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Thus, it predicts simply that the slope of the Scatchard plot will be
reduced by a factor of 1/(1+Fc/Kdc) in the presence of a constant
concentration of free inhibitor F^. We now substitute the total
concentration for the (actually variable) free concentration Fj,.
Thus, the estimated value of KdC derived from the use of this
approximation (which we call K^app) will be given by
Kdc(app) = [reduced slope/(original slope-reduced slope)]S^.
(3-4)
Thus, the percentage error (E) will be given by
E/100 = [KdC(app)/KdC]-l (3-5)
and hence, from above,
E/100 = reduced slope)/Kd^[l+Kd^(reduced slope)]-l.
(3-6)
For the "reduced slope" we substitute the derivative of the equation of
the curvilinear Scatchard plot, d(B^/FL)/dB^, obtained directly from
equation (3-2) above. Thus, if the error is estimated by using as the
"reduced slope" the slope of the tangent to the curve at the abscissa
B^ = Bq/2, then the error in the derived equilibrium constant is given
explicitly by
E/100 = (Kdc[Sc-Kdc]Y-X[Sc+Kdc])/(Kdc2Y+KdcX),
(3-7)