Why, When and How of
Enzyme Kinetics
Esther Bulloch
Crystal Club November 2008
Overview
ƒ Basic theory.
v
Contains equations which may
disturb some viewers.
ƒ Why would I care about basic enzyme kinetics?
[S]
ƒ How do I investigate the kinetics of my enzyme?
ƒ Advanced application: inhibitor testing.
ƒ Where do I go for more information?
Basic Enzyme Kinetics
ka
+
E
kcat
+
kd
S
ES
E
P
How does the rate of an enzyme catalysed reaction vary with substrate concentration?
Assumptions in deriving a model (steady state):
ƒ Catalysis is the slowest step.
ƒ [S]>>>[E]
ƒ [ES] is constant
ƒ Reverse reaction negligible
steady state assumption
+
Demystifying the Michaelis-Menten Model
ka
+
E
kcat
+
kd
S
Rate of reaction:
ES
E
v = kcat[ES]
ka[E][S] = kcat[ES] + kd[ES]
Steady state assumption:
Concentration of free enzyme:
[ET] = [ES] + [E]
[ES] = [ET] [S]
KM + [S]
P
Demystifying the Michaelis-Menten Model
ka
+
Rate of reaction:
kcat
kd
v = kcat[ES]
equivalent to
+
v = kcat [ET] [S]
KM + [S]
Maximum rate of reaction at high [S]:
Vmax =kcat[ET]
Michaelis-Menten equation:
v = Vmax[S]
KM + [S]
Maud Menten
(1879–1960)
Leonor Michaelis
(1875–1949)
v = Vmax[S]
Vmax
v
KM + [S]
Vmax : maximum rate of reaction
Vmax =kcat[ET]
KM
KM: substrate concentration at half Vmax
[S]
KM = kd + kcat
~ Kd
ka
+
ka
kd
kcat
+
Who cares? What does basic kinetic analysis tell me about
my enzyme?
Vmax , kcat – how fast is my enzyme at catalysing this reaction?
KM – how much does my enzyme like this substrate?
kcat /KM
– specificity constant
– how efficient is my enzyme at catalysing this reaction?
Applications of basic kinetic analysis
vs
ƒ Comparison with homologous enzymes
ƒ Analysing enzyme mutants
vs
ƒ Activity of enzyme against alternative substrates
Analysis of enzyme mutants
vs
ƒ Measurements of mutant activity at single [S] provides limited information .
ƒ Determining Vmax and KM of mutant assists in pinpointing role in mechanism.
WT
v
mutant
Catalysis?
Binding?
[S]
Real life example: Anthranilate synthase
AS
KM (μM)
kcat (s-1)
kcat /KM (s-1M-1)
WT
3.5
5.0
(1.4) × 106
Y449F
8.3
5.0
(6.0) × 105
Analysis of enzyme mutants
ƒ Determine difference in transition state energies for rate limiting step.
vs
ES
ES
EP
EP
Free Energy
ES‡
ΔΔGES‡
ΔΔGES‡ = -RTIn (kcat /KM)a
(kcat /KM)b
ES
EP
ƒ May indicate contribution of residue to thermodynamics of reaction.
e.g. hydrogen bond ΔΔGES‡ = 4 kcal/mol
How do I investigate the kinetics of my enzyme?
ƒ Develop an enzyme activity assay.
[S] = 8
[S] = 4
signal
ƒ Measure INITIAL rate of reaction at various
substrate concentrations.
[S] = 2
ƒ Accurately fit data to Michaelis-Menten model to
obtain KM and Vmax.
v
time
[S]
What are important features in setting up an enzyme assay?
ƒ Sensitive and reproducible.
ƒ Consistent with the assumptions of the Michaelis-Menten equation.
[S]>>>[E]
Reverse reaction negligible
+
v
ƒ Linear for range of activity to be measured.
ƒ pH and temperature tightly controlled.
[E]
How can I monitor my enzyme catalysed reaction?
ƒ Optical methods
- absorption
ƒ Radioactivity
- fluorescence
ƒ Electrophoresis
ƒ Chromatography
ƒ Calorimetry
ƒ Immunology
Continuous or stopped assay?
ƒ Continuous
Rate at certain [s] can be determined
with single continuous reading.
signal
[s] = y
time
ƒ Stopped assay
[s] = y
signal
Rate at certain [s] must be determined
by measuring samples stopped at
multiple time points.
time
Direct or coupled assay?
ƒ Direct
ƒ Coupled assay
Æ enzymatically coupled
! Ensure coupling step is not rate limiting and coupling
components do not effect enzyme activity.
signal
Æ chemically coupled
time
Tips in obtaining an accurate Michaelis-Menten curve.
ƒ Use controls to check for non-enzymatic background drift in assay.
signal
ƒ Measure rate before 10% substrate consumed.
100%
substrate
consumed
10% substrate
consumed
time
v
ƒ Preferably determine rates by least-squares fitting.
ƒ Determine rates at [S] range of ½ KM to 10 KM
[S]
Real life example: MbtI
Assay solution
50 mM Tris.HCl
5 mM MgCl2
0.5 to 140 µM chorismate
~200 nM MbtI (initiation, small volume)
Fluorescence assay conditions
excitation 305 nm
emission 440 nm
T = 37 °C (plate pre-incubated)
Real life example: MbtI
Raw data
500
400
0.5 µM
1 µM
2 µM
4 µM
6 µM
12 µM
FU
300
200
100
0
0
5
10
Time (min)
15
Real life example: MbtI
Rates fitted to the Michaelis-Menten equation
3
2.5
Rate (FU/s)
2
KM = 2.1 ± 0.3 μM
1.5
Vmax = 2.6 ± 0.1 FU/s
1
0.5
0
0
20
40
60
80
100
[chorismate], μM
120
140
How do I fit my data to the Michaelis-Menten equation?
ƒ Linear methods
e.g. Lineweaver-Burke plot
1/v
1 = KM
+ 1
v Vmax[S] Vmax
-1/KM
1/Vmax
1/[S]
ƒ Non-linear regression
KM + [S]
v
v = Vmax[S]
e.g. Sigma Plot
Grafit
[S]
What about testing inhibitors against my enzyme?
ƒ Are IC50 (median inhibition concentration) values enough?
Æ Require relatively few experimental measurements
Æ Useful for high-throughput screening.
Æ Value determined highly [S] dependent.
v
Æ Does not indicate mechanism of action.
[I]
What about testing inhibitors against my enzyme?
ƒ What’s so good about KI (inhibition constant) values?
Æ Analyse effect of inhibitor on Michaelis-Menten curve.
Æ Values can be compared between assays and enzymes.
Æ May dissect effect of inhibitor on catalysis vs binding.
Æ Indicates mechanism of action
v
Increasing [I]
[S]
Real life example: MbtI
6
I=0
Rate
I = 200
4
I = 500
I = 1000
I = 2000
2
0
0
20
[chorismate]
40
KI = 500 ± 100 μM
Where can I find more information on enzyme kinetics?
Books
Enzymes : a practical introduction to structure, mechanism, and data analysis, 2000
Robert A. Copeland
Fundamentals of enzyme kinetics, 2004
Athel Cornish-Bowden.
Online
http://www.brenda-enzymes.info/
The End