Enzymes and enzyme kinetics

• enzyme "in yeast"

• proteins and catalysts

• 1860: L. Pasteur "fermentation catalyzed by enzymes"

• 1897: E. Buchner demonstrated alcohol production independent of cells

• 1926: J.B. Sumner isolated pure crystalline urease

milestones

urease

NH2

NH2

C O + H2O 2NH3 + CO2

• accelerates reaction 1014 fold• average for enzymes is 108 – 1020 fold

Don't you hate definitions

• enzyme (catalyst) is substance that increases the rate of chemical reaction without undergoing permanent change itself

• influences rate only, not equilibrium

Units

• 1 IU urease liberates 1 μmole NH3/min at pH 7, 25oC

• generally use initial rate studies

Free energy of activation

L-amino acids from D/L-mixtures

D/L-amino acid

acyl D/L-amino acid

L-amino acid + acyl D-amino acid

acyl D/L-amino acid

acetylation

L-amino acylase

racemization

Enzyme electrodes

Type Enzyme Sensor Stable Time

urea urease pH, NH3 3 weeks few min

glucose glu oxidase pH, O2 wk-months few min

L-glutamate glut dehydrog. various days-wks 1-2 min

lactic acid lact dehydrog. Pt(Fe(CN)) 1 week 3-10 m

alcohols alc oxidase Pt(O2) day-month >1 min

penicillin penicillinase pH 2-3 weeks 2 min

cholesterolchol oxidase Pt(H2O2) 2 min

uric acid uricase Pt(O2) 4 month 30 sec

YSI biochemistry analyzer•glucose, sucrose•lactose•L-lactate•galactose•L-glutamate•choline•L-glutamine•ethanol•hydrogen peroxide•starch

typical enzyme electrode

H5C2 CH2

O

C NH

O

CH

C

CH3

CH3

O

OHC

CH

N CH

CS

NH2

O

CH

C

CH3

CH3

O

OHC

CH

N CH

CS

penicillinacylase

H2O

+ C2H5-CH2COOH

penicillin-G

6-aminopenicillanic acid

ampicillinamoxicillin

Staph (from urine)

semi-synthetic penicillins

sweeteners

lactose (whey) galactose + glucoselactase

heparinase I fromFlavobacterium heparinum

neutralization of heparin in blood and plasma

enzyme kinetic considerations

• rate of reaction (catalytic activity)

• extent of reaction (equilibrium constant)

• duration of usable activity (stability)

• cost

Michaelis Menten kinetic model (1913)

enzyme + reactant enzyme-reactant complex enzyme + product

E + R ER E + Pk1 k2

k-1

Assumptions:• steady state [ER] = constant, d[ER]/dt = 0• single reactant R• [R] >> [E] and [R] >> [ER]• neglect k-2

E + R ER E + Pk1 k2

k-1

from assumption 1 (steady state)

[R] K

][R]E[ ER][

dt

d[P] v rate

[R] K

][R][E [ER]

[ER] - ][E [E]

constant [E] [ER] [E]

K[ER]

[E][R]

[ER])( [E][R]

0 [ER])( - [E][R]dt

d[ER]

m

o22

m

o

o

o

m1

21

211

211

kk

k

kk

kkk

kkk

E + R ER E + Pk1 k2

k-1

v = Vmax when [Eo] ~ [ER]

thus Vmax = k2[Eo]

and

[R] K

[R] V v

m

max

Michaelis-Menten eqn.

ctc

t

k

kkK

ER

REK

Kk

kK

kk

K

m

s

sm

m

11

1

1

21

1

1

21

-1

Units,

][

]][[ where

complex ERfor constant on dissociati the,~then

reactions, somein

substrate)for enzyme of(affinity ~

Saturation kinetics

When R >> Km, v = (Vmax/Km)Rfirst order with respect to R.... R-limiting

When R >> Km, v = Vmax = k2[Eo]zero order wrt R, and E is rate limiting since saturated with R

When v = 0.5 Vmax, then Km = R

[R] K

[R] V v

m

max

R][K

R][Ekv

s

o2

Michaelis-Menten kinetics• theoretical basis• saturation kinetics• single reactant

Monod kinetics• empirical base• saturation kinetics• S is typically C-source]S[K

[S]μμ

m

max

R][K

R][Vv

s

max

double reciprocal plot (Lineweaver Burk plot)

maxmax

m

V

1

R

1

V

K

v

1

max

m

max

maxm

V

K

V

R

v

R

VR

vKv

Eadie-Hofstee plot

Hanes plotLineweaver-Burkplot

Reactant inhibition (uncompetitive)

E + R ER E + P

+

R

ERR

k1

k-1

k2

k3 k-3

v

[R]

v[R]K

1Vv

K

R1

V v,K Rfor

)K

R(1

V

1

R

1

V

K

v

1

[ERR]

[ER][R]

k

kK ere wh

K

R

R

K1

Vv

imax

i

maxm

imaxmax

m

3

3i

i

m

max

1/v

1/R

no inhibition

substrate inhibition

-1/Km

-1/Km(1+R/Ki)

Vmax

Km

slope = Km/Vmax const

v

v/R

slope = -1/Ki

Vmax

product inhibition (competitive)

E + R ER E + P EPk4

k-4

sucrose glucose + fructoseinvertase

E + R P

[EP]

[E][P]

k

kK where

[P]K

KK[R]

[R]Vv

4

4i

i

mm

max

no inhibition

inhibition

-1/Km

Km increaseVmax no change

maxmax

m

i V

1

[R]

1)

V

K)(

K

P(1

v

1

non-competitive inhibition

• urease-Ni + EDTA (chelator)

• heavy metal toxicity, binding to disulfide bridges (cysteine)

• organic acids (acetate, propionate, lactate on hydrolytic enzymes

• inhibitor acts at another site on the enzyme, but changes configuration

maximax

m

i

im

imax

V

1)

K

I(1

R

1)

V

K)(

K

I(1

v

1

[I][R])(K(K

[R]KVv

no inhibition

inhibition

1/v

1/R

Km unchangedVmax reduced

substrate product or substrate reversibleuncompetitive analog, competitive non-competitive

T-effects

RT

EAln kln

eqn. Arrhenius )RT

EAexp(k

][EkV

2

2

o2max

activation

inactivation

ln vorln Vmax

orln k2

1/T (kelvin)