Elementary Reactions
A I 1 I2
P (I: intermediates)
P (A: reactant, P: product)
k
aA + bB + …….+zZ P Rate = k [A]a[B]b…..[Z]z order: a+b+…+z
A
A
P
A+B
v = d[A]/d[t] = k[A] (first-order reaction, k = s-1)
P
v = d[A]/d[t] = d[B]/d[t] = k{A][B] (second-order reaction, k= M-1s-1)
For first-order Rx: d[A]/[A] = -k d[t]
For second-order Rx A+A
P
ln[A] = ln[A]o - kt
d[A]/[A]2 = k d[t]
[A] = [A]oe-kt
t1/2 = ln2/k
1/[A] = 1/[A]o + kt
kcat/Km is a measure of catalytic efficiency
vo =
kcat[E]T[S]
when [S]<<Km, little ES is formed, so [E] ~ [E]T ,vo = (kcat/Km) [E][S]
Km + [S]
kcat/Km is apparent second-order rate constant for an enzyme reaction,
It is smaller than diffusion-controlled limit 108~1010 M-1s-1
fK P
V
max
m
[P]eq
The Haldane Relationship: Keq =
=
VmaxrKmS
[S]eq
k1
The one-intermediate Model
Vmaxf
= k2[E]T
Vmaxr
= k-1[E]T
Competitive inhibitor
k1
k2
ES
E+S
k-1
+
I
KI
EI + S
E+S
No reaction
k-1
k2
EX
KMS
=
E+P
k-2
k-1 + k2
k1
E+P
Vo =
k2[E]T[S]
KM (1+
[I]
) + [S]
KI
KMP
=
K2 + k-1
K-2
Uncompetitive inhibitor
E+S
k1
k-1
KI’
ES
+
I
k2
ESI
E+P
Vmax[S]
Vo =
KM + (1+
No reaction
Mixed or Noncompetitive inhibitor
k2
k1
E+S
ES
E+P
k-1
+
+
I
I
KI
KI’
No reaction
ESI
EI
[I]
KI’
)[S]
Vmax[S]
Vo =
(1+
[I]
[I]
)KM + (1+ )[S]
KI’
KI
pH dependence of simple Michaelis-Menten Enzymes
E-
ES-
EH + S
KE1 H+
k1
k-1
ESH
KES1
EH2+
Vo =
H+
KES2
H+
KE2
k2
EH + P
H+
ESH2+
Vmax’[S]
KM’ + [S]
Vmax’ = Vmax/f2 KM’ = KM(f1/f2)
[H+]
k
f1 =
+ 1 + E2+
kE1
[H ]
f2 =
[H+]
+1+
kES1
kES2
[H+]
Bi-substrate Reactions
A+B
E
P+Q
E
Transfer Reaction
P-X + B
P + B-X
Terminology:
1. Substrates are designated by the letters A, B, C, and D in the order that
they add to the enzyme.
2. Products are designated P, Q, R, and S in the order that leave the enzyme.
3. Stable enzyme forms are designated E, F, and G with E being the free enzyme.
4. The numbers of reactants and products in a given reaction are specified, in
order, by the terms Uni (one), Bi (two), Ter (three), and Quad (four).
Types of Bi Bi reaction:
1. Sequential reactions (single-displacement), can be subclassifieid into
an Ordered mechanism (left) , and a Random mechanism (right).
A
E
A
B
k1 k-1
k2 k-2
EA
P
k3
EAB k-3 EPQ
P
B
Q
Q
k4 k-4
k5 k-5
EQ
E
E
EAB-EPQ
E
B
A
Q
P
2. Ping Pong Reactions
Ping Pong Bi Bi: double displacement
P
A
E
EA-FP
Q
B
F
FB-EQ
E
Rate equations
Ordered Bi Bi
KSAKSB
1
1
KMA
KMB
+
=
+
+
Vo
Vmax Vmax[A] Vmax[B] Vmax[A][B]
Rapid-equilibrium random Bi Bi
Ping Pong Bi Bi
1
1
=
Vo
Vmax
+
KSAKMB
VmaxKS
B[A]
1
1
KMA
KMB
+
=
+
Vo
Vmax Vmax[A] Vmax[B]
+
KMB
Vmax[B]
+
KSAKMB
Vmax[A][B]
slope = KMA/Vmax
Diagnostic plot for Ping Pong Bi Bi
1/vo
increasing
constant [B]
slope =
KM
A
intercept = 1/Vmax + KMB/Vmax[B]
KSAKMB
+ [B]
1/[A]
Vmax
double-reciprocal plots for a Ping Pong Bi Bi mechanism
1/vo
increasing
constant [B]
intercept = 1 + KMB/[B]
Vmax
Diagnostic plot for sequential Bi Bi
1/[A]
double-reciprocal plots for a Sequential Bi Bi mechanism
Differentiating random and ordered sequential mechanisms
1. Product inhibition:
2. isotope exchange
Enzyme catalysis
1.
2.
3.
4.
5.
6.
Acid-base catalysis
Covalent catalysis
Metal ion catalysis
Electrostatic catalysis
Proximity and orientation effects
Preferred binding of the transition state complex
1. Acid-base catalysis
CH2OH
H A
O
O
H
H
H
OH
C
O H
CH2OH
H
OH
:B-
H
H
OH
H
-D-Glucose
H
O
H-B
O
OH
C
H
H :B-
-Pyridone involves
the reaction
OH
N
O
N
CH2OH
H :A
HC
H
H A
OH
-D-Glucose
-
O
H
OH
OH
OH
H
O
O
H
OH
H
OH
H
OH
H
OH
linear form
O
H
O
O
C
H :B-
H
H
O
O
C
H
v=k[-pyridone][tetramethyl--D-glucose]
The bovine pancreatic RNase A-catalyzed hydrolysis of RNA
O
P O CH2 O Base
O
H
H
H
H
NH
H2 O
N
His 12
O OH
O P O CH2
O
Base
O
HO CH2
H
H
O
H
Base
+
H
N
H
H
OH
O
H
O P O
N
OH
O
H
O
O P O
His 119
O
O
P O CH2 O Base
O
H
H
H
H
NH
H+N
O O
His 12
P
O
HO
H
N H O
N
H
His 119
O
P O CH2 O Base
O
H
H
H
H
NH
N
O OH
His 12
O P OH
H
O
N+
N
H
His 119
2. Covalent catalysis
H
+
N
H H
N C OH
H
O
H
H-A
:B
Lys
HC
2-
O3PO
+
N
N+
O
CH2 C
CO2
+ OH-
H+
O-
O
RNH2
OH-
OHCO2
H
H2C
CH3
Acetone
Enolate
RNH2
R
O
H2C
CH2
H2C
-
acetoacetate
H
OCH3
N C
Schiff base (w PLP)
O
H2C
H
N+
H
O
CH2 C
O-
Schiff base (imine)
R
H
+
CH2
H
N
+
H
N
H2C
R
H2C
CH3
3. Metal ion catalysis
1. Metalloenzymes: containing tightly bound metal ions, most commonly transition
metal ions such as Fe2+, Fe3+, Cu2+, Zn2+, Mn2+, or Co3+
2. Metal-activated enzymes: loosely bind metal ions from solution, usually the alkaline
earth metal ions Na+, K+, Mg2+, or Ca2+
Three major roles:
1. By binding to substrates so as to orient them properly for reaction
2. By mediating oxidation-reduction reactions through reversible changes in the
metal ion’s oxidation state.
3. By electrostatically stabilizing or shielding negative charges
Mn+
O CH3
OC
O
Mn+
C C
CH3
C
-
O
O
Im
Im
O-
O-
O
2+
CH3
-
C
CH3
Zn
O
C
Im
H
O
O
O
Im
H O C
O-
Im
O
Mg2+
O
O-
Adenine Ribose O P O P O P OO
O
CH3
O
Zn2+
Im
-
CH3
C CH
O
-
O
O
+ Mn+
4. Electrostatic catalysis
The pK’s of amino acid side chains in proteins may vary by several units
from their nominal values
5. Proximity and orientation effects
a. Proximity alone contributes relatively little to catalysis
b. Properly orienting reactants and arresting their relative motions can
result in large catalytic rate enhancement
O
H3C
O
NO2
k1
N
k2 = 24 x k1[imidazole]
NH
O
H2
C
O
NO2
k2
N
NH
R
R'
R''
Y-
R'
R
R'
R''
R
R''
Y-
Y
6. Preferred binding of the transition state complex
Transition state analogues are competitive inhibitors
proline racemase
-
COO
C
N
H
H
C
H
+
+
H
N
H
H
planar TS
COO-
D-proline
L-proline
C- COON
H
COON
H
N+
H
pyrrole-2-carboxylate
competitive inhibitors
COO-
D-1-pyrroline-2-carboxylate
Lysozyme
A. Enzyme structure: E + (NAG)3 poor substrate
(NAG)6 is a good substrate, 2-fold smaller kcat than (NAG-NAM)3
Modeling suggested that the fourth NAG needs to be distorted to change to half-chair form
Asp52 and Glu35 are close to the cut. For non-enzymatic reaction, oxonium ion can be formed.
OR'
H C OR'
OR'
H C O R"
R H
+
+H
R
R"OH
acetal
R'
O+
C
H
R
R'
OR'
H C OH
O
C+
H R
Hemiacetal
R
oxonium ion (resonance-stabilized)
When the reaction was run in 18O water,
18O
O
was incorporated.
NAM
RO
CH2OH
C
O+
O
H3C
N
H
OH
O
C Glu35
O
O
N
H
O
O
-
H O
NAG HO
H3C
C Asp52
-
O
C
O
Possible covalent catalysis (need proof)
CH2OH
H
O
O
O O C CH2
H
OR
H
H
NHCOCH3
Asp52
covalent catalysis
H
Intermediate can be trapped by speeding up its formation and slowing down its decomposition.
CH2OH
CH2OH
O
H
H
OH OH
H
H
O
O
H
H
OH
NHCOCH3
H
H
H
F
H
(good leaving group)
-
O
O C CH2-Asp52
F
(stabilize the negative charge)
MASS and crystal structure showed unambiguously the intermediate formation
Serine protease
Burst kinetics
assay
chymotrypsin
O
H3C
O
NO2
p-nitrophenyl acetate
fast
rapid
O
H3C
Enzyme
acy-enzyme intermediate
+
-
O
NO2
450 nm
slow
O
H3C
O-
Burst kinetics: A rapid release of p-nitrophenylacetate followed by a slow release of acetate
Asp-His-Ser catalytic triad and oxyanion hole to facilitate tetrahedral intermediate
The tetrahedral intermediate is mimicked in a complex of Trypsin with Trypsin inhibitor
1013
M-1
Trypsin-BPTI (bovine pancreatic trypsin inhibitor)
The side-chain oxygen of Ser95 is in closer than van der Waals contact
with the pyramidally distorted carbonyl carbon of BPTI’s scissile peptide
KA =
Ser195
H
Ala 16I
O
C
O
C N
C
Lys 15I
H
Asp102
His57
H2C C O
O-
Asp102
Ser195
H2C
H2C C O
O-
1
H N
CH2
N
His57
H N
H O
N
C
H O
R
R'
O
H
CH2
N+
R
R'
Ser195
H2C
N
C
O-
H
Tetrahedral intermediate
Asp102
H2C C
His57
O
O-
Asp102
Ser195
H2C
H2O
H N
CH2
N
H2C C O
O-
His57
H N
CH2
N
H O
R'NH2
R
O
Ser195
H2C
C
R
N
O
H
H O
R'
C
O
H
Acyl-enzyme intermediate
Asp102
H2C C O
O-
Asp102
His57
Ser195
H2C
H N
N+
CH2
H2C C O
O-
His57
Ser195
H2C
H N
CH2
N
H O
H O
R
O
H
R
C
O-
O
H
C
O
Drug Discovery
SARs and QSARs (quantitative structure-activity relationship)
Structure-based drug design (rational drug design)
Combinatorial chemistry and High-Throughput Screening
After finding a lead: consider the followings: (1) it must be chemically stable in the
highly acidic (pH 1) environment of the stomach, (2) it must be absorbed from the
gastrointestinal tract into the bloodstream, (3) it must not bind too tightly to other
substances in the body (e.g. albumin), (4) it must survive from the detoxifying
enzymes, (5) it must avoid rapid excretion by the kidney, (6) it must pass from
the capillaries to its target tissue, (7) if it is targeted to the brain, it must cross the
blood-brain barrier, (8) if it is targeted to the intracellular receptor, it must pass
through the plasma membrane and other intracellular membrane.
Pharmacokinetics: The ways in which a drug interacts with these various barriers.
Bioavailability: depends on both dose given and its pharmacokinetics
Lipinski’s rule of five for a compound to exhibit poor absorption or permeation if:
1. Its MW > 500
2. It has >5 hydrogen bond donors (the sums of OH and NH groups)
3. It has > 10 hydrogen bond acceptors (the sum of N and O atoms)
4. Its value of logP is greater than 5 (P is partition coefficient: the conc of
drug in octanol /the conc of drug in water)
Toxicity and adverse reactions eliminate most drug candidates in Clinical trials
phase I: 20-100 of normal healthy volunteers (safety and dosage)
phase II: 100-500 volunteers in single blind tests (efficacy)
phase III: 1000-5000 volunteers in double-blind tests (adverse reactions)
Some statistics
1. Only 5 drug candidates in 5000 that enter preclinical trials reach clinical trials.
2. Preclinical takes 3 years and successful clinical trails take additional 7-10 years.
3. US$300 million is required to bring one drug to the market averagely.
4. Good drug can sell 1 US billion every year and patent is protected for 18 years.
Cytochrome P450
1. The cytochrome P450 metabolize most drugs (the life-time is reduced).
2. Drug-drug interactions are often mediated by cytochrome P450: if drug A
Inhibits cytochrome P450 that metabolizes drug A, co-administration of drugs
A and B will cause the increase of bioavailability of drug B; if drug A induces
the increased expression of cytochrome P450, the co-administrating drugs A
and B will reduce drug B’s bioavailability. Moreover, if drug B is metabolized
to a toxic compound, its increased rate of reaction may result in an adverse
reaction. For example, excess acetaminophen, which reduces fever, can be
converted to acetimidoquinone, which reacts with glutathione to form
conjugate, so the glutathione is used up to cause liver toxicity.
HIV protease and its inhibitors
Aspartic protease
H
C
O
H
O
C
Asp
H
N
R
O
R'
C
O
H
O
O
H
C
O-
N
R
R'
H
-
O
C
Asp
O
H
O
H
O
C
O
Asp
Asp
H
R
O
N
+
C O
R'
H
H
H
O
O
C
Asp
O
-
C
O
Asp
Normal peptide and its isosteres (stereochemical analogs) and HIV protease
inhibitors that are in clinical use
P1’
OH
P1
Ph
N
O
H
N
R'
C
N
CH
CH
R
N
H
C
N
H
O
peptide bond
CH
R
Indinavir (CrixivanTM)
O S
CH
HO
C
N
H
H
N
O
R'
H2
C
H
N
OH
N
N
H
O
Ph
N
OH
H
N
CH
R
Nelfinavir (ViraceptTM)
R'
CH
CH
N
S
O
O
Hydroxyethylene
OH
H
N
CH
R
H
N
CH
R
N
H
O
S
O
NHtBu
N
OH
Saquinavir (InviraseTM)
O
C
H
N
C
H2
N
O
H2N
CH
O
Ph
O
H
N
N
O
Dihydroxyethylene
OH
CH3
N
Ritonavir (NovirTM)
C
OH
H
N
Ph
CH
CH
Ph
O
N
H
R'
CH
OH
H
N
O
C
C
H2
H
H
Reduced Amide
OH
NHtBu
O
CH
H
N
O
R'
Hydroxyethylamine
O
O
Ph
OH
N
S
O O
NH2
Amprenavir (AgeneraseTM)