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First, the bad news. Considerations for measurements of the number of Ag
sites on/in a cell must include the affinity of the Ab, cryptic Ag (or Ag
not accessable to Ab), and signal measurement (fluorescence). Since all
of the thermodynamic considerations posted on this list have been based
on the concept of: Ab + Ag >/< AbAg (sorry, I can't reproduce the
foreward and backward arrows), I would comment that the antibody
generally has 2 hands (or more), and similarly the Ag can be
multi-valent. Thus, the measurement being made with an intact antibody is
actually avidity. For anyone brave enough, I would highly recommend
"Advanced Immunochemistry" by Eugene D. Day, Wiliams & Wilkins. My copy
is the 1972 edition, though I believe there is a revised edition
published sometime in the 1980's. Other technical problems include
inactive antibody (will contribute to the "free" signal), and a
significant number of problems related to measurement of
fluorescence "per cell" (including quenching of fluorescence,
particularly for FITC near the cell surface, measurement of both "bound"
and "free" antibody in the flow sensing zone, etc).
>From a thermodynamic perspective, the equation commonly used (above) is
appropriate for Ab Ag interactions in free solution. The appropriate
model for antibody - Ag binding where the Ag is located on a cell surface is
the adsorbtion isotherm, originally derived by Langmuir for ideal gases
adsorbed to an ideal surface. For an excellent discussion of this, and
other aspects of Ab binding measured by flow cytometry, I recommend (with
some vested interest) "Receptor Quantitation" by Bob Hoffman, Diether
Recktenwald, and Bob Vogt in "Clinical Flow Cytometry: Principles and
Application".
One final point I would make is the very important contribution made to
this field by Chatelier, Ashcroft (wherever he may be!), Lloyd, et al
(Binding of fluoresceinated epidermal growth factor to A431 cell
subpopulations studied using a model-independent analysis of flow
cytometric fluorescence data. EMBO J 5:1181-1186, 1986). The method
developed by these authors, isoparametric titration, measures relative
cell bound fluorescence as a function of total cell and total ligand
concentration, and makes the very important point of expressing all
concentrations (including cell concentration) in moles/L. While this
approach did not solve all the above noted problems, it bypasses a number
of critical constraints, plus it compares the results of the flow
cytometrically derived measurement with a biochemical "gold standard"
(radioactive ligand binding assay).
This area remains one of the central problems of flow cytometry, and one
of its likely unique contributions to cell biology. I would encourage the
dialog, and further developement of models, methods, and standards that
will be widely adapted by the flow (and cell biology) community.
Vince Shankey
Loyola Univ. Medical Center.
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