The effect of SDS on protein zone dispersion in polyacrylamide gel electrophoresis

The zone dispersions of the reduced subunit of β-lactoglobulin B and its derivative with sodium dodecyl sulfate (SDS) were measured during polyacrylamide gel electrophoresis (PAGE) using the apparatus for continuous optical scanning at 280 nm. The ratio of apparent diffusion coefficients (D′) of the reduced subunit of β-lactoglobulin B (1.71 × 10^?6 cm²/s) and of its SDS-derivative (7.1 × 10^?7 cm²/s) was found to be 2.4 under the conditions of PAGE (pH 10.4, 0.015 ionic strength, 1°C, 4 mA/cm² current density, 50 μg protein load, 10% T gel) used. This is nearly twice the value of 1.3 predicted, under the assumption of sphericity for these protein molecules, on the basis of the binding of 1.4 g of SDS per gram of protein. It is postulated that the increment in zone sharpness (decrease in apparent diffusion coefficient) over that predicted by SDS binding alone is a general property of SDS-proteins providing gel electrophoresis in SDS-containing buffers with a resolving power larger than that obtained in the absence of the detergent.     

Factors affecting resolution, band width, number of theoretical plates, and apparent diffusion coefficients in polyacrylamide gel electrophoresis

A systematic study of several variables affecting band width and resolution in polyacrylamide gel electrophoresis (PAGE) has been carried out. This makes it possible to determine resolution, number of theoretical plates, and an apparent diffusion coefficient in PAGE. Measurement of band position yields a linear relationship between logarithm of electrophoretic mobility and gel concentration when other variables are held constant. Similarly, measurement of band width yields a linear relationship between the logarithm of the dispersion coefficient (D′) and gel concentration. This makes it possible to extrapolate to 0 gel concentration and to obtain as estimate of a free dispersion coefficient (D′₀) which is usually one or two orders of magnitude greater than the free diffusion coefficient (D_20,w). D′ depends on protein concentration (which is a function of sample load and time), on ionic strength (I), and on duration of electrophoresis (dependent on field strength which in turn depends on ionic strength and current). Since these several variables introduce nonlinear and interrelated correction factors, extrapolation to “infinite ionic strength,” “zero concentration,” and “infinite time” becomes difficult although it is potentially feasible at both the experimental and the theoretical level, and thus it may be possible to determine diffusion coefficients in PAGE on microgram amounts of material without the need for preliminary purification. Alternatively, PAGE in a nonsieving, anticonvectant gel at high ionic strength and for long duration may be able to provide an estimate of D_20,w. The results also support the validity of previously developed approximations for the relationship between band width and gel concentration, and for the relationship between band dispersion and electrophoretic mobility.     

Transient state isoelectric focusing. Experimental determination of apparent diffusion coefficients in polyacrylamide gels

A photoelectric scanning assembly utilizing uv absorption optics and an on-line digital data acquisition and processing system has been used to follow kinetically zone spreading during the defocusing stage (absence of electric field) of transient state isoelectric focusing (TRANSIF) in polyacrylamide gels. Measurement of the variance (σ²) of a diffusing zone as a function of time yields a linear relationship, the slope of which corresponds to the apparent diffusion coefficient (D) of the protein. A linear relationship is also obtained when the logarithm of the apparent diffusion coefficients (logD) are plotted vs acrylamide concentration (T). This relationship can be used to extrapolate D to zero gel concentration. The apparent diffusion coefficient measured in this way is significantly larger than the true diffusion coefficient. The slope of the plot logD vs T, designated C_R, is expected to be a measure of molecular size related to the retardation coefficient in polyacrylamide gel electrophoresis.     

Transient state isoelectric focusing: effects of zone load and carrier ampholyte concentration on the kinetics of defocusing and refocusing in sucrose density gradients

The kinetics of focusing, defocusing, and refocusing of l-histidyl-l-tyrosine in a sucrose density gradient have been studied utilizing a special apparatus for repetitive scanning of the isoelectric focusing column, employing uv absorption optics and a digital data acquisition system. Starting from a uniform or triangular concentration profile, the band is “focused” and a nearly linear pH gradient is formed during initial focusing. The electrical field is then abolished and free diffusion occurs. The electrical field is then reapplied (“refocusing”) and the band is allowed to sharpen, presumably reapproaching a steady state. The band width was measured quantitatively as the second moment about the mean (square of the standard deviation, σ²). In theory, measurements of σ² versus time permit the estimation of the apparent diffusion coefficient (D) and the isoelectric focusing parameter (pE). If the electrical field strength E and the pH gradient, $\text{d(}\text{pH}\text{)}\text{dx}$, were also measured, then one could calculate the slope of the pH mobility curve of the protein $\text{dM}\text{d(}\text{pH}\text{)}$ evaluated at the isoelectric point. D can be measured during the defocusing stage, and $\text{pE,}\text{D}\text{pE}\text{,}\text{or}\text{D}$ can be measured during focusing or refocusing. Several limitations and difficulties in the verification of this theory have been encountered: First, the apparent diffusion coefficient depends on zone load in approximately a linear fashion. Accordingly, it is necessary to measure D at several zone loads, and then extrapolate to zero load by linear regression techniques. Second, the ampholyte concentration has a marked effect on both D and pE. Here we have no a priori reason to extrapolate to zero ampholyte concentration. Also, at present we have no satisfactory method for measurement of E. These preliminary studies should be helpful in indicating further directions for experimental refinement and for generalization of theory.     

Conformation of <Emphasis Type="Italic">Thermus thermophilus</Emphasis> ribosomal protein S1 in solution at different ionic strengths

Small-angle x-ray and neutron scattering were used to study the structure of the ribosomal protein S1 (61 kDa) from Thermus thermophilus in solution at low and moderate ionic strength (0 and 100 mM NaCl). The protein was found to be globular in both cases. Modeling of the S1 structure comprising six homologous domains on the basis of the NMR data for one domain showed that the best fit to scattering data was provided by compact domain packing. The calculated gyration radius was 28–29 Å, as typical of globular proteins about 60 kDa. The protein was prone to self-association, forming mainly dimers and trimers at moderate ionic strength and higher compact associates at low ionic strength. Neutron scattering assays in heavy water at 100 mM NaCl revealed markedly elongated associates. The translational diffusion coefficient calculated for S1 at 100 mM NaCl from dynamic light scattering was markedly lower than the one expected for its globular monomer (D _20,w = (2.7 ± 0.1)·10^?7 versus (5.8–6.0)·10^?7 cm² s^?1), confirming protein association under equilibrium conditions.     

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).     

Diffusion of insulin-like growth factor-I and ribonuclease through fibrin gels

A fluorescence-based method for simultaneously determining the diffusion coefficients of two proteins is described, and the diffusion coefficient of insulin-like growth factor (IGF-I) and ribonuclease (RNase) in a 0.27% fibrin hydrogel is reported. The method is based on two-color imaging of the relaxation of the protein concentration field with time and comparing the results with a transport model. The gel is confined in a thin (200 μm) capillary and the protein is labeled with a fluorescent dye. The experimentally determined diffusion coefficient of RNase (D = 1.21 × 10⁻⁶ cm²/s) agrees with literature values for dilute gels and bulk aqueous solutions, thus indicating the gel and the dye had a negligible effect on diffusion. The experimental diffusion coefficient of IGF-I (D = 1.59 × 10⁻⁶ cm²/s), in the absence of binding to the fibrin matrix, is consistent with the dimensions of the molecule known from x-ray crystallography and a correlation between D and molecular weight based on 14 other proteins. The experimental method developed here holds promise for determining molecular transport properties of biomolecules under a variety of conditions, for example, when the molecule adsorbs to the gel or is convected through the gel by fluid transport.     

Translational diffusion in the plasma membrane of sea urchin eggs

Translational diffusion in the plasma membrane of individual egg cells from the sea urchin species Paracentrotus lividus has been studied by fluorescence microphotolysis (FM). In order to probe the lipid phase of the membrane, procedures have been worked out by which the fluorescent analog 3,3′-dioctadecyl-oxatricarbocyanine (C₁₈diO) can be incorporated into the membrane. In the unfertilized egg a fraction R = 0.9 of C₁₈diO was mobile having an apparent diffusion coefficient of D = 6.0 × 10^?9 cm² sec^?1. Fifteen to twenty-five minutes after fertilization R and D were reduced to 0.8 and 2.7 × 10^?9 cm² sec^?1, respectively. In order to study diffusion of membrane proteins, procedures have been worked out by which the cell surface can be labeled with fluorescein-isothiocyanate (FITC). FITC binds to both the plasma membrane and the vitelline layer. Together with the vitelline layer two-thirds of the FITC-fluorescence could be removed from the egg surface. Gel electropherograms of isolated egg cortices showed various protein bands; however, only two of the protein bands were labeled with FITC. In the unfertilized egg a fraction R = 0.9 of the FITC-labeled membrane proteins was mobile having an apparent diffusion coefficient of D = 35 × 10^?11 cm² sem^?1. Fiteen to twenty-five minutes after fertilization R and D were reduced to 0.8 and 7.0 × 10^?11 cm² sec^?1, respectively. FITC-labeled proteins of the fertilization envelope were immobile. Our studies have shown (i) that the egg surface can be fluorescently labeled without blocking fertilization and early development, (ii) that the plasma membrane of unfertilized eggs is a fluid environment permitting a rapid movement of lipids and proteins, and (iii) that after fertilization a substantial degree of lipid and protein mobility is maintained.     

Diffusion NMR-based comparison of electrostatic influences of DNA on various monovalent cations

Counterions are important constituents for the structure and function of nucleic acids. Using ⁷Li and ¹³³Cs nuclear magnetic resonance (NMR) spectroscopy, we investigated how ionic radii affect the behavior of counterions around DNA through diffusion measurements of Li⁺ and Cs⁺ ions around a 15-bp DNA duplex. Together with our previous data on ²³Na⁺ and ¹⁵NH₄⁺ ions around the same DNA under the same conditions, we were able to compare the dynamics of four different monovalent ions around DNA. From the apparent diffusion coefficients at varied concentrations of DNA, we determined the diffusion coefficients of these cations inside and outside the ion atmosphere around DNA (D_b and D_f, respectively). We also analyzed ionic competition with K⁺ ions for the ion atmosphere and assessed the relative affinities of these cations for DNA. Interestingly, all cations (i.e., Li⁺, Na⁺, NH₄⁺, and Cs⁺) analyzed by diffusion NMR spectroscopy exhibited nearly identical D_b/D_f ratios despite the differences in their ionic radii, relative affinities, and diffusion coefficients. These results, along with the theoretical relationship between diffusion and entropy, suggest that the entropy change due to the release of counterions from the ion atmosphere around DNA is also similar regardless of the monovalent ion types. These findings and the experimental diffusion data on the monovalent ions are useful for examination of computational models for electrostatic interactions or ion solvation.     

Hydrodynamic properties of nitrogenase — the MoFe protein from Azotobacter vinelandii studied by dynamic light scattering and hydrodynamic modelling

Experimental results for the nitrogenase MoFe protein from Azotobacter vinelandii obtained by dynamic light scattering (DLS) are presented. The translational diffusion coefficient was determined to D=(4.0±0.2)×10⁻⁷ cm²/s. Complementary, we have performed hydrodynamic model calculations based on the X-ray crystallographic data of the MoFe protein. The calculated transport coefficient suggests that the size and shape of the protein in solution is consistent with that in the crystal structure.     

The Molecular Weight and Other Biophysical Properties of Bromegrass Mosaic Virus

Data are presented which show that bromegrass mosaic virus has a particularly low molecular weight and nucleic acid content. A molecular weight of 4.6 × 10⁶ was calculated from the sedimentation coefficient, S°_20,w = 86.2S, the diffusion coefficient, D_20,w = 1.55 × 10^-7 cm²/sec., and an assumed partial specific volume, [UNK] = 0.708 ml/gm. The virus has a ribonucleic acid content of 1.0 × 10⁶ atomic mass units. Electrophoresis experiments showed that the virus is stable in 0.10 ionic strength buffers in the pH range 3-6. Breakdown of the virus was observed outside this pH range. Some characteristics of the breakdown products are described.     

A quasi-elastic laser light scattering study of tubulin and microtubule protein from bovine brain

Quasi-elastic light scattering has been used to characterize the oligomeric properties of solutions of glycerol-cycled bovine microtubule protein, and the properties of the 30 S oligomeric species and 6 S tubulin heterodimer prepared by gel filtration on Sepharose 6B. It is shown that in dimer preparations, as little as 0.04% by number of 30 S rings would account for the difference between an observed mean diffusion coefficient D_{20, W} = 3.1 × 10^?7 cm² s^?1 and the value of D_{20, W} = 5.1 × 10^?7 cm² s^?1 calculated for tubulin dimer of M_rel 100,000. The 30 S ring has an observed diffusion coefficient of D_{20, W} = 0.49 × 10^?7 cm² s^?1. These values are not changed significantly by the presence of 4 m-glycerol, indicating the persistence of 6 S and 30 S forms for dimer and ring, respectively.Mixtures of ring and dimer components of this preparation behave as a non-interacting two-component system, indicating the absence of substantial re-equilibration between the species at 5 °C and pH 6.5.The effect of salt on ring and microtubule protein samples indicates partial dissociation, consistent with the formation of additional intermediate oligomeric forms.In quasi-elastic light scattering measurements adapted to kinetic studies, changes in the oligomeric composition of microtubule protein are detected in the early stages of the reversible assembly process at pH 6.5. A 25% decrease in scattered light intensity, without significant change in mean diffusion coefficient, indicates the lability of the ring oligomeric structures, which undergo partial transformation to alternative oligomeric species under these assembly conditions.     

Signatures of Mechanosensitive Gating

The question of how mechanically gated membrane channels open and close is notoriously difficult to address, especially if the protein structure is not available. This perspective highlights the relevance of micropipette-aspirated single-particle tracking—used to obtain a channel’s diffusion coefficient, D, as a function of applied membrane tension, σ—as an indirect assay for determining functional behavior in mechanosensitive channels. While ensuring that the protein remains integral to the membrane, such methods can be used to identify not only the gating mechanism of a protein, but also associated physical moduli, such as torsional and dilational rigidity, which correspond to the protein’s effective shape change. As an example, three distinct D-versus-σ “signatures” are calculated, corresponding to gating by dilation, gating by tilt, and gating by a combination of both dilation and tilt. Both advantages and disadvantages of the approach are discussed.     

Lateral diffusion and patch formation of H-2Kk antigens on mouse spleen lymphocytes

We have studied the diffusion and aggregation of H-2K^k antigens labeled with a fluorescent anti-H-2K^k monoclonal antibody (IgG) on mouse splenic lymphocytes, employing fluorescence photobleaching recovery and fluorescence microscopy. The H-2K^k antigens were initially distributed homogeneously on all lymphocytes. Upon antibody binding, sub-micron patches were formed on 50–60% of the cells. A lateral diffusion coefficient, D, of 7.1·10^?10 cm²/s and a mobile fraction of 0.73 were found for H-2K^k antigens on diffusely-labeled cells, while these antigens were immobile (D?5·10^?12 cm²/s) on patched cells. The patched and nonpatched sub-populations did not correspond to B- and T-lymphocytes. Subjection to low temperature or treatment with NaN₃ or cytoskeleton-disrupting drugs did not affect the diffusion or patching of H-2K^k, indicating no involvement of metabolic energy or drug-sensitive cytoskeletal components. These findings could be related to the interactions of H-2 antigens on the cell surface, and to the different susceptibilities of various cells to lysis by cytotoxic T-cells.     

Photon correlation spectroscopy of human IgG

The translational diffusion coefficient D _20,w ⁰ , of monomeric human immunoglobulin G (IgG) has been studied by photon-correlation spectroscopy as a function of pH and protein concentration. At pH 7.6, we find D _20,w ⁰ =3.89×10^–7±0.02 cm²/sec, in good agreement with the value determined by classic mehods. This value corresponds to an effective hydrodynamic radius R, of 55.1±0.3 Å. As pH is increased to 8.9; with the same ionic strength, the molecule appears to expand slightly (3.5% increase in hydrodynamic radius). The concentration dependence of the IgG diffusion constant is interpreted in terms of solution electrostatic effects and shows that long-range repulsive interactions are negligible in the buffer used. The diffusion coefficient for dimeric IgG has also been determined to be D_20,w=2.81×10^–7±0.04 cm²/sec at 1.6 mg/ml, which corresponds to a hydrodynamic radius of 75 Å. For light-scattering studies of protein molecules in the dimension range of 5–10 nm (M_r=10⁵–10⁷) we find monomeric horse spleen ferritin well suited as a reference standard. Ferritin is a spherical molecule with a hydrodynamic radius R of 6.9±0.1 nm and is stable for years in our standard Tris-HCl-NaCl buffer even at room temperature.     

Diffusion Coefficients of Endogenous Cytosolic Proteins from Rabbit Skinned Muscle Fibers

Efflux time courses of endogenous cytosolic proteins were obtained from rabbit psoas muscle fibers skinned in oil and transferred to physiological salt solution. Proteins were separated by gel electrophoresis and compared to load-matched standards for quantitative analysis. A radial diffusion model incorporating the dissociation and dissipation of supramolecular complexes accounts for an initial lag and subsequent efflux of glycolytic and glycogenolytic enzymes. The model includes terms representing protein crowding, myofilament lattice hindrance, and binding to the cytomatrix. Optimization algorithms returned estimates of the apparent diffusion coefficients, D(r,t), that were very low at the onset of diffusion (∼10⁻¹⁰ cm² s⁻¹) but increased with time as cytosolic protein density, which was initially high, decreased. D(r,t) at later times ranged from 2.11 × 10⁻⁷ cm² s⁻¹ (parvalbumin) to 0.20 × 10⁻⁷ cm² s⁻¹ (phosphofructose kinase), values that are 3.6- to 12.3-fold lower than those predicted in bulk water. The low initial values are consistent with the presence of complexes in situ; the higher later values are consistent with molecular sieving and transient binding of dissociated proteins. Channeling of metabolic intermediates via enzyme complexes may enhance production of adenosine triphosphate at rates beyond that possible with randomly and/or sparsely distributed enzymes, thereby matching supply with demand.     

Conformational change of core particles studied by quasielastic light scattering

The diffusion translational coefficient D_T of core particles in monodisperse solutions has been measured by the quasielastic light scattering method in a large scale of salinities over the range 6.10⁻⁴ to 2M Na⁺ or K⁺. The observed values of D_T are independent of particle concentration in the range 0.1–2 mg/ml and do not vary with the scattering vector q corresponding to scattering angles between 40°–120°. When the salinity is progressively raised an increase of D_T from 1.9.10⁻⁷ cm²s⁻¹ to 3.2.10⁻⁷ cm²s⁻¹ was observed at about 2.10⁻³ M NaCl followed by a decrease of D_T beyond 0.6 M NaCl.The various possible causes of the changes of D_T such as interactions between particles or between particles and salt ions are discussed. We show that the single low ionic strength change is due to a conformational transition of the core particles, while the second variation of D_T accompanies the disorganization of the core particles.     

Diffusion Coefficients of Endogenous Cytosolic Proteins from Rabbit Skinned Muscle Fibers

Efflux time courses of endogenous cytosolic proteins were obtained from rabbit psoas muscle fibers skinned in oil and transferred to physiological salt solution. Proteins were separated by gel electrophoresis and compared to load-matched standards for quantitative analysis. A radial diffusion model incorporating the dissociation and dissipation of supramolecular complexes accounts for an initial lag and subsequent efflux of glycolytic and glycogenolytic enzymes. The model includes terms representing protein crowding, myofilament lattice hindrance, and binding to the cytomatrix. Optimization algorithms returned estimates of the apparent diffusion coefficients, D(r,t), that were very low at the onset of diffusion (∼10⁻¹⁰ cm² s⁻¹) but increased with time as cytosolic protein density, which was initially high, decreased. D(r,t) at later times ranged from 2.11 × 10⁻⁷ cm² s⁻¹ (parvalbumin) to 0.20 × 10⁻⁷ cm² s⁻¹ (phosphofructose kinase), values that are 3.6- to 12.3-fold lower than those predicted in bulk water. The low initial values are consistent with the presence of complexes in situ; the higher later values are consistent with molecular sieving and transient binding of dissociated proteins. Channeling of metabolic intermediates via enzyme complexes may enhance production of adenosine triphosphate at rates beyond that possible with randomly and/or sparsely distributed enzymes, thereby matching supply with demand.