Measurement of diffusion coefficient and electrophoretic mobility with a quasielastic light-scattering–band-electrophoresis apparatus

We have constructed an apparatus for the simultaneous measurement of electrophoretic mobility, μ, and diffusion coefficient, D, of macromolecules and cells. It combines band electrophoresis in a vertical, sucrose-gradient stabilized column, with quasielastic laser light-scattering determination of the diffusion coefficient of the species within the band. The entire electrophoresis cell is scanned through the laser beam of the quasielastic laser light-scattering apparatus by a vertical translation stage. Total intensity light-scattering measurement at each point in the cell gives the macromolecular concentration at that point. Solvent viscosity and electrical potential are measured at each point in the cell. Application of this apparatus to resealed red blood cell ghosts and to bovine hemoglobin indicates that measurements of field, viscosity, and migration distance are reliable, and that electroosmosis is insignificant. Application to T4D bacteriophage gives μ_20,w = (?1.05 ± 0.05) × 10^?4 cm²/V sec and D_20,w = (3.35 ± 0.10) × 10^?8 cm²/sec for fiberless particles, and μ_20,w = ?(0.59 ± 0.03) × 10^?4 cm²/V sec and D_20,w = (2.86 ± 0.09) × 10^?8 cm²/sec for whole phage with 6 fibers. Approximate analysis of these results with the Henry electrophoresis theory for spheres in dicates that each fiber contributes about 193 positive charges to the phage particle, compared with 327 from amino-acid analysis. The advantages and disadvantages of this apparatus, relative to conventional electrophoresis and to electrophoretic light scattering, are discussed.     

Translational diffusion coefficient of α-chymotrypsinogen A by laser-light-scattering spectroscopy

The translational diffusion coefficient of a pure sample of α-chymotrypsinogen A is measured by laser light scattering to give a value of D_20,w⁰ = (8.40 ± 0.15) × 10^?7 cm²/sec.     

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.     

Histone-induced conformational changes in DNA as probed by quasi-elastic light scattering.

Quasi-elastic light scattering as measured by intensity fluctuation (self-beat) spectroscopy in the time domain can be profitably used to follow both the translational diffusion D and the dominant internal flexing mode τ_int of DNA and its complexes with various histones in aqueous salt solutions. Without histones, DNA is found to have D = 1.6 × 10^?8 cm²/sec and τ_int ? 5 × 10^?4 sec in 0.8 M NaCl, 2 M urea at 20°C. Total histone as well as fraction F2A induce supercoiling (D = 2.6 × 10^?8 cm²/sec, τ_int ? 2.8 × 10^?4 sec) whereas fraction F1 induces uncoiling (D = 1.0 × 10^?8 cm²/sec, τ_int ? 9.4 × 10^?4 sec). Upon increasing the salt concentration to 1.5 M the DNA–histone complex dissociates (D = 1.8 × 10^?8 cm²/sec). Upon decreasing the salt concentration to far below 0.8 M, the DNA–histone complex eventually precipitates as a chromatin gel.     

Photon correlation spectroscopy, total intensity light scattering with laser radiation, and hydrodynamic studies of a well fractionated DNA sample.

A Malvern laser light-scattering instrument has been modified for use at scattering angles down to 5° and both total intensity and quasi-elastic scattering experiments. A sample of sheared, length-fractionated calf-thymus DNA was characterized by sedimentation, viscosity and electron microscopy. Quasi-elastic scattering and absolute intensity determinations were performed with the laser instrument and intensity determinations only with a Fica conventional light-scattering photometer. The total intensity experiments gave M?_w = (3.75 ± 0.15) × 10⁶ and 〈R²〉^1/2_z = (206.9 ± 10.3) nm which yielded a value for the persistence length, allowing for polydispersity, of 66 ± 6nm. The quasi-elastic experiments at scattering angles below 20° gave D⁰_{20, w} = (2.23 ± 0.06) × 10^?8 cm²/sec which combined with S⁰_{20, w} = 15.6 in the Svedberg equation gave M?_w = (3.73 ± 0.18) × 10⁶. In addition, from the higher angle data we extracted a value of the longest intramolecular relaxation time, τ1 of 17.5 msec. This is not in particularly good agreement with τ1 predicted by the Zimm–Rouse theory using our other experimental parameters. The disagreement may be due to the restricted applicability of the Zimm–Rouse spring-bead model as a quantitative representation of DNA molecules. Alternatively, it may be due to present difficulties in the unambiguous interpretation of molecular motions from the experimental autocorrelation functions.     

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.     

Diffusion of bovine serum albumin in a neutral polymer solution

The diffusion coefficient D of bovine serum albumin through various solutions (pH 7.0, 0.5M NaCl) of polythylene oxide (M_w ～ 1 × 10⁵, 3 × 10⁵) was studied with quasielastic light scattering. In solutions of the 1 × 10⁵ polymer solution at polymer concentrations above 0.5 g/L, D is considerably greater than would have been expected from the viscosity of water:polymer mixtures, the deviations being larger at low protein concentration that at high protein concentration. With either polymer, D falls with increasing protein concentration.     

Inelastic light scattering studies of solutions of the chloroplast coupling factor (CF1) at high and low ionic strength

The translational diffusion coefficient of CF₁ at low and high protein concentration as well as at different ionic strength (0.05 – 1.65 M) wsa determined by means of quasi-elastic light scattering experiments. The diffusion coefficient changes from D_20,w^o = 3.12 × 10^?7 cm² · sec^?1 at 0.05 M, pH 7.8, 20°C, to D_20,w^o = 3.52 × 10^?7 cm² · sec^?1 at 1.6 M, pH 7.8, 20°C. At high enzyme concentration (20 mg/ml) and under crystallization conditions (Paradies, BBRC 91: 685, 1979) CF₁ behaves as a solution of “true” hard spheres, whereas at low salt concentration the ionic atmosphere has a larger spatial extent, resulting in a higher effective hydrodynamic radius (R_H = 65 Å).     

Transient electric birefringence of the bacteriophages T3 and T7

Electric birefringence measurements of suspensions of T3 and T7 bacteriophages in 10^?2 M phosphate buffer, pH 6.9, show that there is a difference in their rotational diffusion coefficient. The values corrected to 25°C and water viscosity are D_25,w = 4630 ± 130 sec^?1 and D_25,w = 5290 ± 260 sec^?1 for T3 and T7, respectively. The value obtained from shell model calculations (according to Filson and Bloomfield) is D_25,w = 4500 ± 600 sec^?1. The apparent permanent dipole moments are 4.5 × 10^?26 C·m and 1.7 × 10^?26 C·m for T3 and T7, respectively. For both phage particles the intrinsic optical anisotropy is +7.2 × 10^?3. It is shown that this anisotropy is mainly due to the DNA molecule inside the head of the phage. Its positive value means that there exists an excess orientation of the DNA helix perpendicular to the symmetry axis of the particle. For T7 an unexpectedly large increase of Δn_s and K_sp occurs at a glycerol concentration of about 30% (v/v). This increase is interpreted as being caused by a change of the shape of the particle and/or a change in the secondary structure of the DNA inside the head of the bacteriophage.     

Studies on Sugar-isomerizing Enzyme Purification,Crystallization and Some Properties of Glucose Isomerase from Streptomyces sp.

Glucose isomerase was purified by means of acetone fractionation, DEAE-cellulose column chromatography, DEAE-Sephadex column chromatography and crystallization. The purified enzyme appeared to be homogeneous on ultracentrifugation and electrophoresis. The sedimentation coefficient, s_20,w, the diffusion coefficient, D_20,w, and partial specific volume of the enzyme were 8.0S, 4 × 10^?7cm²/sec and 0.69 ml/g, respectively. The molecular weight of the enzyme was estimated to be 157,000 from the sedimentation and diffusion measurements. The crystalline glucose isomerase contained cobalt and magnesium ions. The properties of the enzyme were also studied.     

Physical properties of type i collagen in solution: Structure of α-Chains and β- and γ-components and two-component mixtures

The structure of thermally denatured Type I collagen has been studied using laser light scattering. The results indicate that the diffusion coefficients of α-chains and β- and γ-components are 1.550 ± 0.08 × 10^?7, 1.000 ± 0.05 × 10^?7, and 0.835 ± 0.04 × 10^?7 cm²/sec, respectively, at temperatures between 20 and 40°C. It is concluded from diffusion data that these species have hydrodynamic radii of about 13.8 nm (α-chain), 21.5 nm (β-component), and 25.7 nm (γ-component), consistent with previous studies of thermal denaturation by light scattering. It is also concluded, based on volume calculations, that a large volume increase occurs when the triple helix unfolds. Homodyne correlation functions for two component mixtures of α-chains and β-and γ-components appeared to decay exponentially. In all but one case discussed the correlation function could be fitted with a single component having a translational diffusion coefficient which was an intensity weighted average of the diffusion coefficient of each component present.     

Li+ counterion self-diffusion in ordered DNA

The anisotropic self-diffusion coefficient of ⁷Li⁺ (I = 3/2) counterions has been studied in hydrated, macroscopically oriented Li-(B)DNA fibers at relatively high water contents, corresponding to approximate DNA-DNA helix axis distances of 22–35 Å, using the pulsed field gradient hmr spin-echo method. Self-diffusion coefficients parallel (D_∥) and perpendicular (D_?) to the DNA helix axis increase with increasing salt content and with increasing DNA-DNA helix axis distance. The observed anisotropy D_∥/D_? decreases from 1.6 to 1.2 with the DNA-DNA separation increasing from 22 to 35 Å in the salt-free sample. This result can be understood by the obstruction effect caused by the DNA molecules themselves. The values of the Li⁺ self-diffusion coefficients in the most water-rich system with no added salt (corresponding to an approximate distance of 35 Å between the DNA helix axes) were D_∥ ～ 1.15 × 10^?10 m² s^?1 and D_? ～ 0.98 × 10^?10 m² s^?1, compared to 9.14 × 10^?10 m² s^?1 for the diffusion of Li⁺ in an aqueous solution of LiCl (～ 2.1M). The possible occurrence of restriction effects in the DNA fibers have also been studied by determining the self-diffusion coefficient at different effective diffusion times. The self-diffusion coefficient of Li⁺ in the sample with the largest DNA-DNA helix axis distance seems to be independent of the effective diffusion time, which indicates that the lithium ions are not trapped within impermeable barriers. The possibility of diffusion through permeable barriers has also been investigated, and is discussed. © 1994 John Wiley & Sons, Inc.     

Transient electric birefringence of T-even bacteriophages. II. T4B in the presence of tryptophan and T4D.

Measurements of electric birefringence, sedimentation velocity, and biological adsorption rate are used to study the properties of bacteriophage T4B in the presence of excess tryptophan. The adsorption rate determined in borate buffer pH 9 (at 25°C) increases from 0.003 × 10^?8 ml min^?1 (0.025 M) to 0.130 × 10^?8 ml min^?1 (0.150 M). The Kerr coefficient, rotational diffusion coefficient, and the sedimentation coefficient of the phage are also dependent on buffer concentration and reach plateau values above 0.12 M given by K_sp = ?(275 ± 18) × 10^?9 OD^?1 cm² statvolt^?2, D_25,w = 133 ± 4 sec^?1, and s_20,w = 818 ± 11 S. From a comparison of electric birefringence measurements of T4B and T4D it is concluded that T4D and T4B (in the presence of excess tryptophan) exhibit a similar hydrodynamic behavior. The change in physical parameters is solely due to a shift in fiber configuration. At high buffer concentrations the fibers make an angle of approximately 3π/4 with the sheath and the permanent dipole moment is about 200,000 D. This dipole moment is roughly ten times as large as that of a phage particle with nonextended fibers. This difference may be due to a change in hydrodynamic center upon fiber extension or to the presence of positive charges on the fiber tips, or both. At intermediate buffer concentrations the phage population behaves as if it were monodisperse. Probably not all six fibers are extended under such conditions.     

Dynamic light scattering of the bacteriophage T4B: determination of translational diffusion coefficients and centres of rotation

Using dynamic light scattering, the translational diffusion coefficient (D_T) and the distance between the hydrodynamic centre and the centre of the head (r₀) of the bacteriophage T4B have been determined. For a particle with retracted tail fibres we found D_T20.w =2.88 (2.88 ± 0.02) × 10^?8cm²s^?1 and r₀ = 52 ± 1 nm. For a phage with fully extended tail fibres D_T20w = (.210 ± 0.02) × 10^?8cm²s^?1 and r₀ = 112 ± nm. These data were obtained by interpreting the correlation function using a theory which takes into account the influence of the lollipop shape of the phage. In the literature this influence has not been taken into account, which has led to erroneous values of diffusion coefficients for T4B and other phages. The sedimentation coefficient of T4B phage is 1040 ± 5 S (fibres retracted) or 829 ± 4 S (fibres extended). With the above mentioned diffusion coefficients, these values correspond to a molecular weight of 236 × 10⁶ ± 3 × 10⁶. Finally, the theory used in this study is applied to other bacterial viruses, to correct reported values of the translational diffusion coefficients and of the corresponding molecular weights of these viruses.     

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.     

Diffusion properties of bacteriophages through agarose gel membrane

A simple two‐chamber diffusion method was developed to study the diffusion properties of bacteriophages (phages). The apparent diffusion coefficients (D_app) of Myoviridae phage T4 and filamentous phage fNEL were investigated, and the diffusion of the phages was found to be much slower than the diffusion of three antibiotics, ciprofloxacin, penicillin G, and tetracycline. D_app of T4 and fNEL in water through filter paper were calculated to be 2.8 × 10^?11 m²/s and 6.8 × 10^?12 m²/s, respectively, and D_app of fNEL through agarose gel membrane, an artificial biofilm, was also calculated to be smaller than that of T4. In addition, D_app of phages through agarose gel was dependent on agarose concentration due to the similar size of phage and agarose gel mesh. We concluded that D_app of phages through an artificial biofilm is dependent on both phage morphology and biofilm density, and suggest the use of this method to study diffusion properties through real biofilms. © 2010 American Institute of Chemical Engineers Biotechnol. Prog., 2010     

Hexamer oligonucleotide topology and assembly under solution phase NMR and theoretical modeling scrutiny

The entire family of noncomplementary hexamer oligodeoxyribonucleotides d(GCXYGC) (X and Y = A, G, C, or T) were assessed for topological indicators and equilibrium thermodynamics using a priori molecular modeling and solution phase NMR spectroscopy. Feasible modeled hairpin structures formed a basis from which solution structure and equilibria for each oligonucleotide were considered. ¹H and ³¹P variable temperature‐dependent (VT) and concentration‐dependent NMR data, NMR signal assignments, and diffusion parameters led to d(GCGAGC) and d(GCGGGC) being understood as exceptions within the family in terms of self‐association and topological character. A mean diffusion coefficient D_{298 K} = (2.0 ± 0.07) × 10^?10 m² s^?1 was evaluated across all hexamers except for d(GCGAGC) (D_{298 K} = 1.7 × 10^?10 m² s^?1) and d(GCGGGC) (D_{298 K} = 1.2 × 10^?10 m² s^?1). Melting under VT analysis (T_m = 323 K) combined with supporting NMR evidence confirmed d(GCGAGC) as the shortest tandem sheared GA mismatched duplex. Diffusion measurements were used to conclude that d(GCGGGC) preferentially exists as the shortest stable quadruplex structure. Thermodynamic analysis of all data led to the assertion that, with the exception of XY = GA and GG, the remaining noncomplementary oligonucleotides adopt equilibria between monomer and duplex, contributed largely by monomer random‐coil forms. Contrastingly, d(GCGAGC) showed preference for tandem sheared GA mismatch duplex formation with an association constant K = 3.9 × 10⁵M^?1. No direct evidence was acquired for hairpin formation in any instance although its potential existence is considered possible for d(GCGAGC) on the basis of molecular modeling studies. © 2010 Wiley Periodicals, Inc. Biopolymers 93: 1023–1038, 2010. This article was originally published online as an accepted preprint. The “Published Online” date corresponds to the preprint version. You can request a copy of the preprint by emailing the Biopolymers editorial office at biopolymers@wiley.com     

Transient electric birefringence of T-even bacteriophages. I. T4B in the absence of tryptophan and fiberless T4 particles

Measurements of the electric birefringence of suspensions of T4B in the absence of tryptophan and of fiberless T4 particles show that both kinds of particles are hydrodynamically equivalent. Their rotational diffusion coefficients corrected to 25°C and water viscosity (D_25,w) are 280 ± 9 sec^?1 and 295 ± 10 sec^?1, respectively. These corrected rotational diffusion coefficients are almost independent of buffer concentration and temperature. The sedimentation coefficient (s_20,w) of T4 B is equal to 1023 ± 12 S, a value which is likewise independent of buffer concentration. By analysis of the field strength dependence of the steady-state birefringence and by reversing pulse experiments it could be shown that the orientation in an electric field is largely due to a permanent dipole moment. This dipole moment is somewhat dependent on buffer concentration and amounts to about 24,000 debye for T4B and 95,000 debye for fiberless T4. An approximate calculation shows that the difference in dipole moment may be ascribed to positive charges on the fiber tip (at least ten per fiber), to negative charges along the fiber or (and) positive charges on the fiberless particle at those places where the fibers are attached in normal particles.     

Molecular weight and shape of the phycocyanin hexamer

The hexamer of phycocyanin from Phormidium luridum has been isolated and purified by ammonium sulfate fractionation and gel chromatography. The protein is characterized by the sedimentation constant S°_{20, w} = 10.2S, the diffusion coefficient D_{20, w} = 4.73 × 10^?7 cm²/sec, and intrinsic viscosity [η] = 3.89 ml/g. The molecular weight of the aggregate is 209,000. The shape and dimensions of the hexamer are discussed in terms of a model consisting of subunits arranged with C₆ symmetry. The monomers, assumed to be spherical, are found to have a radius of 22 Å, and the diameter across the hexamer is 132 Å. The latter figure agrees closely with dimensions observed in electron micrographs.