Sedimentation coefficient concentration dependence

For a given polymer in a given solvent the sedimentation coefficient is dependent on polymer concentration, molecular weight, temperature and pressure. 

For a given polymer-solvent system, the sedimentation coefficient is dependent on temperature, pressure and polymer concentration. For obtaining thermodynamic data from sedimentation coefficients, one additionally has to measure the diffusion coefficient. This can be made with an ultracentrifuge in special diffusion cells or with dynamic light scattering based on the theory of Pecora. Nearly all diffusion coefficients have been measured by this method since it became available in 1970. The determination of sedimen-... 

AUC-SV measures the rate at which proteins sediment in a rapidly spinning rotor. The rate of sedimentation is expressed as a sedimentation coefficient, which depends on both molecular mass and shape. Proteins form concentration gradients, known as boundaries, as they sediment toward the base of a sector-shaped centrifuge cell. An optical detection system based on absorbance, Rayleigh interference, or fluorescence is used to record the movanent of the boundaries at regular intervals of time. The data from an AUC-SV experiment are then used to calculate a continuous distribution of sedimentation coefficients known as c(5). The resulting c(s) distribution provides a measure of... 

As with the diffusion coefficient, sedimentation coefficients are frequently corrected for concentration dependence and reduced to standard conditions ... 

Fig. 3 Concentration dependence of the sedimentation coefficient for wheat amylopectin. The data have been fitted to Eq. 5 (see text) yielding s = (120d= 10)S, = (170=b60)ml/g...

The simplest indicator of conformation comes not from but the sedimentation concentration dependence coefficient, ks. Wales and Van Holde [106] were the first to show that the ratio of fcs to the intrinsic viscosity, [/ ] was a measure of particle conformation. It was shown empirically by Creeth and Knight [107] that this has a value of 1.6 for compact spheres and non-draining coils, and adopted lower values for more extended structures. Rowe [36,37] subsequently provided a derivation for rigid particles, a derivation later supported by Lavrenko and coworkers [10]. The Rowe theory assumed there were no free-draining effects and also that the solvent had suf-... 

The frictional coefficient varies with concentration, but at infinite dilution it reduces to the coefficient (/o) for an isolated polymer molecule moving through the surrounding fluid unperturbed by movements of other polymer molecules (see Chap. XIV). At finite concentrations, however, the motion of the solvent in the vicinity of a given polymer molecule is affected by others nearby binary encounters (as well as ones of higher order) between polymer molecules contribute also to the observed frictional effects. The influence of these interactions will persist to very low concentrations owing to the relatively large effective volume of a polymer molecule, to which attention has been directed repeatedly in this chapter. Since the sedimentation con-stant depends inversely on the frictional coefficient, s must also depend bn concentration. 

Fig. 14. Effects of histone H2A ubiquitination on the folding and solubility of chromatin [221]. A. Magnesium chloride dependence of the sedimentation coefficient (S2o,w) of 208-12 nucleosome arrays. Sedimentation coefficients at a given magnesium chloride concentration are plotted relative...

The thus determined molecular weight is an apparent one since s and D depend on the polymer concentration. Therefore, extrapolation to concentration zero is required. The sedimentation coefficient obtained by extrapolating c —> 0 is called sedimentation constant Sn ... 

The structure of concentrated solutions of branched molecules has also received little attention. It is probable that the network formed by entangled branched molecules displays a topological structure which is different from that formed by linear chains. It is known that the sedimentation properties of branched synthetic polymers differ, especially in good solvents, from those of linear polymers. The concentration dependence of the sedimentation coefficient is relatively more pronounced for branched polymers than that for linear ones 20). 

The sedimentation coefficient depends on concentration consequently, it is usually measured at several different concentrations, and the results are extrapolated to zero concentration. It is customary to designate this limiting value by a superscript zero. Experimental values are also generally labeled with respect to temperature, so a value listed as 520 corresponds to a sedimentation coefficient measured at (or corrected to) 20°C and extrapolated to zero concentration. Under stationary state conditions, the force due to the centrifugal field and the viscous force of resistance will be equal. Therefore, co2r replaces g in Equation (4) to give... 

To minimize the effects of concentration dependence, the sedimentation coefficient is usually determined for a particular system at several concentrations and then extrapolated to infinite dilution (S°). If, on the other hand, the diffusion coefficient is also measured at several concentrations and extrapolated to infinite dilution (D°), then values of S° and D° may be related through the frictional coefficient to determine the molecular weight of the solute molecules... 

In an SV experiment, the sedimentation and the diffusion forces that determine the net rate of movement of the solvent—solution boundary, stem from two intrinsic properties of the solute molecules, their sedimentation coefficient (s) and their diffusion coefficient (D). Whereas D depends predominantly on the shape of the solute particles, s depends both on its shape and on its mass. The diffusion coefficient, D, is defined as the ratio of the flux of molecules (Jx, moving in the direction x under diffusive forces) to the concentration gradient of the molecules (dc/dx). The dependence of D on the molecular shape stems from its relation to the frictional coefficient f ... 

The sedimentation method depends on measuring the sedimentation coefficient (by ultracentrifugation) of the particles, SJ (extrapolated to zero concentration), in the presence of the polymer layer [34]. Assuming that the particles obey Stokes law, SJ is given by the expression ... 

Fig. 5. Dependence of sedimentation coefficient of apoferritin on protein concentration...

Thus since Kf — 7 we expect that the first-order term (in cs) will be very small, and D should show a much smaller concentration-dependence than the sedimentation coefficient or equivalently fs. In fact D might either increase or decrease with cs, depending on which theory is applied. 

Newman et al. (1974) have recently studied the concentration-dependence of the diffusion coefficient and the sedimentation coefficient in a highly monodisperse solution of the single-stranded circular DNA from the fd Bacteriophage. Their results are shown in Fig. 13.5.3. From these data it is possible to determine the coefficients in the expression... 

The solution behavior with a concentration-dependent sedimentation coefficient that decreases with increasing p (hindered settling) has a similar form as for s = constant, but with Eq. (5.5.15b) replaced by... 

In these derivations, it was implicitly assumed that s and D are independent of the concentration. Equation (9-97), therefore, only applies at infinite dilution. However, sedimentation and diffusion coefficients are measured at finite concentrations, and so must be extrapolated to c 0. The extrapolation formula for sedimentation coefficients is obtained from the reasoning that, according to Equation (9-96), the 5 values, and so also the 5c values, are inversely proportional to the frictional coefficients fs. Since fs is proportional to the viscosity rj, and this in turn is proportional to the concentration, 1 /sc must be directly proportional to the concentration. This dependence is usually formulated as... 

Among several other methods proposed for the estimation of c the one using the concentration dependence of the sedimentation coefficient s(c) appears to be most relevant. It has been thoroughly worked out by Roots and Nystriim [8-10] and by Vidakovic et al. [11]... 

Although the theory of sedimentation as described holds for the near-ideal conditions encountered in most dilute biological preparations, refinements of the theory are required to deal with nonideal effects. Deviations from ideal behavior are caused by charge effects, hydration, or steric interference of molecules in concentrated solutions. Nonideal effects may result in an apparent concentration dependence of the sedimentation coefficient and an artificial sharpening of the boundary. 

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