PETER PAZMANY
SEMMELWEIS
CATHOLIC UNIVERSITY
UNIVERSITY
Development of Complex Curricula for Molecular Bionics and Infobionics Programs within a consortial* framework**
Consortium leader
PETER PAZMANY CATHOLIC UNIVERSITY
Consortium members
SEMMELWEIS UNIVERSITY, DIALOG CAMPUS PUBLISHER
The Project has been realised with the support of the European Union and has been co-financed by the European Social Fund ***
**Molekuláris bionika és Infobionika Szakok tananyagának komplex fejlesztése konzorciumi keretben
***A projekt az Európai Unió támogatásával, az Európai Szociális Alap társfinanszírozásával valósul meg. 09/10/11.
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Peter Pazmany Catholic University
Faculty of Information Technology
www.itk.ppke.hu
INTRODUCTION TO BIOPHYSICS
(Bevezetés a biofizikába)
ENZYMES
(Enzimek)
GYÖRFFY DÁNIEL, ZÁVODSZKY PÉTER
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Introduction to biophysics: Enzymes
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Introduction
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Catalysts are substances that can accelerate
reactions taking place spontaneously even in
the absence of the catalyst
Catalysts are reclaimed in unchanged form
after the reaction occurs
Enzymes are catalysts of biological processes
Enzymes are proteins often containing
cofactors such as metal ions
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The substance converted in the reaction
catalyzed by the enzyme is called the
substrate
The substance produced in this reaction is
called product
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Classification of enzymes
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Enzymes are classified into six groups based
on the type of reaction catalyzed by them
The coenzyme is responsible for the type of
reaction to be catalyzed while the apoenzyme
determines the type of the substrate
converted in the reaction
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Classes of enzymes
Class
Catalyzed reaction
Example
Oxidoreductases
Oxidation-reduction
GAPDH
Transferases
Group transfer
ERK2
Hydrolases
Hydrolysis
Trypsin
Lyases
Double bond formation or
removal
Fumarase
Isomerases
Isomerization
Triose phosphate isomerase
Ligases
Ligation
DNA ligase
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GAPDH
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MAP kinase ERK2
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Trypsin
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Fumarase
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Triose phosphate isomerase
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DNA ligase
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Enzymes in action
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Enzymes can catalyze only reactions taking
place spontaneously, i.e. in the absence of
catalyst
Reactions can take place spontaneously if the
free energy of products is less than that of the
reactants
Thus, catalysts such as enzymes do not affect
the thermodynamics of reactions but influence
their kinetics
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Usually, for a reaction to take place, an energy
barrier must be passed
The height of this barrier will determine the
rate of the reaction
The higher the barrier the slower the reaction
Catalysts can make this barrier lower, and thus
accelerate the reaction even by several orders
of magnitude
Now let us examine where this barrier comes
from
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Recall: Arrhenius theory
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The Swedish chemist Arrhenius found a
relation between the rate of reaction and the
temperature
The Arrhenius equation says:
k =A e
−E a / R T
where k is the rate constant, Ea is the activation
energy, R is the gas constant, T is the
temperature and A is a constant called Arrhenius
constant or pre-exponential factor
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k as a function of T
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Recall: Boltzmann distribution
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Ludwig Boltzmann found the energy
distribution of particles in a system at
equilibrium
The Boltzmann distribution is:
1 −E /k
p E i = e
Z
i
B
T
where p(Ei) is the probability that a particle is in a
state having Ei energy, kB is the Boltzmann
constant and Z is the partition function
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The partition function
− Ei / k B T
Z =∑ e
i
is the sum of the Boltzmann factors for all of the i
states and serves as a scaling factor to ensure
that the sum of probabilities equals 1
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Boltzmann distribution
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Thus, the rate of a reaction is proportional to
the fraction of particles having an energy
higher than the activation energy
Hence, if a catalyst lowers the activation
energy, a higher fraction of particles will have
an energy higher than the activation energy
thus, the rate of the reaction will be higher
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Fraction of particles of energy E in an
uncatalyzed and a catalyzed reaction
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Recall: reaction profile
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The progress of a reaction can be
characterized by one or more reaction
coordinates
Now, let us consider a reaction with one
reaction coordinate
The free energy of the system can be plotted
as a function of a reaction coordinate
This plot is called reaction profile
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Reaction profile
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The effect of a catalyst on the reaction profile
is that it lowers the activation energy and thus
lowers the barrier that must be passed for the
system the reaction to occur
It can be seen that a catalyst accelerates a
reaction not only in one direction but in the
opposite direction as well
However, enzymes do not alter the reaction
free energy ∆Gr, and therefore do not
influence whether the reaction occurs
spontaneously
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Effect of a catalyst on the reaction profile
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Hypotheses for enzyme action
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Several hypotheses have been proposed to
explain how enzymes can accelerate reactions
even by several orders of magnitude
Enzymes often open up a by-pass pathway
with lower activation energy for the reaction,
which can thus proceed faster
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Transition state stabilization
●
Let us consider the reaction to be catalyzed by
an enzyme as
K
‡
‡
‡ k
S⇆S P
where S is the substrate, S‡ is the transition
state, P is the product, K‡ is the equilibrium
constant for the formation of the transition state
from the substrate, and k‡ is the rate constant of
the conversion of the transition state to the
product
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It is assumed that the equilibrium step of the
reaction is far faster than the second step
Thus, the overall rate of the reaction can be
approximated by
●
●
‡
‡
v =k [S ]≈ k [S ]
●
It can be seen that the rate of the overall
reaction is proportional to the concentration of
the transition state
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Since
‡
[S ] − G / RT
K =
=e
[S ]
‡
‡
where ΔG‡ is the activation free energy,
describing the stability of transition state relative
to the substrate
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The more stable the transition state the higher
its concentration
Thus, enzymes accelerate reactions by
stabilizing the transition state
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Enzyme-substrate complex
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In the course of catalysis, a complex of the
enzyme and the substrate(s) is formed
The transition state is also formed in an
enzyme substrate complex
The specificity of enzymes is brought about by
the specific binding of substrate
The region of the enzyme where the binding
occurs is called the active site
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Lock and key hypothesis
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To explain substrate specificity, several
theories have been proposed
The lock and key hypothesis assumes that the
shape of the active site is a negative of the
shape of the substrate
Later, several enzymes were found to be able
to catalyze the reaction of substrates having
significantly different shapes but not of
substances having almost the same shape as a
known substrate
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The lock and key hypothesis
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Induced fit hypothesis
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Due to the above mentioned difficulties, a new
model has been proposed to better explain
substrate specificity
This new model, called induced fit model
assumes that, when the substrate approaches
the active site of the enzyme, a conformational
change occurs in the enzyme, allowing the
binding based on shape complementarity
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The induced fit mechanism
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Transition state fit
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According to a more modern view, it is the
transition state whose shape fits the shape of
the active site
Thus, a lock and key binding occurs not
between the enzyme and the ground state but
between the enzyme and the transition state
of the substrate
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Transition state fit
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The transition state is a high-energy state of
the substrate
According to the Boltzmann distribution, states
with high energy have a low but non-zero
probability to occur
Thus, a small amount of substrate molecules in
the transition state is present in the medium
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Transition state fit occurs when the enzyme
selects a substrate molecule being in the
transition state for binding rather than
molecules in the ground state
Not only the enzyme can select from the
reservoir of substrate states but substrates can
also select from the preexisting enzyme
conformations
This mechanism is called conformational
selection or fluctuation fit
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Conformational selection by the enzyme
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Conformational selection by the
substrate
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Transition-state analogues
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Based on the model assuming the selective
binding of the transition state by the enzyme,
it has been proposed that analogues of the
transition state compounds, that is a
compound having similar conformation to it
should be good inhibitors of the enzyme
Indeed, several observations have been
accumulated that support the concept that
transition state analogues are good inhibitors
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Abzymes
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The existence of abzymes lends further
support for the transition state fit model
Abzymes are catalytic antibodies
They have catalytic activity for reactions for
which they can selectively bind the transition
state
Immunizing animals by a transition state
analogue, an effective enzyme can be
obtained
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Michaelis-Menten model for
enzyme kinetics
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The Michaelis-Menten model of enzyme
kinetics accounts for dependence of the rate of
the enzyme reactions on the substrate
concentration
A steady-state approximation has been used to
construct a model fitting well the experimental
results for many enzymes
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Kinetic curves of an enzyme reaction
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●
The following scheme can be proposed for a
generic enzyme reaction
k1
k2
k −1
k −2
E S ⇆ ES ⇆ P
where E is the enzyme and S is the substrate in
their free forms, ES is the enzyme-substrate
complex and P is the product
●
The corresponding rate constants are also
shown
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Assuming that the rate of formation of product
from the enzyme-substrate complex is far
higher than the rate of the reverse reaction,
that is
k 2 ≫k −2
the general scheme of enzyme reactions can be
simplified to be
k1
k2
E S ⇆ ES  P
k −1
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The rate of the reaction is assumed to be
v 0=k 2 [ ES ]
●
Since we do not know the concentration of the
enzyme-substrate complex, we need to
express it in terms of the known quantities
such as the initial substrate or enzyme
concentration
d [ ES ]
=k 1 [ E ][S ]− k −1k 2 [ ES ]
dt
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Making use of the steady state approximation,
i.e. that the concentration of the enzymesubstrate complex does not change for a wide
time range
d [ ES ]
=0
dt
and thus
k 1 [ E ][S ]= k −1k 2 [ ES ]
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After rearrangement we obtain
[ E ][ S ]/[ ES ]=  k −1 k 2 / k 1
●
If we define a new constant called Michaelis
constant, KM
K M = k −1 k 2 / k 1
we get a simpler equation
[ E ][S ]
[ ES ]=
KM
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The concentration of the free enzyme can be
obtained from the equation
[ E ]=[ E ] T −[ ES ]
where [E]T is the total enzyme concentration
●
Since the total amount of the enzyme does not
change through the reaction, it will be equal to
the amount of enzyme initially put into the
reaction mixture
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●
Substituting the expression for the enzyme
concentration into the equation above, we get
[ ES ]=
●
[E ]T −[ ES ] [S ]
KM
Solving the equation for [ES], we obtain
[S]
[ ES ]=[ E ]T
[S ] K M
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●
Substituting this expression into the equation
for the reaction rate, we obtain
[S ]
v 0=k 2 [ E ]T
[S ]K M
●
The reaction can proceed with the maximal
speed when all of the enzyme molecules are in
complex with a substrate molecule, that is
when
[ ES ]=[ E ]T
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Thus the maximal velocity is
v max =k 2 [ E ]T
●
Based on this, the relationship between the
maximal and the actual velocity is
[S]
v 0=v max
[ S ] K M
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●
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It can be seen in the equation above that KM
corresponds to the substrate concentration
where the rate of reaction is half of the
maximal rate
It also shows that the Michaelis constant is an
important kinetic property of enzymes
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The rate of the reaction as a function of
the substrate concentration
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If the substrate concentration is far lower than
the Michaelis constant, that is
[S ]≪ K M
then the rate of reaction is approximately
v max
v 0≈
[S]
KM
●
It can be seen that at low substrate
concentration, the reaction is first-order with
respect to the substrate
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On the other hand, if the substrate
concentration is far higher than the Michaelis
constant, that is
[S ]≫ K M
then the rate of reaction is approximately
v 0≈v max
●
It can be seen that at high substrate
concentration, the reaction is zeroth-order with
respect to the substrate
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Catalytic efficiency
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●
●
The turnover number of an enzyme is the
number of molecules converted into a product
in unit time when the enzyme is fully saturated
by the substrate
The turnover number is equal to the rate
constant k2 which is also called kcat
The maximal velocity, vmax in terms of kcat is
v max =k cat [ E ] T
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●
●
When the substrate concentration is far lower
than the Michaelis constant, the enzymatic
rate is much less than kcat
From equation
v 0=k cat [ ES ]
and
[ E ][S ]
[ ES ]=
KM
we can obtain a new equation
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k cat
v 0=
[ E ][ S ]
KM
●
●
kcat/KM behaves as a second-order rate constant
for the reaction between the substrate and the
free enzyme, and thus can serve as a measure
of catalytic efficiency
The physical limit on the value of kcat/KM is the
rate constant of formation of the enzymesubstrate complex which cannot be faster than
allowed by the velocity of diffusion
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Inhibitors
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Enzymes can be inhibited by specific inhibitors
Two main classes of inhibitors can be
distinguished
– Competitive inhibitors
– Non-competitive inhibitors
●
Competitive inhibitors use the same binding
site on the enzyme as the substrate and a
competition occurs between the substrate and
the inhibitor for the binding site
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●
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Non-competitive inhibitors bind to a different
site on the enzyme than the substrate
They cause a conformational change in the
enzyme, leading to a reduction of the action of
the enzyme
Competitive and non-competitive inhibitors
have a different effect on the kinetics of the
enzyme reaction and thus they can be
kinetically distinguished
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In the case of a competitive inhibitor, if the
concentration of substrate is high enough, the
maximal velocity, vmax, can be attained but the
substrate concentration where the velocity is
the half of vmax, KM, will be higher
In the case of non-competitive inhibitors, the
maximum velocity vmax cannot be attained even
at very high substrate concentration, but the
substrate concentration where the velocity is
the half of the modified maximal velocity is
unchanged
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Competitive inhibitor
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Non competitive inhibitor
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Catalytic strategies
●
The function of enzymes is based on one or
more of a few strategies
– Through covalent catalysis, a reactive group of the
active site becomes covalently modified
• In the active site of trypsin, the catalytic serine
residue forms an acyl-enzyme intermediate with
the N-terminal part of the cleaved polypeptide
chain
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Acyl-enzyme intermediate in the active
site of trypsin
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– In acid-base catalysis, a proton transfer occurs
where the donor or acceptor group is not water
– Metal ions can take part in the catalytic reactions in
several ways, for example they can supply positive
charge if the intermediate is negatively charged, or
they can take part in the substrate binding
– The enzyme can help substrates to approach each
other in a proper orientation, entropically decreasing
the activation free energy
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Ribozymes
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Catalytic capability is a property not
exclusively of proteins but also of RNAs
Several catalytic RNAs called ribozymes are
known
Ribozymes take part mainly in the catalysis of
reactions related to RNA conversion
Ribozymes are important constituents of
ribosomes, the molecular machines
responsible for protein synthesis
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Large subunit of a bacterial ribosome
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Small subunit of a bacterial ribosome
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Another important process catalyzed partly by
ribozymes is splicing through which exons are
cleaved out from the premature mRNA
molecule
Inspired by the discovery of catalytic RNAs, an
evolutionary concept called the RNA world was
proposed
According to these hypothesis, at an earlier
stage of evolution, it was RNA that was
responsible for catalysis and information
storage instead of proteins and DNA,
respectively
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RNA splicing
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The RNA world hypothesis is supported by the
existence of catalytic RNAs and the fact that
many enzymes have a coenzyme, i.e. a
ribonucleotide derivative such as NAD, the
most important electron carrier molecule of
the cell and ATP, the most important energy
currency
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Adenosine triphosphate (ATP)
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Nicotinamid adenine dinucleotide (NAD)
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