Cambridge International A Level Biology Revision Guide

Chapter 3: Enzymes
results to plot the two types of graph. The table in Question
3.8 gives you some results and it is worth spending some
time answering the question before proceeding.
Figure 3.14a shows a double-reciprocal plot. Note that
it is a straight line. Using this graph, we can find V max
in
the following way. First, we find 1/V max
. This is the point
where the line crosses (intersects) the y-axis because this is
where 1/[S] is zero (and therefore [S] is infinite). Once we
know 1/V max
we can calculate V max
.
Another useful value can be obtained from the
double-reciprocal plot, namely the Michaelis–Menten
constant, K m
. The Michaelis–Menten constant is the
substrate concentration at which an enzyme works at half
its maximum rate (½V max
). At this point half the active
sites of the enzyme are occupied by substrate. The higher
the affinity of the enzyme for the substrate, the lower the
substrate concentration needed for this to happen. Thus
the Michaelis–Menten constant is a measure of the affinity
of the enzyme for its substrate. The higher the affinity,
the lower the Michaelis–Menten constant and the quicker
the reaction will proceed to its maximum rate, although
the maximum rate itself is not affected by the Michaelis–
Menten constant. V max
and K m
therefore provide two
different ways of comparing the efficiency of different
enzymes. V max
gives information about the maximum rate
of reaction that is possible (though not necessarily the rate
under cell conditions) while K m
measures the affinity of
the enzyme for the substrate. The higher the affinity, the
more likely the product will be formed when a substrate
molecule enters the active site, rather than the substrate
simply leaving the active site again before a reaction takes
place. These two aspects of efficiency are rather like using
the maximum speed and acceleration to measure the
efficiency of a car.
How can we find K m
from a double-reciprocal plot?
The answer is that the point where the line of the graph
intersects the x-axis is −1/K m
(note that it is in the negative
region of the x-axis). Figure 3.14a shows this point. From the
value for −1/K m
, we can calculate K m
. Figure 3.14b shows
the normal plot (as in Figure 3.7 and your first graph in
Question 3.8). The relationship between ½V max
and K m
is
shown in Figure 3.14b.
The value of K m
for a particular enzyme can vary,
depending on a number of factors. These include the
identity of the substrate, temperature, pH, presence of
particular ions, overall ion concentration, and the presence
of poisons, pollutants or inhibitors.
Turnover numbers, which are related to V max
and K m
values, for four enzymes are shown in Table 3.2. This
shows the great variation in efficiency that is possible
between enzymes, and the fact that V max
and K m
are
independent of each other.
63
V max
1
V max
= intercept on y-axis
–1
K m
= intercept on x-axis
1
v
1
2 V max
Initial rate
1
[S]
K m
Substrate concentration
Figure 3.14 a A double-reciprocal plot of substrate concentration against initial rate: b A graph showing the effect of substrate
concentration on initial rate, with V max
, ½ V max
and K m
values shown.