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superposition of the points from individual Hill plots constructed as
described above. From such a plot only data points corresponding to a
receptor occupancy (e) between 20% and 80% (-0.6 <_ logit e £ 0.6) were
included in the subsequent analysis. A curve was fit to the points by a
computerized cubic spline algorithm (cubic spline Fortran library
subroutine, International Mathematical and Statistical Library; see
Reinsch, 1967) that employs polynomials to smooth data in accordance
with a built-in statistical criterion (Craven and Wahba, 1979); this
method of regression contains no assumptions (other than the continuity
of the function and derivatives and smoothness criterion) restricting
the basic form or shape of the curve, and thus is appropriate for
empirically determining both the shape of the Hill plot and the abscissa
and slope at the 50% occupancy point (where logit e = 0). The slope of
the curve at the x-intercept (50% occupancy) was taken as the combined
Hill coefficient, and the value of F at this point provided a merged
estimate of K^. (The IMSL subroutine is unable to provide summary
statistics for these binding parameters.)
In order to verify that the binding parameters derived from a
least-squares linear regression fit to the points on a Scatchard plot
were not biased seriously (since the Scatchard coordinate system not
only has appreciable error in the independent variable, B but also
unfortunately has correlated error in the independent and dependent
variables; for review see Rodbard, 1973) a standard computer program
(Helwig and Council, 1979) was used to fit some of the binding isotherms
by a weighted, nonlinear regression technique (Marquardt, 1963) using
the relatively error-free independent variable SL (total [ Hjligand).
The model to which the data were fit consisted of the sum of one