Effective hydrodynamic radii

SG Schultz, AK Solomon. Determination of the effective hydrodynamic radii of small molecules by viscometry. J Gen Physiol 44 1189-1199, 1961. 

Figure 2. Effective hydrodynamic radii as a function of polymer concentration for a series of sodium sulfonated polystyrenes In tetrahydrofuran. (Reproduced from ref. 6. Copyright 1987 American Chemical Society.)...

Molecular sizes of the 1 1 pairs were compared as effective hydrodynamic radii, estimated using the Stokes-Einstein equation D = kT/67CT)r, (D is the diffusion coefficient... 

A (3 fibril formation an identifiable nucleating species has yet be isolated. Direct observation has been made difficult by the small size of the (3 peptide, which has an effective hydrodynamic radius of 4 nm [98-100], and by the apparent low abundance of nucleating species due to the low probability of their formation. Such species would be formally akin to an enzyme transition state that is usually kinetically inferred or sometimes trapped with certain kinds of inhibitor. In disaggregated, ultrafiltered (20 nm pore size) preparations, less than 1% of the molar peptide concentration is inferred to be present as seeds or nuclei determined by the kinetics of fibril formation [101]. 

Britzinger and coworkers [306[ have studied the polymerization catalyst MAO/ ZrCp2Me2 in C5D5. The calculated effective hydrodynamic radius of 12.2-12.5 A... 

The z-averag translational diffusion coefficient aj infinite dilution, D, could be determined by extrapolating r/K to zero scattering angle and zero concentration as shown typically in Figs. 4 and 5. D is related to the effective hydrodynamic radius, by the Stokes-Einstein relation ... 

Mobility is q/fl so, the greater the radius, the lower the mobility. Most molecules are not spherical, but Equation 26-9 defines an effective hydrodynamic radius of a molecule, as if it were a sphere, based on its observed mobility. 

Gel permeation chromatography of protein linear random coils in guanidinium chloride allows simultaneous resolution and molecular weight analysis of polypeptide components. Column calibration results are expressed in terms of a log M vs. Kd plot or of effective hydrodynamic radius (Re/). For linear polypeptide random coils in 6M GuHCl, Re is proportional to M0 555, and M° 555 or Re may be used interchangeably. Similarly, calibration data may be interpreted in terms of N° 555 (N is the number of amino acid residues in the polypeptide chain), probably the most appropriate calibration term provided sequence data are available for standards. Re for randomly coiled peptide heteropolymers is insensitive to amino acid residue side-chain composition, permitting incorporation of chromophoric, radioactive, and fluorescent substituents to enhance detection sensitivity. 

Gel permeation studies on agarose-GuHCl columns provide for high resolution and accurate molecular weight determination of linear randomly coiled polypeptide chains. For nonlinear random coils, gel permeation studies provide for accurate determination of the effective hydrodynamic radius of the components. 

Knowing these functions, the mean-square radius of gyration (S2)z and the translational diffusion coefficient Dz can easily be derived eventually by application of the Stokes-Einstein relationship an effective hydrodynamic radius may be evaluated. These five... 

Fig. 14. Translational diffusion coefficients (D) of protein 4 and the corresponding calculated effective hydrodynamic radius (Re) as a function of temperature. From Ahmed et al. (1975), reproduced with permission.

The observable quantity, D or Rj is subject to vario is types of ensemble averages, cind the z-average trcmslatlonal diffusion coefficient (or the z-average of the reciprocal effective hydrodynamic radius) is measured by dyneunic light scattering. 

The function F(F) is expanded in a power series of r. The first moment (cumulant) in the expansion is the average decay constant Favg, which defines an effective diffusion coefficient A for the particle size distribution. A is converted to the effective hydrodynamic radius using the Stokes-Einstein relationship. 

In solution, D is given by the Stokes-Einstein relation which relates D to the viscosity coefficient of the solution, T], and the effective hydrodynamic radius a, where... 

The coil is continually extended and relaxed. If the time between two deformations (c b is longer than the double relaxation time -c no significant changes of the flow properties can be observed. If, however, the velocity is so high that the molecules do not have the time to relax completely between the elongations, then drastic increases in the pressure drop can be detected. In this case, the polymer is permanently deformed in the velocity field. Consequently, the effective hydrodynamic radius of the molecule is higher than that of the random coil in... 

Effective hydrodynamic radius, R, dictates solute partitioning in a gel. This can be related to the number of units in a flexible polymer. It is then a corollary that partitioning of a linear polymer is a function of Its molecular weight. This has been proved experimentally leading to popularization of gel chromatography in 6M guanidinium chloride as a useful method of protein molecular weight determination. 

Fig. 5 Variation in settling velocity with grid location. The effective hydrodynamic radius was determined from U = Ff6nr a and converted to g using (293) g was found to be independent of T) and L, as expected. Results are shown at 56 different grid positions (labeled by the index n), systematically varying the coordinates in steps of 0.1b. Particles with input radius ao = b were placed at coordinates ib/10, jb/10, kb/10), with 0 < i < j < k < 5. Results are shown for the two-point (circles), three-point (squares) and four-point (diamonds) interpolation schemes...

Shifts in the SEC fractionation range are not new. It has been known for decades that adding chaotropes to mobile phases causes proteins to elute as if they were much larger molecules. Sodium dodecyl sulfate (SDS) (9) and guanidinium hydrochloride (Gd.HCl) (9-12) have been used for this purpose. It has not been clearly determined in every case if these shifts reflect effects of the chaotropes on the solutes or on the stationary phase. Proteins are denatured by chaotropes the loss of tertiary structure increases their hydrodynamic radius. However, a similar shift in elution times has been observed with SEC of peptides in 0.1% trifluoroacetic acid (TEA) (13-15) or 0.1 M formic acid (16), even if they were too small to have significant tertiary structure. Speculation as to the cause involved solvation effects that decreased the effective pore size of the... 

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