Proton magnetic relaxation dispersion in human fluoromethaemoglobin solutions.

The solvent proton spin-lattice relaxation time of high spin Fe3+ (S=5/2) human A fluoromethaemoglobin aqueous solutions was measured at 14 Larmor frequencies in the range from 2.2 to 96 MHz. The observed paramagnetic relaxation rates are analysed in terms of the Solomon-Bloembergen theory, with the g-tensor value of 2 based on the consideration of the protein tertiary structure. From the H2O (pH 6) haemoprotein solution relaxation data, tau(c) =(9.3+/-0.3) X 10(-10) sec. If the total relaxation rates are corrected for the "outer-sphere" paramagnetic contribution, tau(c)=(6.5+/-0.4) X 10(-10) sec. The latter correction is obtained from the p.m.r. of the non-exchangeable aliphatic protons of C2H4(OD)2 added to the D2O-solution of fluoromethaemoglobin. Assuming that single proton transfer is taking place through the protein channel along the axis normal to the haem (g=2), the protein "binding" site is at a distance of 3.93 to 3.98 A from the haem Fe3+ ion.     

Lipari-Szabo approach as a tool for the analysis of macromolecular gadolinium(III)-based MRI contrast agents illustrated by the [Gd(EGTA-BA-(CH2)12)] n n + polymer

The parameters governing the water proton relaxivity of the [Gd(EGTA-BA-(CH2)12)]nn+ polymeric complex were determined through global analysis of 17O NMR, EPR and nuclear magnetic relaxation dispersion (NMRD) data [EGTA-BA2- = 3,12-bis(carbamoylmethyl)- 6,9-dioxa-3,12-diazatetradecanedioate(2-)]. The Lipari-Szabo approach that distinguishes the global motion of the polymer (tau g) from the local motion of the Gd(III)-water vector (tau l) was necessary to describe the 1H and 17O longitudinal relaxation rates; therefore for the first time it was included in the global simultaneous analysis of the EPR, 17O NMR and NMRD data. The polymer consists on average of only five monomeric units, which limits the intramolecular hydrophobic interactions operating between the (CH2)12 groups. Hence the global rotational correlation time is not very high (tau g298 = 3880 +/- 750 ps) compared to the corresponding DTPA-BA-based polymer (about 15 monomeric units), where tau g298 = 6500 ps. As a consequence, the relaxivity is limited by the rotation, which precludes the advantage obtained from the fast exchanging chelating unit (kex298 = 2.2 +/- 0.1 x 10(6) s-1).     

High-resolution field-cycling NMR studies of a DNA octamer as a probe of phosphodiester dynamics and comparison with computer simulation

Phosphorus-spin longitudinal relaxation rates of the DNA duplex octamer [d(GGAATTCC)](2) have been measured from 0.1 to 17.6 T by means of conventional and new field-cycling NMR methods. The high-resolution field-cycling method is identical to a conventional relaxation experiment, except that after preparation the sample is moved pneumatically from its usual position at the center of the high-resolution magnet upward to a lower field above its normal position and then returned to the center for readout after it has relaxed for the programmed relaxation delay at the low field. This is the first measurement of all longitudinal relaxation rates R(1) of a nuclear species in a macromolecule over virtually the entire accessible magnetic field range. For detailed analysis, three magnetic field regions can be delineated: (i) dipolar relaxation dominates at fields below 2 T, (ii) chemical shift anisotropy (CSA) relaxation is roughly constant from 2 to 6 T, and (iii) a square-law increasing dependence is seen at fields higher than approximately 6 T due to internal motion CSA relaxation. The analysis provides a rotational correlation time (tau(r) = 4.1 +/- 0.3 ns) for the duplex at both 1.5 and 0.25 mM concentrations (of duplex) at 22 degrees C. For comparison, extraction of tau(r) in the conventional way from the ratio of T(1)/T(2) at 14 T yields 3.2 ns. The tau(r) discrepancy disappears when we exclude the contribution of internal motion from the R(1) in the ratio. The low-field dipolar relaxation provides a weighted inverse sixth power sum of the distances from the phosphorus to the protons responsible for relaxation. This average is similar for all phosphates in the octamer and similar to that in previous B-DNA structures (its inverse sixth root is about 2.40 A for two different concentrations of octamer). The CSA relaxation at intermediate field provides an estimate of the order parameter squared, S(c)(2), for each phosphorus. S(c)(2) is about 0.7-1, clearly different for different phosphate linkages in the octamer duplex. The increasing R(1) at high fields reflects CSA relaxation due to internal motions, for which a correlation time, tau(hf), can be approximately extracted with the aid of additional measurements at 14.0 and 17.6 T. We conclude that tau(hf) values are relatively large, in the range of about 150 ps. Insight into the motions leading to this correlation time was gained by a 28 ns molecular dynamics simulation of the molecule. S(2) and tau(s) (corresponding to tau(hf)) predicted by this simulation were in good agreement with the experimental values from the field-cycling data. Both the effect of Mg(2+) on the dynamic parameters extracted from (31)P relaxation rates and the field dependence of relaxation rates for several protons of the octamer were measured. High-resolution field cycling opens up the possibility of monitoring residue-specific dipolar interactions and dynamics for the phosphorus nuclei of diverse oligonucleotides.     

Internal motions in B- and Z-form poly(dG-dC).poly(dG-dC): 1H NMR relaxation studies

Proton NMR relaxation measurements are used to compare the molecular dynamics of 60 base pair duplexes of B- and Z-form poly(dG-dC).poly(dG-dC). The relaxation rates of the exchangeable guanine imino protons (Gim) in H2O and in 90% D2O show that below 20 degrees C spin-lattice relaxation is exclusively from proton-proton magnetic dipolar interactions while proton-nitrogen interactions contribute about 30% to the spin-spin relaxation. The observation that the spin-lattice relaxation is nonexponential and that the initial spin-lattice relaxation rate of the Gim, G-H8 and C-H6 protons depends on the selectivity of the exciting pulse shows that spin-diffusion dominates the spin-lattice relaxation. The relaxation rates of the Gim, C-H5, and C-H6 in B- and Z-form poly(dG-dC).poly(dG-dC) cannot be explained by assuming the DNA behaves as a rigid rod. The data can be fit by assuming large-amplitude out of plane motions (+/- 30-40 degrees, tau = 1-100 ns) and fast, large-amplitude local torsional motions (+/- 25-90 degrees, tau = 0.1-1.5 ns) in addition to collective torsional motions. The results for the B and Z forms show that the rapid internal motions are similar and large in both conformations although backbone motions are slightly slower, or of lower amplitude, in Z DNA. At high temperatures (greater than 60 degrees C), imino proton exchange with solvent dominates the spin-lattice relaxation of B-form poly(dG-dC).poly(dG-dC), but in the Z form no exchange contribution (less than 2 s-1) is observed at temperatures as high as 85 degrees C. Conformational fluctuations that expose the imino protons to the solvent are strikingly different in the B and Z forms. The results obtained here are compared with those previously reported for poly(dA-dT).poly(dA-dT).     

Hydration of clupeine in solution

Spin-lattice relaxation times, T1, of H2(17) O at 25 degrees were measured for aqueous solutions of clupeine and its constituent amino acids, which are serine, threonine, proline and arginine. The dynamic hydration numbers, nDHN, of clupeine and amino acids were determined from a concentration dependence of T1. The coordination numbers nh, and the rotational correlation times, tau ch, of water molecules around clupeine and amino acids were estimated and compared with that of pure water. The tau ch/tau co of clupeine was 1.85 and close to that of arginine. The experimental value of nDHN of clupeine was in good agreement with that calculated from the nDHN values of the constituent amino acids. This means that the clupeine molecule has a random conformation in solution.     

Self-association of oxyhaemoglobin. A nuclear magnetic relaxation study in H2O/D2O solutions

The proton and deuterium longitudinal relaxation rates were Studied at room temperature up to the highest protein concentrations in oxyhaemoglobin solutions of different H₂O/D₂O composition. The deuterium relaxation rates followed the experimentally well known single linear dependence on protein concentration, the slopes being little influenced by solvent (D₂O/H₂O) composition. The proton ralaxation rates show two different liner dependences on haemoglobin concentration. The entire concentration range is described by two straight lines with the threshold concentration about 11 mM (in haem), The ratio of the slopes is 1.6 (high-to-low Hb-conc.). Only in the higher concentration range two T₁'s were observed if the solvent contained more than half of D₂O. The slow relaxation phase of protons has T₁'s similar to those measured in solutions with less than half of D₂O. The relaxation of the other phase was ten times faster. The ratio of the proton populations in these two phases was equal to 2 (slow-to-fast) and independent of protein concentration. The fast relaxing protons are attributed to water molecules encaged within two or more haemoglobin molecules which associate for times long enough on the PMR time-scale.     

Effects of relaxation processes on the temperature dependence of oxidation rate of photooxidized bacteriochlorophyll on the primary quinone in reaction centers of Rhodobacter sphaeroides

The temperature dependence of the time of dark recombination of charges between photooxidized bacteriochlorophyll and reduced primary quinone acceptor (tau e) in Rhodobacter sphaeroides photosynthetic reaction centers was studied in the temperature range 140-320 K. It was found that the function tau e = tau e(T) is nonmonotonous: in the temperature range from 140 to 290 K, tau e is increased from 40 to 100 ms; however, under further heating to 320 K, tau e decreased to 80 ms. The replacement of H2O by D2O in these preparations caused an acceleration of the recombination process in the range of physiological temperatures, but the nonmonotonous character of the function tau e(T) remained. The theoretical interpretation of the results was made in the framework of the theory of electron-phonon interactions with allowance for the relaxation processes.     

1H and 31P relaxation rate studies of the interaction of phosphoenolpyruvate and its analogues with avian phosphoenolpyruvate carboxykinase

The interactions of the substrate phosphoenolpyruvate and the substrate analogues (Z)-phosphoenol-alpha-ketobutyrate and (E)-phosphoenol-alpha-ketobutyrate with the enzyme-Mn complex of chicken liver phosphoenolpyruvate carboxykinase have been investigated by 1H and by 31P nuclear relaxation rate studies. Studies of the 1H and the 31P relaxation rates of the ligands in the binary Mn-ligand complexes show that these ligands interact with the metal ion via the phosphate group but not through the carboxylate. An inner sphere coordination complex is formed but the metal-ligand complex is not in the most extended conformation. In the relaxation rate studies of the ligands in the presence of the enzyme, conditions were adjusted so that all of the Mn2+ that was added resided in the ternary enzyme-Mn-ligand complex. The 1H relaxation rates for each of the three ligands were measured at 100 and at 300 MHz. In each case the normalized paramagnetic effects showed that 1/(pT2p) was greater than 1/(pT1p). A frequency dependence of the 1/(pT1p) and 1/(pT2p) values was also measured. The correlation time, tau c, for the Mn-1H interaction was calculated from the frequency dependence of 1/(pT1p) assuming a maximal frequency dependence of tau c and assuming no frequency dependence of tau c and from the T1M/T2M ratios at each frequency. The tau c values for all of the complexes, calculated at 100 MHz, varied from approximately 0.3 to 2.0 ns. These values were used to calculate the Mn-1H distances in each of the ternary complexes. The relaxation rates of 31P were also measured.(ABSTRACT TRUNCATED AT 250 WORDS)     

Light scattering studies of the effect of Ca2+ on the structure of porcine submaxillary mucin

The effects of calcium ions on the solution properties of porcine submaxillary mucin (PSM) have been investigated by static and dynamic light scattering. The weight average molecular weights of PSM fractions are unaffected by the addition of up to 0.5M CaCl2: these data are within experimental error of those for solutions in 0.1M NaCl. The distribution of relaxation frequencies derived from the dynamic data shows the existence of two distinct relaxation modes. The average relaxation times have been interpreted to yield the z-average translational diffusion coefficient and the longest intramolecular relaxation time tau1. A plot of tau1 vs the mean value of 1/Rh-3z is linear, and consistent with plots of such data recorded for PSM in 0.1m NaCl and 6M GdnHCl solutions. However, the tau values and the associated results for the mean value of R-1h-1z in 0.5M CaCl2 are smaller than those determined in 0.1M NaCl. This suggests that the conformation of PSM in CaCl2 solution is more contracted than those in the other two solvents. These results are consistent with the compact packaging of mucin in the secretary granules that have elevated Ca2+ levels.     

Nuclear magnetic spin-lattice relaxation of water protons caused by metal cage compounds.

The nuclear magnetic spin-lattice relaxation rates of water protons are reported for solutions of manganese(II), copper(II), and chromium(III) cage complexes of the sarcophagine type. As simple aqueous solutions, the complexes are only modest magnetic relaxation agents, presumably because they lack protons on atoms in the first-coordination-sphere protons that are sufficiently labile to mix the large relaxation rate at the metal complex with that of the bulk solvent. The relaxation is approximately modeled using spectral density functions derived for translational diffusion of the interacting dipole moments with the modification that the electron spin relaxation rate is directly included as a contribution to the correlation time. In all cases studied, the electron spin relaxation rate is sufficiently large that it contributes directly to the water-proton spin relaxation process. The poor relaxation efficiency of the cage compound may, however, be improved dramatically by binding the complex to a protein. The efficiency is improved even further if the rotational motion of the protein is reduced drastically by an intermolecular cross-linking reaction. The relaxation efficiency of the cross-linked protein-cage complexes rivals that of the best first-coordination-sphere relaxation agents like [Gd(DTPA)(H2O)]2- and [Gd(DOTA)(H2O)]-.     

Proton relaxation mechanisms and the measurements of r phi, r psi and transannular interproton distances in gramicidin S

Monoselective, Rio(SE), biselective, Rio(i,j), and nonselective proton spin-lattice relaxation rates have been measured for dilute solutions of gramicidin S in dimethyl sulfoxide and used to evaluate cross-relaxation rates (sigma ij = Rio(i,j)-Rio(SE)) and Fi ratios (Fi = Ri(NS)/Rio(SE)). The cross-relaxation parameters, sigma, and Fi ratios measured for backbone gramicidin S protons predict that the same correlation time, tau c = 1.2 X 10(-9)s, modulates all the dipolar proton-proton interactions and that these interactions represent the main source for the proton spin-lattice relaxation process. The larger relaxation rates for amide versus alpha-protons of the backbone are attributed to dipolar relaxation between 14N and its directly bonded protons and is an approximate measure of the extent of this. The intrabackbone proton-proton distances, evaluated from sigma values, were consistent with the antiparallel beta-plated sheet/beta II'-turn conformation previously proposed for gramicidin S in solution.     

The relationship between the transverse and longitudinal nuclear magnetic resonance relaxation rates of muscle water.

Whole frog sartorius and gastrocnemius muscles were incubated in Ringer's solutions, either unenriched or enriched with H2 17Oor 2D2O. Subsequently, the rates of transverse (1/T2) and of longitudinal (1/T1) nuclear magnetic relaxation were measured for 17O, 2D, and 1H at room temperature and at 8.1 MHz. The ratio (T1/T2) for 17O was measured to be approximately 1.5-2.0, close to the value roughly estimated from the Larmor frequency dependence of 1/T1 alone over the range 4.3-8.1 MHz. On the other hand (T1/T2) for 2D and 1H were both measured to lie in the range 9-11. Insofar as the entire 17O signal was detected, the data indicate the presence of an exchange mechanism between the major fraction of intracellular water and a minor fraction characterized by enhanced rates of relaxation. Possible molecular mechanisms are presented.     

Mathematical description of stress relaxation of bovine femoral cortical bone

In 1993 we proposed an empirical formula for describing the relaxation modulus of cortical bone based on the results of stress relaxation experiments performed for 1 x 10(5) sec: [E(t) = E0{A exp[ -(t/tau1)beta] + (1 - A) exp(-t/tau2)}, (0 < A, beta <1 and tau1 < tau2) where E0 is the initial value of the relaxation modulus, A is the portion of the first term, tau1 and tau2 are characteristic relaxation times, and beta is a shape factor [Sasaki et al., J. Biomechanics 26 (1993), 1369]. Although the relaxation properties of bone under various external conditions were described well by the above equation, recent experimental results have indicated some limitations in its application. In order to construct an empirical formula for the relaxation modulus of cortical bone that has a high degree of completeness, stress relaxation experiments were performed for 6 x 10(5) seconds. The second term in the equation was determined as an apparently linear portion in a log E(t) vs t plot at t>1 x 10(4) sec. The same plot for experiments performed for 6 x 10(5) seconds revealed that the linear portion corresponding to the second term was in fact a curve with a large radius of curvature. On the basis of this fact, we proposed a second improved empirical equation E(t) = E0{A exp [ -(t/tau1)beta] + (1 - A) exp[-(t/tau2)gamma]}, (0相似文献   

Effects of O2 and CO2 on Nonsteady-State Photosynthesis (Further Evidence for Ribulose-1,5-Bisphosphate Carboxylase/Oxygenase Limitation)

The effects of CO2 and O2 on nonsteady-state photosynthesis following an increase in photosynthetic photon flux density (PPFD) were examined in Spinacia oleracea to investigate the hypotheses that (a) a slow exponential phase (the ribulose-1,5-bisphosphate carboxylase/oxygenase [Rubisco] phase) of nonsteady-state photosynthesis is primarily limited by Rubisco activity and (b) Rubisco activation involves two sequential, light-dependent processes as described in a previous study (I.E. Woodrow, K.A. Mott [1992] Plant Physiol 99: 298-303). Photosynthesis was found to be sensitive to O2 during the Rubisco phase in the approach of photosynthesis to steady state. Analyses of this sensitivity to O2 showed that the control coefficient for Rubisco was approximately equal to 1 during this phase, suggesting that Rubisco was the primary limitation to photosynthesis. O2 had almost no effect on the kinetics (described using a relaxation time, [tau] of the Rubisco phase for leaves starting in darkness or for leaves starting in low PPFD, but [tau] was substantially higher in the former case. CO2 was found to affect both the rate of photosynthesis and the magnitude of [tau] for the Rubisco phase. The [tau] value for the Rubisco phase was found to be negatively correlated with intercellular CO2 concentration (ci), and leaves starting in darkness had higher values of [tau] at any ci than leaves starting in low PPFD. The effects of CO2 and O2 on the Rubisco phase are consistent with the existence of two sequential, light-dependent processes in the activation of Rubisco if neither process is sensitive to O2 and only the second process is sensitive to CO2. The implications of the data for the mechanism of Rubisco activation and for the effects of stomatal conductance on nonsteady-state photosynthesis are discussed.     

Role of impaired myocardial relaxation in the production of elevated left ventricular filling pressure

Although present in many patients with heart failure and a normal ejection fraction, the role of isolated impairments in active myocardial relaxation in the genesis of elevated filling pressures is not well characterized. Because of difficulties in determining the effect of prolonged myocardial relaxation in vivo, we used a cardiovascular simulated computer model. The effect of myocardial relaxation, as assessed by tau (exponential time constant of relaxation), on pulmonary vein pressure (PVP) and left ventricular end-diastolic pressure (LVEDP) was investigated over a wide range of tau values (20-100 ms) and heart rate (60-140 beats/min) while keeping end-diastolic volume constant. Cardiac output was recorded over a wide range of tau and heart rate while keeping PVP constant. The effect of systolic intervals was investigated by changing time to end systole at the same heart rate. At a heart rate of 60 beats/min, increases in tau from a baseline to extreme value of 100 ms cause only a minor increase in PVP of 3 mmHg. In contrast, at 120 beats/min, the same increase in tau increases PVP by 23 mmHg. An increase in filling pressures at high heart rates was attributable to incomplete relaxation. The PVP-LVEDP gradient was not constant and increased with increasing tau and heart rate. Prolonged systolic intervals augmented the effects of tau on PVP. Impaired myocardial relaxation is an important determinant of PVP and cardiac output only during rapid heart rate and especially when combined with prolonged systolic intervals. These findings clarify the role of myocardial relaxation in the pathogenesis of elevated filling pressures characteristic of heart failure.     

An improved method to analyze the stress relaxation of ligaments following a finite ramp time based on the quasi-linear viscoelastic theory

The quasi-linear viscoelastic (QLV) theory proposed by Fung (1972) has been frequently used to model the nonlinear time- and history-dependent viscoelastic behavior of many soft tissues. It is common to use five constants to describe the instantaneous elastic response (constants A and B) and reduced relaxation function (constants C, tau 1, and tau 2) on experiments with finite ramp times followed by stress relaxation to equilibrium. However, a limitation is that the theory is based on a step change in strain which is not possible to perform experimentally. Accounting for this limitation may result in regression algorithms that converge poorly and yield nonunique solutions with highly variable constants, especially for long ramp times (Kwan et al. 1993). The goal of the present study was to introduce an improved approach to obtain the constants for QLV theory that converges to a unique solution with minimal variability. Six goat femur-medial collateral ligament-tibia complexes were subjected to a uniaxial tension test (ramp time of 18.4 s) followed by one hour of stress relaxation. The convoluted QLV constitutive equation was simultaneously curve-fit to the ramping and relaxation portions of the data (r2 > 0.99). Confidence intervals of the constants were generated from a bootstrapping analysis and revealed that constants were distributed within 1% of their median values. For validation, the determined constants were used to predict peak stresses from a separate cyclic stress relaxation test with averaged errors across all specimens measuring less than 6.3 +/- 6.0% of the experimental values. For comparison, an analysis that assumed an instantaneous ramp time was also performed and the constants obtained for the two approaches were compared. Significant differences were observed for constants B, C, tau 1, and tau 2, with tau 1 differing by an order of magnitude. By taking into account the ramping phase of the experiment, the approach allows for viscoelastic properties to be determined independent of the strain rate applied. Thus, the results obtained from different laboratories and from different tissues may be compared.     

Tryptophan sidechain dynamics in hydrophobic oligopeptides determined by use of 13C nuclear magnetic resonance spectroscopy.

Two oligopeptides, t-boc-LAWAL-OMe and t-boc-LALALW-OMe, were synthesized for the purpose of examining the sidechain dynamics of the tryptophan residue in hydrophobic environments by 13C nuclear magnetic resonance and fluorescence spectroscopy. In both peptides, the tryptophan sidechain was greater than 95% enriched with 13C at the C delta 1 position. Spin-lattice relaxation time (T1) and steady-state nuclear Overhauser effect (NOE) data were obtained at 50.3 and 75.4 MHz for both peptides in CD3OD, and at 75.4 MHz for t-boc-LALALW-OMe in lysolecithin-D2O micelles. We have adapted the model-free approach of G. Lipari and A. Szabo (1982, J. Am. Chem. Soc. 104:4546) to interpret the 13C-NMR data. Computer-generated curves based on experimental data obtained at a single frequency demonstrate relationships between an effective correlation time for tryptophan sidechain motion (tau e), a generalized order parameter (sigma) describing the extent of motional restriction, and an overall correlation time for the peptide (tau m). Assuming predominantly dipolar relaxation, least-squares fits of the dual frequency relaxation data provide values for these parameters for both peptides. The contribution of chemical shift anisotropy (CSA), however, is also explicitly assessed in the data analysis, and is shown to perturb the predicted sigma, tau e, and tau m values and to decrease chi(2) values observed in nonlinear least-squares analysis of the data. Because of uncertainty in the contribution of CSA to the relaxation of the indole ring 13C delta 1 atom, nonlinear least-squares analysis of the relaxation data were performed with and without inclusion of a CSA term in the appropriate relaxation equations. Neglecting CSA, an overall peptide correlation time of 0.69 ns is predicted for t-boc-LAWAL-OMe in CD3OD at 20 degrees C compared with 1.28 ns for t-boc-LALALW-OMe. Given these tau m values and taking into account the effect of measurement error in the T1 and NOE data, the internal dynamics of the tryptophan residue of t-boc-LAWAL-OMe in this isotropic environment are described by a range of tau e values from 70 to 112 ps and sigma values between 0.22 and 0.36. Similarly, for t-boc-LALALW-OMe, 68 less than or equal to tau e less than or equal to 93 ps and 0.09 less than or equal to sigma less than or equal to 0.17. The Ch-terminal position of the tryptophan residue in the hexapeptide may account for its lower order parameter.(ABSTRACT TRUNCATED AT 400 WORDS)     

Water interactions with varying molecular states of bovine casein: 2H NMR relaxation studies

The caseins occur in milk as spherical colloidal complexes of protein and salts with an average diameter of 1200 A, the casein micelles. Removal of Ca2+ is thought to result in their dissociation into smaller protein complexes stabilized by hydrophobic interactions and called submicelles. Whether these submicelles actually occur within the micelles as discrete particles interconnected by calcium phosphate salt bridges has been the subject of much controversy. A variety of physical measurements have shown that casein micelles contain an inordinately high amount of trapped water (2 to 7 g H2O/g protein). With this in mind it was of interest to determine if NMR relaxation measurements could detect the presence of this trapped water within the micelles, and to evaluate whether it is a continuum with picosecond correlation times or is associated in part with discrete submicellar structures with nanosecond motions. For this purpose the variations in 2H NMR longitudinal and transverse relaxation rates of water with protein concentration were determined for bovine casein at various temperatures, under both submicellar and micellar conditions. D2O was used instead of H2O to eliminate cross-relaxation effects. From the protein concentration dependence of the relaxation rates, the second virial coefficient of the protein was obtained by nonlinear regression analysis. Using either an isotropic tumbling or an intermediate asymmetry model, degrees of hydration, v, and correlation times, tau c, were calculated for the caseins; from the latter parameter the Stokes radius, r, was obtained. Next, estimates of molecular weights were obtained from r and the partial specific volume. Values were in the range of those published from other methodologies for the submicelles. Temperature dependences of the hydration and Stokes radius of the casein submicelles were consistent with the hypothesis that hydrophobic interactions represent the predominant forces responsible for the aggregation leading to a submicellar structure. The same temperature dependence of r and v was found for casein under micellar conditions; here, the absolute values of both the Stokes radii and hydrations were significantly greater than those obtained under submicellar conditions, even though tau c values corresponding to the great size of the entire micelle would result in relaxation rates too fast to be observed by these NMR measurements. The existence of a substantial amount of trapped water within the casein micelle is, therefore, corroborated, and the concept that this water is in part associated with submicelles of nanosecond motion is supported by the results of this study.     

Physical determinants of left ventricular isovolumic pressure decline: model prediction with in vivo validation

The rapid decline in pressure during isovolumic relaxation (IVR) is traditionally fit algebraically via two empiric indexes: tau, the time constant of IVR, or tau(L), a logistic time constant. Although these indexes are used for in vivo diastolic function characterization of the same physiological process, their characterization of IVR in the pressure phase plane is strikingly different, and no smooth and continuous transformation between them exists. To avoid the parametric discontinuity between tau and tau(L) and more fully characterize isovolumic relaxation in mechanistic terms, we modeled ventricular IVR kinematically, employing a traditional, lumped relaxation (resistive) and a novel elastic parameter. The model predicts IVR pressure as a function of time as the solution of d(2)P/dt(2) + (1/micro)dP/dt + E(k)P = 0, where micro (ms) is a relaxation rate (resistance) similar to tau or tau(L) and E(k) (1/s(2)) is an elastic (stiffness) parameter (per unit mass). Validation involved analysis of 310 beats (10 consecutive beats for 31 subjects). This model fit the IVR data as well as or better than tau or tau(L) in all cases (average root mean squared error for dP/dt vs. t: 29 mmHg/s for model and 35 and 65 mmHg/s for tau and tau(L), respectively). The solution naturally encompasses tau and tau(L) as parametric limits, and good correlation between tau and 1/microE(k) (tau = 1.15/microE(k) - 11.85; r(2) = 0.96) indicates that isovolumic pressure decline is determined jointly by elastic (E(k)) and resistive (1/mu) parameters. We conclude that pressure decline during IVR is incompletely characterized by resistance (i.e., tau and tau(L)) alone but is determined jointly by elastic (E(k)) and resistive (1/micro) mechanisms.     

NMR relaxation of protein and water protons in diamagnetic hemoglobin solutions

We have measured T1 and T2 of protein and water protons in hemoglobin solutions using broad-line pulse techniques; selective excitation and detection methods enabled the intrinsic protein and water relaxation rates, as well as the spin-transfer rate between them, to be obtained at 5, 10, and 20 MHz. Water and protein T1 data were also obtained at 100 and 200 MHz for hemoglobin in H2O/D2O mixtures by using commercial Fourier-transform instruments. The T1 data conform to a simple model of two well-mixed spin systems with single intrinsic relaxation times and an average spin-transfer rate, with each phase recovering from a radio-frequency excitation with a biexponential time dependence. At low frequencies, protein T1 and T2 agree reasonably with a model of dipolar relaxation of an array of fixed protons tumbling in solution, explicitly calculating methyl and methylene relaxation and using a continuum approximation for the others. Differing values in H2O and D2O are mainly ascribed to solvent viscosity. For water-proton relaxation, T1, T2, and spin transfer were measured for H2O and HDO, which enabled a separation of inter-and intramolecular contributions to relaxation. Despite such detail, few firm conclusions could be reached about hydration water. But it seems clear that few long-lived hydration sites are needed to explain T1 and T2, and the spin-transfer value mandates fewer than five sites with a lifetime longer than 10(-8) s.