for a quick estimation of the inhibition parameters but also to help determine
the type of inhibition that is occurring. Sometimes, differences in measures of
model differences from nonlinear regression fitting (e.g., F-tests, Akaike
Information Criterion) may be so close as to make determinations between two
models difficult. In this case, graphical plots may serve to help distinguish
between models of inhibition.
Two of the most common plots for determining inhibition constants and the
type of inhibition are those as described by Dixon (1953) and Cornish-Bowden
(1974). The two methods are actually very complementary and can serve as a
double check on determinations of the type of inhibition. In addition, they each
make up for the inability of the other method to estimate the inhibition
constant in all types of inhibition.
In the method of Dixon, plots are constructed with 1/nplotted along the
y-axis and [I] plotted along thex-axis (Fig. 4.10a–c). Experiments are typically
conducted over a range of substrate concentrations (3–4 concentrations of
substrate at values bracketing the Km) and at a range of inhibitor
concentrations (3–4 inhibitor concentrations bracketing the expectedKi)as
well as a control set of incubations with only substrate and no inhibitor
present. In the case of competitive inhibition (Fig. 4.10a), the plotted lines
intersect at a point in the upper left quadrant of the plot. A perpendicular from
the point of intersection to the y-axis gives an estimation of 1/n, while a
perpendicular drawn from the intersection point to thex-axis gives an estimate
of the negative ofKi(Ki). Mixed inhibition gives a slightly different plot in
that the point of intersection is nearer to the x-axis (Fig. 4.10b) and a
perpendicular drawn from the intersection point to thex-axis givesKiand a
perpendicular drawn to they-axis gives 1/(1Ki)Vmax. Finally, a Dixon plot of
uncompetitive inhibition results in parallel lines with no intersection, and thus
the inability to graphically estimate any kinetic parameters (Fig. 4.10c).
As mentioned above, the graphical methods proposed by Cornish-Bowden
are complementary as will be demonstrated below. In these types of plots (Fig.
4.10d–f), [S]/nis plotted along they-axis and the inhibitor concentration [I] is
plotted along thex-axis. In the case of competitive inhibition (Fig. 4.10d) a
series of parallel lines is obtained that can be used to confirm the type of
inhibition, but no kinetic parameter estimates can be made. For mixed
inhibition (Fig. 4.10e) the series of lines intersect in the lower left quadrant of
the plot and can be used to distinguish mixed inhibition from competitive (note
the ambiguity of mixed inhibition plots versus competitive inhibition plots with
the Dixon method). For mixed inhibition, a perpendicular drawn from the
intersection point to thex-axis allows an estimation ofKiand a perpendicular
drawn to thex-axis is equal toKm(1Ki)/Vmax. Finally, in contrast to the
Dixon plot, application of the method of Cornish-Bowden to a case of
uncompetitive inhibition (Fig. 4.10f) results in a series of lines intersecting in
the upper left quadrant of the graph with a perpendicular from the intersection
point to thex-axis giving an estimate ofKiand one drawn from this same
intersection to they-axis giving an estimate ofKm/Vmax.
INHIBITION KINETICS GRAPHICAL PLOTS 107