Mean Rotational Relaxation Time Research Articles

Brownian relaxation of an inelastic sphere in air

The procedures that are used to calculate the forces and moments on an aerodynamic body in the rarefied gas of the upper atmosphere are applied to a small sphere of the size of an aerosol particle at sea level. While the gas-surface interaction model that provides accurate results for macroscopic bodies may not be appropriate for bodies that are comprised of only about a thousand atoms, it provides a limiting case that is more realistic than the elastic model. The paper concentrates on the transfer of energy from the air to an initially stationary sphere as it acquires Brownian motion. Individual particle trajectories vary wildly, but a clear relaxation process emerges from an ensemble average over tens of thousands of trajectories. The translational and rotational energies in equilibrium Brownian motion are determined. Empirical relationships are obtained for the mean translational and rotational relaxation times, the mean initial power input to the particle, the mean rates of energy transfer between the particle and air, and the diffusivity. These relationships are functions of the ratio of the particle mass to an average air molecule mass and the Knudsen number, which is the ratio of the mean free path in the air to the particle diameter. The ratio of the molecular radius to the particle radius also enters as a correction factor. The implications of Brownian relaxation for the second law of thermodynamics are discussed.

Studies on Local Motion of Synthetic Polymers and Dynamics of Polysaccharides

Local motion of synthetic polymers and gellan in dilute solutions was examined by a fluorescence depolarization method. Rheological measurements were also carried out for gellan aqueous solutions. The mean rotational relaxation time, a measure of the local chain mobility, for polystyrene in a good solvent was shorter than that in a poor solvent at all the molecular weights of polystyrene examined including the oligomer region. It was suggested that the local chain mobility was mainly determined by the local potential energy for the conformational transition of main chain bond. The local chain mobility of gellan was independent of the added salt concentration (cs), whereas the cs dependence of zero-shear viscosity indicated that the degree of chain expansion of gellan decreased with increasing cs.

Effect of microsome–liposome fusion on the rotational mobility of cytochrome P450IIB4 in rabbit liver microsomes

Membrane fusion of microsomes with soybean phospholipid vesicles was performed at pH 6.5 to investigate the effect of lipid-enrichment in the membrane on the rotational mobility of cytochrome P450. Rotational diffusion of cytochrome P450 in the microsomal membrane of phenobarbital-induced rabbit liver was measured by detecting the decay of absorption anisotropy after photolysis of the heme CO complex by a vertically polarized laser flash. The fusion procedures yielded three separate fractions upon sucrose density gradient centrifugation with lipid-to-protein ratio in weight (L/P) as follows: 1.5 in the bottom fraction, 2.2 in the middle fraction, and 3.9 in the top fraction. In each fraction, co-existence of mobile and immobile cytochrome P450 was observed. The percentage of rotationally mobile P450 (with the mean rotational relaxation time of φ=505–828 μs) in each of the different bands was found to be 59% in the bottom fraction, 61% in the middle fraction, and 68% in the top fraction. This increase in mobile population of P450 due to lipid-enrichment indicates that aggregated proteins in microsomal membranes dissociate with increasing L/P which is inversely proportional to the protein concentration in the membrane. With freeze-fracture electron microscopy, it was shown that the average distance increased between intramembrane particles by lipid-enrichment. Thus, the significant immobile population (32%) of P450 in microsomal membranes can be explained by nonspecific protein aggregation which is a consequence of the low L/P of 0.8. The decrease in the mobile population in the bottom fraction compared with intact microsomes was shown to be due to the pH 6.5 incubation used for fusion.

The ELLIPS suite of macromolecular conformation algorithms.

This paper describes a series of four programmes for the PC based on ellipsoidal representations of macromolecular shape in solution using Universal shape functions, ELLIPS1 is based on simple ellipsoid of revolution models (where two of the three axes of the ellipsoid are fixed equal to each other). If the user types in a value for a shape function from sedimentation or other types of hydrodynamic measurement, it will return a value for the axial ratio of the ellipsoid. ELLIPS2 is based on the more general triaxial ellipsoid with the removal of the restriction of two equal axes. The user enters the three semi-axial dimensions of the molecule or the equivalent two axial ratios and ELLIPS2 returns the value of all the hydrodynamic shape functions. It also works of course for ellipsoids of revolution. ELLIPS3 and ELLIPS4 do the reverse of ELLIPS2, that is they both provide a method for the unique evaluation of the triaxial dimensions or axial ratios of a macromolecule (and without having to guess a value for the so-called "hydration") after entering at least three pieces of hydrodynamic information: ELLIPS3 requires EITHER the intrinsic viscosity with the second virial coefficient (from sedimentation equilibrium, light scattering of osmometry) and the radius of gyration (from light or x-ray scattering) OR the intrinsic viscosity with the concentration dependence term for the sedimentation coefficient and the (harmonic mean) rotational relaxation time from fluorescence depolarisation measurements. ELLIPS4 evaluates the tri-axial shape of a macromolecule from electro-optic decay based Universal shape functions using another Universal shape function as a constraint in the extraction of the decay constants.

Na+,K(+)-ATPase of human placenta during gestational hypertension: a biochemical-biophysical study.

1. Na+,K(+)-ATPase is the membrane enzyme catalysing the active transport of Na+ and K+ across the plasma membrane of animal cells. A reduced activity of Na+,K(+)-ATPase has been described in gestational hypertension in a variety of cell types, in agreement with the hypothesis that gestational hypertension can induce membrane transport modifications similar to those reported for essential hypertension. The causes of the reduced Na+,K(+)-ATPase activity are still debated. 2. The aim of the present work was to investigate the molecular mechanism of the reduced enzymic activity in gestational hypertension using as a model Na+,K(+)-ATPase purified from human placenta. Na+,K(+)-ATPase obtained from term placentas of eight healthy pregnant women and eight age-matched women with gestational hypertension was purified as previously described. 3. We observed in gestational hypertension: (i) a significant increase in the activation energies above transition temperature; (ii) a significant decrease in the fluorescence polarization of 1-(4-trimethylaminophenyl)-6-phenyl-1,3,5-hexatriene (i.e. increased fluidity) and an increase in the mean lifetime (modified hydrophobicity); (iii) a lower Kq, suggesting an enzymic structural modification; and (iv) an increased mean lifetime and rotational relaxation time of pyrene isothiocyanate, indicating a modified ATP binding site.

Transient electric birefringence study of rod-like triple-helical polysaccharide schizophyllan

The rotational dynamics of the uncharged, triple-helical polysaccharide schizophyllan was determined by transient electric birefingence. The field-free decay of a sample with weight average molecular weight of 437× 10 3gmol −1 deviated from single-exponential behaviour. The relaxation spectra obtained by analysis using the CONTIN program, were bimodal, whereas analysis by the stretched exponentials also accounted well for the field-free decay of the birefringence of the polydisperse sample. The mean rotational relaxation time extrapolated to infinite pulse duration of the orienting pulse for dilute aqueous solution of the 437×10 3gmol −1 sample was determined equal to 61 μs. Analysis of the influence of chain rigidity on the rotational dynamics of the polydisperse sample indicated that the persistence length, L pe , was 70nm.

Aggregation structure of poly(γ-benzyl- l-glutamate) in benzene-DMF mixed solution probed by fluorescence depolarization and non-radiative energy transfer

The aggregation of poly(γ-benzyl- l-glutamate) (PBLG) in mixed solution of benzene and N,N-dimethylformamide (DMF) was studied by the emission probe method. Samples of PBLG with 260 and 790 of average degree of polymerization containing anthryl group (An-PBLG260 and An-PBLG790) and carbazolyl group (Cz-PBLG260 and Cz-PBLG790) were prepared. The mean rotational relaxation times ( ρ rot) of the anthryl probe in An-PBLG260 and An-PBLG790 were evaluated in benzene(Bz)-DMF solutions. The apparent efficiencies of the non-radiative intermolecular energy transfer from the carbazolyl probe to the anthryl probe in different PBLG molecules were estimated spectroscopically in Bz-DMF solutions. In benzene solution, ρ rot for An-PBLG260 is larger than that for An-PBLG790 and the efficiency of the energy transfer for PBLG260 is larger than that for PBLG790. With increase in DMF content in Bz-DMF mixtures, ρ rot decreases up to 15% DMF content and the efficiencies of energy transfer decrease for PBLG260 and PBLG790. These results show that the extent of an anti-parallel aggregation of PBLG260 in benzene is larger than that of PBLG790 and that the mobility of the anthryl probe in PBLG260 is smaller than that in PBLG790 in the aggregated state.

High precision study of chemical relaxation in the system N2O4=2NO2 by photoacoustic resonance spectroscopy

The chemical relaxation of the N2O4 dissociation was studied using Ar+ laser excited acoustic resonances of a cylindrical cavity. The resonance profiles of the first radial mode were measured as a function of pressure and temperature by a computer controlled setup. The N2O4 dissociation rate constant and the mean rotational and vibrational relaxation time of the N2O4–NO2 mixture were obtained for temperatures between 273 and 317 K by fitting a detailed theoretical model of the resonator to the measured values for frequency dispersion, resonance broadening, and strength of the photoacoustic signal. Excellent agreement between theory and experiment was obtained for the frequency dispersion and the photoacoustic signal. An empirical correction function had to be introduced to account for discrepancies between the theoretically predicted and measured values of the resonance broadening which was in the percent region. A value of 6.1×10−15 cm3/molecule s was determined for the rate constant of N2O4 dissociation in the low pressure limit at 298 K. The activation energy of the N2O4 dissociation for 20 mbar pressure was determined to be EA=36 kJ/mol. A comparison of the measured low-pressure limit of the unimolecular rate constant with theoretical predictions of RRKM theory yielded values for the mean collision efficiency of N2O4 and NO2 between 0.95 and 0.5 in the temperature range 273–317 K.

Study on dynamical behaviour of semi-stiff chain polymers. Fluorescence depolarization of proflavine aromatic polyimides

The fluorescence depolarization of proflavine groups incorporated into the backbone of aromatic polyimides has been measured in various solvents. The mean rotational relaxation times of the main chain depend on the structures of aromatic polyimides as planar semi-stiff chain polymers and differ from that of a low molecular analogue.

Adhesive polymer: Intermacromolecular interaction in fluid solution studied by fluorescence depolarization method

The fluorescence depolarization of the anthryl groups attached to poly(styrene-maleic anhydride) [P(St-MA)] has been examined in mixtures of various acrylic adhesive polymers with toluene for weight fractions ranging from 0 to 0.25. It is clear that the relative mean rotational relaxation time of the anthryl groups sharply increases with increasing concentration of poly(2-ethylhexylacrylate) (PEHA) containing about 5% acrylic acid units and 10% vinyl acetate units. It may be concluded that an excellent adhesive polymer is made with acrylic acid units as agents for intra- and interaction and vinyl acetate units as depression agents for acrylic acid units and agents for strong PEHA-P(St-MA) interaction.

Study on polymer induced coil-globule transition—I: Fluorescence depolarization of anthryl groups attached to polymer

The fluorescence depolarization of the anthryl group attached to poly(styrene-maleic anhydride) has been examined in polyoxyethylene ( DP = 8)-toluene mixtures for volume fractions ranging from 0 to 0.91. It is clear that the relative mean rotational relaxation time of the anthryl group sharply increases at 55–60% POE. This change may primarily indicate the polymer induced coil-globule transition behaviour of poly(styrene-maleic anhydride) in the mixture. The experimental and theoretical data are briefly compared for the polymer induced coil-globule transition.

Study on the Fluorescence Depolarization of a Chromophore Attached to Polymer Chain End II. Aggregation and Helix–Coil Transition Behavior of Poly(γ-benzyl L-glutamate) in Various Mixed Solvents

The emission anisotropy of the fluorescence depolarization of rhodamine B chemically bound to the terminal amino group of poly(γ-benzyl L-glutamate) (PBLG) was measured in various helicogenic solvents (benzene, dioxane, etc.). The apparent mean rotational relaxation time of the chromophore attached to chain end corresponded to the aggregation behavior of PBLG in various helicogenic solvents. This shows that the terminal rhodamine B group as a chromophore is tightly bound to the PBLG chain end. The aggregation and helix–coil transition behavior of PBLG has been studied in various solvent mixtures (benzene–dichloroacetic acid, benzene–N,N-dimethylformamide, etc.). In the series of highly aggregation-solvents such as benzene and dioxane, PBLG is aggregated up to an N,N-dimethylformamide content of about 80—90%. The aggregation-breaking (dissociation) and helix-breaking ratios as parameters of aggregation and helix–coil transition behavior of PBLG are briefly discussed for various solvent mixtures.

Study of polysaccharides by the fluorescence method. III. Chain length dependence of the micro‐Brownian motion of amylose in an aqueous solution

AbstractThe fluorescence polarization method was applied to the investigation of the micro‐Brownian motion of amylose chains having a wide range of degree of polymerization (DP). We prepared two types of fluorescent conjugates of amylose: amylose conjugated with fluorescein randomly throughout the chain (F‐amylose) and amylose conjugated locally on a terminal segment (t‐F‐amylose). The degree of fluorescence polarization of these conjugates was measured by changing the solvent viscosity at a constant temperature (25°C). The data obtained were analyzed by a Perrin‐type equation to calculate the mean rotational relaxation time, 〈ρ〉. By examination of the plots of 〈ρ〉 vs DP, and by comparison of 〈ρ〉 with the theoretical rotational relaxation time of the whole molecule at a given DP, it was found that 〈ρ〉 mainly reflects the segmental motion of the amylose chain in the high‐DP range. Thus, the fact that 〈ρ〉 for t‐F‐amylose is much smaller than that for F‐amylose at a sufficiently high DP shows that a terminal segment undergoes a more rapid micro‐Brownian motion than interior segments. In the low‐DP range, we felt that the rotational diffusion of the whole molecule contributes significantly to the relaxation process. We also examined, for comparison, the segmental motion of dextran and pullulan in a similar manner and found that these segmental motions are more rapid than those of amylose. Based on the results obtained, the segmental mobility and conformation of the amylose molecule are discussed in relation to its chain length.

Protein-protein interactions of cytochrome oxidase in inner mitochondrial membranes. The effect of liposome fusion on protein rotational mobility.

Rotational diffusion of cytochrome oxidase in the inner membrane of rat liver mitochondria was measured by detecting the decay of absorption anisotropy after photolysis of the heme a3.CO complex by a vertically polarized laser flash. As in previous experiments with beef heart mitochondria (Kawato, S., Sigel, E., Carafoli, E., and Cherry, R. J. (1980) J. Biol. Chem. 255, 5508-5510), co-existence of rotating cytochrome oxidase (mean rotational relaxation time, phi, of 700 to 1400 microseconds) and immobilized cytochrome oxidase (phi greater than 20 ms) was observed in mitochondria and mitoplasts. The effect of lipid/protein ratio by weight (L/P) on the relative proportions of mobile and immobile cytochrome oxidase was investigated following the fusion of soybean phospholipid vesicles with mitoplasts. The fusion procedure yielded four separate fractions upon sucrose density gradient centrifugation with L/P as follows: 0.3 in Pellet, 0.7 in Band 3, 1.5 in Band 2, and 3.0 in Band 1. The percentage of rotationally mobile cytochrome oxidase (phi = 700 to 1000 microseconds) in each of the different bands was found to be 16% in Pellet, 25% in Band 3, 47% in Band 2, and 76% in Band 1 at 37 degrees C. The dependence of the amount of mobile cytochrome oxidase on L/P indicates that the fraction of aggregated protein progressively decreases with decreasing concentration of proteins in the membrane. Thus, the large immobile fraction of cytochrome oxidase in mitochondrial inner membranes can be explained by nonspecific protein aggregation which is a consequence of the low L/P. The decrease in the mobile fraction in Pellet compared with mitoplasts was shown to be due to the pH 6.5 incubation used for fusion.

Rotation of cytochrome P-450. I. Investigations of protein-protein interactions of cytochrome P-450 in phospholipid vesicles and liver microsomes.

Rotation of cytochrome P-450 was examined in both liver microsomes and reconstituted and phospholipid vesicles. Purified cytochrome P-450 was incorporated into lipid vesicles composed of phosphatidylcholine-phosphatidylethanolamine-Phosphatidylserne. Rotational diffusion was measured by detecting the decay of absorption anisotropy, r(t), after photolysis of the heme. CO complex by a vertically polarized laser flash. No contribution of vesicle tumbling to r(t) was observed over the experimental time range of 0-500 mus for samples in 60% sucrose. Analysis of r(t) was based on a "rotation-about-membrane normal" model. The measurements were used to investigate intermolecular interactions of cytochrome P-450. In vesicles of a high lipid to protein ratio (=30 by weight), the residual time-independent normalized anisotropy, r (infinity)/r (0), reached a limiting low value, implying that all cytochrome P-450 was rotating. The mean rotational relaxation time, phi 1, was about 95 mus. In contrast, about 35% of cytochrome P-450 was immobilized in vesicles of a low lipid to protein ratio (=1), with phi 1 of about 95 mus for the mobile fraction. The immobile fraction is presumably due to self-aggregation of cytochrome P-450. In rat liver microsomes, 0-50% of cytochrome P-450 was mobile with phi 1 of about 120 mus at 20 degrees C, and the rest was immobile. A significant temperature dependence of r(t) was observed in microsomes. All cytochrome P-450 was immobile below 7 degrees C, and about 50% of the enzyme was mobile at 37 degrees C with phi 1 approximately 60 mus. From the limiting value of r(infinity)/r(0) congruent to 0.12, the tilt angle of the heme plane of cytochrome p-450 from the membrane plane was calculated to be about 40 degrees.

Rotation of cytochrome P-450. II. Specific interactions of cytochrome P-450 with NADPH-cytochrome P-450 reductase in phospholipid vesicles.

Purified rat liver microsomal cytochrome P-450 and NADPH-cytochrome P-450 reductase were co-reconstituted in phosphatidylcholine-phosphatidylethanolamine-phosphatidylserine vesicles using a cholate dialysis technique. The co-reconstitution of the enzymes was demonstrated in proteoliposomes fractionated by centrifugation in a glycerol gradient. The proteoliposomes catalyzed the N-demethylation of a variety of substrates. Rotational diffusion of cytochrome P-450 was measured by detecting the decay of absorption anisotropy r(t), after photolysis of the heme.CO complex by a vertically polarized laser flash. The rotational mobility of cytochrome P-450, when reconstituted alone, was found to be dependent on the lipid to protein ratio by weight (L/P450) (Kawato, S., Gut, J., Cherry, R. J., Winterhalter, K. H., and Richter, C. (1982) J. Biol. Chem. 257, 7023-7029). About 35% of cytochrome P-450 was immobilized and the rest was rotating with a mean rotational relaxation time phi 1 of about 95 mus in L/P450 = 1 vesicle. In L/P450 = 10 vesicles, about 10% of P-450 was immobile and the rest was rotating with phi 1 congruent to 55 mus. Co-reconstitution of equimolar amounts of NADPH-cytochrome P-450 reductase into the above vesicles results in completely mobile cytochrome P-450 with a phi 1 congruent to 40 mus. Only a small decrease in the immobile fraction of cytochrome P-450 is observed when the molar ratio of cytochrome P-450 to the reductase is 5. The results suggest the formation of a monomolecular 1:1 complex between cytochrome P-450 and NADPH-cytochrome P-450 reductase in the liposomes.

Study on Polysaccharide by the Fluorescence Method. I. Fluorescence Depolarization of the Fluorescein Conjugates of Amylose and Dextran

Amylose and dextran conjugated with fluorescein were prepared and the degree of fluorescence polarization of these conjugates was measured with changing solvent viscosity at constant temperature (25°C). The results obtained were analyzed by Perrin’s equation to calculate the mean rotational relaxation time. The value for dextran conjugate was very small compared with that for amylose. This suggests that the molecular chain of dextran is more flexible than that of amylose. Polarizations of these conjugates gradually departed from the Perrin equation when the temperature was raised in a given solvent. This discrepancy can be attributed to an accelerated loosening of the internal structure of these polysaccharide chains. Thus it seems that amylose and dextran molecules below the transition temperatures have partly ordered conformations with restricted rotation about glycosidic linkage.

Membrane lipid dynamics and enzymic activity in bovine adrenal cortex microsomes

The lipid dynamics of the adrenocortical microsomal membranes was studied by monitoring the fluorescence anisotropy and excited state lifetime of a set of anthroyloxy fatty acid probes (2-, 7-, 9- and 12-(9-anthroyloxy)-stearic acid (AP) and 16-(9-anthroyloxy)palmitic acid (AS). It was found that a decreasing polarity gradient from the aqueous membrane interface to the membrane interior, was present. This gradient was not modified by the proteins, as evidenced by comparison of complete membranes and derived liposomes, suggesting that the anthroyloxy probes were not in close contact with the proteins. An important change of the value of the mean rotational relaxation time as a function of the position of the anthroyl ring along the acyl chain was evidenced. In the complete membranes, a relatively more fluid medium was evidenced in the C16 as compared to the C2 region, while the rotational motion appeared to be the most hindered at the C7–C9 level. In the derived liposomes, a similar trend was observed but the mobility was higher at all levels. The decrease of the mean rotational relaxation time was more important for 12-AS and 16-AP. Temperature dependence of the mean rotational relaxation time of 2-AS, 12-AS and 16-AP in the complete membranes revealed the existence of a lipid reorganization occurring around 27°C and concerning mainly the C16 region. The extent to which the acyl chain reacted to this perturbation at the C12 level depended on pH. The presence of proteins increased the apparent magnitude of this reorganization and also modified the critical temperature from approx. 23°C in the derived liposomes to approx. 27°C in the complete membranes. Thermal dependence of the maximum velocity of the 3-oxosteroid Δ5−Δ4-isomerase, the second enzyme in the enzymatic sequence, responsible for the biosynthesis of the 3-oxo-Δ4-steroids in the adrenal cortex microsomes, was studied. The activation energy of the catalyzed reaction was found to be low and constant (2–5 kcal · mol−1) in the temperature range 16–40°C at pH 7.5, 8.5 and 9, corresponding to the minimum, intermediate and maximum rate, respectively. A drastic increase of the activation energy (20 kcal · mol−1) was observed at temperature below 16°C at pH 7.5. A correlated change of the pKESapp as function of temperature was detected; at 36°C pKESapp = 8.3 while at 13°C the value shifted to 8.7. The pH range of the group ionization was narrower at 13°C. In contrast with the behaviour of the 3β-hydroxy-Δ5-steroid dehydrogenase, the 3-oxosteroid Δ5−Δ4-isomerase was apparently unaffected by the lipid reorganization at 27°C. It is suggested that this enzyme possesses a different and more fluid lipid environment than the bulk lipids.

The combination of the viscosity increment with the harmonic mean rotational relaxation time for determining the conformation of biological macromolecules in solution

The combination of the viscosity increment with the harmonic mean rotational relaxation time for determining the conformation of biological macromolecules in solution

The combination of the viscosity increment with the harmonic mean rotational relaxation time for determining the conformation of biological macromolecules in solution.

A new hydrodynamic shape function, lambda, is derived for determining the conformation of biological macromolecules in solution, adding to the increasing number of shape parameters whose experimental determination does not require a knowledge of the particle swelling due to solvation in solution. lambda can be found from a knowledge of the molecular weight, intrinsic viscosity and the harmonic mean rotational relaxation time. A table of values and a plot of lambda as a function of axial ratio for both oblate and prolate ellipsoids of revolution are given.