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Chapter 8 Enzymes
Significance of enzyme study:
1. Normal enzyme function is required for life maintenance
2. Medical treatment and diagnostic
3. Drug development
Introduction to Enzymes
1897 Eduard Buchner --- yeast extracts can ferment sugar to alcohol
Frederick W. Kuhne --- the name “enzyme”
1926 James Sumner --- crystallization of urease
John Northrop & Moses Kunitz --- crystallization of pepsin and trypsin
J.B.S. Haldane --- treatise for “Enzymes” (weak-bonding interactions)
Most enzymes are proteins
cofactor
coenzyme
prosthetic group
holoenzyme
apoenzyme
(apoprotein)
Enzymes are classified by the reactions they catalyze
How enzymes work
Binding of a substrate to an enzyme
at the active site
Enzymes affect reaction rates, not equilibria
E+S
ES
EP
E+P
Ground state
Transition state vs. reaction intermediate
Activation energy
Rate-limiting step
C12H22O11 + 12 O2
12 CO2 + 11 H2O
Reaction rates vs. Equilibria
K’eq = [P]/[S]
G’o = -RT ln K’eq
V = k[S]
= k [S1][S2]
k = (k T/h)e-G /RT
A few principles explain the catalytic power
and specificity of enzymes
Binding energy (GB)--- the energy derived from enzyme-substrate interaction
1. Much of the catalytic power of enzymes is ultimately derived from the
free energy released in forming multiple weak bonds and interactions
between an enzyme and its substrate. This binding energy contributes to
specificity as well as catalysis.
2. Weak interactions are optimized in the reaction transition state; enzyme
active sites are complementary not to the substrate per se, but to the
transition state through which substrates pass as they are converted into
products during the course of an enzymatic reaction.
Weak interactions between enzyme and substrate
are optimized in the transition state
“lock and key” model
Dihydrofolate reductase
NADP+
tetrahydrofolate
In reality
stickase
Lock and key
Induced fit
Role of binding energy in catalysis
V = k [S1][S2]
k = (k T/h)e-G /RT
V can be increased 10 fold when -G decreased by 5.7 kJ/mol
Formation of a single weak interaction ~4-30 kJ/mol
Between E and S, GB ~60-100 kJ/mol
Binding energy vs. catalysis and specificity
Specificity --- the ability of enzymes to discriminate between
a substrate and a competing molecule.
High specificity --- functional groups in the active site of enzyme
arranged optimally to form a variety of weak interactions with
a given substrate in the transition state
Physical and thermodynamic factors
Contributing to G , the barrier to reaction
1. The change in enthropy
2. The solvation shell of H-bonded water
3. The distortion of substrates
4. The need for proper alignment of catalytic functional groups
on the enzyme
Binding energy is used to overcome these barriers
Rate enhancement by entropy reduction
Specific catalytic groups contribute to catalysis
General acid-base catalysis
Amino acids in general acid-base catalysis
102 to 105 order of rate enhancement
Covalent catalysis
A B
H2O
A B + X:
A+B
A X+B
H2O
Metal ion catalysis
ionic interaction
oxidation-reduction reactions
A + X: + B
Enzyme kinetics as an approach to understanding mechanism
Enzyme kinetics --- determination of the rate of the reaction and how it changes
in response to changes in experimental parameters
Fig. 8-11. Effect of substrate
Concentration on the initial
velocity of an
enzyme-catalyzed reaction
V0 (initial velocity)
when [S]>>[E], t is short
Vmax (maximum velocity)
when [S] 
The relationship between substrate concentration and
reaction rate can be expressed quantitatively
k1
k2
E + S
ES
E+P
k-1
V0 = k2[ES]
Rate of ES formation = k1([Et]-[ES])[S]
Rate of ES breakdown = k-1[ES] + k2[ES]
Steady state assumption
k1([Et]-[ES])[S] = k-1[ES] + k2[ES]
k1[Et][S] - k1[ES][S] = (k-1 + k2)[ES]
k1[Et][S] = (k1[S] + k-1 + k2)[ES]
[ES] = k1[Et][S] / (k1[S] + k-1 + k2) divided by k1
[ES] = [Et][S] / {[S] + (k-1 + k2)/ k1}
(k-1 + k2)/ k1 = is defined as Michaelis constant, Km
[ES] = [Et][S] / ([S] + Km)
V0 = k2[ES] = k2[Et][S] / ([S] + Km)
Vmax = k2[Et]
V0 = Vmax [S] / ([S] + Km)
Michaelis-Menten equation
V0 = Vmax [S] / ([S] + Km)
When [S] = Km
Michaelis-Menten equation
V0 = ½ Vmax
V0 = Vmax [S] / ([S] + Km)
1/V0 = Km /Vmax [S] + 1 /Vmax
the double-reciprocal plot
Kinetic parameters are used to compare enzyme activities
Km = (k-1 + k2)/ k1
E + S
if k2 << k-1 Km = k-1/ k1 = Kd
if k2 >> k-1 Km = k2/ k1
if k2 ~ k-1
k1
ES
k-1
k2
E+P
Km relates to affinity
Vmax = k2[Et]
E + S
k1
ES
k-1
k2
E+P
kcat, the rate limiting of any enzyme-catalyzed reaction at saturation
kcat = Vmax / [Et] (turnover number)
V0 = Vmax [S] / ([S] + Km)
kcat = Vmax / [Et]
M-M equation
(turnover number)
V0 = kcat [Et] [S] / ([S] + Km)
when [S] << Km
([S] is usually low in cells)
V0 = kcat [Et] [S] / Km
( kcat / Km , specific constant)
kcat / Km has a upper limit (E and S diffuse together in aqueous solution)
~108 to 109 M-1S-1
catalytic perfection
Enzyme are subjected to inhibition
Reversible vs. irreversible inhibition
1/V0 = Km /Vmax [S] + 1 /Vmax
(the double-reciprocal plot)
-1/Km
1/V0 = Km /Vmax [S] + 1 /Vmax
1/Vmax
1/V0 = Km /Vmax [S] + 1 /Vmax
Irreversible inhibition is an important tool
in enzyme research and pharmacology
Irreversible inhibitor
Suicide inactivator
Mechanism-based inactivator
chymotrypsin
Enzyme activity is affected by pH
Enzyme-transition state complementarity
Transition-state analogs
Catalytic antibodies
Reaction mechanisms illustrate principles
chymotrypsin
Amide nitrogens
Aromatic
Side chain
Steps in the hydrolytic cleavage of a peptide bound by chymotrypsin
Pre-steady state kinetic
evidence for an acyl-enzyme
intermediate
Induced fit in hexokinase
P (orange)
O (blue)
The two-step reaction catalyzed by
Enolase in glycolysis
Regulatory enzymes
Allosteric enzymes
vs. allorsteric modulators
Allosteric enzymes undergo
conformational changes
in response to modulator
binding
Two views of the regulatory enzyme aspartate transcarbamoylase
(12 subunits)
The regulatory step in many pathways
is catalyzed by an allosteric enzyme
Feedback inhibition
The kinetic properties of allosteric enzymes diverge from
Michaelis-Menten behavior
Vmax, Km
S as a positive modulator
+ Positive modulator
- Negative modulator
Some regulatory enzymes undergo reversible covalent modification
Phosphoryl groups affect the structure and catalytic activity of proteins
Glycogen phosphorylase
(Glucose)n + Pi
(glucose)n-1 + glucose 1-phosphate
AMP
PLP
Glucose
P-Ser14
Regulation of glycogen phosphorylase
Multiple phosphorylations allow exquisite regulatory control
OH
Protein
phosphatases
Protein
kinases
PO4
Multiple regulatory phosphorylations
Some types of regulation require proteolytic cleavage of
an enzyme precursor --- zymogen
-S-S-