From: Jo Butler <pjgb@mrc-lmb.cam.ac.uk>
  To  : RASMB Noticeboard <rasmb@alpha.bbri.org>
  Date: Wed, 17 Mar 1999 17:00:50 +0000

Concentration units when fitting equilibrium data

I may just be being rather naive, but I am having a problem with
concentration units employed when fitting sedimentation equilibrium data
for aggregating systems and wanting meaningful values for K (whether Kd or
Ka).

Consider for the moment just the simplest ideal monomer/dimer equilibrium.
While the equation:
Ct = Sigma,i(Ci)
    = C1 + ((C1)**2)/Kd;    {or = C1 + Ka(C1)**2 if one wants association
constants}

seems obvious, there is a snag that it is derived from using the defining
equation:

Kd = ((C1)**2)/C2; where concentrations are normally expressed in
molarities.

While one may well know the molar extinction coefficient for the monomer
(and anyway this can be determined), it is extremely unlikely that the
extinction coefficients for monomer and dimer will be identical, thus
invalidating the direct substitution of absorption concentrations for molar
ones.  Agreed one could make the simplifying assumption that the extinction
coefficient of dimer would be twice that of monomer, thus introducing a
factor "2" into the last term in the equation for Ct, but this is done in
neither the Beckman supplied software in Origin nor most of the other
derivations for such fitting.  Admittedly the fit will be fine, since the
system is internally self-consistent, but the magnitude and units for K
will be far from obvious in any usual sense.

As I say above, this is just the simplest case and higher aggregation will
be even worse.  Am I missing something obvious, or is this software fitting
this unusual definition of K?

Jo Butler

Dr P.J.G. Butler,
MRC Laboratory of Molecular Biology,
Hills Road,
Cambridge, CB2 2QH,
UK.
Tel. 01223 248011 (or 01223 402296 DDI)
FAX. 01223 213556