Sedimentation coefficients

At first glance, the contents of Chap. 9 read like a catchall for unrelated topics. In it we examine the intrinsic viscosity of polymer solutions, the diffusion coefficient, the sedimentation coefficient, sedimentation equilibrium, and gel permeation chromatography. While all of these techniques can be related in one way or another to the molecular weight of the polymer, the more fundamental unifying principle which connects these topics is their common dependence on the spatial extension of the molecules. The radius of gyration is the parameter of interest in this context, and the intrinsic viscosity in particular can be interpreted to give a value for this important quantity. The experimental techniques discussed in Chap. 9 have been used extensively in the study of biopolymers. 

The stationary-state velocity per unit acceleration is a parameter which characterizes the settling particle and is called the sedimentation coefficient s ... 

In a solution of molecules of uniform molecular weight, all particles settle with the same value of v. If diffusion is ignored, a sharp boundary forms between the top portion of the cell, which has been swept free of solute, and the bottom, which still contains solute. Figure 9.13a shows schematically how the concentration profile varies with time under these conditions. It is apparent that the Schlieren optical system described in the last section is ideally suited for measuring the displacement of this boundary with time. Since the velocity of the boundary and that of the particles are the same, the sedimentation coefficient is readily measured. 

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

Once a sedimentation coefficient has been measured, there are several ways in which it can be used ... 

The particle can be assumed to be spherical, in which case M/N can be replaced by (4/3)ttR P2, and f by 671770R- In this case the radius can be evaluated from the sedimentation coefficient s = 2R (p2 - p)/9t7o. Then, working in reverse, we can evaluate M and f from R. These quantities are called, respectively, the mass, friction factor, and radius of an equivalent sphere, a hypothetical spherical particle which settles at the same rate as the actual molecule. 

Mandelkern and Floryt have assembled the sedimentation coefficients and intrinsic viscosities for polymers of various molecular weights. As shown... 

Determine the sedimentation coefficient of this enzyme and, from this, its... 

Fig. 2. Ultracentrifugal pattern for the water-extractable proteins of defatted soybean meal in pH 7.6, 0.5 ionic strength buffer. Numbers above peaks are approximate sedimentation coefficients in Svedberg units, S. Molecular weight ranges for the fractions are 2S, 8,000—50,000 7S, 100,000—180,000 IIS, 300,000—350,000 and 15S, 600,000—700,000 (9). The 15S fraction is a dimer of the IIS protein (10).

Centrifugation methods separate macromolecules on the basis of their characteristic densities. Particles tend to fail through a solution if the density of the solution is less than the density of the particle. The velocity of the particle through the medium is proportional to the difference in density between the particle and the solution. The tendency of any particle to move through a solution under centrifugal force is given by the sedimentation coefficient, S ... 

Ribosomes, the supramolecular assemblies where protein synthesis occurs, are about 65% RNA of the ribosomal RNA type. Ribosomal RNA (rRNA) molecules fold into characteristic secondary structures as a consequence of intramolecular hydrogen bond interactions (marginal figure). The different species of rRNA are generally referred to according to their sedimentation coefficients (see the Appendix to Chapter 5), which are a rough measure of their relative size (Table 11.2 and Figure 11.25). 

Sedimentation coefficients are a measure of the velocity witli which a particle sediments in a centrifugal force field. Sedimentation coefficients are typically expressed in Svedbergs (.symbolized S), named to honor The Svedberg, developer of the ultracentrifuge. One S equals 10 . sec. 

Paudjojo was able to show by ultracentrifuge measurements that there is a strong specific interaction between (Lys) and CIO4, however no measurable one between (Lys)n and SO According to her results, the sedimentation coefficient... 

Fig. 9. Sedimentation coefficient of (Lys) in different electrolyte solutions as a function of temperature a) 1,5 m UCIO4 solution 100101> b) 1,0 m LiC104 solution c) 0,5 m LiC104 solution d) 0,2 m LiC104 solution e) 0,1 m LiC104 solution f) 0,1 and 1,5 m Li2S04 solution...

Properties of Latia luciferase and the purple protein. The absorption spectra of purified Latia luciferase and the purple protein are shown in Fig. 6.1.4. The sedimentation coefficient (sjo) of the... 

Ribosomes are ancient ribonucleoprotein complexes that are the sites of protein synthesis in living cells. Their core structures and fundamental functional mechanisms have been conserved throughout the three domains of life bacteria, archaea and eukaryotes. All ribosomes are organized into two subunits that are defined by their apparent sedimentation coefficient, measured in Svedberg units (S). There is a general... 

Keywords Complex Flexibility Molecular weight distribution Mucoadhesion Sedimentation coefficient distribution... 

Analytical ultracentrifugation (AUC) Molecular weight M, molecular weight distribution, g(M) vs. M, polydispersity, sedimentation coefficient, s, and distribution, g(s) vs. s solution conformation and flexibility. Interaction complex formation phenomena. Molecular charge No columns or membranes required [2]... 

Traditional analysis methods on these measurements have been based around recording the movement of the radial position of the boundary r y with time t, from which a sedimentation coefficient, 5 (sec or Svedbergs, S, where 1 S = 10 sec) can be obtained (see, e.g. [30]) ... 

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 way computationally of obtaining a sedimentation coefficient distribution is from time derivative analysis of the evolving concentration distribution profile across the cell [40,41]. The time derivative at each radial position r is d c r,t)/co /dt)r where cq is the initial loading concentration. Assuming that a sufficiently small time integral of scans are chosen so that Ac r t)/At= dc r t)ldt the apparent weight fraction distribution function g (s) n.b. sometimes written as (s ) can be calculated... 

In this relation a(r, t) is the experimentally observed signal, s represents random noise, axi r) represents the time invariant systematic noise and aRi(f) the radial invariant systematic noise Schuck [42] and Dam and Schuck [43] describe how this systematic noise is ehminated. x is the normahsed concentration at r and t for a given sedimenting species of sedimentation coefficient 5 and translational diffusion coefficient D it is normalised to the initial loading concentration so it is dimensionless. 

Although only approximate analytical solutions to this partial differential equation have been available for x(s,D,r,t), accurate numerical solutions are now possible using finite element methods first introduced by Claverie and coworkers [46] and recently generalized to permit greater efficiency and stabihty [42,43] the algorithm SEDFIT [47] employs this procedure for obtaining the sedimentation coefficient distribution. 

The sedimentation coefficient s°, or its normalized form 5 0 w function of the conformation and flexibility of a macromolecule (via its translational frictional property) and its mass. So if we are going to obtain conformation and flexibility information we need to know the molecular weight (molar mass)... 

It is possible to get molecular weight from the sedimentation coefficient if we assiune a conformation or if we combine with other measurements, namely the translational diffusion coefficient via the Svedberg equation [50]... 

A sedimentation coefficient distribution—either c s) versus 5 or g (s) vs. s—for a polysaccharide can also be converted into an apparent molecular weight distribution if the conformation of the polysaccharide is known or can... 

One can see the M procedure has a parallel to either g (s) vs. s or c(s) vs. s in sedimentation velocity where the data are transformed from radial displacement space [concentration, c(r) versus r] to sedimentation coefficient space [g s) or c(s) versus s]. Here we are transforming the data from concentration space [concentration relative to the meniscus j(r) versus r] to molecular weight space [M r) versus r]. 

The sedimentation coefficient provides a useful indicator of polysaccharide conformation and flexibility in solution, particiflarly if the dependence of on Mw is known [62]. There are two levels of approach (i) a general level in which we are delineating between overall conformation types (coil, rod, sphere) (ii) a more detailed representation where we are trying to specify particle aspect ratios in the case of rigid structures or persistence lengths for linear, flexible structures. 

The relation finking the sedimentation coefficient with the molecular weight for a homologous polymer series given above is (see [61, 111]) ... 

Another scaling relation exists between the sedimentation coefficient and ks [see [10]]... 

For a cylindrical rod an expression also exists for the sedimentation coefficient [116] ... 

The sedimentation coefficient for wormlike chains was first worked out by Hearst and Stockmayer [123], later improved by Yamakawa and Fujii [124] to give this expression for s ... 

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