1. CHMI 2227E Biochemistry I Enzymes: Kinetics
CHMI E.R. Gauthier, Ph.D.

2. Enzymatic reactions Let’s set up a typical enzymatic reaction:
Enzyme (each = 1 µmol)
Only concentrations we know  we’re the ones who set up the experiment!
Substrate (each = 1 µmol)
X min
Product
CHMI E.R. Gauthier, Ph.D.

3. Enzymatic reactions How do we measure enzyme activity?
1. Detection of the product(s):
pNA = para-nitroaniline  Absorbs at 405 nm
H3+N-CH-C-NH-CH-C-NH-CH-C-NH-CH-C-OH O
CH2
COO- CH
CH3
H3C
NO2
H2N
pNA (yellow)
H3+N-CH-C-NH-CH-C-NH-CH-C-NH-CH-C-NH-
DEVD-pNA
(uncolored)
DEVD
(uncoloured)
Caspase 3 (proteasehydrolase)
Measure increase
in A405nm
CHMI E.R. Gauthier, Ph.D.

4. Enzymatic reactions How do we measure enzyme activity?
2. Accumulation/utilisation of a co-factor:
NADH = absorbs strongly at 340 nm (e = 6.3 molL-1cm-1 )
NAD+ =does not absorb at 340 nm
Measure increase
in A340nm
Measure decrease
in A340nm
Lactate
dehydrogenase
CHMI E.R. Gauthier, Ph.D.

5. Enzymatic reactions How do we measure enzyme activity?
3. Coupled reactions:
Very useful when neither substrate/product/co-factor can be (easily) detected;
Glutaminase
+ NH4+
1st reaction
Measure increase
in A340nm
Glutamate
Dehydrogenase
+ NAD+
+ NADH +H+
2nd reaction
+ H2O
Detectable by HPLC
but not practical
CHMI E.R. Gauthier, Ph.D.

6. Enzymatic reactions [Product] Time VELOCITY 3 µmol / min or Rate 1 min
15 µmol S vs 1 µmol E
Time
[Product]
Slope = Initial velocity
= v0 = [P] / time
2 min
3 µmol / min
4 min
<3 µmol / min
CHMI E.R. Gauthier, Ph.D.

7. Enzymatic reactions v0 is proportional to [E] 3µmol E 2µmol E
1 min
3 µmol / min
15 µmol S vs 1 µmol E
6 µmol / min
15 µmol S vs 2 µmol E
9 µmol / min
15 µmol S vs 3 µmol E
Time
[Product]
v0 is proportional to [E]
1µmol E
2µmol E
3µmol E
CHMI E.R. Gauthier, Ph.D.

8. Enzymatic reactions Maximum velocity = Vmax Vmax ½ Vmax v0 [Substrate]
1 µmol / min
1 min
[Substrate] v0
Maximum velocity = Vmax
Vmax
½ Vmax
2 µmol / min
1 min
3 µmol / min
1 min
E saturated by S
CHMI E.R. Gauthier, Ph.D.

9. Enzymatic reactions So:
1) v0 (initial velocity) is the rate of the reaction very early on  when [P] is negligeable;
2) v0 can be obtained by taking the slope of the graph of [P] vs Time (units: concentration / time)
3) v0 varies as a function of [E];
4) v0 increases as a function of [S] UNTIL E is saturated by S.
5) When E is saturated with S  v0 = Vmax
CHMI E.R. Gauthier, Ph.D.

10. Michaelis-Menten Equation
The relationship between vo and [S] can be viewed as a 2 step reaction:
This relationship can be expressed by the Michaelis-Menten equation:
[Substrate] v0
Maximum velocity = Vmax
Vmax
½ Vmax
E + S ES E + P k2 k1
k-1
FAST
SLOW
vo = Vmax [S]
Km + [S]
CHMI E.R. Gauthier, Ph.D.

11. Michaelis-Menten Equation
Km can be calculated as the [S] required to acheive half the Vmax;
Km is a measure of the affinity of E for S:
The lower the Km, the less S is requried by E to acheive ½ Vmax, and the greater the affinity of E for S.
[Substrate] v0
Vmax
½ Vmax
Km1
Km2 E2 E1
CHMI E.R. Gauthier, Ph.D.

12. Km
CHMI E.R. Gauthier, Ph.D.

13. Turnover number At saturating [S] :
vo = Vmax
vo is determined by [E]
k2 will drive the rate;
k2= kcat
So: Vmax = kcat [E]total
kcat = Vmax/[E]total
kcat = turnover number = maximum number of substrate molecules converted to product per second by each active site (units = s-1)
1/kcat = amount of time required for E to convert 1 substrate molecule to the product (i.e. time for 1 catalytic event). Units: s.
E + S ES E + P k2 k1
K-1
FAST
SLOW
CHMI E.R. Gauthier, Ph.D.

14. Measuring Km and Vmax
Neither Km nor Vmax can be easily obtained directly from kinetic data because Vmax is rarely acheived (its an hyperbolic curve…);
[Substrate] v0
Vmax
½ Vmax Km
CHMI E.R. Gauthier, Ph.D.

15. Measuring Km and Vmax 1/vo 1 = Km x 1 + 1 vo Vmax [S] 1/Vmax 1/[S]
However, Km and Vmax can be easily obtained if we take the reciprocal of (and slightly rearrange) the Michaelis-Menten equation: the Lineweaver-Burk equation:
The graph of 1/vo vs 1/[S] gives a straight line with:
Intercept on the x axis = -1/Km
Intercept on the y axis = 1/Vmax
This is the BEST and EASIEST way to accurately obtain Vmax and Km since:
You know [S] (you’re the one who did the experiment!!)
V0 is easily obtained in the lab (slope of [P] vs Time).
1/vo
1/[S]
1/Vmax
-1/Km
Lineweaver-Burk plot 1 vo
= Km x
Vmax
[S]
CHMI E.R. Gauthier, Ph.D.