105
isotherm. Both spectra of such a pair were generated by applying the
transformation to smoothed binding functions expressed in the log By -
log F coordinate system. To generate the comparison spectrum (A) the
previously-fit 3-parameter regression equation was transformed to the
log By log F coordinate system before use of the finite differences
algorithm; thus, the binding data for the comparison spectrum were
"smoothed" by force-fit to a specific model containing only one
saturable binding site. The unconstrained spectrum (B) was produced by
smoothing the experimental By data in the same coordinate system with
the cubic spline subroutine before transformation to the affinity
distribution. Thus, to produce this spectrum the data were not
force-fit to any specific biophysical model such as equation (4-6).
For display the spectra were normalized by the total receptor concentra
tion (Bq) estimated by the 3-parameter nonlinear regression; thus, the
finite difference equation (equation 4 of Thakur et al., 1980, which
contains an error in the reference itself) takes the form
N(K) = a(f2 2fy )/(a-l )2]/2BQ log a, (4-7)
where f-j and are as defined in Thakur et al. (1980). The input
spacing for the transformation Alog K = 0.1, and log a = 0.2. The
dimensionality of K is M-"* (1/mole); the normalized N(K) itself is
dimensionless. The peak of the comparison spectrum is located at
(-log K^) on the abscissa, where is the estimate derived from the
3-parameter nonlinear regression.
Data sets from separate isotherms were also combined to generate
pairs of "merged" affinity spectra (e.g., figure 4-24) following the