Nuclear magnetic resonance of tissue Na correlation time

Shporer and Civan (Biochim. Biophys. Acta (1974) 354, 291–304) reported the effect of magnetic-field strength on the NMR relaxation times of ²³Na in frog skeletal muscle. From these data, they estimated the correlation time τ_c for bound ²³Na whose tumbling is severely restricted, and they suggested that the fraction of bound ²³Na does not exceed some few percent of the total ²³Na population. However, a step in their theoretical approach seems oversimplified. With an improved approach, we obtained an effective τ_c of 4–9 ns for bound ²³Na. This value is some 10 times shorter than the corresponding value estimated by them from the same data. On the other hand, their conclusion concerning the amount of bound ²³Na seems to remain valid. The origin of the observed difference between the two transverse relaxation times of tissue ²³Na is also discussed.     

An empirical relationship between rotational correlation time and solvent accessible surface area

Structure–dynamics interrelationships are important in understanding protein function. We have explored the empirical relationship between rotational correlation times (τ_c and the solvent accessible surface areas (SASA) of 75 proteins with known structures. The theoretical correlation between SASA and τ_c through the equation SASA = K_rτ_c ^(2/3) is also considered. SASA was determined from the structure, τ_c ^calc was determined from diffusion tensor calculations, and τ_c ^expt was determined from NMR backbone¹³ C or ¹⁵N relaxation rate measurements. The theoretical and experimental values of τ_c correlate with SASA with regression analyses values of K_r as 1696 and 1896 m²s^-(2/3), respectively, and with corresponding correlation coefficients of 0.92 and 0.70.     

Orientational interactions in low-concentration DNA solutions

The rotational relaxation tiem τ₃ of DNA molecules (M_w ? 5 × 10⁶) in solution has been determined by the transient electric birefringence method. The analysis of the birefringence decay makes it possible to study only the higher-molecular-weight fraction, the molecules being considered as rigid elongated particles in a short time scale. A marked concentration dependence of the relaxation time has been observed for DNA in low ionic strengths. Above a critical concentration c*, τ₃ increases with the DNA concentration, c. The value of c* increases with the ionic strength. For 10^?3 ionic strength (with NaCl), c* is about 10 μg/mL; then we observe the same strong concentration dependence of rotational relaxation times as recently reported for rodlike M-13 viruses [Maguire, J. F., McTague, J. P. & Rondelez, F. (1980) Phys. Rev. Lett. 45 , 1891–1894]. These results may be discussed in terms of the Doi-Edwards theory for rotational relaxation time of rigid macromolecules [Doi, M. (1975) J. Phys. 36 , 607–611; Doi, M. & Edwards, S. F. (1978) J. Chem. Soc. Faraday Trans. 74 , 918–932] and the critical concentration above which the interactions between the molecules begin to appear allows determining the corresponding molecular length. We observe a very good agreement between the DNA lengths obtained from the c* values and by using the infinite dilution value of τ₃ and Broersma's equation. Therefore, only highly diluted solutions can be used if intrinsic molecular properties based on the rotational diffusion of high-molecular-weight elongated molecules are studied.     

Characterization of the dynamic behavior of r(ACC) and r(AAC) with NMR relaxation data and both metropolis monte carlo and molecular dynamics simulations

The solution-state behavior of two triribonucleotides, adenylyl(3′-5′) adenylyl (3′-5′) cytidine [r(AAC)] and adenylyl (3′-5′) cytidylyl (3′-5′) cytidine [r(ACC)], was studied with spectroscopic and molecular modeling methods. Melting temperatures of 299 and 294 K for r(AAC) and r(ACC), respectively, were obtained from ultraviolet absorption (UV) and circular dichroism (CD) temperature profiles of the order-disorder transition. The behavior of the Raman marker modes is consistent with greater stability of r(AAC) compared to that of r(ACC). Nuclear magnetic resonance (nmr) relaxation data (homonuclear cross-relaxation rates, proton selective and nonselective longitudinal relaxation times, and carbon longitudinal relaxation times) were measured at 283, 296, and 318 K for both trimers. In parallel, the major types of conformations were explored with Metropolis Monte Carlo (MMC) and molecular dynamics (MD) simulations to obtain representations of both slow and fast events. Fitting of experimental data showed that although the MMC conformations do not represent an exhaustive list of conformers in solution, the canonical helical form (A-RNA type) should coexist at low temperature with significant populations of other less classical conformers such as half-stacked (HS), bulged (BU), and reverse-stacked (RS). Fitting of the experimental relaxation data ensemble at 283 K led to very different representations for the two trimers. r(AAC) was shown to have a fairly compact, rigid structure (angular order parameter, S²_ang ∼ 0.9, correlation time for internal motion, τ_e ∼ 0.1 ns), which undergoes fairly rapid overall tumbling characterized by the correlation time τ_c ∼ 0.6 ns, whereas r(ACC) exhibits much more flexibility (S²_ang ∼ 0.7, τ_e ∼ 0.1 ns) and slower molecular reorientation (τ_c ∼ 1.0 ns). The values of S²_ang tended to confirm that large amplitude fluctuations did not occur on the relaxation timescale (ns). In the course of this paper, a widely accepted concept was shown to be questionable. As regards the nmr relaxation data, simulations show that for fairly small nucleic acids (τ_c < 2.0 ns) the second term of the model-free spectral densities is not negligible for representative motional models (S²_ang values < 0.9 and τ_e values in the 0.05–0.2 ns range). The difference in the dynamic behavior of r(AAC) and r(ACC) can be explained by the greater propensity of the A-A sequence to stack as compared to that of A-C. © 1996 John Wiley & Sons, Inc.     

An approach at estimating present day base cation weathering rates: a case study for the Hermine watershed,Canada

A new methodological approach is described for estimating Ca, Mg and K fluxes from soil mineral weathering. This method combines Na flux in surface waters in the Hermine watershed with base cation (BC) concentrations to Na molar ratios from the soil weatherable pool obtained using sequential extraction method. Comparison of BC:Na molar ratios of the weatherable pool with those from other compartments of the watershed suggests possible accumulation of base cations in some areas of the watershed, while losses or minimal changes are observed in others. On average, present day Na weathering rates estimated using the watershed input–output budget method was 0.26 (range 0.16–0.36) kmol_c ha^?1 yearr^?1, over the period of 1995–2006. For Ca, Mg and K, present day weathering rates estimated with the new methodological approach averaged 0.44 (range 0.27–0.60), 0.11 (range 0.07–0.15) and 0.02 (range 0.01–0.02) kmol_c ha^?1 year^?1, respectively. These values are within the range of present day rates previously calculated for the same site and for forested soils from similar granitic environments using other methods. Candidate models for predicting BC weathering rates on individual annual observations were developed using Akaike’s information criterion. The best model includes the number of frost days (inverse relationship) and explained 51% of the variation in total BC weathering rates. The newly developed method may be applicable to other watersheds, providing yearly estimates of nutrient BC at the watershed scale.     

Frequency dependence of the proton magnetic relaxation in aqueous solutions iof haemoproteins

The longitudinal proton magnetic relaxation times T₁ were measured for ferri (met)-and carbonmonoxy-bovine haemoglobin and equine myoglobin in 0.1 M KH₂PO₄ aqueous solutions near pH 6 at 5°C and 35°C from 1.5- to 60-MHz Larmor frequencies. It is concluded that the correlation time τ_C for the dipole–dipole interaction of electron and nuclear spins is in fact the electron (ferric) spin relaxation time τ_S being close to 1.5 × 10^?10 sec for both metHb and metMb at 5°C. At 35°C the paramagnetic relaxation rates are not determined solely by the relaxation of protons exchanging from the haem pocket with bulk solvent. Hence, τC at 35°C cannot be calculated from the dispersion data obtained at this temperature. The relevance of this for the determination of interspin distances r is discussed.     

Effects of temperature and field strength on the NMR relaxation times of 23Na in frog striated muscle

Pulsed NMR techniques have been applied to the study of the relaxation parameters characterizing ²³Na within frog striated muscle. Experiments were performed at 3°C, 22–24°C and 39°C at a Larmor frequency of 15.7 MHz; at 22–24°C, measurements were obtained both at 15.7 MHz and at 7.85 MHz.As previously reported, only a single spine-lattice relaxation time (T₁) was observed, but both slow (T₂)_I and fast (T₂)_II components of the spin-spin relaxation time were measured. The effect of temperature (θ) upon (1/T₁) was qualitatively similar to that reported for ²³Na in free solution; (θ) did not significantly affect (1/T₂) over the range of temperatures studied. (1/T₂)_I, and to a lesser degreee, (1/T₁) exhibited a modest inverse dependence of doubtful significance on the Larmor frequency.The data are examined within the framework of a simple specific model; a conservative values in assumed for the quadrupolar coupling constant characterizing immobilized intracellular Na⁺. Within this framework, the results suggest that the fraction of bound ions whose molecular tumbling is severely restricted does not exceed some few percent of the total sodium population.     

Quasielastic light scattering: Effect of ionic strength on the internal dynamics of DNA

Quasielastic light scattering is used to study the effect of ionic strength on the dynamic behaviour of DNA. In a first approach the spectrum of scattered light is analyzed in terms of a single relaxation process. The large difference between the observed behaviour and that expected according to a pure diffusional process reflects the contribution associated with internal modes, which increases with decreasing ionic strength. Such behaviour is better analyzed in terms of a double relaxation process by using two relaxation times, the reciprocals of which are equal to DK² and DK² + τ_i^?1 (K), respectively, where τ_i (K) is an average value describing the set of modes observed at a given K value. Relative intensity and relaxation times, which are the more accurate parameters, were used to interpret the results. The observed increase of the relative contribution of internal modes with decreasing ionic strength is actually a relative decrease of the diffusional contribution induced by a corresponding increase of the radius of gyration R_G. On the other hand, the reciprocal τ_i^?1 (K) of the relaxation time is a linear function of K² in the analyzed KR_G range and is insensitive to ionic strength between 10^?2M and 1M. These results, when discussed according to Rouse's model, lead to define for each value of τ_i^?1 (K) a corresponding mean-squared equilibrium length 〈μ〉 which is found to be a linear function of K^?2.     

Shear stress and sediment resuspension in relation to submersed macrophyte biomass

We examined the impacts of macrophyte beds dominated by a canopy-forming (Myriophyllum sibiricum) and a meadow-forming (Chara canescens) species on bottom shear stress (τ) and resuspension in shallow Lake Christina, Minnesota (U.S.A.). Studies were conducted in late summer, 1998, when macrophyte biomass levels exceeded 200 g m^?2, and in early summer, 2000, when biomass was greatly reduced (<20 g m^?2) in both plant beds. The critical shear stress (τ_c) of sediments, measured experimentally in the laboratory, was low (1.4 dynes cm^?2) indicating potential for resuspension in the absence of macrophytes. During 1998, turbidity was low at the M. sibiricum and Chara station, rarely increasing when calculated bottom τ (calculated from wave theory assuming no biomass obstruction) exceeded τsub c sub, indicating that both beds reduced sediment resuspension at high biomass levels. In situτ (estimated τ), measured via gypsum sphere dissolution, did not exceed τ_c above the sediment interface in either bed during 1998. In contrast, sediment resuspension occurred in both beds during similar high winds in 2000. However, estimated τ was lower than calculated bottom τ, suggesting that at low biomass, macrophytes were having some impact on τ.     

31P nmr spin-lattice relaxation studies of deoxyoligonucleotides

Temperature-dependent conformational transitions of deoxyoligonucleotides have been monitored by measuring ³¹P chemical shifts, spin-lattice relaxation times (T₁), and ³¹P-{H} nuclear Overhauser enhancements (NOEs). The measured NOE ranged from 30 to 80%, compared to the theoretical maximum of 124% for a dipolar relaxation mediated by rapid isotropic rotation. The observed 3′-5′ phosphate diester ³¹P T₁ showed a similar temperature dependence over the range 2–75°C for both double- and single-stranded oligonucleotides, and for dinucleotides. The results show that dipole–dipole interactions dominate the internucleotide phosphate relaxation rate in oligonucleotides. The same is true of terminal phosphate groups at low temperature; but at higher temperature another process, possibly due to contamination by paramagnetic ions, becomes dominant. The rotational correlation time τ_R calculated from the dipole–dipole relaxation rate of the internucleotide phosphate in d(pA)₂ at 16°C is τ_R = 5.0 × 10^?10 sec, implying a Stokes radius for isotropic rotation of 7.6 Å. The T₁ and NOE values for the double-helical octanucleotide d(pA)₃pGpC(pT)₃ are consistent with dominance of dipole–dipole relaxation and isotropic rotation of a sphere of radius 14 Å, a reasonable dimension for the double helix. Activation energies for the rotation of dinucleotides range from 4 to 6 kcal/mol, close to the value of 4 kcal/mol expected for isotropic rotation. In order to test the possible effect of internal motion of correlation time τ_G on the results, we considered a model in which the nucleotide chain rotates about the P-O bonds. Comparison of the calculation with our experimental results shows that internal motion with τ_G ? 10^?9 sec, as found from other studies to be present for large nucleic acids, would not influence out T₁ and NOE values enough to be distinguished from isotropic rotation. However, we can conclude that τ_G cannot be as fast as 10^?10 sec, even for dinucleotides.     

Molecular states in single-stranded adenylate chains by relaxation analysis

The single-strand helix-coil transition in various oligo- and polyadenylates is characterized by means of an improved cable temperature-jump technique. In all the polymers studied {poly(rA), poly(dA), poly[A(m^2′)] and poly[A(e^2′)]} helix-coil relaxation is observed in the time range from 30 to 1000 nsec. Relaxation-time constants observed at wavelengths λ<280 nm (τ_α) are different from those found at λ >280 nm (τβ), indicating the presence of more than two conformational states. The time constants τ_α increase in the series poly(dA), poly[A(m^2′)], constants τ_β/τ_α is approximately 2.5, except in poly(dA) where τ_β/τ_α ≈ 9. Relaxation measurements with r(A)_n- oligomers show a decrease in conformational mobility with increasing chain length. The relaxation curves also demonstrate that “internal” residues have lower reaction rates than residues at the ends of the oligomer chain. Measurement in D₂O reveal a solvent isotope effect for τ_α of +87% for poly(rA), and of +53% for poly(dA), whereas no isotope effect is found in τ_β. The absence of “slow” relaxation processes in the model compound 9,9′ -trimethylenebisadenine shows that the relatively low rate of the single-strand helix-coil transitions is due to the coupling of base stacking with the folding of the sugar–phosphate chain. The absence of a seprate relaxation process (corresponding to τ_β) in 9,9′-trimethylenebisadenine, as well as in the dinucleotides ApC and CpA, suggests that this relaxation process is dependent upon the presence of both the sugar–phosphate chain and of adjacent adenine bases. The experimental data provide evidence that there is more than one ordered conformation in various single-stranded oligo- and polyadenylates and that the transition between these conformations is influenced by the sugar conformation.     

Conformation and dynamic structure of poly(inosinic acid) in neutral aqueous solution by 1H-, 2H-, 13C-, and 31P-NMR spectroscopy

The conformation and dynamic structure of single-stranded poly(inosinic acid), poly(I), in aqueous solution at neutral pH have been investigated by nmr of four nuclei at different frequencies: ¹H (90 and 250 MHz), ²H (13.8 MHz), ¹³C (75.4 MHz), and ³¹P (36.4 and 111.6 MHz). Measurements of the proton-proton coupling constants and of the ¹H and ¹³C chemical shifts versus temperature show that the ribose is flexible and that base-base stacking is not very significant for concentrations varying from 0.04 to 0.10M in the monomer unit. On the other hand, the proton T₁ ratios between the sugar protons, T₁ (H₁′)/T₁ (H₃′), indicate a predominance of the anti orientation of the base around the glycosidic bond. The local motions of the ribose and the base were studied at different temperatures by measurements of nuclear Overhauser enhancement (NOE) of protonated carbons, the ratio of the proton relaxation times measured at two frequencies (90 and 250 MHz), and the deuterium quadrupolar transverse relaxation time T₂. For a given temperature between 22 and 62°C, the ¹³C-{¹H} NOE value is practically the same for seven protonated carbons (C₂, C₈, C_1′, C_2′, C_3′, C_4′, C_5′). This is also true for the T₁ ratio of the corresponding protons. Thus, the motion of the ribose–base unit can be considered as isotropic and characterized by a single correlation time, τ_c, for all protons and carbons. The τ_c values determined from either the ¹³C-{¹H} NOE or proton T₁ ratios, T₁(90 MHz)/T₁(250 MHz), and/or deuterium transverse relaxation time T₂ agree well. The molecular motion of the sugar-phosphate backbone (O-P-O) and the chemical-shift anisotropy (CSA) were deduced from T₁ (³¹P) and ³¹P-{¹H} NOE measurements at two frequencies. The CSA contribution to the phosphorus relaxation is about 12% at 36.4 MHz and 72% at 111.6 MHz, corresponding to a value of 118 ppm for the CSA (σ = σ∥ ? σ?). Activation energies of 2–6 kcal/mol for the motion of the ribose–base unit and the sugarphosphate backbone were evaluated from the proton and phosphorus relaxation data.     

Dielectric relaxation of collagen in aqueous solutions

The complex dielectric constant of collagen in aqueous solutions (polymer concentration, C_p = 0.02–0.2%) was measured at 10°C in the frequency range from 3 Hz to 30 kHz. The loss peak for C_p = 0.02% is located at 90 Hz and the dielectric relaxation time τ_D is estimated to be 1.8 ± 0.3 msec. The τ_D agrees well with the rotational relaxation time estimated from the reduced viscosity, and the relaxation is ascribed to the end-over-end rotation of the molecule. The C_p dependence of τ_D and the dielectric increment Δε are interpreted in terms of the aggregation of molecules. The dipole moment of a molecule, obtained from Δε at C_p = 0.02% and pH 6.5, is (5.2 ± 0.2) × 10⁴D, which is explained by the asymmetrical distribution of the ionized side chains of the molecule.     

31P Magnetic relaxation studies of yeast transfer RNAPhe.

The molecular mechanism of thermal unfolding of yeast tRNA^Phe in 20 mM NaCl, 1 mM EDTA, and 10 mM MgSO₄, pH 7.1 ± 0.1, has been examined by ³¹P magnetic relaxation and the nuclear Overhauser effect methods at 40.48 MHz in the temperature range of 22.5–80°C. Two partially resolved ³¹P resonance peaks of yeast tRNA^Phe have been found to behave distinctively different in their longitudinal relaxation times. Individual intensities of the two partially resolved peaks have been quantitatively estimated by the use of relaxation data and the nuclear Overhauser effect as a function of temperature. The results of these observations largely support the earlier suggestion by Guéron and Shulman that the high- and low-field parts of the main ³¹P resonance cluster originate from phosphorus nuclei belonging to the double-helical and nonhelical regions of the tRNA, respectively. The spin-lattice relaxation of the phosphorus nucleus has been found to be determined dominantly by the dipolar interaction with the surrounding ribose protons at this observing frequency. Rotational correlation times for the two portions of the ribose-phosphate backbone of the tRNA have been separately deduced from the quantitative treatment of the ³¹P nuclear spin-lattice relaxation times (T₁) and the nuclear Overhauser effect. The result indicates that the two portions undergo internal motions at distinctively different rates of 10⁸–10¹⁰ sec^?1 order in the temperature range of 22.5–80°C, and that the thermal activation of these motions occurs at least in three distinctive steps, i.e., 22.5–31, 31–40, and 40–80°C. The rates of the internal motions and the associated activation energies in respective steps give some insight into the thermo-induced change of the yeast tRNA^Phe structure.     

23Na-NMR investigations of counterion exchange reactions of helical DNA

Changes in Δν_½, the nmr linewidth of ²³Na, have been determined during titrations of helical DNA with polyamines (divalent putrescine and trivalent spermidine) and with inorganic cations (Mg²⁺ and Co(NH₃)). In each case additions of a multivalent cation (M^z+) to a solution containing NaDNA and NaCl cause decreases in Δν_½, which is a population-weighted average of contributions from nuclei in bound and free environments. Thus, the binding of M^z+ to DNA displaces sodium ions from regions where the quadrupolar relaxation of ²³Na is relatively efficient. At a given extent of titration, the binding of a polyamine produces a smaller decrease in Δν_½ than does the binding of an inorganic ion of the same valence. The concentration dependence of Δν_½ during the course of a titration can be interpreted most simply as a two-state ion-exchange reaction by assuming that the binding of M^z does not alter R_B, the average relaxation rate of sodium nuclei that remain bound. On the basis of this assumption, the initial linear portions of titration curves can be analyzed to determine upper bounds for r°, the number of sodium ions bound per DNA phosphate in the absence of any competing counterion. Analyzing the titration curves for the four multivalent competitors leads to a range of upper-bound estimates for r°: 0.5–0.8. The differences in these estimates could indicate that polyamines displace fewer sodium ions from DNA than do their smaller inorganic counterparts. Alternatively, the range in upper-bound estimates for r° could also reflect specific differences in the effects of the various multivalent cations on R_B, if this relaxation rate does change during titration.     

Effects of temperature and field strength on the NMR relaxation times of Na in frog striated muscle

Pulsed NMR techniques have been applied to the study of the relaxation parameters characterizing ²³Na within frog striated muscle. Experiments were performed at 3°C, 22–24°C and 39°C at a Larmor frequency of 15.7 MHz; at 22–24°C, measurements were obtained both at 15.7 MHz and at 7.85 MHz.As previously reported, only a single spine-lattice relaxation time (T₁) was observed, but both slow (T₂)_I and fast (T₂)_II components of the spin-spin relaxation time were measured. The effect of temperature (θ) upon (1/T₁) was qualitatively similar to that reported for ²³Na in free solution; (θ) did not significantly affect (1/T₂) over the range of temperatures studied. (1/T₂)_I, and to a lesser degreee, (1/T₁) exhibited a modest inverse dependence of doubtful significance on the Larmor frequency.The data are examined within the framework of a simple specific model; a conservative values in assumed for the quadrupolar coupling constant characterizing immobilized intracellular Na⁺. Within this framework, the results suggest that the fraction of bound ions whose molecular tumbling is severely restricted does not exceed some few percent of the total sodium population.     

Pulsed nuclear magnetic resonance studies on 23 Na, 7 Li and 35 Cl binding to human oxy- and carbon monoxyhaemoglobin

Pulsed nuclear magnetic resonance studies of the longitudinal (T₁) and transverse (T₂) quadrupolar relaxation times of ⁷Li, ²³Na, ³⁵Cl ions in the absence and presence of human oxy- and carbon monoxyhaemoglobin have been used to investigate the interaction of the ions and the macromolecule.The relaxation data show that Cl^? interacts strongly with the haemoglobin but provide no evidence for binding of Na⁺ up to concentrations of 0.5 m. In the case of Li⁺, evidence for interaction is obtained at concentrations of about 0.1 m.The dependence of relaxation rate on frequency was followed over a limited frequency range in an attempt to separate the effects of correlation times and exchange rates of the bonded ions on the relaxation. In the case of Cl^?, an upper limit for the mean lifetime divided by the number of sites can be set at about 1 × 10^?6 second, and a lower limit at about 1 × 10^?8 second.     

NMR relaxation processes of 31P in macromolecules

³¹P-Nmr relaxation parameters (spin-lattice relaxation time, linewidth, and nuclear Overhauser effect) were obtained at three different frequencies for poly(U) and a well-defined (145 ± 3 base-pair) fragment of DNA in solution. Data sets for the two samples were analyzed by theories which included relaxation by the mechanisms of ³¹P chemical shift anisotropy as well as by ¹H-³¹P dipole–dipole interaction. Neither data set could be satisfactorily described by a single correlation time. A model of a rigid rotor most nearly fits the data for the DNA molecule. Parameters obtained from the least-square fit indicate (1) that the DNA undergoes anisotropic reorientation with a correlation time τ₀ = 6.5 × 10^?7 sec for the end-to-end motion, (2) the ratio of diffusion constants D_∥/D_⊥ is 91, and (3) that the linewidth is due to chemical shift dispersion to the extent of 0.5 ppm. Some deviations of the calculated from the observed values suggested that significant torsional and bending motions may also take place for this DNA. Another model which contains isotropic motion but with a broad distribution of correlation times was required to fit the data for poly(U). A log ? χ² distribution function of correlation times [Scheafer, J. (1973) Macromolecules 6 , 881–888] described well the motion of poly(U) with the average correlation time τ = 3.3 × 10^?9 sec and a distribution parameter p = 14.     

Sodium ion and solvent nuclear relaxation results in aqueous solutions of DNA

The field-dependent ²³Na nuclear relaxation in aqueous DNA solutions has been obtained for a range of temperatures, including the DNA melting region. At least two correlation times are needed to characterize the spectral density function for the ²³Na relaxation. For the slow process (with the largest correlation time), the temperature dependence of the coupling constant and the correlation time were determined, and important premelting effects were observed. Possible origins of the slow process are discussed. The last process is shown to be correlated with the properties of the hydration water of DNA as reflected by the ¹⁷O relaxation rates in these solutions. The influence of the polyelectrolyte and NaCl concentrations on the ²³Na relaxation rate is compared with previous results from solutions of linear flexible polyelectrolytes.     

Hydrodynamic properties of a rigid molecule: Rotational and linear diffusion and fluorescence anisotropy

The fluorescence anisotropy of a general rigid body is formally the sum of five exponentials. We show that, to a high degree of approximation, there are relationships between the five time constants. As we define the time constants here, τ₁ ? τ₅, τ₂ ? τ₃, and τ₁^?1 + 3τ₄^?1 ? 4τ₂^?1. In practical cases, at most only three exponentials will be observed, and, of these, only two are independent. Using a numerical integration procedure, Perrin's equations for the rotational and translational diffusion of a general ellipsoid are solved. Rotational friction coefficients, frictional ratio, rotational relaxation times, and the five exponential terms in the fluorescence anisotropy are tabulated as functions of the axial ratios of the ellipsoid. In principle, the three axes of a general ellipsoid may be determined by a simultaneous measurement of the anisotropy and the linear diffusion constant. We examine, and illustrate, the effect of experimental error on such a determination.