From: Marc S. Lewis <mslewis@helix.nih.gov>
  To  : RASMB <rasmb@alpha.bbri.org>
  Date: Thu, 9 Sep 1999 15:56:44 -0500

Associating Systems

<fontfamily><param>Times</param>Dear RASMBers:


Being much occupied with keeping a number of collaborators happy, I
have taken the easy route of waiting until a number of good replies
have come in regarding this messy problem so that I only needed to
comment on what I felt needed to be considered that had not already
been very well covered by a number of respondents.


The first of these is that fitting absorbance data can lead to
erroneous results because the error distribution of absorbance data is
not a normal distribution but is a logarithmically skewed Cauchy
distribution.  See the recent publications of Dimitriadis, et al for
details.  The best solution that we have found for this is direct
fitting of the intensity data from the XL-A (or XL-I), using the
mathematical model:

		Z(r,Ii,It) = Ii * (10^ -F(r)) - It

where r = radius, Ii = incident intensity, It = transmitted intensity,
and F(r) is the function that you would normally use to fit absorbance
data for an assumed association.  The data matrix is simply the data
returned by the XL-A, which represent the independent variables with
the addition of a fourth column of zero's representing the dependent
variable for this model.  Needless to say, global fitting with multiple
concentrations and, if practical, multiple rotor speeds is mandatory. 
Use of this approach does not guarantee a definitive answer, but,
because it eliminates certain inherent defects in absorbance data, in
some cases it <bold>may </bold>be useful.  I prefer it because 
intensiÝy data has normally distributed error while absorbance data
does not and non-linear least-squares curve-fitting assumes that the
fit data either has normally distributed error or that the error
distribution is unknown.   Interference data does not have this
problem.  With respect to interference data, I would recommend use of
the recent noise reduction analytical techniques  developed by Peter
Schuck for this optical system.


The other technique that I have found useful on occasion is to do
temperature dependence studies  over as wide a temperature range as
possible with temperature increments not in excess of 4 deg.  It has
been my experience that if one fits values of delta G as a function of
T with values of delta H, delta S, delta Cp, and, if possible, the
derivative of delta Cp with respect to T as fitting parameters, one
association model will sometimes permit significantly  better fitting
of delta G(T) than others.  It must be emphasized that this absolutely
does not prove that the mødel that gives the best fit is the correct
mødel; it simply suggests that it does have a higher probability of
being correct, and this caveat must be so stated..


As Tom Laue so ably stated, this is indeed an ill conditioned problem
and ultimately, there is absolutely no substitute for having the best
data possible.  Then, you must devise the best possible way of using
that data and be prepared to accept the fact that a definitive answer
may simply not be possible.

  

Good luck   -


Marc Lewis

</fontfamily>
Marc S. Lewis, Ph. D., Chief

Molecular Interactions Resource

Bioengineering and Physical Science Program

Office of Research Services

National Institutes of Health

Buiding 13  Room 3N17

13 South Drive  MSC 5766

BETHESDA MD 20892-5766


Phone: 301-496-9044;  Fax:  301-496-6608