Using Kinetics to Elicit Mechanistic Information

1
Using Kinetics to Elicit Mechanistic Information

• as a model, look at movement of some substrate,
  S, across cell wall.
• A. By Diffusion.

S
P
out in
?
S rate 1 1 2 2 3
3 4 4 6 6 8
8 10 10 12 12
?
?

rate
?
?
first-order reaction rate k S
?
?
?


S
2
Using Kinetics to Elicit Mechanistic Information

• as a model, look at movement of some substrate,
  S, across cell wall.
• B. By Active Transport.

door can only revolve fast enough to pass
4S/minute
S
P
out in
S rate 1 1 2 2 3
3 4 4 6 6 8
8 10 8 12 8
kmax
?
?
?

rate
?
hyperbolic
?
?
?
?


S
3
Derivation of Kinetic Equation
k1 k-1
kp
E S ES
P E
second step is rate limiting
rate kp ES cannot measure ES directly
express as fraction of total E concentration,
Eo ES
1 rate kp
Eo kp Eo
ES E
1 (E/ES) steady
state approximation formation of ES rate of
reaction of ES k1 ES kp ES k-1
ES k1 ES kp k-1 or
(E/S) ((kp
k-1)/k1)(1/S) ES or (E/S)
km(1/S) substitute in
above equation
( ) ( )
4
Derivation of Kinetic Equation
k1 k-1
kp
E S ES
P E
1
1
S rate
kp Eo
kp Eo
kp Eo 1
(E/ES) 1
km(1/S) S
km kmax kpEo maximum rate would be
when all of E is in the form of ES
kmax S rate
equation for a hyperbola km
S
( ) ( ) (
)
kmax
?
?
?

rate
?
hyperbolic
?
?
?
?


S
5
Lineweaver-Burke Plots
k1 k-1
kp
E S ES
P E

kmax S 1/rate km
S take inverse of both sides
km S km S 1/rate

kmax S kmax S kmax
S km 1
1 1/rate
kmax S kmax y
m x b Plot 1/rate vs.
1/S
it is difficult to look at these plots and
predict km and kmax values
( )
kmax
?
?
?

rate
?
hyperbolic
?
?
?
?


S
6
Lineweaver-Burke Plots
k1 k-1
kp
E S ES
P E

kmax S 1/rate km
S take inverse of both sides
km S km S 1/rate

kmax S kmax S kmax
S km 1
1 1/rate
kmax S kmax y
m x b Plot 1/rate vs.
1/S
it is difficult to look at these plots and
predict km and kmax values
Lineweaver- Burke Plot
( )
slope km/kmax

1/rate
intercept 1/kmax


1/S
7
Competitive Inhibition
S
PS or PI
I
out in
In competitive inhibition, the inhibiting
species competes for uptake by the receptor. This
is a reversible process that may be overcome by
adding more substrate. Thus, at a particular
concentration of substrate, the greater the
concentration of inhibitor, the slower the rate
of reaction. However, for the same inhibitor
concentration, an increase in substrate concentrat
ion will eventually approach kmax.
kmax

rate
no inhibitor some inhibitor more inhibitor


S
8
Kinetic Example
Coprogen
Ferrichrome
out in
Many microbial cells use siderophores to
transport iron into the cell. There are two types
of siderophores recognized by the cell 1.
coprogens, and 2. the ferrichromes. Question Do
the coprogens and ferrichromes use the same
or different transport systems to get into the
cell? How can we determine this? Radiolabel
coprogen and watch its uptake (at various
concentrations) by itself and then when a certain
concentration of ferrichrome is also present. If
using different transport systems, what effect
should the ferrichrome have on coprogen uptake?
NONE Results at right. Therefore,
coprogen and ferrichrome DO use the same
transport system.
kmax

rate
no ferrichrome with ferrichrome


S