Download Enzyme Properties

Enzyme Properties and
Kinetics
Andy Howard
Introductory Biochemistry, Fall 2008
14 October 2008
Biochemistry: Enzyme Properties
10/14/2008
Enzymes catalyze reactions
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We need to classify them and get an
idea of how they affect the rates of
reactions.
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Plans for Today
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Classes of
enzymes
Enzyme kinetics
Michaelis-Menten
kinetics: overview
Kinetic Constants
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Kinetic
Mechanisms
Induced Fit
Bisubstrate
reactions
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Enzymes
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Okay. Having reminded you that not all
proteins are enzymes, we can now zero
in on enzymes
Understanding a bit about enzymes
makes it possible for us to characterize
the kinetics of biochemical reactions and
how they’re controlled
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Enzymes have 3 features
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Catalytic power (they lower G‡)
Specificity
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They prefer one substrate over others
Side reactions are minimized
Regulation
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Can be sped up or slowed down by
inhibitors and accelerators
Other control mechanisms exist
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IUBMB Major Enzyme Classes
EC # Class
Reactions
Sample
Comments
1
oxidoreductases
Oxidationreduction
LDH
NAD,FMN
2
transferases
Transfer
big group
AAT
Includes
kinases
3
hydrolases
Transfer of
H 2O
Pyrophos
hydrolase
Includes
proteases
4
Lyases
Addition
across =
Pyr decarboxylase
synthases
5
Isomerases
Unimolecular rxns
Alanine
racemase
Includes
mutases
6
Ligases
Joining 2
substrates
Gln
synthetase
Often need
ATP
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EC System
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4-component naming system,
sort of like an internet address
Pancreatic elastase:
Category 3: hydrolases
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Subcategory 3.4: hydrolases acting on
peptide bonds (peptidases)
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Sub-subcategory 3.4.21: Serine
endopeptidases
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Porcine
pancreatic
elastase
PDB 3EST
1.65 Å
26kDa
monomer
Sub-sub-subcategory 3.4.21.36:
Pancreatic elastase
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Category 1:
Oxidoreductases
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General reaction:
Aox + Bred  Ared + Box
One reactant often a cofactor (see ch.7)
Cofactors may be organic (NAD or FAD)
or metal ions complexed to proteins
Typical reaction:
H-X-OH + NAD+  X=O + NADH + H+
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Category 2:
Transferases
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These catalyze transfers of
groups like phosphate or amines.
Example: L-alanine + a-ketoglutarate 
pyruvate + L-glutamate
Kinases are transferases:
they transfer a phosphate from ATP to
something else
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Category 3:
hydrolases
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O
O-
HO-P-O-P-OH
O-
O
Water is acceptor of
transferred group
Ultrasimple: pyrophosphatase:
Pyrophosphate + H2O ->
2 Phosphate
Proteases,
many other sub-categories
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C=C
Category 4:
Lyases
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Non-hydrolytic, nonoxidative elimination
(or addition) reactions
Addition across a double bond or reverse
Example: pyruvate carboxylase:
pyruvate + H+  acetaldehyde + CO2
More typical lyases add across C=C
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Category 5:
Isomerases
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Unimolecular interconversions
(glucose-6-P  fructose-6-P)
Reactions usually almost exactly isoergic
Subcategories:
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Racemases: alter stereospecificity such that
the product is the enantiomer of the substrate
Mutases: shift a single functional group from
one carbon to another (phosphoglucomutase)
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Category 6: Ligases
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Catalyze joining of 2 substrates,e.g.
L-glutamate + ATP + NH4+ 
L-glutamine + ADP + Pi
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Require input of energy from XTP (X=A,G)
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Usually called synthetases
(not synthases, which are lyases, category 4)
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Typically the hydrolyzed phosphate is not
incorporated into the product
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iClicker quiz, question 1
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Collagenase catalyzes the cleavage
of the -glycosidic bonds holding
collagen together. Which IUBMB
enzyme category would collagenase
fall into?
(a) ligases (6)
(b) oxidoreductases (1)
(c ) hydrolases (3)
(d) isomerases (5)
(e) none of the above.
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iClicker quiz, question 2
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Triosephosphate isomerase, whose
structure we discussed earlier,
interconverts glyceraldehyde-3phosphate and dhydroxyacetone
phosphate. What would you expect
the approximate G value for this
reaction to be?
(a) -30 kJ mol-1
(d) 0 kJ mol-1
(b) 30 kJ mol-1
(e) no way to tell.
(c ) -14 kJ mol-1.
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Enzyme Kinetics
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Kinetics: study of reaction rates and the
ways that they depend on concentrations
of substrates, products, inhibitors,
catalysts, and other effectors.
Simple situation A B under influence of
a catalyst C, at time t=0, [A] = A0, [B] = 0:
then the rate or velocity of the reaction is
expressed as d[B]/dt.
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[B]
Kinetics, continued
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t
In most situations more product will be produced
per unit time if A0 is large than if it is small, and
in fact the rate will be linear with the
concentration at any given time:
d[B]/dt = v = k[A]
where v is the velocity of the reaction and k is a
constant known as the forward rate constant.
Here, since [A] has units of concentration and
d[B]/dt has units of concentration / time, the
units of k will be those of inverse time, e.g. sec-1.
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More complex cases
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More complicated than this if >1 reactant
involved or if a catalyst whose concentration
influences the production of species B is
present.
If >1 reactant required for making B, then
usually the reaction will be linear in the
concentration of the scarcest reactant and
nearly independent of the concentration of
the more plentiful reactants.
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Bimolecular reaction
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If in the reaction
A+DB
the initial concentrations of [A] and [D]
are comparable, then the reaction rate
will be linear in both [A] and [D]:
d[B]/dt = v = k[A][D] = k[A]1[D]1
i.e. the reaction is first-order in both A
and D, and it’s second-order overall
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Forward and backward
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Rate of reverse reaction may
not be the same as the rate at
which the forward reaction
occurs. If the forward reaction
rate of reaction 1 is designated
as k1, the backward rate
typically designated as k-1.
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Multi-step reactions
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In complex reactions, we may need to keep
track of rates in the forward and reverse
directions of multiple reactions. Thus in the
conversion A  B  C
we can write rate constants
k1, k-1, k2, and k-2
as the rate constants associated with
converting A to B, converting B to A,
converting B to C, and converting C to B.
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[ES]
Michaelis-Menten
kinetics
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t
A very common situation is one in which for
some portion of the time in which a reaction is
being monitored, the concentration of the
enzyme-substrate complex is nearly constant.
Thus in the general reaction
E + S  ES  E + P
where E is the enzyme, S is the substrate, ES is
the enzyme-substrate complex (or "enzymeintermediate complex"), and P is the product
We find that [ES] is nearly constant for a
considerable stretch of time.
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Michaelis-Menten rates
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Rate at which new ES molecules are being
produced in the first forward reaction is
equal to the rate at which ES molecules are
being converted to (E and P) and (E and S).
Rate of formation of ES from left =
vf = k1([E]tot - [ES])[S]
because the enzyme that is already
substrate-bound is unavailable!
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Equating the rates
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Rate of disappearance of ES on right
and left is
vd = k-1[ES] + k2[ES] = (k-1+ k2)[ES]
This rate of disappearance should be
equal to the rate of appearance
Under these conditions vf = vd.
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Derivation, continued
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Thus since vf = vd.
k1([E]tot - [ES])[S] = (k-1+ k2)[ES]
Km  (k-1+ k2)/k1 =
([E]tot - [ES])[S] / [ES]
[ES] = [E]tot [S] / (Km + [S])
But the rate-limiting reaction is the
formation of product: v0 = k2[ES]
Thus v0 = k2[E]tot [S] / (Km + [S])
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Maximum velocity
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What conditions would produce the
maximum velocity?
Answer: very high substrate
concentration ([S] >> [E]tot),
for which all the enzyme would be
bound up with substrate. Thus
under those conditions we get
Vmax = v0 = k2[ES] = k2[E]tot
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Using Vmax in
M-M kinetics
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Thus since
Vmax = k2[E]tot,
v0 = Vmax [S] / (Km+[S])
That’s the famous Michaelis-Menten
equation
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Graphical interpretation
0.01
Michaelis-Menten kinetics
0.009
Initial velocity v0, Ms-1
0.008
0.007
Vmax = 0.01 Ms -1
0.006
Km = 0.03M
0.005
[E]tot = 10 -7M
0.004
kcat = 10 5 s-1
0.003
0.002
0.001
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Substrate conc, M
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Physical meaning of Km
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As we can see from the plot, the
velocity is half-maximal when [S] = Km
Trivially derivable: if [S] = Km, then
v0 = Vmax[S] / ([S]+[S]) = Vmax /2
We can turn that around and say that
the Km is defined as the concentration
resulting in half-maximal velocity
Km is a property associated with
binding of S to E, not a property of
turnover
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kcat
A quantity we often want is the
maximum velocity independent of
how much enzyme we originally
dumped in
 That would be kcat = Vmax / [E]tot
 Oh wait: that’s just the rate of our
rate-limiting step, i.e. kcat = k2
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Physical meaning of kcat
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Describes turnover of substrate to
product:
Number of product molecules produced
per sec per molecule of enzyme
More complex reactions may not have
kcat = k2, but we can often approximate
them that way anyway
Some enzymes very efficient:
kcat > 106 s-1
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Specificity constant, kcat/Km
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kcat/Km measures affinity of enzyme for a
specific substrate: we call it the specificity
constant or the molecular activity for the
enzyme for that particular substrate
Useful in comparing primary substrate to
other substrates (e.g. ethanol vs.
propanol in alcohol dehydrogenase)
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Kinetic Mechanisms
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If a reaction involves >1 reactant or >1 product,
there may be variations in kinetics that occur
as a result of the order in which substrates are
bound or products are released.
Examine eqns. 13.48, 13.49, 13.50, and the
unnumbered eqn. on p. 430 in G&G, which
depict bisubstrate reactions of various sorts. As
you can see, the possibilities enumerated
include sequential, random, and ping-pong
mechanisms.
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Historical thought
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Biochemists, 1935 - 1970 examined effect
on reaction rates of changing [reactants] and
[enzymes], and deducing the mechanistic
realities from kinetic data.
In recent years other tools have become
available for deriving the same information,
including static and dynamic structural
studies that provide us with slide-shows or
even movies of reaction sequences.
But diagrams like these still help!
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Sequential, ordered
reactions
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W.W.Cleland
Substrates, products must bind in
specific order for reaction to complete
A
B
P
Q
_____________________________
E
EA (EAB) (EPQ) EQ E
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Sequential, random reactions
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Substrates can come in in either order, and
products can be released in either order
A
B
P Q
EA
EQ
__
E
(EAB)(EPQ)
E
EB
EP
B
A
Q P
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Ping-pong mechanism
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First substrate enters, is altered, is
released, with change in enzyme
Then second substrate reacts with
altered enzyme, is altered, is released
Enzyme restored to original state
A
P
B
Q
E EA FA F
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FB FQ E
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Induced fit
Daniel
Koshland
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QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Conformations of enzymes
don't change enormously
when they bind substrates,
but they do change to some
extent. An instance where
the changes are fairly
substantial is the binding of
substrates to kinases.
Cartoon from
textbookofbacteriology.net
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Kinase reactions
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unwanted reaction
ATP + H-O-H ⇒ ADP + Pi
will compete with the desired reaction
ATP + R-O-H ⇒ ADP + R-O-P
Kinases minimize the likelihood of this
unproductive activity by changing
conformation upon binding substrate so that
hydrolysis of ATP cannot occur until the
binding happens.
Illustrates the importance of the order in which
things happen in enzyme function
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