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.     

Characterization of Phospholipid Mixed Micelles by Translational Diffusion

The concentration dependence of the translational self diffusion rate, D (s), has been measured for a range of micelle and mixed micelle systems. Use of bipolar gradient pulse pairs in the longitudinal eddy current delay experiment minimizes NOE attenuation and is found critical for optimizing sensitivity of the translational diffusion measurement of macromolecules and aggregates. For low volume fractions Phi (Phi\\ le 15% v/v) of the micelles, experimental measurement of the concentration dependence, combined with use of the D (s)= D (o)(1-3.2lambdaPhi) relationship, yields the hydrodynamic volume. For proteins, the hydrodynamic volume, derived from D (s) at infinitely dilute concentration, is found to be about 2.6 times the unhydrated molecular volume. Using the data collected for hen egg white lysozyme as a reference, diffusion data for dihexanoyl phosphatidylcholine (DHPC) micelles indicate approximately 27 molecules per micelle, and a critical micelle concentration of 14 mM. Differences in translational diffusion rates for detergent and long chain phospholipids in mixed micelles are attributed to rapid exchange between free and micelle-bound detergent. This difference permits determination of the free detergent concentration, which, for a high detergent to long chain phospholipid molar ratio, is found to depend strongly on this ratio. The hydrodynamic volume of DHPC/POPC bicelles, loaded with an M2 channel peptide homolog, derived from translational diffusion, predicts a rotational correlation time that slightly exceeds the value obtained from peptide (15)N relaxation data.     

Diagnostic of precipitant for biomacromolecule crystallization by quasi-elastic light-scattering

The translational diffusion coefficient D25,w of hen egg-white lysozyme and concanavalin A from the jack bean is measured in various precipitating agent solutions as a function of salt and protein concentration using quasi-elastic light-scattering. With some precipitants, in undersaturated protein solutions, a protein or salt concentration dependence of the diffusion coefficient of the scatters is observed. It can be correlated with the inability of the protein to crystallize in this precipitant once the solution is supersaturated. These variations of D25,w are interpreted in terms of non-specific interactions and/or aggregation that prevent the protein from making appropriate contacts to form a crystal. With other precipitants known to lead to crystallization, no significant variation of the diffusion coefficient with increasing concentration was observed, indicating that under such conditions up to saturation the proteins remain essentially monodisperse. Application of this technique to find crystallization conditions of other proteins is discussed.     

Hyperthermophilic redox chemistry: a re-evaluation

The redox chemistry of Pyrococcus furiosus rubredoxin and ferredoxin has been studied as a function of temperature in direct voltammetry and in EPR monitored bulk titrations. The E_ms of both proteins, measured with direct voltammetry, have a normal (linear) temperature dependence and show no pH dependence. EPR monitoring is not a reliable method to determine the temperature dependence of the E_m: upon rapid freezing the proteins take their conformation corresponding to the freezing point of the solution.     

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.     

The binding of a neutral aromatic molecule to a negatively-charged lipid membrane. II. Kinetics and mechanism

The kinetics of the binding of the fluorescence indicator N-phenyl naphthylamine to bilayer vesicles of C12-methyl-phosphatidic acid have been investigated by means of the temperature-jump relaxation technique utilizing fluorescence light detection. Single-exponential relaxation curves were observed, with time constants in the range 0.2-3 ms. The concentration dependence of the relaxation time yielded an apparent association rate constant (expressed in terms of monomeric phospholipid) of k(on) = 5 x 10(6) M(-1) s(-1) in aqueous solution at 25 degrees . The activation energy and viscosity dependence associated with the binding rate show that this process is actually diffusion-controlled. The theory of diffusion-controlled reactions then allows a determination of the average size of the bilayer vesicles and of the true rate constant for the association of the indicator molecules with the vesicles. Assuming spherical geometry for the vesicles, the values are: r(ves) = 190 A, which corresponds to 20000 lipid molecules per vesicle and k'(on) = 1 x 10(11) M(-1) s(-1) (25 degrees). The correctness of this size-determination was confirmed semi-quantitatively by electron microscopy. Since in fact a distribution of vesicle sizes must be present, a discussion is included of the relaxation function which the system is expected to take in the general case. Biological implications of diffusion control for the transport of non-polar substances and for lipid mixing are indicated.     

Diffusion of H-meromyosin in F-actin plus ATP solution at a very low electrolyte concentration

The translational diffusion coefficient (D) of H-meromyosin in actin (F-actin) and ATP solution was measured under conditions wherein the actin-activated ATPase activity is close to its maximal value at a very low electrolyte concentration. The results were compared with similar data obtained with 0.1 M KCl, where H-meromyosin and actin were almost completely dissociated. With 0.1 M KCl, it was found that there was no dependence of the D of H-meromyosin on actin concentration. On the other hand, at a very low electrolyte concentration, it was found that the D of H-meromyosin did depend on actin concentration; at a rather high actin concentration (and activation of ATPase), it was slightly larger than at low or zero actin concentrations. This behavior of D at a low electrolyte concentration is interpreted on the assumption that even in solution, H-meromyosin molecules can actively slide on actin filaments due to the ATPase activity.     

Anomalous diffusion of proteins due to molecular crowding

We have studied the diffusion of tracer proteins in highly concentrated random-coil polymer and globular protein solutions imitating the crowded conditions encountered in cellular environments. Using fluorescence correlation spectroscopy, we measured the anomalous diffusion exponent alpha characterizing the dependence of the mean-square displacement of the tracer proteins on time, r(2)(t) approximately t(alpha). We observed that the diffusion of proteins in dextran solutions with concentrations up to 400 g/l is subdiffusive (alpha < 1) even at low obstacle concentration. The anomalous diffusion exponent alpha decreases continuously with increasing obstacle concentration and molecular weight, but does not depend on buffer ionic strength, and neither does it depend strongly on solution temperature. At very high random-coil polymer concentrations, alpha reaches a limit value of alpha(l) approximately 3/4, which we take to be the signature of a coupling between the motions of the tracer proteins and the segments of the dextran chains. A similar, although less pronounced, subdiffusive behavior is observed for the diffusion of streptavidin in concentrated globular protein solutions. These observations indicate that protein diffusion in the cell cytoplasm and nucleus should be anomalous as well, with consequences for measurements of solute diffusion coefficients in cells and for the modeling of cellular processes relying on diffusion.     

Electron paramagnetic resonance characterization of the exopolysaccharide layer produced by bacteria

In order to establish a method to characterize the structural heterogeneity of the bacterial surface, research was conducted with a combination of experiments based on electron paramagnetic resonance (EPR) concentration-imaging (CI) and the modeling of translational diffusion with local restrictions. The benefits and drawbacks of this approach are discussed for the Vibrio sp. exopolysaccharide (EPS) layer.     

A method for estimating lateral diffusion coefficients in membranes from steady-state fluorescence quenching studies.

The Stern-Volmer theory, in which the quantum yield ratio (Io/I) depends linearly on the quencher concentration, will typically be inapplicable to fluorescence quenching in membranes. Numerical analysis shows that diffusion-controlled quenching results in a nonlinear concentration dependence for diffusion coefficients less than or of the order of 10(-6) cm2 s-1 and probe fluorescence lifetimes in the region of 10-100 ns. Lateral diffusion coefficients in membranes are typically overestimated an order of magnitude or more by the Stern-Volmer theory. An alternative empirical method is presented, which represents nonlinear concentration curves by a single parameter linear approximation determined by a least-squares analysis. The fitting parameter, P, depends on the interaction distance, the membrane thickness, the maximum extent of quenching and, in the case of biexponential probe fluorescence decay, the fluorescence kinetic parameters. P is presented in tabular form for a useful range of these parameters. The method is used to estimate diffusion coefficients for plastoquinone and plastoquinol from pyrene fluorescence quenching in soya bean phosphatidylcholine liposomes. It is found that the diffusion coefficients are nearly equal and in the region of 1.3-3.5 X 10(-7) cm2 s-1 for interaction radii of 1.5-0.5 nm, respectively.     

Size dependence of the translational diffusion of large integral membrane proteins in liquid-crystalline phase lipid bilayers. A study using fluorescence recovery after photobleaching

The translational diffusion of bovine rhodopsin, the Ca2+-activated adenosinetriphosphatase of rabbit muscle sarcoplasmic reticulum, and the acetylcholine receptor monomer of Torpedo marmorata has been examined at a high dilution (molar ratios of lipid/protein greater than or equal to 3000/1) in liquid-crystalline phase phospholipid bilayer membranes by using the fluorescence recovery after photobleaching technique. These integral membrane proteins having molecular weights of about 37 000 for rhodopsin, about 100 000 for the adenosinetriphosphatase, and about 250 000 for the acetylcholine receptor were reconstituted into membranes of dimyristoylphosphatidylcholine (rhodopsin and acetylcholine receptor), soybean lipids (acetylcholine receptor), and a total lipid extract of rabbit muscle sarcoplasmic reticulum (adenosinetriphosphatase). The translational diffusion coefficients of all the proteins at 310 K were found to be in the range (1-3) X 10(-8) cm2/s. In consideration of the sizes of the membrane-bound portions of these proteins, this result is in agreement with the weak dependence of the translational diffusion coefficient upon diffusing particle size predicted by continuum fluid hydrodynamic models for the diffusion in membranes [Saffman, P. G., & Delbrück, M. (1975) Proc. Natl. Acad. Sci. U.S.A. 72, 3111-3113]. Lipid diffusion was also examined in th same lipid bilayers with the fluorescent lipid derivative N-(7-nitro-2,1,3-benzoxadiazol-4-yl)dimyristoylphosphatidylethanolamine. The translational diffusion coefficient for this lipid derivative was found to be in the range (9-14) X 10(-8) cm2/s at 310 K. In consideration of the dimensions of the lipid molecule, this value for the lipid diffusion coefficient is in agreement with the continuum fluid hydrodynamic model only if a near-complete slip boundary condition is assumed at the bilayer midplane. Alternatively, kinetic diffusion models [Tr?uble, H., & Sackmann. E. (1972) J. Am. Chem. Soc. 94, 4499-4510] may have to be invoked to explain the lipid diffusion behavior.     

Analysis of Reaction-Diffusion Systems with Anomalous Subdiffusion

Reaction-diffusion equations are the cornerstone of modeling biochemical systems with spatial gradients, which are relevant to biological processes such as signal transduction. Implicit in the formulation of these equations is the assumption of Fick's law, which states that the local diffusive flux of species i is proportional to its concentration gradient; however, in the context of complex fluids such as cytoplasm and cell membranes, the use of Fick's law is based on empiricism, whereas evidence has been mounting that such media foster anomalous subdiffusion (with mean-squared displacement increasing less than linearly with time) over certain length scales. Particularly when modeling diffusion-controlled reactions and other systems where the spatial domain is considered semi-infinite, assuming Fickian diffusion might not be appropriate. In this article, two simple, conceptually extreme models of anomalous subdiffusion are used in the framework of Green's functions to demonstrate the solution of four reaction-diffusion problems that are well known in the biophysical context of signal transduction: fluorescence recovery after photobleaching, the Smolochowski limit for diffusion-controlled reactions in solution, the spatial range of a diffusing molecule with finite lifetime, and the collision coupling mechanism of diffusion-controlled reactions in two dimensions. In each case, there are only subtle differences between the two subdiffusion models, suggesting how measurements of mean-squared displacement versus time might generally inform models of reactive systems with partial diffusion control.     

The concentration dependence of the diffusion coefficient for bovine pancreatic trypsin inhibitor: a dynamic light scattering study of a small protein

This paper reports the use of dynamic light scattering to investigate the concentration dependence of the diffusion coefficient for bovine pancreatic trypsin inhibitor (BPTI). BPTI is a small molecular weight protein (6511 Da) that has been the subject of numerous experimental studies. In addition to addressing questions that remain in the literature concerning the aggregation behavior of BPTI, we show that dynamic light scattering can be practically applied to proteins as small as BPTI, and that it can provide a useful means of parameterizing the solution behavior for proteins. We obtained values for the apparent diffusion coefficient of BPTI as a function of concentration over a range of pH values from 2.59 to 9.92 at an ionic strength of 0.3M, and over a range of ionic strength values from 0.1 to 0.5M at a pH of 7.0. The concentration dependence is linear for nearly all the conditions examined, even up to concentrations as high as 65 mg/mL. The average diffusion coefficient obtained at infinite dilution is 14.4 +/- 0.2 x 10(-7) cm2/s. This value agrees with that expected for a BPTI monomer hydrated with less than a monolayer of water. We used the theories of Felderhof, of Batchelor, and of Phillies, along with the DLVO theory to interpret the concentration dependence of the apparent diffusion coefficient. The variations observed with pH and ionic strength can be primarily attributed to screened coulombic interactions. In addition, there is an attractive interaction that is slightly stronger than the repulsive coulombic one, and that is essentially independent of pH and ionic strength. The attractive interactions appear to arise from nonspecific van der Waals interactions and do not lead to the formation of stable aggregates of BPTI.     

Intensity-fluctuation spectroscopy and tRNA conformation. II. Changes of size and shape of tRNA in the melting process

We have measured the translational (D^T) and rotational (D^R) diffusion coefficients of bulk tRNA from baker's yeast during the thermal unfolding process by means of photon-correlation spectroscopy. It should be noted that our estimate of the rotational diffusion coefficient represented, for the first time, measurements on a small macromolecule in solution by the photoelectron time-of-arrival technique with a delay-time resolution of 1 nsec. The melting curves expressed in terms of δD^T vs temperature were consistent with the literature data in revealing the melting steps and their dependence on NaCl concentration. Additionally, it was possible to prove the existence of an intermediate, more compact structure during the initial steps of the thermal unfolding process. We found that the temperature ranges over which this intermediate structure appears depend strongly on salt concentration. By utilizing both translational and rotational diffusion coefficients and Perrin's equations for ellipsoids of revolution, we have computed the values of the equivalent length and width of tRNA molecules in solution at four different temperatures for NaCl concentrations of 0.2, 0.5, and 1M. The approximate model of ellipsoids of revolution also permits us to obtain an estimate of the radius of gyration, which is in very good agreement with literature data measured by means of small-angle x-ray scattering. Furthermore, we have measured the shape and size changes of tRNA with varying NaCl concentrations at room temperatures (25°C). The molecule becomes smaller and more spherical when NaCl concentration increases. As a result of partial melting at 70°C, the macromolecule is surprisingly elongated with an approximate axial ratio of 8:1 and has dimensions of about 180/22Å. Such information on conformational changes by a simultaneous determination of rotational and translational diffusion coefficients illustrates the potential of this approach, not available by other methods.     

A kinetic, chromatographic method for studying protein hydrodynamic behavior

A chromatographic method based on "split-peak" behavior was described for the determination of the coefficient of mass transfer of proteins on small reversed-phase columns. The coefficient of mass transfer was found to be a linear function of the protein translational diffusion coefficient and inversely proportional to the square of the support particle diameter, as predicted by chromatographic theory. As an example of the practical application of this method for the measurement of protein diffusion coefficients, the denaturation of bovine serum albumin with decreasing solution pH was followed by measuring the change in the coefficient of mass transfer. A major advantage of this method was that the results were not affected by the interaction of the protein with the stationary phase.     

Translational diffusion of fluorescent proteins by molecular fourier imaging correlation spectroscopy

The ability to noninvasively observe translational diffusion of proteins and protein complexes is important to many biophysical problems. We report high signal/noise (>or=250) measurements of the translational diffusion in viscous solution of the fluorescent protein, DsRed. This is carried out using a new technique: molecular Fourier imaging correlation spectroscopy (M-FICS). M-FICS is an interferometric method that detects a collective Fourier component of the fluctuating density of a small population of fluorescent molecules, and provides information about the distribution of molecular diffusivities. A theoretical analysis is presented that expresses the detected signal fluctuations in terms of the relevant time-correlation functions for molecular translational diffusion. Furthermore, the role played by optical orientational degrees of freedom is established. We report Fickian self-diffusion of the DsRed tetramer at short timescales. The long-time deviation of our data from Fickian behavior is used to determine the variance of the distribution of the protein self-diffusion coefficient. We compare our results to the expected outcomes for 1), a bi-disperse distribution of protein species, and 2), dynamic disorder of the host solvent.     

Probe diffusion in aqueous poly(vinyl alcohol) solutions studied by fluorescence correlation spectroscopy

We report fluorescence correlation spectroscopy measurements of the translational diffusion coefficient of various probe particles in dilute and semidilute aqueous poly(vinyl alcohol) solutions. The range of sizes of the particles (fluorescent molecules, proteins, and polymers) was chosen to explore various length scales of the polymer solutions as defined by the polymer-polymer correlation length. For particles larger than the correlation length, we find that the diffusion coefficient, D, decreases exponentially with the polymer concentration. This can be explained by an exponential increase in the solution viscosity, consistent with the Stokes-Einstein equation. For probes on the order of the correlation length, the decrease of the diffusion coefficient cannot be accounted for by the Stokes-Einstein equation, but can be fit by a stretched exponential, D approximately exp(-alphacn), where we find n = 0.73-0.84 and alpha is related to the probe size. These results are in accord with a diffusion model of Langevin and Rondelez (Polymer 1978, 19, 1875), where these values of n indicate a good solvent quality.     

Salt dependent changes in structure and dynamics of circular single stranded DNA of filamentous phages of Escherichia coli

We have analyzed the static and dynamic behaviour of the circular single stranded DNA of the filamentous Escherichia coli phages F1 and M13mp8 in solution as a function of salt concentration using static and dynamic light scattering and sedimentation analysis in the analytical ultracentrifuge. We show by static light scattering that native and denatured single stranded DNA behave like a randomly coiled macromolecule at all salt concentrations used. The size of the native single stranded DNA is governed by the formation of secondary structures. While the radius of gyration decreases with increasing salt concentration the translational diffusion of the center-of-mass of native single stranded DNA and the sedimentation coefficient increase with increasing salt concentration in a biphasic manner. Below 100 mM monovalent cation concentration there is a strong dependence of the hydrodynamic parameters upon salt which is reduced approx. 3-fold at higher salt concentrations. We attribute the compaction of single stranded DNA by salt to electrostatic shielding and, in case of native single stranded DNA, secondary structure formation. Internal motions of the native single stranded DNA are observable at all salt concentrations and can be interpreted with a model of segmental diffusion of the elements of the polymer chain. The observed segmental diffusion coefficient of the native single stranded polynucleotide increases with increasing salt under the conditions investigated.     

A method for measuring sedimentation and diffusion of macromolecules in capillary tubes by total intensity and quasi-elastic light-scattering techniques.

Light scattered from a macromolecular solution in a capillary tube is used to determine both the sedimentation and translational diffusion coefficients. The capillary tube is spun in a preparative centrifuge, removed, and placed in a light-scattering photometer equipped with a scanning mechanism. The intensity distribution of scattered light along the tube represents the concentration profile in the tube and provides the measure of boundary migration. The sedimentation coefficient is determined from this measure and the applied centrifugal field. The diffusion coefficient is obtained from a time-autocorrelation analysis of fluctuations in intensity of light scattered from any fixed point of the profile. These coefficients were obtained for two monodisperse systems, R17 bacteriophage and 28s ribosomal rat liver RNA. The molecular weights obtained from ratios of these coefficients are in good agreement with literature values. In the sedimentation analysis, deviations from linearity between boundary displacement and applied field were found to be less than 1%. This precision confirms that the boundary is stable for the capillary geometry even in the absence of a preformed density gradient. The sedimentation coefficients of identical samples were also measured with the Spinco Model E analytical ultracentrifuge; results of the two methods agree to within 4%. As a consequence of the capillary tube geometry and light-scattering detection, sedimentation coefficients can be obtained from sample volumes of less than 100 μl. This detection techniques is thus far demonstrated to be at least an order of magnitude more sensitive than Schlieren optics, thereby useful when uv absorption is not applicable. For diffusion measurements there are also several inherent advantages. The diffusion coefficient is obtained from the identical sample, and scanning provides the capability to measure D from various parts of the sedimentation profiles and thereby directly explore concentration dependence, homogeneity, and integrity of the sample. The capillary tube with a layer of silicone oil over the sample and centrifugation provides an effective method to cleanse the solution and trap all dust.