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Enzyme mechanisms and
kinetics
Enzyme kinetics is the field of biochemistry concerned with the quantitative
measurement of the rates of enzyme catalyzed reactions and the study of factors that
affect these rates
A+B
P+Q
-One molecule of each substrate A and B forms one molecule of each product P and Q
-Double arrows indicate a reversible reaction, an intrinsic property of all chemical
reactions
-Single arrows are used where
1
...
Reactions in living cells where the products of the reaction are
immediately consumed by a subsequent enzyme catalyzed reaction
rendering the reaction functionally irreversible
A+B
P+Q

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Introduction to Enzyme Kinetics
•
•
•

•

Kinetics is the branch of science concerned with the rates of chemical
reactions
...

In enzyme kinetics, the maximum reaction velocity that the enzyme can
attain is determined and its binding affinities for substrates and inhibitors
...
That is,

– For this case, the rate law is

– The rate is proportional to the concentration of A, and k is the proportionality
constant, or rate constant
2

•
•

V is a function of [A] to the first power, or, in the terminology of kinetics, v is
first-order with respect to A
...
Because it is
proportional to the product of two concentration terms, the reaction is
second-order overall, first-order with respect to A and first-order with
respect to B
...

This transition state sits at the apex of the energy profile in the energy
diagram describing the energetic relationship between A and P
The average free energy of A molecules defines the initial state and the
average free energy of P molecules is the final state along the reaction
coordinate
...

5

•

The relationship between activation energy and the rate constant of the
reaction, k, is given by the Arrhenius equation,

•

where A is a constant for a particular reaction (not to be confused with the
reactant species, A, that we’re discussing)
...

Therefore, if the energy
of activation decreases, the reaction rate increases
...
This will increase the average energy of
reactant molecules, which in effect lowers the energy needed to reach the
transition state
– Second, the rates of chemical reactions can also be accelerated by catalysts
...
Raising the temperature
raises the average energy of A molecules, which increases the population of A molecules
having energies equal to the activation energy for the reaction, thereby increasing the
reaction rate
...
The effect of
the catalyst is to lower the free energy of activation for the reaction
...

At low concentrations of the substrate S, v is proportional to [S], as
expected for a first-order reaction
...

At high [S], v becomes virtually independent of [S] and approaches a
maximal limit
...

Because rate is no longer dependent on [S] at these high concentrations,
the enzyme-catalyzed reaction is now obeying zero-order kinetics

9

Substrate saturation curve for an enzyme-catalyzed reaction
...
The reaction rate, v, as a function of [S] is described by
a rectangular hyperbola
...
That is, the velocity is limited
only by conditions (temperature, pH, ionic strength) and by the amount of
enzyme present; v becomes independent of [S]
...
Under zero-order conditions, velocity is directly dependent on
[enzyme]
...

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•

The physical interpretation is that every enzyme molecule in the reaction
mixture has its substrate-binding site occupied by S

11

Reaction profile for a reaction associated with a negative overall charge
in free energy
ΔG activation
for S → P

Free energy G

S----P

ΔG activation
for P → S

S
Ground state

P
Ground state

Reaction coordinate
Overall free
energy change

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Reaction profile for a reaction in the presence of an enzyme

Free energy G

Enzymes accelerate reaction rates by providing transition states with lowered activation
energy
No enzyme
ΔG activation
S----P
for S → P

EP

ES

With enzyme

ΔG activation
for P → S

S
Ground state

P
Ground state

Reaction coordinate
ES and EP intermediates occupy valleys in a reaction
Overall free
coordinate diagram
energy change
-A higher activation energy corresponds to a slower reaction
-Enzymes enhance the reaction rates by lowering the activation energy
-Where several steps are involved in enzyme catalyzed reactions, the one with the
highest Eact is the rate limiting step
-An enzyme that catalyzes S→P also catalyzes P→S, and the direction and position
of equilibrium are not affected by the enzyme

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Enzymes do not affect Keq
• Enzymes emerge unchanged at the completion of a reaction
...

• It’s a dynamic state; individual substrates and products are continually being
interconverted
• The numerical value of the equilibrium constant Keq can be calculated
either from the concentrations of substrates and products at equilibrium or
from the ratio of k1/k-1

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Multiple factors affect the rate of enzyme catalyzed
reactions
These include, temperature, hydrogen ion concentration, substrate concentration, end
products, allosteric factors, covalent modification, hormones etc
Temperature
• Rising temperature increases the rate of both uncatalyzed and enzyme-catalyzed
reactions
-increase kinetic energy of the reactants
-increase the collision frequency of the reactants
• Heat energy can also increase kinetic energy of the enzyme to the point of disrupting
the noncovalent interactions that maintain the enzyme’s three dimensional structure
-polypeptide chain unfolds or denatures
-loss of catalytic activity
• The temperature range over which an enzyme maintains a stable , catalytically
competent conformation depends upon (and typically moderately exceeds) the
normal temperature of the cells in which it resides
-in humans enzymes generally exhibit stability at temperatures up
to 45 – 55oC
-in thermophilic microorganisms that reside in volcanic hot springs
enzymes may be stable at 100oC
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•

Q10, or temperature coefficient , is the factor by which the rate of a biologic process
increases for a 10oC increase in temperature
...

-enzymes whose mechanism depends on acid-base catalysis, the
residues involved must be in the appropriate state of protonation for
the reaction to proceed
-the binding and recognition of substrate molecules with dissociable
groups also typically involves the formation of salt bridges with
the enzymes
•
The most common charged groups are the negative carboxylate groups and the
positively charged groups of protonated amines
• Gain or loss of charged groups thus will affect substrate binding and hence retard
catalysis

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Enzyme concentration

•

•
•

Measurements of the rates of enzyme-catalyzed reactions employ short
periods which approximate initial rate conditions
-traces of products accumulate
-rate of the reverse reaction is negligible
The initial velocity (vi) of the reaction is essentially that of the rate of the
forward reaction
If a large molar excess of substrate over enzyme is employed
- vi is directly proportional to the concentration of the enzyme
-measurement of the initial velocity permits one to estimate the
concentration of enzyme in the biological sample
- but as stated above enzyme concentration has no effect on
Keq and ΔGo

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Substrate concentration affects reaction rate
•

•
•
•

•
•

The approach to understanding enzyme mechanism is to determine the rate of the
reaction and show changes in response to changes in experimental parameters
Follow the increase in reaction product as a function of time
Because [S] changes during reaction as substrate is converted to product, the initial
rate (Initial velocity) is the is the one that is measured
In a typical reaction [S] is much higher than [E]
...
C

Vmax

vi

Vmax/2


...
A
Km

Vmax/2
[S]

Effects of substrate concentration on the initial velocity of an
enzyme-catalyzed reaction

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-As substrate concentration is increased , the vi increases until it reaches a
maximum value Vmax
...

Because it is slow it must be rate limiting

E+S
•

•
•

•
•

ES

At low [S] most of the enzyme is in the uncombined E form
...
x intercept is -1/Km
-called a double reciprocal or Lineweaver-Burk plot
Slope =

1
vi

─

1
Km

Km
Vmax

Km is most easily calculated
from the x intercept

1
Vmax
1
[S]

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-The Lineweaver-Burk plot
-has the advantage of allowing a more accurate determination of Vmax,
which can only be approximated from a simple plot of vi Vs [S]
-also useful in distinguishing between certain types of enzymatic
reaction mechanisms and in analyzing enzyme inhibitions
The relationship of Km to Kd, the dissociation constant of the enzyme
substrate complex
• The affinity of the enzyme for its substrate is equal to the inverse of the
dissociation constant, Kd for ES
E+S

k1

ES

K-1

k 1
Kd= k
1

i
...

If k2 + k-1  k-1, then 1/Km underestimates the affinity 1/Kd
•
•

Km equals to the dissociation constant of the ES complex if K2 is much smaller than
K-1
When this condition is met , Km is a measure of the strength of the ES complex: a
high Km indicates weak binding ; a low Km indicates strong binding

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The Hill equation describes the behaviour of enzymes that exhibit
cooperative binding of substrate
-Some enzymes bind their substrates in a cooperative fashion analogous to the
binding of oxygen by hemoglobin
-Cooperative binding is encountered in multimeric enzymes that bind
substrates at multiple sites
-In enzymes that display positive cooperativity in binding to substrate, the
shape of the curve that relate vi to changes in [S] is sigmoidal
-Neither the Michaelis-Menten equation nor the Lineweaver-Burk plot can be
used to evaluate cooperative saturation kinetics
vi
Sigmoid saturation kinetics

[S]

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