Rotational Diffusion Constants Research Articles

Lipid--protein interactions in bacteriorhodopsin--dimyristoylphosphatidylcholine vesicles.

Bacteriorhodopsin (BR) was incorporated into large unilamellar dimyristoyl- and dipalmitoylphosphatidylcholine vesicles (100--300-nm radius). The effect of this intrinsic membrane protein on the order and dynamics of the lipid and on the cooperativity and transition temperature (Tc) of the gel to liquid-crystalline phase transition was investigated as a function of the lipid:protein ratio (L/BR). The lipid phase transition induces protein segregation. Above Tc, bacteriorhodopsin is in the monomeric state. Below Tc, BR is aggregated in the same hexagonal lattice as in the purple membrane (PM). In this reconstituted system, BR has a photochemical cycle similar to that in the PM and is active as a light-driven proton pump. The lipid phase transition which was monitored by using the steady-state anisotropy of the fluorescent probe 1,6-diphenyl-1,3,5-hexatriene (DPH) broadens with decreasing L/BR but occurs at approximately the same Tc. Below Tc, the fluorescence anisotropy of DPH is quite high (0.35) and independent of the L/BR. Above Tc, however, the anisotrophy increases markedly with decreasing L/BR. It was recently pointed out that the fluorescence anisotropy of probes like DPH contains information not only on the dynamics (correlation times) but also on the order parameters of the lipids [Heyn, M. P. (1979) FEBS Lett. 108, 359--364]. The most likely explanation of the observed increase in anisotropy above Tc is that the perturbation of the lipid bilayer caused by the incorporation of BR leads both to an increase in order and to a slowing of the rotational diffusion of the lipids (increased viscosity). In agreement with this latter dynamical effect, the rotational diffusion constant of BR itself decreases above Tc with decreasing L/BR. Above Tc, the membrane viscosity as determined from the rotational diffusion constant of BR is at least 1.5 times larger than that obtained from the fluorescence depolarization of DPH. The formation of the BR lattice as a function of temperature was followed by using the circular dichroism (CD) exciton effect together with measurements of the rotational diffusion of BR. Both methods show similar transition curves for the protein crystallization whose midpoints, however, occur several degrees below Tc.

Nuclear relaxation and molecular motion of pyridine-N-oxide in carbon tetrachloride

Proton spin lattice relaxation of pyridine-N-oxide-2,6-d2 in dilute solution (0·2 M) with carbon tetrachloride has been measured at -12·6, 6·5, and 26·6°C. Using 2H and 14N decoupling, eight transitions were resolved and recovery was monitored after non-selective inversion. In absence of 14N decoupling, scalar relaxation produced clearly visible effects on the proton recovery curves. Combined with measurements of deuterium relaxation of the 2,6-d2 and 4-d derivatives, proton relaxation data (including effects of dipolar cross correlation) were used to determine all three rotational diffusion constants at each temperature. The in-plane spinning motion was found to be ∼four-fold more strongly dependent on viscosity than predicted by the slip rotational diffusion model, while motion about the other two principal axes proceeds at rates within ∼40 per cent of slip predictions. 14N spin lattice relaxation data were combined with the anisotropic reorientation rates in efforts to determine liquid phase values of the 14N quadrupole coupling parameters. A very small decrease from solid phase values provides the best overall fit to the relaxation data.

Fourier transform carbon-13 spin–lattice relaxation study of motion of cyclic hydrocarbons

The molecular dynamics in solution for a series of cyclic and bicyclic hydrocarbon derivatives has been investigated by C-13 pulsed Fourier Transform nuclear magnetic resonance spin–lattice relaxation experiments. Molecular motion has been analysed in terms of an anisotropic rotational diffusion model, and an attempt has been made to assess the effects of structure on the observed rotational diffusion constants. Errors in the diffusion constants are discussed, and some of the other problems inherent in the use of these parameters to obtain structural information are outlined.

Orientation of membrane fragments by electric field

Purple membrane fragments from Halobacterium halobium were oriented by a static electric field in a water suspension. It was found that an electric field of approx. 20 V/cm is sufficient to achieve practically complete orientation; the purple membranes have a permanent electric dipole moment of (6 ±1)· 10 −23 C · m, the orientation of the retinal transition moment relative to the direction of the electric dipole moment, θ, is (59 ± 1) 0, and the purple membrane rotational diffusion constant D rot = 0.65 s −1. It was found that because of the electrophoretic movement of the particles a hydrodynamic velocity gradient builds up which also orients the purple membranes.

1-H and 14-N NMR relaxation studies on solutions of Mn(ClO4)2 in acetonitrile

Proton spin-lattice and spin-spin relaxation times of acetonitrile solutions of Mn(ClO4)2 between 298°K≤T≤413°K have been measured over a wide frequency range (10 kHz≤v≤90 MHz). From these data and corresponding 14-N NMR line width measurements of acetonitrile at varying temperatures, it is possible to extract structural and dynamical parameters such as the number of complexed acetonitrile molecules, their mean lifetime in the first solvation sphere of the manganese ions, and the rotational diffusion constant of the [Mn(CH3CN)6]2+ complex.

Rotational diffusion tensors for non-spherical molecules

The rotational diffusion tensors of several rigid molecules are determined from the rotational friction tensor. The molecular friction tensor is modeled as a sum over the translational Stokes law friction coefficients of the constituent atoms of the molecule. Agreement of the theory with experimental rotational diffusion constants and onentational correlation times is surprisingly good.

Raman study of rotational motion of benzene in solution

Raman line widths of v 1 and v 15 of benzene were measured in a number of solvents, and rotational diffusion constants were determined. Experimental Dz as well as Dx showed the solvent dependence. Theoretical diffusion constants were computed for each solution, on the basis of the Hynes-Kapral-Weinberg model. The theory well explains the solvent dependence of experimental diffusion constants, and it is suggested that intermolecular association of benzene with some solvent molecules is not so strong as to affect significantly the rotational motion of benzene.

Comparative study of Raman and i.r. band widths of acetonitrile

Raman and i.r. band widths of all the vibrational bands of acetonitrile, CH 3CN and CD 3CN, have been measured in the pure liquid and in solutions of isotopic compounds. Widths arising from the vibrational relaxation, reorientational relaxation and resonance energy transfer have been separated on the basis of the current theories on vibrational band widths. The vibrational relaxation widths estimated for i.r. a 1 bands agree well with the observed isotropic Raman widths. Acceptable values of the rotational diffusion constants have been obtained from the band width data.

The structure and conformational dynamics of yeast phenylalanine-accepting transfer ribonucleic acid in solution

The solution structure of yeast tRNAPhe was investigated by using ethidium as a fluorescent probe in the D loop and the anticodon loop. For this purpose the dihydrouracils in position 16/17 and wybutine in position 37 were substituted by ethidium. The lifetimes and the time-dependent anisotropy of ethidium fluorescence were measured by pulsed nanosecond fluorometry. The kinetics of the transitions between different states of the tRNAPheEtd derivatives were determined by chemical relaxation measurements. It was found that the ethidium label irrespective of its position exhibits three different states called T1, T2 and T3 characterized by lifetimes tau 1 = 30 ns, tau 2 = 12 ns, and tau 3 = 3 ns. The lifetime differences are due to different accessibilities of ethidium for solvent quenching in the three states. Thus, there are three different defined structural environments of the ethidium in both the anticodon and the D loop. The distribution of the three states was measured as a function of Mg2+ concentration and temperature; it was found that state T3 is favored over states T2 and T1 by both increasing Mg2+ concentration and increasing temperature. The chemical relaxation kinetics exhibit a fast transition between T1 and T2 (10--100 ms) and a slow transition between T2 and T3 (100--1000 ms). The rates of both transitions depend likewise on Mg2+ concentration and temperature. The equilibrium and kinetic data clearly show the presence of strong and weak interactions between Mg2+ and tRNA. A cooperative model accounting for this behavior is developed. The ethidium probe behaves identically when located in different regions of the tRNA regarding both its distribution of states and its transition kinetics. This suggests that the different spectroscopic states report different conformations of the tRNA structure. The dependence of the three states on Mg2+ and spermine indicates that conformation T3 is closely related to or identical with the crystal structure. The rotational diffusion constants indicate that of all three states T3 is most extended while T2 is most compact. The thermodynamic analysis reveals that the strongly bound Mg2+ ions reduce both the activation entropy and enthalpy of all transitions. The weakly bound Mg2+ ions increase both the activation enthalpy and entropy of the slow transition between T2 and T3. It is suggested that the breaking of several intramolecular bonds, e.g., hydrogen bonds, is involved in this transition.

The rotational diffusion of cytochrome b5 in lipid bilayer membranes. Influence of the lipid physical state

A derivative of the integral membranes protein, cytochrome b5, has been prepared in which the native heme group has been replaced by the structurally similar rhodium(III)-protoporphyrin IX. This metalloporphyrin has a finite triplet yield with a single exponential decay time of 22 microsecond in water. After insertion of the metalloporphyrin into the protein, its triplet-state decay becomes strongly nonexponential with at least three equal amplitude components with time constants varying over a range of 100. The derivatized protein has been incorporated into unilamellar liposomes prepared from dimyristoyllecithin, and the rotational diffusion of the protein in the lipid bilayer has been studied at temperatures above and below the lipid phase transition temperature via triplet absorbance anisotropy decay. The anisotropy decay curves are biphasic both above and below the lipid phase transition. The rotational diffusion constant is found to be 2.4 X 10(5) s-1 at 35 degrees C, and 1.1 X 10(4) s-1 at 10 degrees C, both being calculated from the fast decay component. The ratio of the limiting anisotropy to the initial anisotropy is 0.6 at both temperatures. This implies a cone of restricted motion of 34 degrees for the protein in the bilayer.

Rotational diffusion in solvents with large characteristic lengths

A theory, based upon mode coupling, is given for the rotational diffusion constant of a tagged particle in a solvent characterized by a large macroscopic length. The theory is used to explain rotational diffusion near a critical point or in the presence of polymer molecules.

Determination of rotational diffusion constants of liquid benzene from measurements of infrared and raman line widths

Line widths are measured for the Raman v 1, v 15 and infrared v 12 of C 6ll 6 in C 6D 6 solution. Rotational diffusion constants are determined from the observed line widths, and compared with literature values. A rather anisotropic rotation of benzene molecules is suggested.

Effect of flexible polymers on the dielectric dispersion of rod-like macromolecules

The rotational diffusion of rod-like polar macromolecules (poly-γ-benzyl- l-glutamate or poly- n-hexylisocyanate) within entangled non polar polymer coils (polystyrene) is studied by dielectric absorption in solution. The dielectric increment as well as the rotatory diffusion constant is studied as a function of molecular weight of both components and increasing concentration of the non-polar polymer as well as the temperature. The classical theory of rotational diffusion is not obeyed if the viscosity of the polystyrene solution is taken as the medium viscosity. An increase in molecular aggregation on polystyrene addition is suspected.

Etude de la Dynamique Orientationnelle des Molécules d'Allène a l'Etat Liquide par Spectrométrie Raman

AbstractThe orientational dynamics of liquid allene has been studied by means of the analysis of the isotropic and anisotropic profiles of the symmetrical A1 band at 1074 cm−1 and of the anisotropic profile of an E band at 3067 cm−1. These profiles have been studied in the temperature range from 300 to 150 K and for pressures ranging from 100 to 3000 atm.Using the hypothesis of a diffusional rotation, the analysis of the former band allows the determination of the principal component D⊥ of the diffusion tensor, as well as of the associated activation energy and activation volume. The comparison of the observed orientational correlation times with the free‐rotation times and the shape of the correlation functions are not in too bad agreement with this hypothesis. The second band of E symmetry, which corresponds to a vibration whose Coriolis constant is very small, allows the evaluation of the diffusional Constant D∥ associated to the rotation of the molecule about its axis. A strong anisotropy in the rotations of the allene molecule in the liquid state is evidenced: D∥/D⊥ ≃ 7. Furthermore, the rotational motion about the axis seems to digress from a diffusional motion more than the reorientation of the axis itself. Finally, the paper discusses those conditions in which the evaluation of the rotational diffusion constant from the Raman profile of a depolarized band is valid.

Molecular rotation and reorientation: Microscopic and hydrodynamic contributions

The relative roles of microscopic and hydrodynamic contributions to molecular rotation and reorientation are examined within the framework of the microscopic boundary layer theory recently proposed by the authors. The theory is applied to rough spheres, for which computer simulation data are available, and to experimental results on spherical top molecules. Attention is focused on rotational diffusion constants, the kappa parameter introduced by Kivelson et al., and orientational relaxation times. It is shown that, while collective effects are present and often nonnegligible, the motion of small molecules is dominated by its microscopic aspects. Experimental trends which can incorrectly suggest dominance by hydrodynamic contributions are discussed in some detail. Finally, the transition to the regime where collective effects are dominant is considered.

Raman study of reorientational motion of liquid benzene

Raman spectra of the 943 cm −1 band of liquid benzene- d 6 were measured at temperatures up to 120°C and at pressures up to 4000 bar. Rotational diffusion constants for tumbling and spinning motions were obtained from Raman band widths and NMR T 1 data. Experimental results were compared with theoretical diffusion constants computed on the basis of various models. It is found that the Hynes—Kapral—Weinberg theory gives the best prediction for the temperature and pressure dependence of the diffusion constants and for the rotational anisotropy in liquid benzene.

The phenyl group motion in polystyrene and a model of restricted internal rotation

AbstractThe 13C NMR relaxation functions are calculated for the case of restricted rotational diffusion of a CH dipole pair about an internal rotational axis. The model is applied to the interpretation of recent 13C experiments of polystyrene in a region where the relaxation of all C atoms of the phenyl ring exhibits the same temperature coefficient. It is concluded that the velocity of the phenyl group motion may be overestimated if complete rotation is assumed. By means of the model of restricted internal rotation one finds D/D0<0,1 for the ratio of internal and mean segmental rotational diffusion constants.

Proton NMR Relaxation Studies on Solutions of Mn(ClO4)2 in Dimethylsulfoxide

AbstractProton spin‐lattice and spin‐spin relaxation times of DMSO solutions with Mn(ClO4)2 between 298 K ⩽ T ⩽ 413 K have been measured over a relatively wide frequency range (10 kHz ⩽ v ⩽ 90 MHz). Three regions exist where the relaxation times of solvent DMSO are frequency dependent. It is possible to extract from these experimental data structural and dynamical parameters such as the number of complexed DMSO molecules, their mean lifetime in the first solvation sphere around the metal ions, and/or the rotational diffusion constant of the [Mn(DMSO)6]2+ complex. These data are necessary for a better understanding of the EPR relaxation mechanism of manganese ions in the same environment, where considerable line broadening at higher temperatures (T ⩾ 373 K) has been observed.

Particle size distributions from transient electric birefringence data: I. polydisperse rods by two-parameter distribution functions

Many dilute solutions or suspensions of rod-like particles become birefringent when subjected to electric fields. On switching off the applied field the birefringence decays away as the particles revert from an ordered to a random orientation state. For polydisperse suspensions it is possible to evaluate well defined, experimental average values 〈D〉 of the rotary diffusion constant D by an analysis of the decay process. The nature of the average depends on the electrical and geometrical properties of the particle, on the experimental conditions of orientation and on the particle size distribution. Experimentally two such averages may always be isolated. A method is described whereby, if the particle size distribution is describable by a two-parameter distribution function | (L) then the parameters of | (L) may be readily evaluated from the two measured 〈D〉 averages. Equations are presented for three skew and two symmetric standard distribution functions. A method is also described whereby the most appropriate distribution function can be identified.

Relation between the initial slope of some electro-optic decays and the moments of the distribution of size

Several well defined average values of the rotatory diffusion constant D of a polydisperse system can be obtained using the initial slope of the free decay of different electro-optical phenomena and different degrees of orientation. The type of average depends also on the orientation mechanism. The type of average and its relation to the corresponding moments of the size distribution, which have been previously misused, are derived for rod-like and disc-like particles, different mechanisms of orientation, and two types of electro-optical effect: birefringence (or dichroism) and light scattering in an electric field. Re-examination of the agreement claimed by previous authors between averages of D measured by this technique and calculated from a distribution of size derived from electron micrographs illustrate the difficulties of the measurements at saturation of orientation, and the role of an exact knowledge of the orientation mechanism. Possible experiments are discussed. Two parameters analytical distribution functions, well suited for the expression of the differen moments appearing in the theory, are indicated.