KAPITOLA 3KAPITOLA 3Enzymová katalýza IEnzymová katalýza I

• katylytická aktivita enzymůkatylytická aktivita enzymů• interakce enzym - substrátinterakce enzym - substrát• koenzymykoenzymy• vazebné místo pro substrátvazebné místo pro substrát• fyzikálně chemické vlastnostifyzikálně chemické vlastnosti• nomenklatura enzymůnomenklatura enzymů

An imaginary enzyme (stickase) designed to catalyze the breaking of a metal stick. (a) To break, the stick must first be bent (the transition state). In the stickase, magnetic interactions take

the place of weak-bonding interactions between enzyme and substrate.(b) An enzyme with a magnet-lined pocket complementary in structure to the stick (the substrate) will

stabilize this substrate . Bending will be impeded by the magnetic attraction between stick and stickase.

(c) An enzyme complementary to the reaction transition state will help to destabilize the stick, resulting in catalysis of the reaction. The magnetic interactions provide energy that compensates for the increase in free energy required to bend the stick. Reaction coordinate diagrams show the energetic consequences of complementarity to substrate versus complementarity to transition state. The term GM represents the energy contribued by the magnetic interactions between the stick and stickase. When the enzyme is complementary to the substrate, as in (b), the ES complex is more stable and has less free energy in the ground state than substrate alone. The result is an increase in the activation energy. For simplicity, the EP complexes are not shown.

Reaction coordinate

Free

ene

rgy,

G

The role of binding energy in catalysis. To lower the activation energy for a reaction, the system must acquire an amount of energy equivalent to the amount by which DG# is lowered. This energy comes largery from binding energy ( GB) contribued by formation of weak noncovalent interactions between substrate and enzyme in the transition state. The role of GB is analogous to that of GM.

Many organic reactions are promoted by proton donors (general acids) or proton acceptors (general bases). The active sites of some enzymes contain amino acid functional groups, such as those shown here, that can participe in the catalytic process as proton donors or proton acceptors.

Enzymes

What? Proteins which catalyse biological reactions

Properties? Highly specificUnchanged after reactionCan accelerate reactions >106 foldTurnoverCannot alter reaction equilibria

Conversion of substrate to product:S P

2 factors determine the appearance of product:i. Thermodynamicii. Kinetic

Enzyme Classification

Rawn Biochemistry, International edition

Reaction profile for a simple reaction

Rawn Biochemistry, International edition

UncatalysedEnzyme catalysed

Reaction profile for an enzyme-catalysed reaction

0

200

400

600

800

1000

1200

0

Conc

entra

tion

(micr

omol

ar)

50 100 150 200 250 300 350

S

P

Time (secs)

Change in [S] and [P] with time

Enzyme kinetics

0

0.5

1

1.5

2

2.5

3

0

Rate

(v) m

icrom

olar

per

sec

1 2 3 4 5 6[Enzyme] micromolar

Rate versus [enzyme]

Impact of changing enzyme concentration

0

0.2

0.4

0.6

0.8

1

0

Rate

(v) m

icom

olar

per

sec

200 400 600 800 1000 1200[Substrate] micromolar

Rate versus [substrate]

Impact of changing substrate concentration

E + S ES E + P

k1

k-1

k2

Derivation of the Michaelis-Menten equation

Rate of reaction: v k2[ES] Equation (1)

During the steady-state, [ES] is constant i.e. the rate of formation = rate of breakdown

k 1[E ][S] k 1[ES]k 2[ES]Therefore:

[ES]

k1[E][S]k 1 k2

[ES]

k1[E][S]k 1 k2

KM

k 1k 2

k1

[ES]

[E][S]KM

Equation (2)

If we introduce a constant KM defined as

This equation becomes

The total concentration of enzyme introduced at the start of the reaction is still present, it is either bound to substrate or it is not, i.e.

[E0] = [E] + [ES]Or rearranged: [E] = [E0] - [ES]Substituting this into Equation (2) gives us:

[ES]

([E0] [ES])[S]KM

Opening the bracket on the right-hand side gives:

[ES] = [E0][S] - [ES][S]

KM

[ES] = ([E0] - [ES])[S]

KM

Therefore: KM [ES] = [E0][S] - [ES][S]

KM [ES] + [S][ES] = [E0][S]

(KM + [S])[ES] = [E0][S]

Collect [ES]:

Therefore:[ES] =

[E0][S] [S] + KM

[ES] = [E0][S]

[S] + KM

Substituting this back into equation (1): v k2[ES]Gives us:

v = k2 [E0][S]

[S] + KM

The maximum rate for the enzyme (Vmax) will be achieved when all of the Enzyme is saturated with substrate, i.e. [ES] = [E0]

Putting this again into equation (1) we get: Vmax = k2 [E0]

Notice that the term k2[E0] features in equation (3), which can now be written

Equation (3)

v = Vmax [S] KM + [S]

Michaelis-Mentenequation

What does the KM actually tell us?

Consider the case when the reaction rate (v) is half of the maximum rate (Vmax). Under these conditions the MM equation becomes:

= Vmax [S] KM + [S]

Vmax 2

This leaves us with:2[S] = KM + [S]

Which simplifies to:[S] = KM

KM is the substrate concentration at which the reaction proceeds at half of the maximum rate (Vmax)

KM

Vmax

Initialrate, V

Substrate concentration, [S]

Vmax/2

Plot of rate (V) against substrate concentration ([S])

v = Vmax [S] KM + [S]

= KM 1 1 1

v [S] Vmax +

Vmax .

Taking the reciprocal of both sides can give

This is in the general form y = m x + c

i.e. a plot of 1/v against 1/[S] will give straight line

This is a Lineweaver-Burk plot

1/V

1/[S]

-1/KM 1/Vmax

KM/Vmaxslope =

Lineweaver-Burk plot

KAPITOLA 4KAPITOLA 4Enzymová katalýza IIEnzymová katalýza II

• kinetika reakcí katalyzovaných enzymykinetika reakcí katalyzovaných enzymy• analýza reakční rychlostianalýza reakční rychlosti• inhibice a regulace katalytické aktivityinhibice a regulace katalytické aktivity• metody studiametody studia

Dependence of initial velocity on substrate concentration, showing the kinetic parameters that define the limits of the curve at hight and low [S]. At low [S], Km>>[S], and the [S] term in the denominator of the Michaelis-Menten equation becomes insignificant; the equation simplifies to V0 = Vmax[S]/Km, and V0 exhibits a linear dependence on [S], as observed. At high [S], where [S]>>Km, the Km term in the denominator of the Michaelis-Menten equation becomes insignificant, and the equation simplifies to V0=Vmax; this is consistent with the plateau observed at high [S]. The Michaelis-Menten equation is therefore consistent with the observed dependence of V0 on [S], with the shape of the curve defined by the terms Vmax/Km at low [S] and Vmax at high [S].

]S[K]S[V

2V

m

maxmax

The Michaelis-Menten equation

maxmax

m

0 V1

]S[1

VK

V1

A double-reciprocal, or Lineweaver-Burk, plot.

The Lineweaver-Burk equation

Common mechanisms for enzyme-catalyzed bisubstrate reactions. (a) the enzyme and both substrates come together to form a ternary complex. In ordered binding, substrate 1 must be bound before substrate 2 can bind productively.(b) an enzyme-substrate complex forms, a product leaves the complex, the altered enzyme forms a second complex with another substrate molecule, and the second product leaves, regenerating the enzyme. Substrate 1 may transfer a functional group to the enzyme (forming E´), which is subsequently transferred to substrate 2. This is a ping-pong or double-displacement mechanism.

A B

A shows a set of double-reciprocal plots obtained in the absence of the inhibitor and with two different concentrations of a competitive inhibitor. Increasing inhibitor concentration [I] results in the production of a family of lines with a common intercept on the 1/V0 axis but with different slopes. Because the intercept on the 1/V0 axis is equal to 1/Vmax, we can see that Vmax is unchanged by a presence of a competitive inhibitor. That is, regardless of the concentration of a competitive inhibitor, there is always some high substrate concentration that will displace the inhibitor from the enzyme´s active site.

In noncompetitive inhibition, similar plots of the rate data give the family of lines shown in B, having a common intercept on the 1/[S] axis. This indicates that Km for the substrate is not altered by a noncompetitive inhibitor, but Vmax decreases.

Three types of reversible inhibition.Competitive inhibitors bind to the enzyme´s active site. Noncompetitive inhibitors generally bind at a separate site. Uncompetitive inhibitors also bind at a separate site, but they bind only to the ES complex. KI is the equilibrum constant for inhibitor binding.

Some well-studied examples of enzyme modification reactions.

Allosteric Enzymes

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