CHMI 2227 - E.R. Gauthier, Ph.D. 1

CHMI 2227EBiochemistry I

Enzymes:- Kinetics

CHMI 2227 - E.R. Gauthier, Ph.D. 2

Enzymatic reactions

Let’s set up a typical enzymatic reaction:

Enzyme (each = 1 µmol)

Substrate (each = 1 µmol)

Only concentrations we know we’re the ones who set up the experiment!

X min Product

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Enzymatic reactionsHow 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 O O O

CH2

COO-

CH2

CH2

COO-

CHCH3H3C

CH2

COO-

NO2H2N

pNA (yellow)

H3+N-CH-C-NH-CH-C-NH-CH-C-NH-CH-C-NH-

O O O O

CH2

COO-

CH2

CH2

COO-

CHCH3H3C

CH2

COO-

NO2DEVD-pNA(uncolored)

DEVD(uncoloured)

Caspase 3 (proteasehydrolase)Measure increase

in A405nm

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Enzymatic reactionsHow do we measure enzyme activity? 2. Accumulation/utilisation of a co-factor:

NADH = absorbs strongly at 340 nm ( = 6.3 molL-1cm-1 ) NAD+ =does not absorb at 340 nm

Measure increase in A340nm

Measure decrease in A340nm

Lactate dehydrogenase

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Enzymatic reactionsHow 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

GlutamateDehydrogenase

+ NAD+ + NADH +H+

2nd reaction

+ NH4++ H2O

Detectable by HPLC but not practical

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Enzymatic reactions

1 min

3 µmol / min VELOCITYor Rate

15 µmol S vs 1 µmol E

Time

[Pro

duct

]

Slope = Initial velocity = v0 = [P] / time

2 min

3 µmol / min

4 min

<3 µmol / min

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Enzymatic reactions

Time

[Pro

duct

]

v0 is proportional to [E]

1µmol E

2µmol E

3µmol E

1 min

3 µmol / min

15 µmol S vs 1 µmol E

1 min

6 µmol / min

15 µmol S vs 2 µmol E

1 min

9 µmol / min

15 µmol S vs 3 µmol E

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Enzymatic reactions

1 min

2 µmol / min

1 µmol / min

1 min

3 µmol / min

1 min

[Substrate]

v 0

Maximum velocity = Vmax

Vmax

½ Vmax

E saturated by S

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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

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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]

v 0

Maximum velocity = Vmax

Vmax

½ Vmax

E + S ES E + Pk2

k1

k-1

FAST SLOW

vo = Vmax [S] Km + [S]

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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:

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]

v 0

Vmax

½ Vmax

Km1 Km2

E2

E1

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Km

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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

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 + Pk2

k1

K-1

FAST SLOW

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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…); [Substrate]

v 0

Vmax

½ Vmax

Km

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Measuring Km and Vmax 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 1 + 1

Vmax [S] Vmax