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Size-and-Shape distributions

Model | continuous c(s,ffo)

Model | continuous c(s,ffo) with 1 discrete component


A detailed description of this model can be found in the Biophys. J. 2006 paper (preprint).  The practical use is illustrated in the getting started tutorial part c(s,M). Since most of the computational effort resides in operations dealing with the experimental data points, reducing the radial density of points can speed up calculation of these distributions significantly.

This model calculates general size-and-shape distributions free of scale-relationship assumptions on the frictional ratio.  This can be used to calculate two-dimensional distributions, or general diffusion deconvoluted sedimentation coefficient distributions:

Size-and-Shape Distributions c(s,ffo), c(s,M), etc.

General c(s,*)

Their application can be indicated, for example, when there is a mixture of macromolecules exhibiting microheterogeneity in s and M, with species of widely different frictional ratios. 

Essentially, both are based on fitting the data with a two-dimensional distribution


In contrast to the c(s) distribution, there is no scale-relationship assuming similar frictional ratio values for each s-value.  Instead, all frictional ratio values are permitted in the fit for each s-value. Therefore, we have a two-dimensional grid.  This will be entered here:

This works just like a conventional c(s) (and it's counterpart with the extra discrete species), but instead of fitting for f/f0, we enter a minimum value, a maximum value, and a resolution in f/f0. 

Note that in the bottom there are two fields for regularization.  The first one (which currently holds the value 0.95) is the overall P-value for the regularization.  The second field is the relative amount of regularization applied to the s-direction, relative to the f/f0-direction of the two-dimensional distribution.  Since the resolution in f/f0 is likely much lower than in s, it might be advantageous to increase the regularization in f/f0 direction (e.g. enter a value of 10).  This does not influence the overall level of regularization.  Only Tikhonov-Phillips regularization is currently implemented.

After calculating the distribution (using the RUN or FIT command), there will be two kinds of outputs:


Size-and-Shape Distributions c(s,ffo), c(s,M), etc.

These are representations of the two-dimensional distribution.  The default representation is c(s,ff0).  For example, it may look like this.

The height of the c(s,ff0) distribution is indicated by the color temperature.  The vertical axis is the f/f0 dimension, always automatically scaled from f/f0 min to f/f0 max.  The horizontal axis is the s-axis.  (The solid line is the general c(s,*) distribution derived from the two-dimensional c(s,ff0) distribution.)

The display can be changed by using the buttons on the right-hand side of the parameter box.

These are all equivalent representations of the same distribution, since the diffusion coefficient, Stokes radius, and molar mass are all automatically determined once s and f/f0 are fixed. Of course that requires proper values for vbar, buffer density, buffer viscosity, etc.  (Note the s-values will always remain experimental s-values.). 

For example, as s-M distribution, it looks like this:

Integration over a region can be done using the conventional integration tool (control-I), but only the s-range can be determined. (The integration tool will not work if the horizontal axis is not showing sedimentation coefficients.)

For the molar mass, the following average values are reported:



The two-dimensional distribution can be copied using the copy command, and pasted into a spreadsheet with columns s, M, f, D, R, and c(s,ff0). A MATLAB script for creating publication quality 3d representations is available for download here (this assumes linearly spaced s-values). 3d plots can be made also by other commercial plotting programs.


General c(s,*)

In many cases, the molar mass (or f/f0) information is actually not well determined by the sedimentation data, or it may not be of interest.  In these cases, it makes sense to give up the second dimension, and integrate along the f/f0 axis to arrive back at a one-dimensional sedimentation coefficient distribution, termed general c(s,*):

This shown as the black solid line.  This is equivalent to the conventional c(s) distribution, except for the absence of scale-relationships in f/f0.


It can be copied using the copy command.