Dynamic light scattering from solutions of microtubules.

Calf brain microtubule protein was assembled in vitro to form dilute solutions of microtubules (240 A diameter) having lengths greater than 1 micrometer. The microtubule solutions were examined by dynamic laser light scattering techniques. The angular dependence of the correlation function leads to the conclusion that the correlation function is measuring the translational diffusion constant of the particles. The length dependence of the correlation function, however, shows that the translational diffusion constant is not being measured and that the diffusion constant for the microtubules cannot be straightforwardly determined. These results suggest that a collective property of the rods is being measured by the laser light scattering. Although specific microtubule-microtubule interactions are a possible explanation for the observed results, we present arguments that suggest that the solution can be adequately modeled as a network of entangled polymers.     

Dynamic light scattering from collagen solutions. I. Translational diffusion coefficient and aggregation effects

Solutions of native collagen extracted from rat tail tendons in neutral salt solution have been studied by dynamic light scattering. The spectra obtained are consistent with the presence in solution of both single rod-shaped collagen molecules and aggregates of molecules. No contribution to the spectrum has been detected at any scattering angle from rotational diffusion of single molecules, although a measurable broadening effect is expected at high angles. The translational diffusion coefficient D of single molecules, calculated from the broader spectral component, shows an anomalous dependence on collagen concentration with a maximum value of D_20,w = 8.6 ± 0.2 × 10^?12 m²/sec near the concentration 0.04% by weight. Above 0.05% D falls linearly with increasing concentration and takes the value D _20,w = 8.1 ± 0.2 × 10^?12 m²/sec at 0.064% collagen.     

Photon correlation spectroscopy and light scattering of eye lens proteins at high concentrations.

The bovine eye lens protein, alpha L crystallin, has been studied with photon correlation spectroscopy and statical light scattering in the concentration range up to 200 g/l in different solvent conditions. At higher concentration (c greater than 70 g/l) the scattering behavior is quite complicated, which results in nonexponential correlation functions. Three methods have been used for the analysis of these correlation functions, namely, cumulant analysis, sum of two exponentials analysis, and exponential sampling method. These methods resulted in very similar results. The highly concentrated solutions contain two scattering entities: the single alpha L crystallin and a rather heterogeneous population of large clusters. The statical light-scattering experiments can be interpreted in the same way and gave consistent results for the dimensions of the large scattering units. The formation of these clusters, which are strong light scatterers, is superimposed on an increasing degree of correlation between the bulk of the alpha L-crystallins, resulting in a net decrease of light scattering as a function of concentration.     

Observation of flagellation of spermatozoa by depolarized laser light scattering.

Depolarized laser light-scattering theory was applied to derive the autocorrelation function of laser light scattered by motile spermatozoa, assuming that each spermatozoon is a chain of rotatable rigid ellipsoids of revolution and also that the rotational velocity about an axis perpendicular to the symmetry axis of the ellipsoid is constant for times of the order of the characteristic decay time of the autocorrelation function. The rotations are produced by flagellar movements of the spermatozoa. The correlation function thus obtained was related to the second-order coefficient of a Legendre polynomial expansion of the rotation of the direction angle of the ellipsoidal axis. The experimental fact that the correlation function for dead spermatozoa of sea urchin resembled that for flagella mechanically separated from spermatozoa indicated to us that the depolarized light was scattered mainly by flagella. The rotational velocity distribution of the flagella was determined by comparing the theoretical analysis with the experimentally obtained correlation functions for the motile and dead spermatozoa. The value of the average velocity caused by the flagellation, 230 rad/s, was in good agreement with that measured under an optical microscope.     

Dynamic light scattering by kappa- and lambda-carrageenan solutions

The intensity correlation functions of kappa- and lambda-carrageenan in various salt solutions and at different concentrations have been determined with the help of dynamic light scattering. From the first cumulant of these correlation functions the values of the translational diffusion coefficients D have been derived. They increase with macromolecular concentration. The extrapolated values to infinite dilution of the diffusion coefficients increase with increasing salt concentration as expected from the salt concentration dependence of the r.m.s. radii of gyration determined previously by static light scattering. The translational diffusion coefficient of lambda-carrageenan in 0.1 M NaCl is smaller than the corresponding value for the kappa species. This is consistent with the difference in contour length and linear charge density of the two samples used. No satisfactory interpretation for the concentration dependence of the diffusion coefficient seems to be possible at present. Although current theories for the macromolecular and salt concentration dependence of D, taking into account charge effects, seem to be applicable, they do not allow for a consistent interpretation of the data. No specific difference between the solution behaviour of kappa- and lambda-carrageenan has been detected.     

Quasielastic light scattering from solutions of filamentous viruses. II. Comparison between theories and experiments

We have compared four theoretical effects of rodlike macromolecules with the fast components, i.e., components other than translational diffusion, of our experimental data, which are presented as amplitude autocorrelation functions of electric field scattered from dilute solutions of monodisperse rodlike viruses with lengths from 3300 Å for tobacco mosaic virus to 20,000 Å for Pf1. The four effects are (1) the optic anisotropy treated by Aragón and Pecora, (2) coupled translational–rotational diffusion due to anisotropy in translational mobility recently reformulated by Gierke, (3) anisotropic rotational diffusion with respect to the direction of translational displacement first discussed by Berne and Pecora, and (4) the bending mode of a rod by Fujime and Maruyama. We show that both the first and second effects are required to explain the enhancement of amplitude of the translational diffusion at the expense of fast components. The experimental decay rates of the fast component exceed that of the rotational diffusions. In order to explain the excessive decay rate in the fast component, we need to include a minute amount (～1%) of bending mode of rodlike viruses, especially in longer viruses such as M13 and Pf1.     

Dynamic light scattering study of muscle F-actin

By use of digital autocorrelation and fast Fourier methods, dynamic light-scattering studies of in vitro reconstituted muscle F-actin were made over a wide range of concentrations, 0.01-2 mg/ml F-actin. Measurements of correlation function [g1(t)]2 showed that a transition from a dilute to a semidilute regime for the Brownian motions of filaments occurred at around 0.3 mg/ml F-actin. Beyond this concentration, profiles of successively measured [g1(t)]2 showed very poor reproducibility. This resulted from the existence of very slow components, which could not be measured with a high statistical accuracy even for a measuring time of 3600 s/run. On the other hand, subtraction of these components automatically by an electronic circuit, [g-1(t)]2, or by computer processing, [g1(t)]2, resulted in a fairly good reproducibility of the profiles. The decay characteristics of [g1(t)]2 (and [g-1(t)]2) were very similar to those of [g1(t)]2 for dilute solutions. A theoretical model will be discussed which could account for the above situation. The time sequence [n(t,T)] of photoelectron counts at a sampling time T of light scattered from semidilute solutions of F-actin was stored on magnetic tapes, and both power spectra S(f) and correlation functions [g-1(t)]2 were computed by taking the ensemble average over many short records with duration 1024T. Since both S(f) and [g-1(t)]2 lacked frequency components lower than 1/(2048T) Hz, their profiles were highly reproducible. An analysis of S(f) confirmed our earlier results which had shown an apparent contradiction to later results by a correlation method. A comparison of S(f) and [g-1(t)]2 based on the same [n(t,T)] clarified the reasons why the bandwidth gamma of S(f) largely differed from the bandwidth gamma of [g1(t)]2 and [g-1(t)]2. The temperature dependence of gamma suggested that F-actin would be flexible and that the flexibility parameter would change with temperature.     

Photon and fluorescence correlation spectroscopy and light scattering of eye-lens proteins at moderate concentrations

The bovine eye-lens protein, alpha L-crystallin, has been studied with photon correlation spectroscopy to obtain the mutual diffusion coefficient, Dm, with fluorescence correlation spectroscopy to determine the tracer diffusion coefficient, DT, and with light scattering to get the isothermal osmotic compressibility (delta pi/delta c) P,T. The concentration dependence of Dm, DT, and (delta pi/delta c) P,T up to a volume fraction phi of the protein of 2.5 x 10(-2) has been interpreted on the basis of four different interaction potentials: (a) an extended hard-sphere potential; (b) a shielded Coulomb potential; (c) a shielded Coulomb interaction where the effect of counterions is included; (d) a simple mixed potential. The three parameters Dm, DT, and (delta pi/delta c) P,T have also been combined in the generalized Stokes-Einstein equation, Dm = [(delta pi/delta c)P,T . (1--phi) . (DT)]/(kappa B . T). Our results indicate that, in the case that photon correlation spectroscopy gives the mutual diffusion coefficient Dm, the applicability of the Stokes-Einstein equation can be questioned; or that, when one assumes the Stokes-Einstein equation to be valid, there is significant discrepancy between the result of photon correlation spectroscopy and Dm.     

Translational and rotational diffusion of tobacco mosaic virus from polarized and depolarized light scattering

The translational and rotational dynamics of tobacco mosaic virus in sodium phosphate buffer (pH =7.5) solutions has been investigated by polarized and depolarized light scattering Rayleigh linewidth studies. For concentrations ranging from 1.75 × 10^?4 g ml^?1 to 0.25 × 10^?4 g ml^?1 the translational diffusion coefficient (D_T) has been found to be slightly concentration dependent and extrapolation to zero concentration gives D₀^20°C = 0.34 ± 0.01 × 10^?7 cm²S^?1. A full analysis of the polarized spectra obtained at high and low scattering angles and the depolarized spectra at near zero scattering angles has enabled these techniques to be compared and the rotational diffusion constant D_R to be determined. At a solution concentration of 1.75 × 10^?4 g ml^?1 a mean value is found to be D_R^20°C = 350 ± 30s^?1. These values of D_T and D_R are in approximate agreement with calculations based on models of the tobacco mosaic virus molecule as a cylindrical rod.     

Quasielastic light scattering from solutions of filamentous viruses. I. Experimental

Intensity fluctuations of laser light scattered from filamentous viruses Pf1 [length L (Å) × diameter d (Å) = 20,000 × 90], M13 (9000 × 90), potato virus X (5150 × 130), and tobacco mosaic virus (3000 × 180) in sucrose density gradients were measured with a photon correlation spectrometer over a range of scattering angles from 15° to 120°. The experimental data can be approximated by two exponential decays, “slow” and “fast.” The slow decay rate constant t corresponds to the translational diffusion D of the virus, i.e., t = K²D, where K is the magnitude of the scattering vector. The amplitude of the slow component, i.e., translational diffusion, remains greater than that of the fast component, even at high KL. The fast decay rate constant t is also proportional to K² for viruses such as Pf1, M13, and even potato virus X. In the companion paper, we shall attribute the amplitude enhancement of the translational diffusion to the coupling of its anisotropy to the rotational diffusion modes. In order to explain the excessive decay rates in the fast component, we need to consider the bending mode of rodlike viruses, especially in the longer viruses such as M13 and Pf1, in addition to the usually expected rotational diffusion modes.     

Dynamic light scattering study of calcium-induced fusion in phospholipid vesicles.

Acidic sonicated phospholipid vesicles can undergo dramatic morphological changes due to fusion in the presence of divalent metal ions. For example, small spherical phosphatidylserine vesicles can form scroll-like cylinders which precipitate in the presence of Ca2+ above a threshold concentration. Subsequent addition of EDTA will yield large, unilamellar vesicles. These events have previously been established through the combined use of differential scanning calorimetry and freeze-fracture electron microscopy. We have applied the technique of dynamic light scattering to follow these fusion events rapidly, accurately, and non-perturbatively as they occur in solution at calcium concentrations slightly below threshold for precipitation.     

Dynamic light scattering study of calmodulin-target peptide complexes

Dynamic light scattering (DLS) has been used to assess the influence of eleven different synthetic peptides, comprising the calmodulin (CaM)-binding domains of various CaM-binding proteins, on the structure of apo-CaM (calcium-free) and Ca(2+)-CaM. Peptides that bind CaM in a 1:1 and 2:1 peptide-to-protein ratio were studied, as were solutions of CaM bound simultaneously to two different peptides. DLS was also used to investigate the effect of Ca(2+) on the N- and C-terminal CaM fragments TR1C and TR2C, and to determine whether the two lobes of CaM interact in solution. The results obtained in this study were comparable to similar solution studies performed for some of these peptides using small-angle x-ray scattering. The addition of Ca(2+) to apo-CaM increased the hydrodynamic radius from 2.5 to 3.0 nm. The peptides studied induced a collapse of the elongated Ca(2+)-CaM structure to a more globular form, decreasing its hydrodynamic radius by an average of 25%. None of the peptides had an effect on the conformation of apo-CaM, indicating that either most of the peptides did not interact with apo-CaM, or if bound, they did not cause a large conformational change. The hydrodynamic radii of TR1C and TR2C CaM fragments were not significantly affected by the addition of Ca(2+). The addition of a target peptide and Ca(2+) to the two fragments of CaM, suggest that a globular complex is forming, as has been seen in nuclear magnetic resonance solution studies. This work demonstrates that dynamic light scattering is an inexpensive and efficient technique for assessing large-scale conformational changes that take place in calmodulin and related proteins upon binding of Ca(2+) ions and peptides, and provides a qualitative picture of how this occurs. This work also illustrates that DLS provides a rapid screening method for identifying new CaM targets.     

Quasielastic light scattering from solutions of lollipop-shaped particles

An expression is derived for the field correlation function of the light scattered from a solution of lollipop-shaped particles. Such particles are a tractable model of certain bacteriophages. They are assumed to consist of an ellipsoidal head containing optically anisotropic scattering material and a tail which does not scatter. Because of the tail, Brownian rotational movement occurs around a center of rotational friction which is at a distance r₀ from the center of the head. The dependence of the field correlation function C(τ) on the rotational diffusion coefficient D_R is given by the factor Σ_lB_l exp[?l(l + 1)D_Rτ]. It is shown that the tail causes the coefficients B_l to be different from zero for all values of l. Therefore, C(τ) contains a term proportional to exp(?2D_Rτ), which is not present when r₀ = 0. We give plots of B_l for various combinations of parameters. It turns out that dynamic light scattering may be used to measure r₀.     

Dynamic light scattering measurements of the diffusion of probes in filamentous actin solutions

The diffusion coefficients of monodisperse polystyrene latex spheres in solutions of polymerized actin were measured using dynamic light scattering. Four different probes with radii R, ranging from 50 to 500 nm, were separately used in actin solutions with concentrations c, ranging from 1.5 to 21 microM, which had been polymerized with either 1 mM MgCl2, 1 mM CaCl2, or 100 mM KCl. Under all conditions, and at four different scattering angles in the range of 30 degrees-90 degrees, the measured average diffusion coefficients D of the probes were systematically smaller for samples of increased actin concentration or of increased probe radius. Control experiments indicated that the probes did not bind to the actin. These data for Mg2+- and Ca2+-polymerized actin agree and were found to be quite well summarized by the scaling relation D/D0 = exp[-alpha R delta c nu], where D0 is the measured diffusion coefficient of the probes in water (and, as also measured, in the starting actin solutions prior to polymerization with added salt), with values of delta = 0.73 +/- 0.05, nu = 1.08 +/- 0.09, and alpha = (1.1 +/- 0.6) x 10(-3) (with c in microM and R in nm). Data for KCl-polymerized actin show much more restricted diffusivities of the probes at comparable actin concentrations. Inhomogeneities in the solution are reflected in the "effective polydispersity" of the probe diffusion coefficients, which depend on local microviscosity differences.     

A rotational diffusion coefficient of the 70S ribosome determined by depolarized laser light scattering.

We have obtained a rotational diffusion coefficient of the 70S ribosome isolated from Escherichia-coli (MRE-600), from the depolarized light scattering spectrum measured by photon correlation spectroscopy. The intensity correlation function of depolarized scattered light contains contributions due to multiple scattered and anisotropy scattered light from the ribosomal particle. We discuss extensively the subtraction procedure used to obtain the rotational correlation from the time from the experimental correlation function. We have also obtained the translational diffusion coefficient from the same sample by determining the polarized correlation function. The hydrodynamic radius determined from the rotational diffusion coefficient is only slightly larger than the radius obtained from the translational diffusion coefficient. Therefore the ribosomal particle has a non-spherical shape. This conclusion, however, could be impaired by the effect of free draining of the ribosome.     

Dynamic light scattering study of suspensions of purple membrane

Purple membrane from Halobacterium halobium in suspensions has been studied by quasielastic light scattering. The intensity correlation functions of polarized scattered light were measured at various K2 values (K being the magnitude of the scattering vector), and the first cumulant Gamma of the field correlation function G1(tau) was obtained by a cumulant expansion method. The apparent diffusion coefficient Gamma /K2 did not increase monotonically with K2 values and showed a distinct anomaly in an intermediate range of K. A theoretical formulation of G1(tau) for a disc and an extremely oblate ellipsoidal shell of revolution (S. Fujime and K. Kubota, Biophys. Chem. 23 (1985) 1) was applied to the analysis of the spectra, and characteristic features of experimental spectra were well reproduced. It was suggested that a strong interference effect between scattered rays on Gamma /K2 should be attributed to a slight noncircular shape of the purple membrane and that a contribution to Gamma /K2 from membrane flexibility should be taken into account. This study will provide experimental evidence of the feasibility of membrane studies by dynamic light scattering.     

Dynamic light scattering studies of internal motions in DNA. II. Clean viral DNAs

Internal Brownian motions of clean ?29 and λ-DNAs have been studied using photon-correlation techniques at both visible (λ₀ = 632.8 nm) and uv (λ₀ = 363.8 nm) wavelengths. The present dynamic light scattering data, which extend to K² = 19 × 10¹⁰ cm^?2, can in every case be satisfactorily simulated by a Rouse-Zimm model polymer with an appropriate choice of the three model parameters. The effects of pH, salt concentration, single-strand breaks, and molecular weight on those model parameters have also been investigated. Intact clean DNAs exhibit surprisingly little variation with pH from 7.85 to 10.25, with salt concentration from 0.01 NaCl to 5.4M NH₄Cl, or with molecular weight or GC content. The single-strand breaks have no effect at pH 9.46, but produce dramatic changes in the model parameters at pH 10.0 and 10.25, indicating the introduction of titratable joints at those pHs. The failure of either single-strand breaks or a large change in GC content to alter the model parameters in the neutral pH range is a strong indication that local denaturation is not required for those flexions and torsions that dominate the relaxation of fluctuations in the scattered light. The Langevin relaxation time for the slowest internal mode of a particular Rouse-Zimm model derived from the dynamic light scattering data is compared with pertinent literature data extrapolated to the same molecular weight. The present algorithm for determining model parameters from the light-scattering D_app vs K² curve actually yields a Langevin time in fairly good agreement with the literature value. For unknown reasons the light-scattering D₀ values generally exceed those obtained from the molecular weight and sedimentation coefficient by about 20%.     

Quasi-elastic laser light scattering from solutions and gels of hemoglobin S.

Quasi-elastic light scattering has been used to examine solutions and gels of deoxyhemoglobin S. The autocorrelation function is found to decay with a characteristic exponential relaxation which can be ascribed to the diffusion of monomer (64,000 molecular weight) hemoglobin S molecules. In the absence of polymers, the relaxation time is in good agreement with previous measurements of the diffusion coefficient for solutions of normal human hemoglobin. In the presence of the polymer phase, a large (greater than 200-fold) increase in the scattered intensity is observed but no contribution to the decay of the autocorrelation function from the motion of the aligned polymer phase can be detected. Heterodyning between the time-independent scattering amplitude from the polymers and the time-dependent scattering of the diffusing monomers results in a twofold increase in the relaxation time arising from monomer diffusion.