R.B. Barlow et al
Antagonist effect curves and operational windows
1093
system accordingly operates within a window, which excludes
the lower part of the signal curve and so shifts, the EC50
towards higher concentrations (see Part 1).
As in the other type of experiments, there was great
variation between animals and the ratio (RA) is bigger with
isotonic recording (see above and Figure 4). This is to be
The signi®cant correlation between the EC50 values
obtained by the two methods has a slope close to one for
expected because with a higher threshold for isotonic
recording, negative eects recorded as zero occur at lower
concentrations (see Figure 1, lower left). This should be
associated with a smaller reduction in M%, which is certainly
true for the experiments with (7) adrenaline.
In conclusion, the work not only shows the in¯uence of the
method of recording on concentration-eect curves but also
the results to be expected with this type of antagonism: it is
important because many drugs aecting airways and blood
¯ow act in this way. The results suggest a possible mechanism
that the two types of drugs produce opposing eects on a
common eector, such as the internal calcium ion concentra-
tion (see Part 1), which operates between limits.
(
7)isoprenaline but less than one for (7)adrenaline, which
has more eects on the maximum response to carbachol, even
though higher concentrations are needed. With a competitive
antagonist the EC50 ratio, RA, is a valid measure (`dose-
ratio') of its eect at the concentration used: with the
compounds used in this work it is not, because they reduce
the maximum response obtainable with the agonist. They can
serve, nevertheless, as a measure of the shift and show that
the pattern is quite dierent from competition. With a ratio
of two produced by 0.3 nM, a competitive antagonist should
produce a ratio of 11 with 3 nM and 101 with 30 nM.
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(Received April 10, 2001
Revised May 14, 2001
Accepted May 15, 2001)
Appendix
A method for standardizing the effects of physiological
antagonists.
isometric results `low' agonist AS=0.27, IC50=0.12, M%=136,
P'=70.43; with `high' agonist AS=1.37, IC50=0.33, M%=58,
P'=70.79, and the interpolated values for AS=1 are IC50=0.26
(
0.29), M%=84(73), P'=70.67 (70.72).
In experiments with values of IC50, M and P obtained for AS51
and AS41, the values for AS=1 must lie between the two and as
a ®rst approximation might be calculated by simple proportion.
Another possibility is that there is a linear relation with log.AS, so
values could be calculated as in a three-point bioassay which
assumes a linear relation between response and log.dose (e.g.
Edinburgh Sta, 1970). There are reasons (discussed below) for
believing that this is more appropriate but when the range of
values of AS is small the dierences between the two methods are
also small. With the results shown in Figure 2 the two pairs of
curves become the two lines shown in Figure 6: for the isotonic
results with `low' agonist AS=0.59, IC50=0.014 (610 M),
M%=165, P'=70.64; with `high' agonist AS=1.76, IC50=0.62,
M%=110, P'=70.88, so the interpolated values for AS=1 (with
those assuming a linear relation with log.AS in parentheses) are
IC50=0.23 (0.31), M%=146 (138), P'=70.73 (70.76). With the
Values of IC50, P' and M% for AS=1 obtained from the results
in Table 1 assuming a linear relation with log.AS are shown in
Table 3, which includes mean estimates of log.IC50 calculated
assuming
a linear relation with AS for comparison. In all
experiments with histamine and isotonic recording the curve is
steeper and IC50 is lower (P=0.016) but there is little eect on
M%. With carbachol, which is a stronger agonist, there is a
reduction in M% with isometric recording and the eects on IC50
and P' are less clear. The same conclusions are obtained by
examining the (slightly dierent) values obtained assuming a linear
relation with AS and reinforce the ®ndings already presented.
Values of pIC50 for AS=1 are useful because they indicate the
concentrations at which antagonistic eects may be expected
(comparable with pD for a single agonist). The standard errors of
mean values of pIC50 are around 0.3 compared with less than 0.1
for log.antagonist constants in competition experiments. If they
7
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British Journal of Pharmacology vol 133 (7)