Elementary Reactions
A P (A: reactant, P: product) A I1 I2 P (I: intermediates)
aA + bB + …….+zZ P Rate = k [A]a[B]b…..[Z]zk
order: a+b+…+z
A P v = d[A]/d[t] = k[A] (first-order reaction, k = s-1)
A + B 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] ln[A] = ln[A]o - kt [A] = [A]oe-kt t1/2 = ln2/k
For second-order Rx A+A P d[A]/[A]2 = k d[t] 1/[A] = 1/[A]o + kt
kcat/Km is a measure of catalytic efficiency
vo = when [S]<<Km, little ES is formed, so [E] ~ [E]T
kcat[E]T[S]
Km + [S],vo = (kcat/Km) [E][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
The Haldane Relationship: Keq = = [P]eq
[S]eq
VmaxfKm
P
VmaxrKm
S
The one-intermediate Model E + S EX E + P
Vmaxf = k2[E]T Vmax
r = k-1[E]T KMS =
k-1 + k2
k1
KMP =
k1 k2
K2 + k-1
K-2
k-1 k-2
Competitive inhibitor
E + S k1
k-1
ESk2 E + P
+I
EI + S No reaction
KI
Vo = k2[E]T[S]
KM (1+ ) + [S][I]KI
Uncompetitive inhibitor
E + S ES E + Pk1
k-1
k2
+I
ESI No reactionKI’
Vo = Vmax[S]
KM + (1+ )[S][I]
KI’
Mixed or Noncompetitive inhibitor
E + S ES E + Pk1
k-1
k2
+I
EI
+I
ESI No reactionKI KI’
Vo = Vmax[S]
(1+ )KM + (1+ )[S][I] [I]
KIKI’
pH dependence of simple Michaelis-Menten Enzymes
E- ES-
EH + S ESH EH + P
EH2+ ESH2
+
H+KE2
H+KE1
H+KES2
H+KES1
k2k1
k-1
Vo = Vmax’[S]
KM’ + [S]
Vmax’ = Vmax/f2 KM’ = KM(f1/f2)
f1 = + 1 + f2 = + 1 + [H+]kE1
kE2
[H+][H+]
kES1
kES2
[H+]
Bi-substrate Reactions A + B P + Q E
Transfer Reaction P-X + B P + B-XE
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 intoan Ordered mechanism (left) , and a Random mechanism (right).
A
k1 k-1
E EA
B
EAB EPQ EQ E
P Q
k2 k-2 k4 k-4 k5 k-5k3
k-3
A B
B A
E EAB-EPQ
P Q
Q P
E
2. Ping Pong Reactions Ping Pong Bi Bi: double displacement
A P B Q
E EA-FP F FB-EQ E
Rate equations
Ordered Bi Bi1Vo
=1
Vmax
KMA
Vmax[A]
KMB
Vmax[B]+ + +
KSAKS
B
Vmax[A][B]
Rapid-equilibrium random Bi Bi 1Vo
=1
Vmax
KSAKM
B
VmaxKSB[A]
KMB
Vmax[B]+ + +
KSAKM
B
Vmax[A][B]
Ping Pong Bi Bi1Vo
=1
Vmax
KMA
Vmax[A]
KMB
Vmax[B]+ +
Diagnostic plot for Ping Pong Bi Bi
Diagnostic plot for sequential Bi Bi
Differentiating random and ordered sequential mechanisms1. Product inhibition: 2. isotope exchange
1/vo
1/[A]
increasing constant [B]
slope = KMA/Vmax
intercept = 1/Vmax + KMB/Vmax[B]
double-reciprocal plots for a Ping Pong Bi Bi mechanism
1/[A]
increasing constant [B]
intercept = 1 + KMB/[B]
double-reciprocal plots for a Sequential Bi Bi mechanism
Vmax
Vmax
[B]KS
AKMB
KMA+
slope =
1/vo
Enzyme catalysis1. Acid-base catalysis2. Covalent catalysis3. Metal ion catalysis4. Electrostatic catalysis 5. Proximity and orientation effects6. Preferred binding of the transition state complex
1. Acid-base catalysis
O
CH2OH
H
OH
H
OHOH
H
H
OH
H
OH
CH2OH
H
OHOH
H
H
OH
HO
linear form
-D-Glucose -D-Glucose
O
CH2OH
OH
H
H
OHOH
H
H
OH
HO
CH
O H
H A
:B-
O
HC
H :A-
H-B
O
O
C
OH
H
H A
:B-
O
C
O
H :B-
NOH
H
NO
O
H
CO
H
H
-Pyridone involvesthe reaction
v=k[-pyridone][tetramethyl--D-glucose]
O
H
O
H
O
Base
H
H
P-O OO
CH2 O
H
O
P-O OO
Base
H
CH2
H
OP
O
O
H
OH
N NH
His 12
NH
N+H
His 119
H2O
HO CH2 O
H
O
P-O OO
Base
H
H
OH
O
H
O
H
O
Base
H
PHO
CH2
H
OP
O
O
O
NH
N
His 119
H
OH
H+N NH
His 12
O
H
O
H
OH
Base
H
P-O OHO
CH2
H
OP
O
O
NH
N+H
His 119
N NH
His 12
The bovine pancreatic RNase A-catalyzed hydrolysis of RNA
2. Covalent catalysis
N
H
H
:B
O+
H-A
N
H
CH
HOH N
H
C + OH-
Schiff base (w PLP)
N+
HCN+
H
Lys
CH3
2-O3PO
H
O-
H2CO
CH2 CO
O-
CO2
H2C
O-
CH2
H+
H2CO
CH3
acetoacetate Enolate Acetone
RNH2
OH-
N+R H
H2C CH2 CO
O-
CO2
H2C
N
CH2
H+
H2C
N+
CH3
OH-
RNH2
R HR H
Schiff base (imine)
3. Metal ion catalysis1. Metalloenzymes: containing tightly bound metal ions, most commonly transitionmetal ions such as Fe2+, Fe3+, Cu2+, Zn2+, Mn2+, or Co3+2. Metal-activated enzymes: loosely bind metal ions from solution, usually the alkalineearth metal ions Na+, K+, Mg2+, or Ca2+
Three major roles:1. By binding to substrates so as to orient them properly for reaction2. By mediating oxidation-reduction reactions through reversible changes in the metal ion’s oxidation state.3. By electrostatically stabilizing or shielding negative charges
O-
C
O
OC
CH3
CH3
CO
O-
Mn+
O-
C
O-
OC
CH3
CH3
Mn+
-O
CO
CHCH3
CH3O+ Mn+
Im Zn2+
Im
O-
Im H
C
O
O
H O C
O
O-
Im Zn2+
Im
Im
Adenine Ribose O P O P O P O-
O- O- O-
O O O
Mg2+
4. Electrostatic catalysisThe pK’s of amino acid side chains in proteins may vary by several unitsfrom their nominal values
5. Proximity and orientation effectsa. Proximity alone contributes relatively little to catalysisb. Properly orienting reactants and arresting their relative motions canresult in large catalytic rate enhancement
H3C
O
O NO2
NH
N
k1
H2C
O
O NO2
NH
N
k2
k2 = 24 x k1[imidazole]
R'R''
R
Y-
RR'
R''
Y-
R R'R''
Y
6. Preferred binding of the transition state complexTransition state analogues are competitive inhibitors
N
CCOO-
H
H
N
C-
H
COO-
N
CH
COO-
H
L-proline
proline racemase
planar TSD-proline
H+ H+
NCOO-
H
pyrrole-2-carboxylate
N+COO-
H
D-1-pyrroline-2-carboxylate
competitive inhibitors
LysozymeA. 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.
When the reaction was run in 18O water, 18O was incorporated.
CH
R
OR'OR' + H+ CH
R
OR'O R"
H
R'O+
CH R
R'O
C+
H R
oxonium ion (resonance-stabilized)
CH
R
OR'OH
Hemiacetal
acetal R"OH
O
O
O+
CH2OH
O
RO
N
H
CO
H3C
O
OC
-OAsp52
OC
OGlu35
NAM
NAG HO
N
H
CO
H3C
HOH-
OCH2OH
H
H
O C
O
CH2 Asp52H
O OR
H
H
NHCOCH3
covalent catalysis
Possible covalent catalysis (need proof)
Intermediate can be trapped by speeding up its formation and slowing down its decomposition.
MASS and crystal structure showed unambiguously the intermediate formation
OCH2OH
H
H
H
OH OH
H
H
NHCOCH3
OH O
CH2OH
H
H
F
OH
H
H
F
(good leaving group)
-O CO
CH2-Asp52
(stabilize the negative charge)
Serine protease
assay
Burst kinetics: A rapid release of p-nitrophenylacetate followed by a slow release of acetate
H3C
O
O NO2
p-nitrophenyl acetate
chymotrypsin
H3C
O
Enzyme + -O NO2
450 nm
rapid
acy-enzyme intermediate
fast
slow
H3C
O
O-
Burst kinetics
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
Ser195
O
C
H
NH
CO
CLys 15I
Ala 16IKA = 1013 M-1 Trypsin-BPTI (bovine pancreatic trypsin inhibitor)
The side-chain oxygen of Ser95 is in closer than van der Waals contactwith the pyramidally distorted carbonyl carbon of BPTI’s scissile peptide
H2C CO
O-H N
N
H2C
His57Asp102
H O
CH2
Ser195
N C
R
O
R'
H
1 H2C CO
O-H N
N+
H2C
His57Asp102
H O
CH2
Ser195
N C
R
O-
R'
HTetrahedral intermediate
H2C CO
O-H N
N
H2C
His57Asp102
H O
CH2
Ser195
N C
R
O
R'
HAcyl-enzyme intermediate
H2O
R'NH2
H2C CO
O-H N
N
H2C
His57Asp102
H O
CH2
Ser195
O C
R
OH
H2C CO
O-H N
N+
H2C
His57Asp102
H O
CH2
Ser195
O C
R
O-H
H2C CO
O-H N
N
H2C
His57Asp102
H O
CH2
Ser195
O C
R
OH
Drug DiscoverySARs 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 thehighly 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 fromthe 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 > 5002. 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 ofdrug in octanol /the conc of drug in water)
Toxicity and adverse reactions eliminate most drug candidates in Clinical trialsphase 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 statistics1. 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.
1. The cytochrome P450 metabolize most drugs (the life-time is reduced).
2. Drug-drug interactions are often mediated by cytochrome P450: if drug AInhibits 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 Aand B will reduce drug B’s bioavailability. Moreover, if drug B is metabolizedto a toxic compound, its increased rate of reaction may result in an adverse reaction. For example, excess acetaminophen, which reduces fever, can beconverted to acetimidoquinone, which reacts with glutathione to form conjugate, so the glutathione is used up to cause liver toxicity.
Cytochrome P450
HIV protease and its inhibitors
CN
R'R
O
H
HO
C
Asp
OH
OH
O
CO-
Asp
O-
C
Asp
OH
OH
O
CO
Asp
H
OC
R N
H
R'
R
CO
OH
+H
NR'
H
HO
C
Asp
O
O
C-O
Asp
Aspartic protease
Normal peptide and its isosteres (stereochemical analogs) and HIV proteaseinhibitors that are in clinical use
N
NN
PhHN
OH
O
OH
NH
Indinavir (CrixivanTM)
NH
N
NHtBuO
OH
SPh
O
HO
H
H
Nelfinavir (ViraceptTM)
N
SO
HN
OPh
OHPh
NH
O HN N
S
N
CH3
O
Ritonavir (NovirTM)
NHN
NH
OHN
O NHtBuPhO
H2N O
O
Saquinavir (InviraseTM)
O
O
O
HN
Ph
NS NH2
OH
O O
Amprenavir (AgeneraseTM)
HN
CH
C
NH
CH
C
O
O R'
peptide bond
HN
CH
H2C
NH
CH
C
O
R'
Reduced Amide
HN
CH
CH
CH2
CH
C
O
R'
Hydroxyethylene
OH
HN
CH
CH
CH
CH
C
O
R'
Dihydroxyethylene
OH
OH
HN
CH
CH
CH2
HN
CH
C
R'Hydroxyethylamine
OH O
R
R
R
R
R
P1 P1’
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