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which is responsible for the binding of the component to a specific
target, and the other for an essential biological activity other than
binding. A lethal mutant of this component could be constructed by
introducing a mutation into the functional domain while keeping the
binding domain intact. If this mutant component retains a binding
affinity equal to the wild-type component, then the stoichiometry of
this component could be determined by mixing the wild type with the
mutant in the reaction to access the probability of the distribution and
combination of the mutant and wild type. This method is intended to
determine the stoichiometry of components that participate in one
single step of the reaction.
Here “receptor” represents the reaction assemblage, and “ligand”
represents the component to be measured for stoichiometry. The
probability that the receptor possesses a certain amount of mutant
and a certain amount of wild-type ligand can be predicted through
binomial expansion (Eq. (1)).
Z
0
p Z
Z
1
p Z −1 q
Z
2
p Z −2 q 2
Z
Z
pq Z −1
( p
+
q ) Z
=
+
+
+
1
Z
Z
q Z
Z
M
p Z −Μ q M .
Z
+
=
(1)
M
=
0
where p and q are the known ratios (percentage) of mutant and wild-
type ligands, respectively, in the reaction mixture, where p
1;
Z is the total number of ligands per receptor, that is, the unknown
stoichiometry to be determined; M is the number of mutants bound
to the receptor. Therefore:
+
q
=
Z
M
Z !
=
.
(2)
M !( Z
M )!
The probability of different combinations of mutant and wild type
can be predicted to produce theoretical curves. Using various ratios
of mutant to wild-type components in an experimental setting, the
percentage of mutant vs. the yield of products of the empirical data can
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