[RASMB] Fitting Sedimentation Equilibrium Data

[James Cole]

Dear All:
There is a set of help pages for NONLIN available at the UCONN NAUF FTP site
(ftp://spin6.mcb.uconn.edu/pub/pc/win95/winnonln) and at the RASMB software
archive. Jack Correia's recent emails and previous postings to this list
have nicely addressed one of the more confusing aspect of NONLIN: units
conversion for LnK. In our recent software we find it more convenient to
always work in molar units for the equilibrium constants. We are working to
port the current package running under IGOR into a windows-based program
suitable for distribution.

Concerning the issue of the analysis of sedimentation equilibrium
experiments by direct analysis of  absorption /interference gradients or
analysis of transformed data, many people have shown that there is no
substitute for obtaining lots of high-quality data. Problems with baselines
or Weiner skewing cannot be eliminated by any transformation of the data.
Model independent analysis (point-average molecular weight, Mw values from
short column experiments, omega function) can be very helpful to determine
whether a system is undergoing reversible association, assess homogeneity
and even to define the self-association mechanism. However, if one wishes to
extract parameters from the data, at some point you need to fit data to a
theoretical model. If the model is nonlinear and complex (as is the case in
analysis of association by sedimentation equilibrium), then you need to have
good guesses for the initial values of the parameters and you can run into
problems with finding unique and well-defined best fit values for the
adjustable parameters. This is not a unique problem in using NONLIN to
analyze raw sedimentation equilibrium data but occurs all over biophysics.
The usual solution is to somehow constrain the fitting process by reducing
the number of adjustable parameters and by using global analysis of multiple
data sets that are obtained over a wide range of experimental conditions. It
can be really useful to do simulations to design the experiments to make
sure that you have a good chance of extracting meaningful results. Finally,
NONLIN and the other packages that most people use have the ability to
determine the confidence intervals on the fitted parameters: problems with
poorly defined error surfaces and cross-correlation in the fitted parameters
will show up as broad confidence intervals.

You can choose to fit the primary absorbance or fringe displacement data to
a model using NONLIN-type approaches or you can fit the transformed data.
The advantage of fitting primary data is that the error statistics are well
defined in terms of the random noise in the data. Also, less manipulation of
data results in a more objective fitting process. Alternatively, it can be
more intuitive to fit the transformed data than to watch fit lines going
through 20 exponential concentration gradients. Also, Allen Minton has shown
that for complex, hetero-association models it can be useful to fit
weight-average molecular mass data as a function of loading concentrations
for each reactant. Essentially, this eliminates the reference concentrations
as fitting variable. Marc Lewis, Allen and John Philo have shown that this
is also useful in the analysis of primary data by incorporating conservation
of mass or signal in the analysis.


Jim


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James Cole
Department of Molecular and Cell Biology
University of Connecticut
75 North Eagleville Road, U-3125
Storrs, CT 06269-3125, USA
Tel.:   (860) 486-4333
FAX:  (860) 486-4331
E-mail: james.cole at uconn.edu
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