CHMI 2227E
Biochemistry I
Enzymes:
-
Kinetics
CHMI 2227 - E.R. Gauthier, Ph.D.
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Enzymatic reactions

Let’s set up a typical enzymatic reaction:
Enzyme (each = 1 µmol)
Substrate (each = 1 µmol)
X min
Only concentrations we know  we’re
the ones who set up the experiment!
Product
CHMI 2227 - E.R. Gauthier, Ph.D.
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Enzymatic reactions
How do we measure enzyme activity?

1. Detection of the product(s):

pNA = para-nitroaniline  Absorbs at 405 nm
O
DEVD-pNA
(uncolored)
O
O
O
H3+N-CH-C-NH-CH-C-NH-CH-C-NH-CH-C-NHCH2
COO-
CH2
CH
CH2 H3C CH3
COO-
CH2
COOMeasure increase
in A405nm
Caspase 3 (proteasehydrolase)
O
O
NO2
O
O
DEVD
H3+N-CH-C-NH-CH-C-NH-CH-C-NH-CH-C-OH
(uncoloured)
CH2
CH2
CH
CH2
COOCH2 H3C CH3
COOCOO
CHMI 2227 - E.R. Gauthier, Ph.D.
H2N
NO2
pNA (yellow)
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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
Lactate
dehydrogenase
CHMI 2227 - E.R. Gauthier, Ph.D.
Measure decrease
in A340nm
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Enzymatic reactions
How do we measure enzyme activity?

3. Coupled reactions:

Very useful when neither substrate/product/co-factor can be
(easily) detected;
Detectable by HPLC
but not practical
Glutaminase
1st reaction
+ NH4+
2nd reaction
+ NAD+
+ H2O
Glutamate
Dehydrogenase
+ NADH +H+
+ NH4+
CHMI 2227 - E.R. Gauthier, Ph.D.
Measure increase
in A340nm
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Enzymatic reactions
3 µmol / min
VELOCITY
or Rate
1 min
Slope = Initial velocity
= v0 = [P] / time
3 µmol / min
2 min
<3 µmol / min
[Product]
15 µmol S vs 1 µmol E
Time
4 min
CHMI 2227 - E.R. Gauthier, Ph.D.
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Enzymatic reactions
3 µmol / min
1 min
v0 is proportional to [E]
15 µmol S vs 1 µmol E
6 µmol / min
1 min
[Product]
3µmol E
2µmol E
1µmol E
15 µmol S vs 2 µmol E
9 µmol / min
Time
1 min
15 µmol S vs 3 µmol E
CHMI 2227 - E.R. Gauthier, Ph.D.
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Enzymatic reactions
1 µmol / min
1 min
Maximum velocity = Vmax
Vmax
2 µmol / min
1 min
v0
½ Vmax
3 µmol / min
[Substrate]
1 min
E saturated by S
CHMI 2227 - E.R. Gauthier, Ph.D.
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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 2227 - E.R. Gauthier, Ph.D.
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Michaelis-Menten Equation

The relationship between vo
and [S] can be viewed as a 2
step reaction:
E +S
k1
k-1
Vmax
E+P
SLOW
½ Vmax
v0
FAST
k2
ES
Maximum velocity = Vmax

This relationship can be
expressed by the MichaelisMenten equation:
[Substrate]
vo = Vmax [S]
Km + [S]
CHMI 2227 - E.R. Gauthier, Ph.D.
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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:
E1
Vmax
E2
v0
½ Vmax

Km1 Km2
[Substrate]
The lower the Km, the less
S is requried by E to
acheive ½ Vmax, and the
greater the affinity of E for
S.
CHMI 2227 - E.R. Gauthier, Ph.D.
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Km
CHMI 2227 - E.R. Gauthier, Ph.D.
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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
E +S
k1
K-1
FAST
ES
k2
E+P
SLOW

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.
CHMI 2227 - E.R. Gauthier, Ph.D.
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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…);
Vmax
½ Vmax
v0

CHMI 2227 - E.R. Gauthier, Ph.D.
Km
[Substrate]
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Measuring Km and Vmax

1/vo
However, Km and Vmax can be easily obtained if
we take the reciprocal of (and slightly rearrange)
the Michaelis-Menten equation: the LineweaverBurk equation:
1 = Km
vo
Vmax

1/Vmax

1/[S]
-1/Km
+
1
Vmax
The graph of 1/vo vs 1/[S] gives a straight line
with:


x 1
[S]
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).
Lineweaver-Burk plot
CHMI 2227 - E.R. Gauthier, Ph.D.
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