Biomedical Engineering Reference
In-Depth Information
=
interval. Because [E
0
], the enzyme concentration at t
0, is the sum
of [E] plus [ES], and because the substrate conversion is maximal
when enzyme molecules are saturated with substrate and involved
within the catalytic process (v
max
=
[E
0
]), it is possible to
transform the rate equation into theMichaelis-Menten equation
k
3
·
[S]
K
M
+[S]
K
M
is the Michaelis constant or the enzymatic reaction and is
defined by
v
max
·
=
v
k
2
+k
3
k
1
If the reaction rate v is plotted against the substrate concentration
[S] (measuring v at different substrate concentrations within a lin-
ear range of substrate conversion), v
max
is calculated for [S]
=
K
M
→∞
and the value of 0.5
·
v
max
gives K
M
.If[S]
>>
K
M
,thenvbecomes
v
max
.
K
M
and v
max
are mostly determined from linearized plots de-
rived from conversions of the Michaelis-Menten equation. Some
of these linearizations are given in Table 9.3.
The Lineweaver-Burk plot is very useful for descriptions
of type and effects of inhibitors: Competitive inhibitors have the
same intercept on the ordinate and different intercepts on abscissa,
non-competitive inhibitors give the same intercept at the abscissa
but different at the ordinate. In the case of (partially) inhibited
reactions, the slope is larger than at the respective non-inhibited
reaction.
If the effect of an inhibitor on an enzyme is to be investigated,
the Dixon plot is recommended. To obtain data for the Dixon plot,
estimate the reaction rate at constant substrate concentration and
vary the inhibitor concentration [I]. At competitive inhibition, all
the obtained straight lines coincide at a point with the coordinates
x
=
=
/
v
max
, and at non-competitive inhibition all the
straight lines have the same intercept on abscissa at x
−K
I
,y
1
=
−K
I
.At
Table 9.3.
Transformations for graphic determination of K
M
and v
max
Plot according to
Plot on
Intercept with the
Slope
Abscissa
Ordinate
Abscissa
Ordinate
Lineweaver
1/[S]
1/v
−1/K
M
1/v
max
K
M
/v
max
and Burk
Hanes
[S]
[S]/v
−K
M
K
M
/v
max
1/v
max
Eadie and Hofstee
v/[S]
v
v
max
/K
M
v
max
−K
M
1/v
a
max
Dixon
[I]
1/v
a
At high excess of substrate
