Titration curve and pKa value
Using titration curves to determine pKa values
The pH value where the titratable group is half-protonated is equal to the pKa if the titration curve
follows the Henderson-Hasselbalch equation. Most pKa calculation methods silently assume that all
titration curves are Henderson-Hasselbalch shaped, and pKa values in pKa calculation programs are
therefore often determined in this way.
In chemistry, the Henderson-Hasselbalch equation describes the derivation of pH as a measure of
acidity (using pKa, the acid dissociation constant) in biological and chemical systems. The equation is
also useful for estimating the pH of a buffer solution and finding the equilibrium pH in acid-base
reactions It is widely used to calculate isoelectric point of the proteins.
The general equations for acid-base reactions and the basic theory behind pKa calculations.
The basic equations for acid-base reactions
The dissociation of a proton from an acid generally takes the form
HA + H2O -> H3O+ + A- (Eq. 4.1)
The free energy change for this reaction (DGa) can be related to an equilibrium constant (Ka) for the
reaction (we exclude water and replace H3O+ with H+ for simplicity):
For acid-base reactions it is customary to report the pKa values, which is simply –log(Ka). The
Henderson-Hasselbalch equation is a rearrangement of equation
From the Equation,. it is seen that the pKa value of an acid is the pH value where the concentrations of
the protonated and deprotonated forms of the acid are present at the exact same concentrations.
Furthermore by rearranging Eq.
and plotting fHA as a function of pH we get the well-known sigmoid titration curve
The titration of an acid with a pKa value of 5.0
For the association of a proton with a base, a similar set of equations can be produced. The major
difference being that the base reaction is:
B + H3O+ -> BH+ + H2O
The corresponding equilibrium constant thus becomes
Calculating titration curves
We now know the energy of every possible protonation state of a protein at a given pH value, and the
next step is the conversion of these energies into fractional charges at each pH value for each residue in
order to get the titration curves.
A straight-forward way to find the occupancy of the different states in Table 4.1 is to evaluate the
Boltzmann sum for each state.
Here pi is the fraction of molecules in state i. Ei is the energy of state i, and the sum in the denominator
is over all possible states of the system. k is Boltzmann’s constant and T is the temperature in Kelvin.
The fractional charge of a particular group is simply the sum of the pi’s for all the states where the
group is charged. Thus for group 1 in Table 4.1, for example, the charge is the sum of p1, p2, p3 and
p4.
From the calculated titration curves the pKa value for each group is determined as the pH where the
group is half-protonated. This gives an accurate result only if the titration curve follows a HendersonHasselbalch shape. This is the case for most groups, but especially in active sites it is quite common to
find groups that have very irregular titration curves. In these cases manual inspection of the titration
curves is necessary in order to obtain meaningful results.
Significance of pKa calculations
Tell you which pKa values are highly shifted, and their approximate value.
Give you the overall shape of the pH stability curve