Lecture 2 question

1
Lecture 2 question
A binding constant of 10 micromolar is good but
not great. How many well placed hydrogen bonds
would it take to increase this binding constant
to 1 nanomolar (a binding constant that reflects
a tight interaction)?
DDGA-B -RTln KaA/KbB -RTln 10-5/10-9
-0.6 ln 104 -5.5 kcal/mol -5.5 kcal/mol
represents 1-2 hydrogen bonds.
2
Catalytic Mechanisms and Strategies

• Lecture 3 What drives catalysis?
• Reaction pathways - enthalpy, entropy and free
  
• energy
• Electrostatics and electrostatic potentials in
  catalysis
• pKa changes

3
Reading Fersht Chapter 5 pH dependence of
enzyme catalysis Chapter 11 Forces between
molecules and binding energies Chapter 12
Enzyme-substrate complementarity and the
use of binding energy in catalysis Chapter 16
Case studies of enzyme structure and
mechanism Creighton Chapter 1 Chemical
properties of polypeptides Chapter 4
Physical interactions that determine the
properties of proteins Chapter 9 Enzyme
catalysis
4
Catalytic Mechanisms and Strategies

• What drives catalysis?
• Reaction pathways - enthalpy, entropy and free
  energy
• Electrostatics and electrostatic potentials in
  catalysis
• pKa changes

5
transition state
Decrease of entropy Destabilizing electrostatic
interactions Km S
E S
Increase of entropy Stabilizing electrostatic
hydrogen bonding van der Waals
interactions Km
DGf
EP complex
ES complex
6
What can you do with binding energy?
O
C
O
H
RO
O
HOCH2
O
..
R
HOCH2
O
..
HOCH2
..
O
O
O
HO
HO
HO
NHAc
NHAc
NHAc
O
O
C

• Orient substrate
• Exclude water
• Alter structure of substrate
• to resemble the transition
• state

7
Coulombs Law
Force (F) is proportional to q1q2/er2 Electric
potential (U) is proportional to W/qo Work
(W) kq1q2/er DE (relative to energy when
the charges are far apart). (-)(-) and ()()
repulsive (-)() attractive
8
Dielectric constant
- O-C
NH3
- O-C
NH3
O
O
ewater, salt 80
ewater 80
evacuum 1
eprotein interior 2-10
Partial Charges
-0.6
O
C O
N - H
0.4
-0.4
0.2
-0.2
H
H
0.3
0.3
If you know the position of every partial (and
full) charge (including water), you do not need a
dielectric constant.
9
Dielectric constant
- O-C
NH3
- O-C
NH3
O
O
ewater, salt 80
ewater 80
evacuum 1
eprotein interior 2-10
You can calculate the electrostatic potential at
any point relative to fixed known charges even in
the presence of mobil charges using the Poisson
- Boltzmann Equation.
10
Chymotrypsin Dimer
PDB accession code 4CHA
11
Blue positive
Electrostatic Potential
Red negative
12
Electrostatic Potential
Blue positive
Red negative
13
Na
Cl-
Na
Cl-
-120 kcal/mol
NH3
- O-C
- O-C
NH3
O
O
substrate
enzyme
favorable - van der Waals - free water
unfavorable - ordered water
hydrophobic effect 50 cal/mol/Å2
14
Dipole - Monopole Interactions
monopole
r1
qo
q
r
U S U (n) U1 U2
q
a
r2
U 1/4peo (q/r1 - q/r2) q/4peo (r1 - r2/
r1r2)
q-
dipole
if r a then r2 - r1 a cos q and r1r2
r2 U qa/4peo (cos q/ r2)
U is a function of q and r. If you rotate
around the dipole axis, there is no change in
the value of U
15
Dipole - Monopole Interactions
qo
r
q
q
q
r
q
a
qo
q-
q-
q 90 cos q 0 U 0
q 0 cos q 1 U qa/4peo r2
16
Dipole - Dipole Interactions
E -2ma mb/ er3

-

-

-
E -ma mb/ er3
-

• dipole moment Zd
• (Zseparated excess charge)
• water 1.85 Debye units (D)
• peptide bond 3.5 D
• retinal 15 D

Eavg (-2/3kT) ma2 mb2/ er6
Interaction energy is dependent on orientation
and distance
17
Whats the point?
q
r

-

-
qo
q-

-

-
-
-

-

-


-
Van der Waals interactions (i.e. dipole-monopole,
dipole-dipole, induced dipole-induced dipole,
etc.) are all based on Coulombs law, can be
substantial, and can be calculated.
18
Summary of binding energies
Table 8.3 (Creighton) Free energy contribution
to Group binding to protein (kcal/mol) -CH3
-2.0 to -3.9 -CH2CH3 -6.5 -CH-(CH3)2 -9.6 -SCH3
-4.9 -SH -5.4 to -9.1 -OH -8 -NH2 -4.5 -N
H3 -6.7 -CO2- -4.3
DDGA-B -RTln KaA/KbB
Measure Ka with group A and remeasure Ka with
group B
19
Some limiting values of binding energies
Binding cavity Unfavorable binding
energy Constructed for Occupied
by kcal/mol -CH3 -OH 3.5 -H
-CH3 7.6 -H -OH 3.7 -OH
-H 7.0 -NH3 -H 4.3 Determined from
measurements on aminoacyl-tRNA synthetase Table
11.8 (Fersht)
20
Example - Recognition of G-U duplexes as
substrates for Group 1 ribozymes.
U
O --------H - N
N
G
R
N
NH2
G interacts with minor groove of ribozyme Kd for
substrate binding is 0.05 nM Estimate Kd if the
exocyclic amine is removed?
21
Example - Recognition of G-U duplexes as
substrates for Group 1 ribozymes.
U
O --------H - N
N
G
R
N
NH2
Assume NH2 is hydrogen bonding. Estimate
contribution to interaction as 5 kcal/mol.
DDGA-B -RTln KaA/KbB
5 kcal/mol -0.6 ln 0.05 nm/KbB
KbB 208 nm
22
Catalytic Mechanisms and Strategies

• What drives catalysis?
• Reaction pathways - enthalpy, entropy and free
  
• energy
• Electrostatics and electrostatic potentials in
  catalysis
• pKa changes

23
(No Transcript)
24
acetylcholine esterase
25
acetylcholine esterase with acetylcholine
26
active site
emerging field lines

• white lines calculated with uniform dielectric
• green lines calculated with 280 dielectric
  (inout), note that in
• this case they go through water to get from (-)
  to ().

27
Catalytic Mechanisms and Strategies

• What drives catalysis?
• Reaction pathways - enthalpy, entropy and free
  
• energy
• Electrostatics and electrostatic potentials in
  catalysis
• pKa changes

28
Linderstrom - Lang
protein
high e
low e
uniform smear of charge
discrete point charges
Tanford-Kirkwood
high e
low e
mobile ions eeff ewaterekr
ion exclusion region
k is a function of ionic strength
29
Simple idea
Ka acid dissociation constant Ka H A- /
HA
HA H A-
Stabilize A-, increase Ka, decrease pKa
HA H A-
B B
A-
B
Destabilize A-, decrease Ka, increase pKa
HA H A-
A- A-
Destabilize A-, decrease Ka, increase pKa
HA H A-
-CH3 -CH3 Hydrophobic environment
KNOW THIS FOR EXAM
30
pKa differences in free amino acids
pKa 3.7
H3N - CH - C - O-
C - O-
Unusual pKas in maleic acid
pKa 4.4
pKa 1.9
pKa 6.2
C - O-
H-O-C
31
pKa differences due to helix dipoles
d
N
d
C
pKa of His decreases
His
O
d -
HHis H His
H
d
d
N
C
d -
O
d -
pKa of Asp increases
Asp
H
d
HA H A-
C
N
d -
d -

• CO dipole is larger than N-H dipole, and
  therefore dominates.
• Helix dipoles can influence pKas.

32
Helix dipoles in the K channel
Selectivity filter strips K ion of water. K is
stabilized by glycine CO groups while in
selectivity filter.
Two mechanisms by which the K channel stabilizes
a cation in the middle of the membrane. First, a
large aqueous cavity stabilizes an ion (green) in
the otherwise hydrophobic membrane interior.
Second, oriented helices point their partial
negative charge (carboxyl end, red) towards the
cavity where a cation is located. B. Roux and R.
Mackinnon (Doyle et al. 1998, Science).
33
HA H A-
More detail
Ka H A- / HA
DG -RTlnKeq -2.3RTlogKa 2.3RTpKa
pKaintrinsic pKa0 pKapartial charges
pKa pKaintrinsic pKacharge-charge
non-titratable
electrostatic interactions, titratable
DDG 2.3RTDpKa Change in pKa by 1 pH unit
1.38 kcal/mol
34
Some highly perturbed pKas of groups in proteins
Lysozyme Glu35 6.5 Lysozyme-glycolchitin
complex Glu35 8.2 Acetoacetate
decarboxylase Lys (e-NH2) 5.9 Chymotrypsin Il
e16 (a-NH) 10.0 a-Lactoglobulin CO2H 7.5 Pap
ain His-159 3.4
Fersht - Table 5.4
35
Titration curve for Ribonuclease
pH optimum 6.2
activity
5.0
6.0
7.0
pH
Ribonuclease catalyzes the hydrolysis of RNA
36
Reaction mechanism for Ribonuclease
substrate
Asp121
Lys41
His 119
OR
His 12
-O - P O

N - H
HN
O
O - H
NH
N
catalytic acid
catalytic base
O
B
HHis H His
Ka H His / HHis
37
Reaction mechanism for Ribonuclease
cleaved product
HOR
Lys41
His 119
O
-O
H
His 12
P
N
HN
H - O
O
O

NH
H - N
catalytic base
O
catalytic acid
B
Lys41 swings over to stabilize the phosphate
intermediate
38
1a. Draw the individual titration curves for
His119 and His12 in ribonuclease if Asp121 is
mutated to alanine. Combine the titration curves
and show an activity profile (activity vs.
pH). 1b. Draw the individual titration curves
for His119 and His12 in ribonuclease if Ala40
near His12 is mutated to lysine. Combine the
titration curves and show an activity profile
(activity vs. pH). 2. DNA precipitations are
often carried out with salt and ethanol. How
does salt change the dielectric constant of the
solution (increase, decrease, no change)? How
does ethanol change the dielectric
constant(increase, decrease, no change)? Why
does the DNA precipitate?