Analysis of sedimentation velocity data

Example

The plot below shows successive radial absorbance scans of a protein with a monomeric mass of 16.4 kDa centrifuged at 55000 rpm for 5 hours at 10°C in 50 mM Tris-HCl (pH 7.95), 0.5 M KCl, 0.6 mM imidazole. This buffer was used as reference.

From the first scan the maximum absorbance can be read. This corresponds to the total loading concentration providing that there has been no significant pelleting of sample. The optical pathlength of the cells is 1.2 cm, so this initial lower plateau absorbance should be 1.2 times the absorbance measured in a spectrophotometer before loading sample into the centrifuge cell, bearing in mind that the accuracy of the wavelength setting in the analytical centrifuge is ± 1 nm.  The upper plateau is so called because it forms near the top of the liquid column towards the end of the run. This represents absorbance contributed by substances which do not sediment away from the meniscus at the speed of the experiment, such as proteolytic fragments or small contaminants. In the example shown the upper plateau absorbance is zero, indicating that all of the sample has sedimented away from the meniscus, and that the effect of imidazole absorbance has been corrected by the reference.

Looking at the shape of the scans it can be seen that early on the boundary is very sharp, then as time progresses the boundary spreads out, spanning a greater radial distance. This is caused by diffusion of the sample. The height of the lower plateau decreases progressively during the run. This is caused by radial dilution due to the wedge shape of the cell sectors. This radial dilution is corrected for by the analysis software.

Here at the Astbury Centre for Structural Molecular Biology, University of Leeds, U.K. one of the analysis methods we use is the g(s*) method (pronounced “g of s”) which is also called the dc/dt method. [Stafford 1992, Philo, 2000]  The essence of this technique is to select a set of scans which span a time range short enough that the difference in concentration between first and last scan approximates to the derivative of concentration with respect to time, dc/dt.

 

 

 

dc/dt analysis 

 

 

 

Initial A280                              0.72

Co(1)  (AU)                           0.6523      [ 0.6470, 0.6578 ]  (91% of total loading concentration)

s20,w(1)  (S)                             2.410         [ 2.406, 2.414 ]

D20,w(1)  (F)                            7.28            [ 7.13, 7.43 ]

calculated mass [kDa]:        28.23       [27.61, 28.87]

Values in square brackets are the 95% confidence limits, and approximate to the standard deviation, but are not necessarily symmetrical about the mean.

s* is the apparent sedimentation coefficient and has units of Svedbergs (S), where 1 Svedberg = 1 x 10-13 sec. g(s*) is the distribution function of apparent sedimentation values, and has units of absorbance units per Svedberg (AU  S-1). Thus if you measure the area under the calculated (blue) line by integration the result has units of absorbance. This result is fitted as part of the program’s algorithm and appears as Co(1)  (AU), the loading concentration for the fitted species. This can be compared with the observed starting absorbance and expressed as a percentage of the total loading concentration, in this case 91%. By looking at the graph, it can be seen that part of the data has higher g(s*) values than the fitted line: visual evidence that less than 100% of the sedimentation is described by the fitted species. As the region where this discrepancy occurs is at S values greater than 2.4, we conclude that the 9% not described by species 1 is larger than that species.

The other parameters derived  from this analysis:

 s20,w(1) is the sedimentation coefficient of species 1. The suffix 20,w indicates that the parameter has been corrected to 20.0°C and the density of water. This correction enables one to compare results from experiments performed in different buffers and temperatures.

D20,w(1) is the diffusion coefficient of species 1. It has units of Fick (F) where 1 Fick = 1x10-7 cm2 s-1 .

The suffix 20,w has the same meaning as for the diffusion coefficient.

calculated mass [kDa] The molecular mass of the solute (in this case protein) in units of kDa.

The molecular weight is calculated from the ratio S/D using the Svedberg equation:

 

where S0 and D0 are the coefficients extrapolated to zero solute concentration, R is the gas constant, T the temperature in °K, (1-vr) is the buoyancy term: r is the buffer density in units of g/ml, and v   (v-bar), the solute partial specific volume, is the volume excluded by the solute in units of ml/g.  

We calculate protein partial specific volume, and buffer densities and viscosities using the program Sednterp (Dr. Thomas Laue, Department of Biochemistry, University of New Hampshire, Durham, New Hampshire  03824.  Telephone 603-862-2459, FAX 603-862-4013.)

Use of the term apparent, as in s*,  takes account of uncertainty about the nature of the sample. If the sample is a pure, monodisperse solute the width of the g(s*) vs s* plot will be due to diffusion alone. However, this width could also arise from sedimentation of a mixture of solutes with slightly different sedimentation rates, either because of heterogeneity in mass or shape. In the example shown above the calculated solute mass is 28.2 kDa with confidence limits of 27.6 to 28.9 kDa. The protein monomer molecular weight is calculated from amino acid sequence to be 16.4 kDa, so the value obtained from sedimentation velocity is 5.2 kDa smaller than dimer, and 11.2 kDa larger than monomer. However, the accuracy of this method is ±  5%, and John Philo reports that his program usually results in underestimates of the mass by 2%, so the upper 95% confidence limit could be 31.0 kDa. The conclusion in this experiment was that more than 90% of the protein is in the form of dimers, and that no monomer is present. However, the slight underestimate of MW could be due to a weak reversible association of dimers to larger aggregates. In this case the width of the peak would be due to a mixture of dimers and tetramers (say) in rapid reversible equilibrium. A series of velocity experiments at a range of protein concentrations would test this hypothesis: there should be more tetramer at higher protein concentration, showing up as widening of the g(s*) vs s* peak and, contrary to intuition, reduction of the calculated mass to a value lower than that of the smallest species present.

In fact an equilibrium run was performed to obtain an accurate measure of mass. The average mass determined was 33.2 kDa, very close to the expected dimer mass 32.8 kDa. A dimer-tetramer model resulted in a marginally better fit, with a Kd of 1.3 mM, a very weak affinity.

Examples of previous results

Protein                                   S20,w        D20,w        M
Fetuin                                     3.3           7.0           43 kDa
BSA                                        4.9           6.8           66 kDa
small alpha helical protein  1.1           7.4           13.1kDa
PNPase                                  1.5           3              48 kDa
alpha peptide                        1.1           4.5           19 kDa
virus capsid                          50            2.3           2.4 MDa
whole phage                         80                            3.6 MDa

Whole boundary analysis using Sedfit

(See http://www.analyticalultracentrifugation.com/sedfit_help.htm)

The plot produced by this analysis is similar to the g(s*) plot produced by DCDT+ in that the distribution of sedimentation coefficients is plotted against s. The calculation involves iterative fitting to solutions of the Lamm equation (a differential equation that describes the change in boundary shape during sedimentation). A second stage of the analysis is to make assumptions about the sample, and then to calculate the most probable distribution of species by maximum entropy techniques. (If you have had mass spec done you might be familiar with this last technique.) The resolution is very good, so that, for example, a mixture of BSA (67kDa) and Fetuin (45kDa) were resolved as two distinct peaks whereas g(s*) analysis produced a single asymmetrical peak.

 The values derived are uncorrected for changes in density and temperature, so here S = 1.9, compared to s20,w = 2.4 calculated by DCDT.

 Sedfit c(s) analysis of fetuin, BSA, and mixture of both proteins

 

Same three datasets analysed by the g(s*) method

 

 


References

Stafford, W.F., III. (1992).  Boundary analysis in sedimentation transport experiments: A procedure for obtaining sedimentation coefficient distributions using the time derivative of the concentration profile.  Analytical Biochemistry  203:295-301.

Philo, J.S. (2000). A method for directly fitting the time derivative of sedimentation velocity data and an alternative algorithm for calculating sedimentation coefficient distribution functions. Analytical Biochemistry 279, 151-163.

Schuck, P. (2000). Size distribution analysis of macromolecules by sedimentation velocity ultracentrifugation and Lamm equation modeling. Biophysical Journal 78:1606-1619.

Web sites

A central site linking many AUC practitioners: http://www.bbri.org/RASMB/rasmb.html

Sedfit: http://www.analyticalultracentrifugation.com/sedfit_help.htm

DCDT+ and Sednterp: http://www.jphilo.mailway.com/