Biochemistry 462a - Enzyme Kinetics
Reading - Chapter 14 & 15
Practice problems - Chapter 14 - 1,2,4,6,7; Chapter 15 - 1,2; Enzymes extra problems
Introduction
Enzymes are Biological Catalysis
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A catalyst is a substance that increases the rate (velocity) of a chemical reaction.
Most biological catalysts are proteins.
The material acted upon by the catalyst is the substrate.
Although a catalyst participates in the reaction process, it is unchanged after the process is
complete.
A catalyst increases the rate at which a reaction reaches equilibrium but does not alter Keq
or Go' for the reaction.
A thermodynamically favorable process is not made more favorable by the presence of a
catalyst.
A thermodynamically unfavorable process is not made favorable by the presence of a
catalyst.
Kinetics
The Rate Constant
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For the irreversible reaction A  B.
This is a first order reaction (there is only a single reactant).
The velocity (v) or reaction rate is given by the rate of
formation of product or the rate of disappearance of
reactant.
The velocity (v) or reaction rate is, where k= the rate
constant.
For the reaction A + B products, v = k[A][B]. This is a second order reaction (there are two
reactants).
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Reaction Rate Theory
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What determines the rate of a
reaction?
For every reaction there is a highenergy transition state through
which the reactants must pass in
order for the reaction to occur.
The height of the energy barrier,
Go‡, determines the rate of the
reaction. k=Qe-Go‡/RT
Q is a collection of constants.
Catalysis
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A catalyst functions by lowering the
activation energy for a reaction by
amount = Go‡.
A catalyst does not alter the G for
the reaction.
Go‡ =Ho‡ -TSo‡ - a catalyst can
accelerate a reaction by affecting
either Ho‡ or So‡, or both.
Strong binding of the transition state
to the catalyst lowers Ho‡ - makes it
more negative.
Proximity and orientation of the
substrates on the catalyst favors
formation of the transition state by
reducing So‡.
Enzymes
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Enzymes are highly effective catalysts that carry out complex chemical transformations
under mild conditions (water, neutral pH).
Enzymes show great specificity with regard to the reactions they catalyze and the substrates
they react with.
Enzymes can be regulated.
Enzymes carry out their catalytic role by binding the substrate to a specific area of the protein
called the active site (Companion: Enzymes/Enzyme Kinetics).
Several amino acid side chains comprise the active site.
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Coenzymes are small organic molecules, derived from vitamins that participate in the chemical
reactions catalyzed by many enzymes.
Coenzyme
Vitamin
Reaction Mediated
Biotin
Biotin
Carboxylation
Cobalamin
B12
Alkylation
Coenzyme A
Pantothenic acid Acyl Transfer
Flavin
Riboflavin
Oxidation-Reduction
Lipoic Acid
Lipoamide
Acyl Transfer
Nicotinamide
Niacin
Oxidation-Reduction
Pyridoxal Phosphate
Pyridoxal
Amino Group Transfer
Tetrahydrofolate
Folate
One-Carbon Group Transfer
Thiamine Pyrophosphate Thiamine
Aldehyde Transfer
Summary of factors responsible for the rate enhancement seen with enzyme catalysis
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Uncatalyzed reactions in solution can be slow because
o They involve the formation of unstable positive and negative charges in the transition
state.
o They frequently require several molecules to be brought together with a concomitant
loss of entropy.
These difficulties are lessened with enzymes because
o Strategically placed acids, bases, metal ions, or dipoles that are part of the structure of
the enzyme stabilize charges.
o Covalent catalysis is used to give reaction pathways of lower energy.
o Entropy losses are minimized because the necessary catalytic groups are part of the
enzyme structure.
These features are paid for in two ways.
o The original synthesis of the enzyme costs energy, although the enzyme is used
repeatedly.
o The enzyme-substrate binding energy is used to immobilize the substrate at the active
site and hold it next to the catalytic groups.
This binding energy is inherently available for use but it is generally not utilized in
uncatalyzed reactions.
Enzyme Kinetics
The simplest enzyme mechanism involves the
following two steps
The rate of the enzymatic reaction is:
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In order to derive a useful equation describing this
reaction we make the steady-state assumption,
which assumes that over most of the reaction course
[ES] is small and does not change, i.e., d[ES]/dt=0.
Using this assumption, one
Michaelis-Menten equation.
can
derive
the
Plotting Kinetic Data
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The Michaelis-Menten equation describes a
rectangular hyperbole.
The enzyme is characterized by two constants:
KM and Vmax
o Vmax is the maximal rate of the reaction
which occurs when [S] >> KM
o KM is the substrate concentration that
gives 1/2 maximal velocity.
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For determination of KM and Vmax a linear
transformation - the Lineweaver-Burke plot is
useful.
Turnover Number
The turnover number of an enzyme, kcat, is the maximal
velocity per enzyme molecule per unit of time.
Enzyme Efficiency
We can rewrite the rate equation as
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When [S] << KM, then kcat/KM is a second order rate constant, and is a measure of the
efficiency of the enzyme at low [S].
The maximal value of kcat/KM is 108-109, which is diffusion-controlled.
Enzyme
Substrate
kcat (sec-1)
KM(M)
kcat/ KM (M-1) (sec-1)
Catalase
H2O2
4.0x107
1.1
4.0x107
Carbonic
anhydrase
CO2
1.0x104
1.2x10-2
8.3x107
Acetylcholine
esterase
Acetylcholine
1.4x104
9.0x10-5
1.6x108
Fumarase
Fumarate
8.0x102
5.0x10-6
1.6x108
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For different substrates, kcat/KM is also the best way to determine the specificity of an enzyme.
For hydrolysis of a peptide bond by the proteolytic enzyme
chymotrypsin, the nature of the R1 sidechain is critical
.
R1
kcat/ KM (M-1sec-1)
Gly
1.3x10-1
Val
3.6x102
Leu
3.0x103
Phe
1.0x105
The Phe-containing substrate is best!
Enzyme Regulation
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Amount of enzyme (transcriptional).
Amount of substrate.
Control of activity.
o Allosteric regulation.
o Covalent modification.
o Inhibitors.
Allosteric Regulation (remember hemoglobin!!).
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Multisubunit enzymes
Homoallostery - cooperative substrate binding
and activation.
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Heteroallostery - regulation by effector
molecules, which can be positive or
negative.
Allosteric effectors bind at a site different
from the active site.Allosteric effectors can
activate (favor R state) or inhibit (favor T
state).
Reversible
covalent
modification is widely used to
regulate
enzyme
activity.
Phosphorylation of a Ser is a
common reaction.
Irreversible covalent modification. Many enzymes are
made as inactive precursors - zymogens. Activation of the
zymogen involves proteolytic removal a peptide from the
amino terminal.
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Enzyme Inhibitors
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The use of enzyme inhibitors can often provide valuable information about an enzymatic
mechanism. Many drugs are based on the use of enzyme inhibitors, e.g., penicillin inhibits
an enzyme involved in bacterial cell wall synthesis.
A competitive inhibitor competes with the substrate for binding at the active site.
A noncompetitive inhibitor binds to a site other than the active site and inhibits product
formation
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Covalent Inhibition
Irreversible or covalent inhibition involves chemical
modification of the protein.
Effect of pH
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pH is not an important regulatory mechanism, but
the effect of pH can be highly informative about the
mechanism.
Changing pH can increase or decrease the rate.
This pH-rate profile suggests that a deprotonated
histidine is involved in the catalytic step.
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This pH-rate profile suggests that a protonated
lysine is involved in the catalytic step.
Note that the apparent pKa derived from inspection of kinetic data may be significantly
different than the actual pKa of the sidechain. More sophisticated analysis is required to obtain
an accurate estimation of the pKa in the enzyme.
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