| Graphical and Mathematical Analysis
of the Reversible Inhibition of Enzyme Kinetics |
|
|
Graphical
Formats |
Michaelis-Menten
Rectangular
Hyperbolic Plot |
Lineweaver-Burke Double-Reciprocal
Plot |
|
Y vs. X Empirical Variables |
Vo vs. [S]o |
1/Vo vs. 1/[S]o |
Functional Relationships
Y = f(X) |
| V0 |
= |
(Vmaxapp)*[S]0h |
|
| [S]0h+
(KMapp)h |
|
1/V0
= (1/[S]0h)*(KMapp)h/(Vmaxapp)
+ 1/Vmaxapp |
|
|
Graphical
formats: |
Eisenthal-Cornish-Bowden Direct
Linear Plot |
Scatchard
Plot |
| Y vs. X Empirical Variables
|
Vo vs. -[S]o
Vmaxapp
& KMapp
are pseudo-variables. |
r/[S]0
vs. r
where r =
n*(V0/Vmaxapp) |
Functional Relationships
Y = f(X) |
Vmaxapp=
(V0/[S]0h)*(KMapp)h
+ V0 |
r/[S]0
= ([S]0h-1/(KMapp)h)*(n-r) |
|
|
Graphical
Formats |
Hill
Plot |
| Y vs. X empirical plots |
log (V0/Vmaxapp-V0) vs.
log [S]0 |
Functional Relationships
Y = f(X) |
log
(V0/(Vmaxapp-V0)) = log
([S]0/KMapp)h =
h*log ([S]0/KMapp) |
|
|
Constants and
Definitions |
| KMapp
= [S]50%
@ V0
= Vmaxapp/2 |
h =
Hill
coefficient,
h = 1 for Michaelis-Menten Kinetics |
n =
# of identical catalytic sites per E molecule.
r = average # of S molecules converted
to P molecules per enzyme. molecule per unit time. |
| Competitive Inhibition |
Uncompetitive Inhibition |
Mixed Inhibition |
Vmaxapp
= Vmax
- unchanged
KMapp
= a*KM
where
a
= (1 + [I]/KI) |
Vmaxapp
= Vmax/a'
(mM/sec)
KMapp
= KM/a where a'
= (1 + [I]/KI') |
Vmaxapp
= Vmax/a'
& KMapp
= a*KM/a'
where a
= (1 + [I]/KI)
&
a'
= (1 + [I]/KI') |