Enzyme Kinetics

vo=Vmax [S]Km + [S]

Km Vmax &

E1E2E3

1st order

zero order

Competitive

Non-competitive

Uncompetitive

Direct plot

Double reciprocal

Bi-substrate reaction alsofollows M-M equation, butone of the substrate shouldbe saturated when estimate the other

Affinity withsubstrate

Maximumvelocity Inh

ibition

Activity

Observe vo change under various [S], resulted plotsyield Vmax and Km

k3 [Et]

kcatTurn overnumber

kcat / Km

Activity Unit

1 molemin

Specific Activity

unitmg

Significance

Juang RH (2004) BCbasics

Significance of Enzyme Kinetics

vo =Vmax [S]Km + [S]

Obtain Vmax and Km

[S] = Low → High [S] = Fixed concentration

zero order

1st order

E3

E2E1

Proportional to

enzyme concentration

v0 = Vmax × K = k3 [Et] × K

Juang RH (2004) BCbasics

Km = [S]

Km + [S] = 2 [S]

Vmax

2=

Vmax [S]Km + [S]

Km: Affinity with Substrate

If vo =Vmax

2

S2S1 S3

S1 S2 S3

Vmax

1/2

When using different substrate

Affinity changesKm

vo =Vmax [S]Km + [S]

Jua

ng

RH

(2

00

4)

BC

ba

sics

Km: Hexokinase Example

Glucose + ATP → Glc-6-P + ADP

1

2

3

4

5

6

Glucose Allose Mannose Substratenumber

Km = 8 8,000 5 M

CHO H-C-OH HO-C-H H-C-OH H-C-OH H2-C-OH

CHO H-C-OH H-C-OH H-C-OH H-C-OH H2-C-OH

CHO HO-C-H HO-C-H H-C-OH H-C-OH H2-C-OH

Juang RH (2004) BCbasics

Turn Over Number, kcat

vo =Vmax [S]Km + [S]

(vo)E + S ES E + P

k2

k1 k3

When substrate excess, k3 = kcat, turn over number (t.o.n)

When [substrate] is low

=k3 [E][S]

Km + [S]=

Km

k3 [E][S]

Omit the [substrate] Substrate specificityStart from M-M eq.

Second order(IV)

Juang RH (2004) BCbasics

Turn Over Numbers of Enzymes

Catalase H2O2

Carbonic anhydrase HCO3-

Acetylcholinesterase Acetylcholine

40,000,000

400,000

140,000

-Lactamase Benzylpenicillin 2,000

Fumarase Fumarate 800

RecA protein (ATPase) ATP 0.4

Enzymes Substrate kcat (s-1)

The number of product transformed from substrate by one enzyme molecule in one second

Adapted from Nelson & Cox (2000) Lehninger Principles of Biochemistry (3e) p.263

Chymotrypsin Has Distinct kcat / Km to Different Substrates

O R O

H3C–C–N–C–C–O–CH3

H H

= – =––

–HGlycine

kcat / Km

1.3 ╳ 10-1

–CH2–CH2–CH3Norvaline 3.6 ╳ 102

–CH2–CH2–CH2–CH3Norleucine 3.0 ╳ 103

–CH2–Phenylalanine 1.0 ╳ 105

(M-1 s-1)

R =

Adapted from Mathews et al (2000) Biochemistry (3e) p.379

Enzyme Activity Unit

Reaction time (min)P

rodu

ct [P

]0 10 20 30 40

Slopetan

S → P mole

vo = [P] / min

Unit =

Activity Units

Protein (mg)

t

mole/min

yx

yx = tan

Jua

ng

RH

(2

00

4)

BC

ba

sics

Specific Activity =