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Aulani " Biokimia Enzim Lanjut" Presentasi 5
Basic enzyme kineticsBasic enzyme kinetics
Aulanni’am
Biochemistry Laboratory
Brawijaya University
Aulani " Biokimia Enzim Lanjut" Presentasi 5
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.
Aulani " Biokimia Enzim Lanjut" Presentasi 5
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]
Aulani " Biokimia Enzim Lanjut" Presentasi 5
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.
Aulani " Biokimia Enzim Lanjut" Presentasi 5
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.
Aulani " Biokimia Enzim Lanjut" Presentasi 5
Equilibrium approximationEquilibrium approximation
k 1c k1se
And thus, since
c ee0
c e0s
Ks sThus
V k2c k2e0s
Ks sVmaxs
Ks sreaction velocity
Aulani " Biokimia Enzim Lanjut" Presentasi 5
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!
Aulani " Biokimia Enzim Lanjut" Presentasi 5
Basic saturating velocityBasic saturating velocity
s
V
Vmax
Km
Vmax/2
Aulani " Biokimia Enzim Lanjut" Presentasi 5
Lineweaver-Burke plotsLineweaver-Burke plots
1
V
1
Vmax
KmVmax
1
s
Plot, and determine the slope and intercept to get the required constants.
Aulani " Biokimia Enzim Lanjut" Presentasi 5
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
Aulani " Biokimia Enzim Lanjut" Presentasi 5
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
Aulani " Biokimia Enzim Lanjut" Presentasi 5
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
Aulani " Biokimia Enzim Lanjut" Presentasi 5
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.
Aulani " Biokimia Enzim Lanjut" Presentasi 5
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.
Aulani " Biokimia Enzim Lanjut" Presentasi 5
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
Aulani " Biokimia Enzim Lanjut" Presentasi 5
Monod-Wyman-Changeux modelMonod-Wyman-Changeux model
A more mechanistic realisation of cooperativity.
Aulani " Biokimia Enzim Lanjut" Presentasi 5
Equilibrium approximationEquilibrium approximation
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
Aulani " Biokimia Enzim Lanjut" Presentasi 5
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
Aulani " Biokimia Enzim Lanjut" Presentasi 5
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