aulani " biokimia enzim lanjut" presentasi 5 basic enzyme kinetics aulanni’am...

Aulani " Biokimia Enzim Lanjut" Presentasi 5

Basic enzyme kineticsBasic enzyme kinetics

Aulanni’am

Biochemistry Laboratory

Brawijaya University


EnzymesEnzymes

• Enzymes are catalysts, that speed up the rate of a reaction, without changing the extent of the reaction.

• They are (in general) large proteins and are highly specific, i.e., usually each enzyme speeds up only one single biochemical reaction.

• They are highly regulated by a pile of things. Phosphorylation, calcium, ATP, their own products, etc, resulting in extremely complex webs of intracellular biochemical reactions.


Law of mass actionLaw of mass actionGiven a basic reaction

A + B Ck1

k-1

we assume that the rate of forward reaction is linearly proportional to the concentrations of A and B, and the back reaction is linearly proportional to the concentration of C.

d[A]

dtk 1[C] k1[A][B]


EquilibriumEquilibrium

Equilibrium is reached when the net rate of reaction is zero. Thus

k 1[C] k1[A][B] 0

K1[C] [A][B], K1 k 1

k1

or

This equilibrium constant tells us the extent of the reaction, NOT its speed.

Aulani " Biokimia Enzim Lanjut" Presentasi Aulani " Biokimia Enzim Lanjut" Presentasi 55

Basic problem of enzyme Basic problem of enzyme kineticskinetics

Suppose an enzyme were to react with a substrate, giving a product.

S + E P + E

If we simply applied the law of mass action to this reaction, the rate of reaction would be a linearly increasing function of [S]. As [S] gets very big, so would the reaction rate.

This doesn’t happen. In reality, the reaction rate saturates.


Michaelis and MentenMichaelis and Menten

In 1913, Michaelis and Menten proposed the following mechanism for a saturating reaction rate

S + E k1

k-1

C k2 P + E

Complex. product

• Easy to use mass action to derive the equations.• There are conservation constraints.


Equilibrium approximationEquilibrium approximation

k 1c k1se

And thus, since

c ee0

c e0s

Ks sThus

V k2c k2e0s

Ks sVmaxs

Ks sreaction velocity


Pseudo-steady state approximationPseudo-steady state approximation

(k 1 k2)c k1se

And thus, since

c ee0

c e0s

Km sThus

V k2c k2e0s

Km sVmaxs

Km s

reaction velocityLooks very similar to previous, but is actually quite different!


Basic saturating velocityBasic saturating velocity

s

V

Vmax

Km

Vmax/2


Lineweaver-Burke plotsLineweaver-Burke plots

1

V

1

Vmax

KmVmax

1

s

Plot, and determine the slope and intercept to get the required constants.


CooperativityCooperativity

S + E k1

k-1

C1k2 P + E

S + C1 k3

k-3

C2k4 P + E

Enzyme can bind two substrates molecules at different binding sites.

or

E C1 C2

E E

S S

S S

P P


Pseudo-steady assumptionPseudo-steady assumption

c1 K2e0sK1K2 K2s s

2

c1 e0s

2

K1K2 K2s s2

V k2c1 k4c2 (k2K2 k4s)e0s

K1K2 K2s s2

Note the quadraticbehaviour


Independent binding sitesIndependent binding sites

k1 2k3 k

2k 1 k 3 k2k2 k4

E C1 C2

E E

S S

S S

P P

2k+ k+

2k-k-

V 2k2e0s

K sJust twice the single binding rate, as expected


Positive/negative cooperativityPositive/negative cooperativity

Usually, the binding of the first S changes the rate at which the second S binds.

• If the binding rate of the second S is increased, it’s called positive cooperativity

• If the binding rate of the second S is decreased, it’s called negative cooperativity.


Hill equationHill equationIn the limit as the binding of the second S becomes infinitely fast, we get a nice reduction.

Let k3 , and k1 0, while keeping k1k3 constant.

V (k2K2 k4s)e0s

K1K2 K2s s2

Vmaxs2

Km2 s2

Hill equation, withHill coefficient of 2.This equation is used all the time to describe a

cooperative reaction. Mostly use of this equation is just a heuristic kludge.

VERY special assumptions, note.


Another fast equilibrium model of Another fast equilibrium model of cooperativitycooperativity

E C1 C2

E E

S S

S S

P P

Let C=C1+C2

V k2c1 k4c2 k2K3 k4s

sK3

c (s)c

k-1

k1 k3

k-3

k2 k4

S + E k1

k-1

C s)P + E


Monod-Wyman-Changeux modelMonod-Wyman-Changeux model

A more mechanistic realisation of cooperativity.



Don’t even think about a pseudo-steady approach. Waste of valuable time.

Y r1 2r2 t1 2t22(r0 r1 r2 t0 t1 t2)

K1r1 2sr0,

which gives

Y sK1

1(1 sK1 1) K2

1[sK3 1(1 sK3

1)]

(1 sK1 1)2 K2

1(1 sK3 1)2

occupancy fraction

and so on for all the other states

Note the sigmoidal character of this curve


Reversible enzymesReversible enzymes

Of course, all enzymes HAVE to be reversible, so it’s naughty to put no back reaction from P to C. Should use

S + E k1

k-1

Ck2

P + Ek-2

I leave it as an exercise to calculate that

V e0(k1k2s k 1k 2p)

k1s k 1p k 1 k2


Allosteric modulationAllosteric modulation

substrate binding

inhibitorbinding at adifferent site

this state canform no product

(Inhibition in this case, but it doesn’t have to be)

X

Y Z



(e0 x y z)s K1x 0

(e0 x y z)i K3y 0

ys K1z0

and thus

x e0K3

K3 is

K1 s

V k2x Vmax

1 i /K3

s

K1 s

X

Y Z

Could change these rate constants, also.Inhibition decreases the Vmax in

this model

aulani " biokimia enzim lanjut" presentasi 5 basic enzyme kinetics aulanni’am...

Documents

reaction velocity slide

basic reaction

net rate of reaction

rate of forward reaction

c s p e slide

cooperative reaction

binding rate

s ep e