Nanosecond spectroscopy of a dimeric enzyme: plasma amine oxidase.

The fluorescence dye 1-anilino-naphthalene-8-sulphonic acid (ANS) was used as a probe of non-polar binding sites in the enzyme plasma amine oxidase. Steady fluorescence measurements indicate that ANS binds to a single binding site of the dimeric enzyme with a dissociation constant of 5 microns. This binding site is different from the catalytic binding site. Nanosecond emission anisotropy measurements were performed on the ANS-enzyme in an effort to detect independent rotation of the subunits in the native enzyme. The observed rotational correlation time (phi = 105 ns) corresponds to the rotation of a rigid dimeric macromolecule. A rotational correlation time of 120 ns was obtained with the enzyme labelled with pyrenebutyric acid. It is concluded that the dimeric enzyme does not exhibit any modes of flexibility due to independent rotation of the subunits in the nanosecond range.     

Fluorescence correlation spectroscopy in the nanosecond time range: rotational diffusion of bovine carbonic anhydrase B

A fluorescence correlation experiment for measurement of rotational diffusion in the nanosecond time scale is described. Using this method, the rotational diffusion coefficient of bovine carbonic anhydrase B labelled with tetramethylrhodamine isothiocyanate was estimated to be D _r=(1.14±0.15)×10⁷ s^-1 at 22°C. The experiment is based on a cw argon ion laser, a microfluorimeter with local solution flow inside the sample cell, and two photon detectors. The fluorescence intensity autocorrelation function in the nanosecond time range is computed with the help of a time-to-amplitude converter and a multichannel pulse-amplitude analyser.     

Fluorescence lifetime and rotational correlation time of bovine serum albumin-sodium dodecyl sulfate complex labeled with 1-dimethylaminonaphthalene-5-sulfonyl chloride: Effect of disulfide bridges in the protein on these fluorescence parameters

A fluorescent dye, 1-dimethylaminonaphthalene-5-sulfonyl chloride, was used to label bovine serum albumin (BSA), intact and disulfide bridges-cleaved. The fluorescence lifetime and fluorescence anisotropy of the adducts in sodium dodecyl sulfate (SDS) solutions were studied by the nanosecond fluorescence depolarization method. The volume of equivalent sphere (V _e) was calculated to be 2.1×10^–19 cm³ for BSA with the intact disulfide bridges from the rotational correlation time. The value ofV _e was 4.4×10^–19 cm³ for the disulfide bridges-cleaved BSA. With an increase in SDS concentration, the rotational correlation time of the intact BSA became longer, while that of the disulfide bridges-cleaved BSA became shorter. This suggests that upon the binding of SDS, the total volume of the intact BSA increases while the expanded state of the protein, caused by the cleavage of the disulfide bridges, becomes compact.     

Rotational dynamics of 4-aminobutyrate aminotransferase

The fluorescence dye 1-anilinonaphthalene-8-sulfonate (ANS) was used as a probe of non-polar binding sites in 4-aminobutyrate aminotransferase. ANS binds to a single binding site of the dimeric protein with a K_d of 6 μM. Nanosecond emission anisotropy measurements were performed on the ANS-enzyme in an effort to detect independent rotation of the subunits in the native enzyme. The observed rotational correlation time (φ = 65 ns) corresponds to the rotation of a rather rigid dimeric structure. The microenvironment surrounding the natural probe pyridoxal-5-P covalently bound to the dimeric structure was explored using ³¹P-NMR at 72.86 MHz. In the native enzyme, the pyridoxal-5-P ³¹P-chemical shift is pH-independent, indicating that the phosphate group is well protected from the solvent. The correlation time determined from the ³¹P-spectrum of the aminotransferase exceeds the value calculated for the hydrated spherical model (φ = 40 ns). It is concluded that the phosphate of the pyridoxal-5-P molecule is rigidly bound to the active site of 4-aminobutyrate aminotransferase.     

Interaction between brain enzymes glutamate dehydrogenase and aspartate aminotransferase.

Fluorescence spectroscopic methods were used to study the interaction between aspartate aminotransferase and glutamate dehydrogenase isolated from pig brain. The conversion of the P-pyridoxal form of the aminotransferase to the P-pyridoxamine form of the enzyme is easily monitored by recording emission spectra upon excitation at 330 nm. Evidence for the interaction between the enzymes was obtained from fluroescence measurements conducted on aspartate aminotransferase label with a fluorescence probe (1-5-AEDANS) attached to one sH residue of the protein. The interaction of the aminotransferase (1μM) with glutamate dehydrogenase (2μM) brings about an enhancement as well as a blue shift in the band position of the fluorescence emitted by the dansyl chromophore. Polarization of fluorescence measurements conducted over a wide range of temperatures reveal that the rotational correlation time of aspartate aminotransferase (35 n.seconds) is increased to a value of 100 n.seconds upon addition of glutamate dehydrogenase.     

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.     

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.     

Chlorophyll fluorescence phenomena in chloroplasts on subnanosecond time-scales probed by picosecond pulse pairs

Fluorescence enhancement phenomena and quenching by exciton-exciton annihilation on subnanosecond and nanosecond time-scales were investigated in spinach chloroplasts utilizing picosecond laser pulse pairs (530 nm, 30 ps wide) of equal intensity, spaced apart in time by variable delays of Δt = 0−6 ns. This new method was devised to study the effect of pulse energies (1·10¹⁰–2·10¹⁵ photons per cm²) on the overall fluorescence yield in order to deduce the degree of correlation between the two pulses as a function of Δt. In the case of open reaction centers (F₀ state) in Photosystem II (PS II), it is shown that the quenching effect of excitons generated by the first pulse on the fluorescence yield of the second pulse diminishes with increasing Δt with a characteristic decorrelation time of 140 ± 60 ps. This effect is attributed to either (1) the decay of mobile excitons in the light-harvesting antenna pigment bed as these excitons migrate towards the PS II reaction centers and the associated smaller core antenna pigment pools, or (2) the decay of a quenching state of the reaction center (and/or core antenna) which appears following a rapid (less than 140 ps) trapping of the excitons initially created in the antenna pigment bed. The absence of a significant decay component of exciton quenchers with a lifetime comparable to the 300–600 ps intermediate phase of fluorescence decay kinetics suggests that this phase, although contributing to more than half of the integrated fluorescence emission signal, is not caused by freely mobile exitons migrating in a lake of pigments, but originates instead from smaller pigment pools to which the excitons have migrated. It is proposed that bimolecular exciton-exciton annihilation in these smaller domains dominates annihilation in the larger antenna pigment bed. In the case of closed reaction centers (F_max state), the decorrelation time between the two pulses is increased to 400 ± 100 ps, which is also attributed to either a mobile exciton component or to the decay of a quenching state of the reaction center. At low pulse intensities (below approx. 2 · 10¹² photons per cm²) anomalous fluorescence enhancement effects are noted, which are clearly linked to the existence of initially open PS II reaction centers. These enhancement effects are different from the well-known fluorescence induction phenomena which occur on longer time-scales, and are tentatively attributed to variations in the quenching efficiencies of transitory photochemical states of PS II reaction centers.     

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.     

The Tryptophan Fluorescence of Tetracarbidium conophorum Agglutinin II and a Solution-Based Assay for the Binding of a Biantennary Glycopeptide

The plant lectin Tetracarbidium conophorum agglutinin II binds to glycoproteins and glycopeptides in a structurally specific manner [Animashaun et al., (1994) Glycoconjugate J. 11, 299–303]. We have characterized the steady-state and time-resolved fluorescence of the tryptophan residues of this lectin. The fluorescence (λ_ex = 295 nm, λ_em = 350 nm) decay is complex and can be described by four decay times with the following values: τ₁ = 7.4nsec, α₁ = 0.22; τ₂ = 2.9 nsec, α₂ = 0.25; τ₃ = l.0 nsec, α₃ = 0.34; τ₄ = 0.2 nsec, α₄ = 0.18. The addition of a biantennary glycopeptide $\begin{array}{*{20}c} {Gal\beta (1 \to 4)GlcNAc\beta (1 \to 2)Man\alpha (1 \to 6)\neg } \\ {Man\beta (1 \to 4)GlcNAC\beta (1 \to 4)GlcAc\beta (1 \to )\begin{array}{*{20}c} {Glu - Nh_2 } \\ | \\ {Asn} \\ | \\ {COOH} \\ \end{array} } \\ {Gal\beta (1 \to 4)GlcNAc\beta (1 \to 2)Man\alpha (1 \to 3)} \\ \end{array} $ to the lectin results in a quench and an 8 nm blue shift of the emission spectrum. The effect is saturable, and is described by an association constant of 1.8×10⁵ M^?1. The tryptophan fluorescence of Tetracarbidium conophorum agglutinin II may therefore be utilized to characterize thermodynamically the binding interactions between this lectin and complex glycoprotein.     

Fluorescence anisotropy of labelled F-actin: Influence of Ca2+ on the flexibility of F-actin

We measured the fluorescence static anisotropy and the time-resolved fluorescence anisotropy decay of F-actin labelled with N-iodoacetyl-N'-(5-sulfo-1-naphthyl)ethylenediamine at 20°C in solutions containing 100 mM KCl and free Ca²⁺ at various concentrations. The average fluorescence anisotropy and the fluorescence rotational correlation time of actin decreased in the presence of micromolar concentrations of free Ca²⁺. The change of the rotational correlation time of labelled actin could not be explained by a variation of the actin critical concentration. We concluded therefore that F-actin undergoes a conformational change induced by Ca²⁺ binding. The binding constant was 6 × 10⁶ M^?1.     

Effects of trypsin and bivalent cations on P-680+-reduction,fluorescence induction and oxygen evolution in Photosystem II membrane fragments from spinach

Laser-flash-induced absorption changes at 830 nm, fluorescence-induction curves and the average oxygen yield per flash have been measured in spinach Photosystem II membrane fragments as a function of trypsin treatment and its modification by CaCl₂. The following was found. (i) The relative contribution of the nanosecond relaxation to the overall decay kinetics of 830 nm absorption changes reflecting the P-680⁺-reduction decreases as a function of incubation time with trypsin. Simultaneously, mild treatment at pH = 6.0 markedly increases the extent of 200 μs kinetics that highly revert back to nanosecond kinetics by CaCl₂ addition. After harsher trypsin treatment (pH = 7.5) pH-dependent 2–20 μs kinetics appear that cannot be reverted to nanosecond kinetics by CaCl₂. (ii) The CaCl₂-induced restoration of nanosecond kinetics is mainly due to a Ca²⁺-induced effect rather than to a functional role of Cl⁻. Sr²⁺ can substantially substitute for Ca²⁺, whereas Mg²⁺, Mn²⁺ and monovalent ions are almost inefficient. (iii) A quantitative correlation between the extent of the nanosecond kinetics and the average oxygen yield per flash was not observed. (iv) If CaCl₂ is present in the assay medium for trypsin treatment the samples are markedly protected to proteolytic degradation. This effect mainly refers to the reaction pattern of the acceptor side. Other bivalent cations can substitute Ca²⁺ for its protective function. (v) The CaCl₂-induced protection to proteolytic attack is extremely sensitive to a very short trypsin pretreatment that does hardly affect the shape of the fluorescence induction curve. The results are discussed in relation to the functional and structural organization of Photosystem II.     

Characterization of Horizontal Lipid Bilayers as a Model System to Study Lipid Phase Separation

Artificial lipid membranes are widely used as a model system to study single ion channel activity using electrophysiological techniques. In this study, we characterize the properties of the artificial bilayer system with respect to its dynamics of lipid phase separation using single-molecule fluorescence fluctuation and electrophysiological techniques. We determined the rotational motions of fluorescently labeled lipids on the nanosecond timescale using confocal time-resolved anisotropy to probe the microscopic viscosity of the membrane. Simultaneously, long-range mobility was investigated by the lateral diffusion of the lipids using fluorescence correlation spectroscopy. Depending on the solvent used for membrane preparation, lateral diffusion coefficients in the range D_lat = 10-25 μm²/s and rotational diffusion coefficients ranging from D_rot = 2.8 − 1.4 × 10⁷ s⁻¹ were measured in pure liquid-disordered (L_d) membranes. In ternary mixtures containing saturated and unsaturated phospholipids and cholesterol, liquid-ordered (L_o) domains segregated from the L_d phase at 23°C. The lateral mobility of lipids in L_o domains was around eightfold lower compared to those in the L_d phase, whereas the rotational mobility decreased by a factor of 1.5. Burst-integrated steady-state anisotropy histograms, as well as anisotropy imaging, were used to visualize the rotational mobility of lipid probes in phase-separated bilayers. These experiments and fluorescence correlation spectroscopy measurements at different focal diameters indicated a heterogeneous microenvironment in the L_o phase. Finally, we demonstrate the potential of the optoelectro setup to study the influence of lipid domains on the electrophysiological properties of ion channels. We found that the electrophysiological activity of gramicidin A (gA), a well-characterized ion-channel-forming peptide, was related to lipid-domain partitioning. During liquid-liquid phase separation, gA was largely excluded from L_o domains. Simultaneously, the number of electrically active gA dimers increased due to the increased surface density of gA in the L_d phase.     

Nanosecond time-resolved emission anisotropy of the fluorescent probe 1,6-diphenyl-1,3,5-hexatriene in human amniotic fluid

The fluorescence emission anisotropy of 1,6-diphenyl-1,3,5-hexatriene in human amniotic fluid has been studied using nanosecond time-resolved emission techniques. These studies demonstrate that the previously reported decrease in the steady state emission anisotropy, 〈r〉, with gestational age is due to a change in the rate of rotational motion of the probe. The emission anisotropy decays to a limiting value (r_∞) greater than zero, suggesting a hindered rotation of the probe, and this is independent of gestational age. The decay function for the emission anisotropy of amniotic fluids from 17, 29, 40 and 41 weeks in gestational age can be best expressed as a single exponential plus a constant term, with rotational correlation times varying from 17 ns to 2.2 ns, respectively. The zero time emission anisotropy remains approx. 0.30 for both early and late gestational times.     

Alanine Aminotransferase and Aspartate Aminotransferase in Leishmania tarentolae1

SYNOPSIS. Culture stages (promastigotes) of Leishmania tarentolae were tested for alanine aminotransferase (E.C.2.6.1.2) and aspartate aminotransferase (E.C.2.6.1.1.). Neither enzyme was detected in crude cell extracts. After starch block electrophoresis, however, both transaminase activities were found in proteins migrating toward the anode. Only one species of each enzyme was found. Using coupled enzyme assay systems, the following physical and kinetic properties were seen: 1) aspartate aminotransferase was inhibited by α-ketoglutarate concentrations above 1.68 × 10^?2 M and alanine aminotransferase was inhibited by concentrations higher than 1.34 × 10^?2 M; 2) the Michaelis constant (Km[α-ketoglutarate]) was 5.4 × 10^?4 M for aspartate aminotransferase and 3.0 × 10^?4 M for alanine aminotransferase; 3) maximum activity was found at ?pH 8.5 (broad range between pH 7.75–9.0) for aspartate aminotransferase whereas maximum activity for alanine aminotransferase was ?pH 7.2 (range between pH 7.0–7.5); 4) both enzymes lost half of their activity after 4 days at 8 C; 5) aspartate aminotransferase was most active at 35 C and completely inactivated at 59.5 C, alanine aminotransferase exhibited maximum activity at 29.5 C and was completely inactivated at 61 C; and 6) neither enzyme showed enhanced activity with added pyridoxal phosphate.     

K-35, a fluorescent probe for albumin study: Optical properties

Fluorescent probe N-(carboxyphenyl)imide of 4-(dimethylamino)naphthalic acid, K-35, is used as an indicator of structural changes of human serum albumin molecules in pathology. The probe occupies albumin binding pockets where the probe environment is of very high polarity; probably, the pockets contain protein polar groups and also water molecules. At the same time the rather small Stokes shift of K-35 fluorescence spectrum shows that the polar group motion is one-two orders of magnitude lower than the mobility of polar molecules in polar fluids. K-35 fluorescence decay in HSA can be described as a sum of three exponentials with time constants close to τ₁ = 9 ns; τ₂ = 3.6 ns and τ₃ = 1.0 ns. The difference between excitation maxima of these three decay components shows that the environment of these three species of K-35 molecules has been different before excitation. Different τ values are probably a consequence of nonidentical structure of several binding sites, or the binding site(s) can have variable conformation.     

Local mobility of the lac repressor molecule

The rotational mobility of lac repressor from Escherichia coli was investigated by nanosecond fluorescence depolarization spectroscopy. A single rotational correlation time (φ) of the repressor was observed by monitoring the emission anisotropic decay of the intrinsic tryptophan fluorescence. The small value of φ (9·5 ns) suggests that one or both of the two tryptophan residues in the repressor are located in a flexible segment of the protein molecule. This segmental flexibility is enhanced by binding of inducer (isopropyl-β-d-thiogalactoside) to the repressor while it is restrained by binding of anti-inducer (glucose) or small DNA fragments, as indicated by the changes in φ. Further time-dependent emission anisotropy studies with an extrinsic fluorescent probe, N-(iodoacetylaminoethyl)-5-naphthylamine-1-sulfonate, covalently attached to the repressor yielded two rotational correlation times. The shorter φ_S (6·7 ns) also corresponds to a segmental flexibility whereas the longer φ_L (118 ns) represents the rotational motion of the entire repressor molecule. Both the values of φ_S and φ_L vary by addition of inducer or anti-inducer in a manner similar to that observed for the intrinsic tryptophan fluorescence but they are insensitive to addition of DNA fragments. The changes in local mobility of the lac repressor molecule observed in these studies may provide some insight into how inducer (or anti-inducer) destabilizes (or stabilizes) the repressor-operator complex.     

Fluorescence studies on the coat protein of Alfalfa Mosaic Virus

Abstract

The intrinsic luminescence of different forms of the alfalfa mosaic virus (AMV) strain 425 coat protein has been studied, both statically and time resolved. It was found that the emission of the protein (M_r24,250), which contains two tryptophans at positions 54 and 190 and four tyrosines, is completely dominated by tryptophan fluorescence. The high fluorescence quantum yield indicates that both tryptophans are emitting. Surprisingly, the fluorescence decay is found to be strictly exponential, with a lifetime of 5.1 nsec. Similar results were obtained for various other forms of the protein, i.e. the 30-S polymer, the mildly trypsinised forms of the protein lacking the N-terminal part and the protein assembled into viral particles. Virus particles and proteins of stains S and VRU gave similar results, as well as the VRU protein polymerised into tubular structures. The fluorescence decay is also monoexponential in the presence of various concentrations of the quenching molecules acrylamide and potassium iodide. Stern-Volmer plots were linear and yield for the coat protein dimer with acrylamide a quenching constant of 4.5 ^* 10⁸ M^?1sec^?1. This indicates that the tryptophans are moderately accessible for acrylamide. For the 30-S polymer a somewhat smaller value was found, whereas in the viral Top a particles the accessibility of the tryptophans is still further reduced. From the decay of the polarisation anisotropy of the fluorescence of the coat protein dimer the rotational correlation time was obtained as 35 nsec. Since this roughly equals the expected rotational correlation time of the dimer as a whole, it suggests that the tryptophans are contained rigidly in the dimer.

The results show that in the excited state of the protein the two tryptophans are strongly coupled and suggest that the trp-trp distance is smaller than 10 A. Because the coat protein occurs as a dimer, the coupling can be inter- or intramolecular. The implications for the viral structure are discussed.     

Time resolved spectroscgpy of tryptopkyl fluorescence of yeast 3-phosphoglycerate kinase

The tryptophyl fluorescence emission of yeast 3-phosphoglycerate kinase decreases from pH 3.9 to pH 7.2 following a normal titration curve with an apparent pK of 4.7. The fluorescence decays have been determined at both extreme pH by photocounting pulse fluorimetry and have been found to vary with the emission wavelength. A quantitative analysis of these results according to a previously described method allows to determine the emission characteristics of the two tryptophan residues present in the protein molecule. At pH 3.9, one of the tryptophan residues is responsible for only 13% of the total fluorescence emission. This first residue has a lifetime τ₁= 0.6 ns and a maximum fluorescence wavelength λ_2max = 332 nm. The second tryptophan residue exhibits two lifetimes τ₂₁= 3.1 ns and τ₂₂= 7.0 ns (λ_2max= 338 nm). In agreement with the attribution of τ₂₁and τ₃₂ to the same tryptophan residue, the ratio β = C₂₁/C₂₂ of the normalized amplitudes is constant along the fluorescence emission spectrum. At pH 7.2, the two tryptophan residues contribute almost equally tc the protein fluorescence. The decay time of tryptophan 1 is 0.4 ns. The other emission parameters are the same as those determined at pH 3.9. We conclude that the fluorescence quenching in the range pH 3.9 to pH 8.0 comes essentially from the formation of a non emitting internal ground state complex between the tryptophan having the longest decay times and a neighbouring protein chemical group. The intrinsic pK of this group and the equilibrium constant of the irternal complex can be estimated. The quenching group is thought to be a carboxylate anion. Excitation transfers between the two tryptophyl residues of the protein molecule appear to have a small efficiency.     

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.