Biology Reference
In-Depth Information
55
and
The value of c is then about 8.57 X in reasonably good agreement with
what Monod
et al.
(1965) found originally. The value of K, however, is
quite different. More accurate values of these equilibrium constants can be
obtained by least square fitting of the theoretical equation to the
experimental data as discussed below.
LEAST SQUARE FITTING
The three models discussed above can all be fitted to experimental measured
data of hemoglobin saturation plotted against oxygen pressure, i.e. the y vs.
plot. However, for the same data displayed by the Hill's plot, the one-
constant model does not fit at all. The two-constant model can be fitted
reasonably closely, but not completely, due to the symmetry property of the
model. On the other hand, the three-constant model may be fitted quite
closely. But, what is “fitting”? To define “fitting” precisely, we need to
introduce the idea of least square.
In our present discussion, for any experimentally measured oxygen pressure,
the corresponding experimentally determined percentage saturation, y,
is converted to ln {y/(1-y)}, to give an experimental data point on the Hill's
plot. On the other hand, we can substitute the experimentally measured
value of
into the equation derived from the MWC model:
to obtain a theoretical value of ln (y/(1-y)} which depends on the three
equilibrium constants. The difference between the experimental and
