phase) was demonstrated that was inversely proportional to a function of the hemoglobin concentration and that occurred without alteration in temperature, pH, or oxygen tension. 2). As determined by the Schachman modification of the capillary viscometer, preparations of oxyhemoglobin S and A and deoxyhemoglobin A were indistinguishable when compared over a wide range of concentrations. Up to the concentration at which gelling occurred, deoxyhemoglobin S exhibited the same viscosity behavior. The viscosity of deoxygenated hemoglobin S within the lower gelling concentration range was normal during the lag phase and became abnormally high only at the time of gelation.     

Inhibition of the gelation of extracellular and intracellular hemoglobin S by selective acetylation with methyl acetyl phosphate

Methyl acetyl phosphate binds to the 2,3-diphosphoglycerate (2,3-DPG) binding site of hemoglobin and selectively acetylates three amino groups at or near that site. The subsequent binding of 2,3-DPG is thus impeded. When intact sickle cells are exposed to methyl acetyl phosphate, their abnormally high density under anaerobic conditions is reduced to the density range of oxygenated, nonsickling erythrocytes. This change is probably due to a combination of direct and indirect effects induced by the specific acetylation. The direct effect is on the solubility of deoxyhemoglobin S, which is increased from 17 g/dL for unmodified hemoglobin S to 22 g/dL for acetylated hemoglobin S at pH 6.8. Acetylated hemoglobin S does not gel at pH 7.4, up to a concentration of 32 g/dL. The indirect effect could be due to the decreased binding of 2,3-DPG to deoxyhemoglobin S within the sickle erythrocyte, thus hindering the conversion of oxyhemoglobin S to the gelling form, deoxyhemoglobin S.     

Gelling properties of apohemoglobin S alone and in mixtures with hemoglobin S

Apohemoglobin S formed a gel in the cold (5 degrees C) with a protein concentration in the supernatants after centrifugation of the gels (Csat) near 27 g/dl, in 0.02 M phosphate buffer at pH 7.2. Under the same experimental conditions in mixtures of apohemoglobin S and deoxyhemoglobin S the solubility of hemoglobin S in the cold was decreased from Csat greater than 40 g/dl in the absence to about 18 g/dl in the presence of apohemoglobin S. Conversely, in the same mixture, Csat of apohemoglobin S was decreased to about 5 g/dl. Also, gelling occurred in mixtures of oxyhemoglobin S and its apoderivative. Apohemoglobin A alone did not form gels; however, it induced fiber formation in deoxyhemoglobin S in the cold; unlike apohemoglobin S, it was not included in the precipitate. Gels of apohemoglobin S were not birefringent, and inspection at the electron microscope failed to show the presence of organized structures. Excluded volume effects were probably at the origin of the decreased solubility of hemoglobin S and apohemoglobin S in the presence of each other.     

Transformation of hemoglobin a into methemoglobin by sesamol

Sesamol (3,4-methylenedioxyphenol), a monophenolic antioxidant in sesame iol, produced methemoglobin from hemoglobin A (oxyhemoglobin and deoxyhemoglobin) and from red cells. The activity of the compound was more extensive than the polyphenolic compounds. The profiles of the methemoglobin formation by the compound were compared with those by nitrite and hydroxylamine. The formation of methemoglobin from oxyhemoglobin by the compound was rather slowly progressed, but the amount of methemoglobin formed was proportional to the concentration of oxyhemoglobin even when the concentration of the compound was low. The sesamol-induced methemoglobin formation was influenced by inositol hexaphosphate, an allosteric effector of hemoglobin. Thus, the phosphate enhanced the transformation of oxyhemoglobin and inhibited the transformation of deoxyhemoglobin.     

The effect of potassium chloride on the Bohr effect of human hemoglobin.

The normal and differential titration curves of liganded and unliganded hemoglobin were measured at various KCl concentrations (0.1 to 2.0 M). In this range of KCl concentrations, the curves for deoxyhemoglobin showed no salt-induced pK changes of titratable groups. In the same salt concentration range oxyhemoglobin showed a marked change in titration behavior which could only be accounted for by a salt-induced increase in pK of some titratable groups. These results show that the suppression of the alkaline Bohr effect by high concentrations of neutral univalent salt is not caused by a weakening of the salt bridges in deoxyhemoglobin but is due to an interaction of chloride ions with oxyhemoglobin. Measurements of the Bohr effect at various KCl concentrations showed that at low chloride ion concentration (5 times 10-3 M) the alkaline Bohr effect is smaller than at a concentration of 0.1 M. This observation indicates that at a chloride ion concentration of 0.1 M, part of the alkaline Bohr effect is due to an interaction of chloride ions with hemoglobin. Furthermore, at low concentrations of chloride ions the acid Bohr effect has almost vanished. This result suggests that part of the acid Bohr effect arises from an interaction of chloride ions with oxyhemoglobin. The dependence of the Bohr effect upon the chloride ion concentration can be explained by assuming specific binding of chloride ions to both oxy- and deoxyhemoglobin, with deoxyhemoglobin having the highest affinity.     

Effect of oxygen concentration on trasverse water proton relaxation times in erythrocytes homozygous and heterozygous for hemoglonin S.

The transverse water proton relaxation times (T₂) of erythrocytes homozygous and heterozygous for hemoglobin S have been measured as a function of oxyhemoglobin concentration at 37 °C. An immediate decrease in T₂ is observed in S/S erythrocytes as the amount of oxyhemoglobin is decreased and the maximum change is observed at 50% deoxyhemoglobin S. In heterozygous erythrocytes, the T₂ remains unchanged until a critical level of deoxyhemoglobin is attained. The critical level of deoxyhemoglobin is a function of the percentage of hemoglobin S in the heterozygous erythrocytes. A Hill plot of the data obtained from S/S erythrocytes gives an n value of around 2.4. These results suggest that the measurement of T₂ is sensitive to the very early stages of the polymerization process. This suggestion is supported by calculations; our T₂ measurements are sensitive to a range of correlation times expected for hemoglobin monomers at one extreme and linear polymers of seven hemoglobin molecules at the other extreme.     

Oxygenation of hemoglobin: Correspondence of crystal and solution properties using diffusion coefficient measurements

Quasi-elastic light scattering has been used to measure the change in the translational diffusion coefficient of hemoglobin upon oxygenation and the difference in the diffusion coefficients of oxy- and methemoglobin. The diffusion coefficients of oxy- and methemoglobin were found to be the same within the experimental accuracy of 0.2%, while the diffusion coefficient of oxyhemoglobin tetramers in solution at 13 mg/ml was found to be 0.8% smaller than that of deoxyhemoglobin at the same concentration, when the reversible dissociation of oxyhemoglobin tetramers into dimers was taken into account. In the limit of zero concentration, the oxyhemoglobin diffusion coefficient was found to be 1.5% ± 1.0% smaller than that of deoxyhemoglobin. This result is in very good agreement with what we predict using atomic coordinates to model the liganded and unliganded hemoglobin molecules as ellipsoids of revolution.     

The binding of folyl- and antifolylpolyglutamates to hemoglobin

A binding method that detects only the strongest binding site for a ligand on a protein has been used to show that folates and folate analogs, conjugated with poly-gamma-glutamates, are bound to hemoglobin. When the concentration of hemoglobin is much larger than that of the polyglutamate, as is the case in the red cell, the fraction bound is a direct function of the hemoglobin concentration and is independent of the total polyglutamate concentration. Binding to deoxyhemoglobin tetramers is competitive with 2,3-diphosphoglycerate. In oxyhemoglobin the folyl and methotrexate polyglutamates are bound preferentially by free alpha beta dimers, but removal of the pteridine moiety leads to tetramer binding even in oxyhemoglobin. Changes in the length of the polyglutamate side chain and alterations of the pteridine structure such as reduction and/or methylation have a much larger effect on the constant for binding to deoxyhemoglobin tetramers than on that for oxyhemoglobin dimers. The implications of these results for the storage of pteroylpolyglutamates in the erythrocyte and their release from the red cell under the influence of the degree of oxygenation and variations in the 2,3-diphosphoglycerate level are discussed.     

The gelation of deoxyhemoglobin S in erythrocytes as detected by transverse water proton relazation measurements

At 37 °C, when samples of blood, washed erythrocytes, or isolated hemoglobin from individuals with sickle cell disease are deoxygenated, the transverse water proton relaxation time is sharply decreased. In similar samples from normal adults homozygous for hemoglobin A, only a slight decrease in t₂ is observed upon deoxygenation at 37 °C. In samples containing deoxyhemoglobin S the value of t₂ increases as the temperature is decreased from 37 °C to 4 °C, in contrast to samples containing oxyhemoglobin S, oxyhemoglobin A, or deoxyhemoglobin A where t₂ decreases as the temperature decreases. It is suggested that this decrease in t₂ observed in samples of deoxyhemoglobin S at 37 °C is the result of an increase in the amount of preferentially oriented water at macromolecular interfaces which occurs under conditions known to produce deoxyhemoglobin S gelation. Conditions which reverse deoxyhemoglobin S gelation such as lowering the temperature to 4 °C decrease the amount of preferentially oriented water which results in an increase in the value of t₂. Thus, measurement of the transverse water proton relaxation time can be used to monitor the gelation of deoxyhemoglobin S inside the erythrocyte.     

Observation of allosteric transition in hemoglobin

Two conclusions have been drawn from NMR studies of mixed state hemoglobins. First the α and β subunits in hemoglobin are not equivalent in their conformational properties. Second the mixed state hemoglobin (α^IIICN β^II)₂ can take two different quaternary structures without changing the degree of ligation. One of the two structures is similar to that of deoxyhemoglobin and the other to that of oxyhemoglobin.     

Gelation of sickle cell hemoglobin in mixtures with normal adult and fetal hemoglobins.

We report the results of thermodynamic and kinetic studies on the gelation of mixtures of sickle cell (S) deoxyhemoglobin with normal human adult (A) and fetal (F) deoxyhemoglobins. The delay time of thermally induced gelation was monitored by the increase in turbidity. At the completion of gelation the solubility was determined by sedimenting the polymers and measuring the supernatant concentration spectrophotometrically. Addition of hemoglobins A or F, at mole fractions from 0 to 0.6, resulted in large increases in both the solubility and the delay time. For a 50:50 mixture of deoxyhemoglobin F with deoxyhemoglobin S, the solubility increased by a factor of 1.8 and the delay time by a factor of 10⁷ relative to pure deoxyhemoglobin S at the same total concentration, while for a 50:50 mixture of deoxyhemoglobins A and S the solubility increased by a factor of 1.4 and the delay time by a factor of 10⁴. The relative delay times were independent of both temperature and total hemoglobin concentration. The data have been analyzed according to theoretical models which treat the effects of temperature, concentration, non-ideality and solution composition on the thermodynamics and kinetics of gelation. The increased solubility in mixtures with deoxyhemoglobin F is fully explained by a model in which only deoxyhemoglobin S molecules polymerize. The effect of fetal hemoglobin (α₂γ₂) and hybrid α₂γβ^S molecules is to increase the solution non-ideality through the contribution of their excluded volume. The smaller increase in the solubility observed in comparable mixtures with deoxyhemoglobin A requires that the hybrid α₂β^Aβ^S molecules copolymerize with the deoxyhemoglobin S. The kinetic results for the mixtures can be quantitatively accounted for using a nucleation model in which the equilibrium properties of the polymer are used to describe the critical nucleus. The very large increases in delay time observed for the $\text{S}\text{F}$ mixtures can be explained by assuming that only α₂β₂^S molecules participate in the formation of a nucleus containing about 25 monomers. As in the thermodynamic analysis, the smaller effect of adding deoxyhemoglobin A can be attributed to the contribution of the hybrid molecules in forming the critical nucleus. Thus the difference between the polymerization properties of mixtures of deoxyhemoglobin S with deoxyhemoglobins A and F can be attributed solely to the copolymerization of the α₂β^Aβ^S hybrid molecule and the absence of any significant copolymerization of the α₂γβ^S hybrid.     

Kinetics of polymerization of deoxyhemoglobin S and mixtures of hemoglobin A and hemoglobin S at high hemoglobin concentrations

Transverse water proton relaxation times (T₂) have been measured as a function of time after deoxygenation of solutions containing hemoglobin S. The shortened T₂ values observed upon deoxygenation of hemoglobin S result from an increase in the correlation time (τ_c) of the water fraction irrotationally bound to deoxyhemoglobin S as it polymerizes. Therefore, the change in τ_c as a function of time after deoxygenation can be used to measure the rate of polymer formation. The change in τ_c observed is reasonably fit by the first-order equation τ = τ₀ (1 ? e^?kt) + τ_oxy. At a total hemoglobin concentration of approximately 300 mg/ml, the pseudo-first-order rate constant in a heterozygous AS sample is 25 times slower than in a homozygous S sample, k = 0.019 and 0.47 s^?1, respectively. Since the transit time for an erythrocyte in vivo is approximately 15 s, these results suggest that the heterozygous A/S erythrocyte would traverse the circulation and become reoxygenated before extensive polymerization and, therefore, cell sickling could occur. For the homozygous S/S erythrocyte, there is ample time for polymerization and for cell sickling during circulation.     

Hemoglobin oxygen fractional saturation regulates nitrite-dependent vasodilation of aortic ring bioassays

Nitrite reacts with deoxyhemoglobin to generate nitric oxide (NO). This reaction has been proposed to contribute to nitrite-dependent vasodilation in vivo and potentially regulate physiological hypoxic vasodilation. Paradoxically, while deoxyhemoglobin can generate NO via nitrite reduction, both oxyhemoglobin and deoxyhemoglobin potently scavenge NO. Furthermore, at the very low O(2) tensions required to deoxygenate cell-free hemoglobin solutions in aortic ring bioassays, surprisingly low doses of nitrite can be reduced to NO directly by the blood vessel, independent of the presence of hemoglobin; this makes assessments of the role of hemoglobin in the bioactivation of nitrite difficult to characterize in these systems. Therefore, to study the O(2) dependence and ability of deoxhemoglobin to generate vasodilatory NO from nitrite, we performed full factorial experiments of oxyhemoglobin, deoxyhemoglobin, and nitrite and found a highly significant interaction between hemoglobin deoxygenation and nitrite-dependent vasodilation (P < or = 0.0002). Furthermore, we compared the effect of hemoglobin oxygenation on authentic NO-dependent vasodilation using a NONOate NO donor and found that there was no such interaction, i.e., both oxyhemoglobin and deoxyhemoglobin inhibited NO-mediated vasodilation. Finally, we showed that another NO scavenger, 2-carboxyphenyl-4,4-5,5-tetramethylimidazoline-1-oxyl-3-oxide, inhibits nitrite-dependent vasodilation under normoxia and hypoxia, illustrating the uniqueness of the interaction of nitrite with deoxyhemoglobin. While both oxyhemoglobin and deoxyhemoglobin potently inhibit NO, deoxyhemoglobin exhibits unique functional duality as an NO scavenger and nitrite-dependent NO generator, suggesting a model in which intravascular NO homeostasis is regulated by a balance between NO scavenging and NO generation that is dynamically regulated by hemoglobin's O(2) fractional saturation and allosteric nitrite reductase activity.     

Crystallization of deoxyhemoglobin S by fiber alignment and fusion.

Fibers of deoxyhemoglobin S obtained directly from lysed sickled red blood cells have been compared with fibers from chromatographically pure deoxyhemoglobin S solutions of known chemical composition. Electron micrographs of negatively stained specimens reveal that the molecular packing within the fibers remains largely invariant with changes in pH, ionic strength, Mg²⁺ concentration, 2,3-diphosphoglycerate concentration, temperature or the method of deoxygenation.When solutions of chromatographically pure deoxyhemoglobin S are stirred, the fibers align into well defined fascicles. After several hours of stirring, long needles and twisted ribbons develop and in a relatively short time replace the fascicles in solution. With continued stirring all forms are replaced by small crystals. By use of electron microscopy and low-angle X-ray diffraction we have found these crystals to have cell parameters indistinguishable from those of crystals grown in polyethylene glycol and citrate/phosphate buffer at pH 5 to 6 (Wishner et al., 1975a).Our evidence indicates that crystal formation in stirred solutions of deoxyhemoglobin S is the result of a progressive alignment and fusion of the fibers, and that the molecular arrangement within the fibers is closely related to that within the crystal. The remarkable pH invariance of the molecular packing within the fiber and crystal structures is consistent with the dominance of hydrophobic bonding between molecules. The β6-valine contact observed by Wishner et al. (1975b) is apparently the pathological contact responsible for the polymerization of deoxyhemoglobin S in vivo. On the basis of our observations and knowledge of the crystal structure we propose that the deoxyhemoglobin S fiber consists of eight molecular double strands, four of which run in each direction along the length of the fiber.     

The Binding of Asparagine,Glutamine and Homoserine to Human Erythrocytes Containing Hemoglobins S and CS and to Soluble Hemoglobins S and CS

Abstract

Tritium labeled asparagine binds to oxyhemoglobin S and to a mixture of hemoglobins C and S in the molar ratio of 3.38:1 and 8.2:1 respectively. From the dialysis equilibrium studies it appears that labeled asparagine does not bind to oxy- or deoxy- hemoglobin A nor to deoxyhemoglobin S. The constant for equilibrium association of asparagine for oxyhemoglobin S is 7.38 × 10⁷ M^?1 and for'oxyhemoglobin CS 4.8 × 10⁴ M^?1 at 23°C. Tritium labeled asparagine is bound to oxyhemoglobin S and CS sufficiently strongly to prevent dissociation under the conditions of gel electrophoresis at pH 9.50. The protein with and without bound asparagine, gluta-mine or homoserine, is indistinguishable in molecular net charge and size by the criteria of quantitative polyacrylamide gel electrophoresis (PAGE). Also there were no significant differences in mobility between hemoglobin S and hemoglobin C in the presence and absence of asparagine, glutamine and homoserine as detectable in agar coated cellulose acetate electrophoresis at pH 6.3. Erythrocytes containing hemoglobin S and CS, after incubation with tritium labeled asparagine and lysis under the conditions of gel electrophoresis at pH 9.5, release hemoglobin S and C with bound tritiated asparagine. No tritiated asparagine remains bound to the ghost.     

Ligand binding and the gelation of sickle cell hemoglobin.

The solubility equilibrium between monomer and polymer which has been shown to exist in deoxyhemoglobin S solutions is examined in solutions partially saturated with carbon monoxide. The total solubility is found to increase monotonically with increasing fractional saturation. At low fractional saturations the increase is nearly linear, amounting roughly to an increase of 0.01 g cm^?3 in solubility for each 10% increase in fractional saturation. Linear dichroism measurements on the spontaneously aligned polymer phase are used to examine the composition of the polymer as a function of the fractional saturation of the corresponding solution phase. The dichroism experiments show that the polymer phase contains less than 5% of CO-liganded hemes even at supernatant fractional saturations in excess of 70%. The polymer selects against totally liganded hemoglobin molecules by a minimum factor of 65 and against singly liganded molecules by a factor of at least 2.5. Consequently, polymerized hemoglobin S has a ligand affinity which is significantly lower than that of monomeric hemoglobin S in the deoxy quaternary structure.The kinetics of the polymerization reaction in the presence of CO are similar to those observed in pure deoxyhemoglobin S solutions. The polymerization is preceded by a pronounced delay, the duration of which, t_d, is proportional roughly to the 30th power of the solubility. At low fractional saturations, this amounts to a tenfold increase in t_d for each 10% increase in the fractional saturation.These results show that the polymerization reaction is nearly specific for deoxyhemoglobin. Models for the dependence of the solubility and the polymer saturation on ligand partial pressure demonstrate the importance of solution phase non-ideality in determining the solubility of mixtures. The results require selection against partially liganded species which is significantly greater than is predicted by the two-state allosteric model. The data are compatible with either sequential or allosteric models in which the major polymerized component is the unliganded hemoglobin molecule.     

Rheologic behavior of deoxyhemoglobin S gels

The physical properties of deoxyhemoglobin S gels formed from solutions at concentrations and temperatures approaching those in vivo have been characterized by stress relaxation using a rotational rheometer. Gels were annealed in the rheometer and then subjected to a constant shear strain; thereafter the stress sustained was followed with time. Gels with solid-like behavior held stress indefinitely, and were characterized by yield temperature (the temperature at which stress decreased). Gels with less solid behavior were unable to hold target stress, and were characterized by yield stress (maximum stress attained) and equilibrium stress (final stress held). The samples were ultracentrifuged to calculate pellet and polymer masses. The solidity of the gels, as measured by yield temperature or yield stress, was related to the initial hemoglobin concentration, pellet and polymer masses, shear history, temperature, and the temperature and time of annealing. Solidity increased significantly with time when gels were annealed at 37 degrees C, whereas, when annealed at 25 degrees C, no or minimal increases in solidity were noted. Studies suggest that polymerization occurs rapidly and is completed early in or before the gel annealing period and that the increase in solidity with time of annealing is mainly due to factors other than polymer mass, i.e. alignment, increasing bond strength, water loss. The chemical activity of deoxyhemoglobin S did not affect the solidity of the formed gels. When the resultant polymer masses were comparable, gels formed from samples with albumin present (higher initial total protein concentration, but lower initial deoxyhemoglobin S concentration), had the same behavior as gels formed from solutions with higher initial hemoglobin S concentration. These findings demonstrate that gel annealing conditions must be standardized when comparing the rheologic behaviors of deoxyhemoglobin S gels and indicate that the gel's physical properties (influenced by polymer mass, shear history, annealing time) must be considered in understanding pathophysiology of sickling disorders.     

Electrostatic effects in hemoglobin: hydrogen ion equilibria in human deoxy- and oxyhemoglobin A.

The modified Tanford-Kirkwood theory of Shire et al. [Shire, S. J., Hanania, G.I.H., & Gurd, F.R.N. (1974) Biochemistry 13, 2967] for electrostatic interactions was applied to the hydrogen ion equilibria of human deoxyhemoglobin and oxyhemoglobin. Atomic coordinates for oxyhemoglobin were generated by the application of the appropriate rigid rotation function to alpha and beta chains of the deoxyhemoglobin structure [Fermi, G. (1975) J. Mol. Biol. 97, 237]. The model employs two sets of parameters derived from the crystalline protein structures, the atomic coordinates of charged amino acid residues and static solvent accessibility factors to reflect their individual degrees of exposure to solvent. Theoretical titration curves based on a consistent set of pKint values compared closely with experimental potentiometric curves. Theoretical pK values at half-titration for individual protein sites corresponded to available observed values for both quaternary states. The results bring out the cumulative effects of numerous electrostatic interactions in the tetrameric structures and the major effects of the quaternary transition that result from changes in static solvent accessibility of certain ionizable groups.     

Electron Spin Resonance Analysis of the Nitroxide Spin Label 2,2,6,6-Tetramethylpiperidone-N-Oxyl (Tempone) in Single Crystals of the Reduced Tempone Matrix

The nitroxide spin label Tempone (2,2,6,6-tetramethylpiperidone-N-oxyl) can be reduced with ascorbic acid to give a nonparamagnetic species. Single crystals of reduced Tempone serve as a suitable host matrix to orient trace quantities of Tempone for ESR analysis. In these crystals the majority of the Tempone molecules are well-oriented, but a smaller fraction of the molecules tumble freely to give an isotropic electron spin resonance (ESR) spectrum. ESR transitions for the oriented molecules are saturated at much lower microwave power levels than for the tumbling molecules. For the oriented molecules, an analysis of the anisotropy of the spectroscopic splitting factor (g) gives principal values of g₁ = 2.0094, g₂ = 2.0061, g₃ = 2.0021. The hyperfine coupling tensor is nearly axially symmetric, with principal values (in gauss) of A₁ = 6.5, A₂ = 6.7, A₃ = 33.0. Within experimental error, the principal axis systems for the g tensor and the hyperfine tensor are identical. Comparison of the average values of g and A with the isotropic values of these parameters for Tempone in solvents of different polarity suggests a method for choosing the most appropriate tensor elements to be used for spin label experiments in various solvent systems.