What is the pKa

1

• What is the pKa?
• Microscopic and macroscopic pKas
• Measurement by acid-base titration
• Measurement by pH dependent properties (activity,
  reactivity, fluorescence)
• Calculation
• examples

2

• Protonation as ligand binding
• Protonation of a basic group can be described as
  a special case of ligand binding
• B H BH
• or dissociation
• AH A- H
• Ka A-H/AH, pKa -log(Ka)
• The dissociation constant Ka and pKa are normally
  used for characterization of these processes.

3

• Pitfalls
• Dissociation constants (and pKas) are only
  constant for one species. Varying conditions can
  change the state of the molecule (conformation,
  binding of other ligands, protonation at other
  sites) and thereby its pKa!
• The overall description as acid and base do
  not specify where and how the protons are bound!

4

• Acid-base titration
• Consumption of H or OH- is directly measured
  by pH measurement.
• Curves can be calculated (and fitted) with the
  Henderson-Hasselbalch equation
• pH pKa log(A-/HA)

5

• Example titration of 100 ml MES with 1 M NaOH

pKa
equivalence point
MES morpholinoethansulfonic acid, buffer
substance
6

• Problems with biological samples
• Extreme pH values upon acid/base addition
• Large amounts of sample required
• All protonable groups are measured

7

• Example with one pKa

One site, protonated or deprotonated
8

• Example with two pKas
• (Biochemical Methods, Pingoud et al.)

9

• Example with two pKas
• (Biochemical Methods, Pingoud et al.)

10

• Interacting protonation sites
• The protonation state of one site can influence
  the pKa of the other site and vice versa
• Without interaction
• A1H A1- H
  A2H A2- H
• With interaction
• A1H A2H A1- A2H H
• A1H A2- H A1- A2-
  2H

Ka1
Ka2
Ka1
Ka2
Ka12
Ka21
11

• The four Ka values can be described with three
  independent numbers (because of the cycle
  Ka1Ka12 Ka2Ka21).
• The three numbers can also be represented as two
  Kas and an interaction energy (Ka1, Ka2 and
  W12).
• In an example the intrinsic (isolated) pKa values
  are 7.0 and 7.1, the interaction energy is 12
  kJ/mol.
• The apparent pKa values are 4.6 and 7.4.

12
The individual sites show two step deprotonation.
pKa2
pKa1
Total protonation Protonation of the quasi
sites Protonation of the individual sites
13
With more sites unexpected effects can occur
Nonmonotonic titration curves for individual
sites.
DTPA Diethylenetriaminepentaacetate
Protonation of the middle amino group
14

• pKa calculation
• For the deprotonation reaction energies for all
  steps can be calculated separately.

15

• For the GFP chromophore many states can be drawn

positive
neutral
zwitterionic
negative
16
The pKa values can be calculated for the ground
state and the excited state. The large
differences lead to different preferences for the
neutral and zwitterionic state.
Zwitterion stable in the excited state
Neutral form stable in the ground state
17
Problem 1 reported values in the literature
differ widely. Problem 2 the values are only
for the isolated chromophore, not for the
chromophore in the protein environment.