Intramolecular interference effects in dynamic light scattering: rigid double spirals and superhelical DNAs

A theory is developed for dynamic light scattering (DLS) from rigid double spirals by treating an invisible rigid cylinder with two helical scattering stripes on opposite sides of its cylindrical surface. The exact initial, or first cumulant, diffusion coefficient Dapp (K) is obtained in terms of the translational diffusion coefficients (D parallel and D perpendicular) parallel and perpendicular to the symmetry axis, the rotational diffusion coefficients (DR parallel and DR perpendicular) around the symmetry and transverse axes, the length (L) and radius (b) of the cylindrical surface bearing the stripes, and the pitch (p). Interference effects, namely geometrical antiresonances, between strands, produce deep minima in the static structure factor S (K) and corresponding prominent peaks in Dapp (K). These peaks in Dapp (K) depend sensitively on the rotational dynamics around the symmetry axis, and nearly vanish when DR parallel = 0. Some results for single spirals are also presented. A simpler model in which scattering points are attached at opposite ends of an otherwise invisible thin rigid rod is also treated, and shown to exhibit modest minima in S (K) and corresponding maxima in Dapp (K). Confining this rod to a plane containing K enhances the amplitudes of the oscillations in S (K) and Dapp (K), as expected. Rigid double spirals are employed as crude models for interwound supercoiled DNAs in order to assess the possible occurrence of interference effects. Although native supercoiled DNAs exhibit a cylinder diameter that is much too small to exhibit geometrical antiresonances in the presently accessible range of K2, nearly relaxed supercoiled DNAs are predicted to exhibit their first maximum in Dapp (K) just inside this range. Previously reported data for the effect of Escherichia coli single-strand binding (ssb) protein on the DLS of supercoiled pBR322 DNA cannot be mimicked by a gradual homogeneous reduction of superhelix density with increasing ssb, but instead can be mimicked by inhomogeneous all-or-none binding in which uncomplexed native DNAs and nearly relaxed saturated ssb/DNA complexes coexist in varying proportions. Experimental Dapp (K) and S (K) data for a sample of relaxed pUC8 dimers display, respectively, a broad maximum and a corresponding minimum, in qualitative agreement with rough theoretical predictions.     

Quasielastic light scattering from long rigid rods

The purpose of this work was to improve our understanding of quasielastic light scattering from long rigid rods (QL >> 1). For these scatterers, only small angular displacements are required to produce dephasing of the scattering light. This plus the fact that only rods lying perpendicular to Q contribute to the scattered light allow one to simplify the intermediate scattering function to an analytic form. This form is shown to be nonexponential, exhibiting (t)^?½ behavior at long delay times. This new scattering function can then be fit to experimental functions using standard methods.     

Static and dynamic light scattering from aggregating particles

We use standard hydrodynamic and light scattering theories to calculate the total intensity and dynamic light scattering properties of random aggregates of spherical particles containing up to ten spheres. When the aggregates have dimensions comparable to the wavelength of light, intraaggregate interference effects can dramatically reduce the apparent size of the aggregates. These results could be significant in interpreting DNA condensation, protein polymerization, and other biomolecular aggregation reactions.     

Static and dynamic light scattering from dilute insulin solutions

Static and dynamic light-scattering measurements are reported on zinc-insulin at room temperature (21 ± l°C) and pH = 6.88 in 0.1M NaCl aqueous solution. The experiments were performed at very low concentration, in the range 0.12 × 10^?4 to 0.90 × 10^?4 g cm^?3. Within experimental error, we find no evidence for a critical micellar concentration in this system. The aggregation phenomenon starts immediately after preparation of the solutions, and takes several days to come to stable equilibrium. The concentration dependence of the diffusion coefficients, D _z, = D_o (1 — k_DC), is negative, and k_D was observed to decrease as a function of time, while the aggregate size was found to increase. The equivalent concentration coefficient, ?2BM _W, obtained from static light scattering, showed a similar behavior, and, within experimental error, was found to be numerically equal to k_D. From the relation found between the diffusion coefficient at infinite dilution and the molecular weight of the aggregates, log D₀ = ?0.240 log M _w ? 5.077, we deduce that the insulin aggregates are compact structures with a characteristic radius of 0.71 Å/(dalton)^1/3, surrounded by a hydration layer of a thickness of 8.0 Å. The equilibrium aggregation number is approximately 10.     

Size distributions of chylomicrons from human lymph from dynamic light scattering measurements

Chylomicrons, the vehicles for the transport of exogeneous triglycerides and cholesterol in the lymph and the blood, were characterized by their size from dynamic light scattering measurements. To achieve an appropriate resolution, correlation data were collected over several hours. Analysis was performed with an extended version of the regularization method CONTIN, and special attention was given to errors in the experimental baseline and to randomness of the residuals. The solutions selected by means of Fisher's F-test by CONTIN agreed with those obtained with the stability plot of Schnablegger and Glatter, when in the case of data of lower statistical accuracy the solution was taken from the lower part of the confidence interval of the F-test. The intensity-weighted size distributions indicated two classes of particle, their mean diameters being 100–140 nm and 330–350 nm. The ability to resolve two peaks of such a size ratio is demonstrated. The numbers of particles associated with the two peaks were estimated by means of the scattering properties of the particles, which showed that the overwhelming majority were small ones. This estimation also suggested that the mean size of the first peak of the number distribution is significantly smaller than the typical size of chylomicrons. This was consistent with the finding that the sample contained not only apolipoprotein B-48 but also a similar amount of apolipoprotein B-100, which is associated with lipoproteins of smaller size. The larger particles of the second peak are probably dietary triglyceride-rich chylomicrons. Received: 12 October 1997 / Revised version: 26 June 1998 / Accepted: 7 August 1998     

Rotational effects in quasielastic laser light scattering from T-even bacteriophage.

We have applied a theory of dynamic light scattering from large anisotropic particles, developed by Aragón and Pecora [J. Chem. Phys. 66 , 2506–2516 (1977)] to calculate the scattering expected from T-even phage models. The results indicate that the off-center rotation of the massive virus head with respect to the center of frictional resistance introduces significant rotational contributions to the light-scattering time autocorrelation function. The effect is particularly important when the fibers of the phage are extended. Reanalysis of previously published data [J. B. Welch III and V. A. Bloomfield, Biopolymers 17 , 2001–2014 (1978)], taking into account rotational corrections, confirms the equality of molecular weights of the slow- and fast-sedimenting forms of T2L bacteriophage.     

Measurement of inherent particle properties by dynamic light scattering: introducing electrorotational light scattering.

Common dynamic light scattering (DLS) methods determine the size and zeta-potential of particles by analyzing the motion resulting from thermal noise or electrophoretic force. Dielectric particle spectroscopy by common microscopic electrorotation (ER) measures the frequency dependence of field-induced rotation of single particles to analyze their inherent dielectric structure. We propose a new technique, electrorotational light scattering (ERLS). It measures ER in a particle ensemble by a homodyne DLS setup. ER-induced particle rotation is extracted from the initial decorrelation of the intensity autocorrelation function (ACF) by a simple optical particle model. Human red blood cells were used as test particles, and changes of the characteristic frequency of membrane dispersion induced by the ionophore nystatin were monitored by ERLS. For untreated control cells, a rotation frequency of 2 s-1 was induced at the membrane peak frequency of 150 kHz and a field strength of 12 kV/m. This rotation led to a decorrelation of the ACF about 10 times steeper than that of the field free control. For deduction of ERLS frequency spectra, different criteria are discussed. Particle shape and additional field-induced motions like dielectrophoresis and particle-particle attraction do not significantly influence the criteria. For nystatin-treated cells, recalculation of dielectric cell properties revealed an ionophore-induced decrease in the internal conductivity. Although the absolute rotation speed and the rotation sense are not yet directly accessible, ERLS eliminates the tedious microscopic measurements. It offers computerized, statistically significant measurements of dielectric particle properties that are especially suitable for nonbiological applications, e.g., the study of colloidal particles.     

Chain stiffness of heteropolysaccharide from Aeromonas gum in dilute solution by dynamic light scattering

Dynamic light scattering measurements have been made on 15 fractions of aeromonas (A) gum, an extracellular heteropolysaccharide produced by the strain Aeromonas nichidenii, with dimethylsulfoxide containing 0.2M lithium chloride as the solvent at 25 degrees C. Data for the translational diffusion coefficient D covering a molecular weight range from 4.5 x 10(5) to 2.1 x 10(6) and ratios of the z-average radius of gyration (z) (1/2) to the hydrodynamic radius R(H) (calculated with previous (z) data) suggest that the polymer behaves like a semiflexible chain in this solvent similar to the stiffness of cellulose derivatives. Thus the D data are analyzed on the basis of the Yamakawa-Fujii theory for the translational friction coefficient of a wormlike cylinder by coarse-graining the heteropolysaccharide molecule. Excluded-volume effects are taken into account in the quasi-two-parameter scheme, as was done previously for (z) and [eta] (the intrinsic viscosity) of A gum in the same solvent. The molecular weight dependence of R(H) is found to be explained by the perturbed wormlike chain with a persistence length of 10 nm, a linear mass density of 1350 nm(-1), an excluded-volume strength parameter of 1.3 nm, and a chain diameter of 2.8 nm. These parameters are in substantial agreement with those estimated previously from (z) and [eta] data, demonstrating that the solution properties (D, (z), and [eta]) of the heteropolysaccharide are almost quantitatively described by the current theories for wormlike chains in the molecular weight range studied.     

Dynamic light scattering from thin rigid rods: Anisotropy of translational diffusion of tobacco mosaic virus

An Exact theoretical expression for the apparent diffusion coefficient D_app(K) of a thin rigid rod with arbitrary anisotropy of its translational diffusion diffusion coefficient is derived from the first cumulant of its dynamic structure factor. D_app(K) is predicted to reach a limiting plateau value at extermely large values of KL, where K is the scattering vector and L the rod length. Howerver, that limiting plateau value is approached only very slowly along a quasi-plateau with a very gradual slope. Dynamic light-scattering studies have been performed on tobacco mosaic virus from K² = (0.4–20) × 10¹⁰ cm^?2 using 632-8-nm laser radiation. The present data yield D₀ = (4.19 ± 0.10) × 10^?8 cm²/s (corrected to 20,w conditions) and, with literature data to establish L = 2980 Å and the rotational diffusion coefficient D_R = 318s^?1, yield also Δ ≡ D_∥ ? D_⊥ = (1.79 ± 0.38) × 10^?8 cm²/s. The experimental data closely follow the curve of D_app(K) vs K² calcuated for these parameters. The present value of D₀ substantially exceeds all previous dynamic light-scattering values, but is in good aggreement with previous sedimentation data, which were confirmed for the presemt sample. The anisotropy ratio Δ/D₀ = 0.43 ± 0.09 is in accord with theoretical predictions based on the modified Kirkwood algorithm, despite the fact the D₀ lies significantly below its corresponding theoretical value. The present data largely predlude the possibility that both D₀ and Δ/D₀ could simultaneously match their theoretical predictions. We present a detailed comparison of the experimental data with the calculations of Tirado and Garcia de la Torre based on the modified Kirkwood algorithm and with the Broersma formulas.     

Vesicle sizing: Number distributions by dynamic light scattering

A procedure is described which optimizes nonnegative least squares and exponential sampling fitting methods for analysis of dynamic light scattering (DLS) data from aqueous suspensions of vesicle/liposome systems. This approach utilizes a Rayleigh-Gans-Debye form factor for a coated sphere and yields number distributions which can be compared directly to distributions obtained by freeze-fracture electron microscopy (EM). Excellent agreement between the DLS and EM results are obtained for vesicle size distributions in the 100-200-nm range.     

Gelatin-alpha olefin sulfonate interactions studied by dynamic light scattering

Dynamic light scattering (DLS) measurements were performed to study the binding of anionic surfactant alpha olefin sulfonate (AOS) to gelatin chains at various NaCl concentrations at 30 degrees C in aqueous sodium phosphate buffer (pH = 6.8) solutions. The surfactant concentration was varied from 0 to 80 mM and the NaCl concentrations chosen were 0.025, 0.05, and 0.1 M. AOS exhibited electrostatic binding to the positively charged sites of the polypeptide chain resulting in considerable reduction in its hydrodynamic radius up to critical micellar concentration (cmc = 8 mM for no salt, 0.01 and 0.025 M, and 5 mM for 0.05 M and 2 mM for 0.1 M solutions). The correlation function revealed the presence of two types of structures above cmc; namely the micelles of AOS and gelatin-AOS micelle complexes. The micellar radii (Rm), the effective gelatin-surfactant complex radii (Rc), have been determined as a function of salt concentration. No critical aggregation concentration (cac) was observed. The inter-gelatin-surfactant complex (kD1) and inter-micellar interactions (kD2), were determined by fitting the concentration dependence of Rm and Rc to a virial expansion in reduced concentration (c - cmc), which are compared. While kD1 showed strong ionic strength dependence, kD2 remained invariant of the same. The protein to surfactant binding ratio was found to be smaller than normal. Results have been discussed within the framework of the necklace-bead model of polymer-surfactant interactions.     

Acid denatured apo-cytochrome c is a random coil: evidence from small-angle X-ray scattering and dynamic light scattering

The conformation of a denatured protein has been investigated, since the experimental data on the structure of denatured proteins have been incomplete until now. The Stokes' radius Rs and the radius of gyration Rg of apo-cytochrome c at pH 2.3 have been determined by dynamic light scattering and small-angle X-ray scattering, respectively. The values of these structure parameters, extrapolated to zero protein concentration, are Rs = 3.0 nm and Rg = 4.6 nm. The ratio Rg.Rs-1 is a sensitive indicator of the molecular conformation. The ratio of 1.55 obtained by us is typical for a random-coil polymer. The persistence length--the characteristic of the molecular flexibility--was determined to be a = 1.81 nm. From this results the root-mean-square average end-to-end distance of the molecules [h2] 1/2 = 11.2 nm and the characteristic ratio [h2]/npl2p = 8.43, where np = 104 is the number of amino acid residues and lp the distance between C alpha-atoms. We obtained a second virial coefficient A2 = 8.2.10(-3) mol cm3 g-2. The experimentally determined structure parameters are in approximate agreement with those predicted by Flory and others for an unperturbed, randomly coiled polypeptide. The expansion factor lies between 1.1 and 1.2. In conclusion, we have shown that apo-cytochrome c at pH 2.3 and at low concentrations has the conformation of a perturbed random coil with repulsive potentials between the chain segments.     

Effects of normalization errors on size distributions obtained from dynamic light scattering data.

This paper presents a study of the influence of normalization errors on size distributions obtained from the analysis of intensity fluctuations by photon correlation spectroscopy. The effects of these errors are demonstrated by means of computer-generated autocorrelation functions simulating light scattered from a monomodal Schulz distribution of small, spherical, unilamellar lipid vesicles. The calculations show that even small errors in the baseline, modifying the data upon normalization systematically, will cause serious errors in the estimated size distribution. As it turns out this is due to the peculiar characteristics of normalization errors in data of the first order autocorrelation function. The errors introduced there are described in parts by functions of the delay time having positive exponents. Such components are not considered in the integral equations commonly used to analyze the measured data. The error's property to be a function of delay time in turn enables us to obtain the relative baseline error from the inversion of the data. The new method for its determination is described in some detail. Here, it has been realized with a modified version of the size distribution algorithm CONTIN.     

Localized dynamic light scattering: a new approach to dynamic measurements in optical microscopy.

We present a new approach to probing single-particle dynamics that uses dynamic light scattering from a localized region. By scattering a focused laser beam from a micron-size particle, we measure its spatial fluctuations via the temporal autocorrelation of the scattered intensity. We demonstrate the applicability of this approach by measuring the three-dimensional force constants of a single bead and a pair of beads trapped by laser tweezers. The scattering equations that relate the scattered intensity autocorrelation to the particle position correlation function are derived. This technique has potential applications for measurement of biomolecular force constants and probing viscoelastic properties of complex media.     

Characterization of Caulobacter crescentus FtsZ protein using dynamic light scattering

The self-assembly of the tubulin homologue FtsZ at the mid-cell is a critical step in bacterial cell division. We introduce dynamic light scattering (DLS) spectroscopy as a new method to study the polymerization kinetics of FtsZ in solution. Analysis of the DLS data indicates that the FtsZ polymers are remarkably monodisperse in length, independent of the concentrations of GTP, GDP, and FtsZ monomers. Measurements of the diffusion coefficient of the polymers demonstrate that their length is remarkably stable until the free GTP is consumed. We estimated the mean size of the FtsZ polymers within this interval of stable length to be between 9 and 18 monomers. The rates of FtsZ polymerization and depolymerization are likely influenced by the concentration of GDP, as the repeated addition of GTP to FtsZ increased the rate of polymerization and slowed down depolymerization. Increasing the FtsZ concentration did not change the size of FtsZ polymers; however, it increased the rate of the depolymerization reaction by depleting free GTP. Using transmission electron microscopy we observed that FtsZ forms linear polymers in solutions which rapidly convert to large bundles upon contact with surfaces at time scales as short as several seconds. Finally, the best studied small molecule that binds to FtsZ, PC190723, had no stabilizing effect on Caulobacter crescentus FtsZ filaments in vitro, which complements previous studies with Escherichia coli FtsZ and confirms that this class of small molecules binds Gram-negative FtsZ weakly.     

Rheology and dynamic light scattering of octa-ethyleneglycol-monododecylether/chitosan solutions

In this work we used rheometry and DLS to probe relaxation phenomena in solutions of chitosan and octa-ethyleneglycol-monododecylether. The dispersions had a marked pseudoplastic behavior, which became less evident, as surfactant concentration was increased. Arrhenius plots showed that systems with surfactant presented a characteristic temperature at which apparent enthalpy of activation (varying from 3 to 40 kJ mol⁻¹) changed: this change was correlated to a possible transition of colloidal aggregates to a wormlike configuration. DLS intensity correlation functions were described by KWW equation: pure chitosan solutions had relaxation rate distributions centered at a characteristic relaxation rate around 4.6 × 10⁻⁶ μS⁻¹; as surfactant was added, a new component, with a faster characteristic relaxation rate with a magnitude order of 10⁻³ μs⁻¹, appeared. It was shown that the dependence between these relaxation rates and surfactant concentration could be used to describe DLS-related relaxation phenomena as an Arrhenius-activated process, agreeing with results obtained using rheometry.     

Solution dimensions of the gramicidin dimer by dynamic light scattering

Gramicidin is thought to form dimeric helical rods in alcohol solutions. In addition, there is evidence that the rod dimensions change upon addition of potassium ions. The present work reports values for the translational and rotational diffusion coefficients of gramicidin in methanol and 95% ethanol and in these same solvents with added KSCN. Solution dimensions are calculated from the diffusion coefficients. The results suggest that gramicidin exists primarily as dimers in these solutions and that the gramicidin rod does indeed become shorter upon addition of potassium ion. These results are consistent with those obtained from X-ray studies on single crystals grown from alcohol solutions.