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’