Protonation States and pKa

Munia Mukherjee
April
16th,
2007
munia@medusa.bioc.aecom.yu.edu
Protonation States and pKa
Suggested Readings:
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Markley, J. L. (1975). “Observation of Histidine Residues in Proteins by Nuclear Magnetic
Resonance Spectroscopy.” Acc. Chem. Res. 8, 70-80.
Cosgrove, M.S. et.al (2002), “The Catalytic Mechanism of G-6-P Dehydrogenases,…”
Biochemistry, 41, 6939-6945.
Bartik, K. et al. (1994), “ Measurement of the Individual pKa Values of Acidic Residues of Hen
And Turkey Lysozymes by Two Dimensional 1H NMR.” Biophysical J., 66, 1180-1184
Anderson, D.E. et al. (1990). “pH induced denaturation of proteins: A single salt bridge
contributes 3-5 kCal/mol to the free energy of folding of T4 lysozyme.” Biochemistry, 29, 24032408.
Smith, R. et al. (1996) “Ionization states of the catalytic residues in HIV-1 protease”. Nat. Struct.
Biol., 3, 946-950.
Dyson, H.J. et al. (1996) “Direct Measurement of the Aspartic Acid 26 pKa for reduced E.coli
Thioredoxin by 13C NMR” Biochemistry, 35, 1-6
Pujato, M. (2006), “The pH-dependence of amide chemical shift of Asp/Glu reflects its pKa in
intrinsically disordered proteins with only local interactions” Biochimica Biophysica Acta, 12271233
Deprotonation reaction:
HA + H2O
A- + H 3 O+
Ka = [A-] [H3O+]
(1)
[HA]
Henderson-Hasselbach equation:
1
1
[A-]
[H3O+] = Ka [HA]
-log [H 3O+] = -log Ka + log [A-] / [HA]
(2)
(3)
pH = pKa + log 1- θ
(4)
θ
θ is degree of protonation or occupancy: Number of bound protons as a
function of pH
The pKa of a titrating site is defined as the pH for which the site is 50%
occupied: The pH for which the occupancy θ is 0.5.
Definition of pKa
pH = pKa + log 1- θ
θ
θ (pH ) =
1
1 + e −ln10(pKa −pH )
Titration curve
One state transition
pK a = 4.0
Titration curves of amino acids
Since amino acids are (at least) diprotic their titration curves appear a little
different from a simple acid
-each proton will have a pKa value and thus there are two or more stages in the
titration curve
Depending on where in the titration you are looking (i.e. at which pH) a
different form of the amino acid will be prevalent
Remember that pH is notation for proton concentration and that pKa is the
equilibrium constant for ionization
- thus pKa is a measure of the tendency for a group to give up a proton
-as the pKa increases by one unit the tendency to give up the proton
decreases tenfold
The positively charged amino group attached to the acarbon helps to push the departing proton of the carboxyl
group out more easily.
The inflection point pI is the point when removal of the
first proton is complete and he second has just begun so
the amino acid’s prevalent form is as a dipolar ion
pH < pI: net positive charge
pH > pI: net negative charge
pKa of ionizable side chains
pKa = pH for 50%
dissociation,
Note range
pKa of some amino acids
Factors that affect pKa values
Ionizable residues encounter two differences inside folded proteins
compared to water
They are partly desolvated by the protein
This is especially unfavorable for the charged form (because it’s an
ion) but it’s also unfavorable for the neutral form (because it’s a
dipole.
They form new interactions with other residue.
These new interactions may be energetically favorable or unfavorable.
Usually the charged form is more affected than the neutral form due
to these interactions
e.g. an aspartate with a low pKa
this aspartate is partly buried but it
accepts ~4 hydrogen bonds from
nearby residues
it’s also close to some positively
charged residues
the charged form is very happy
here, so it becomes more difficult to
add a proton to it
so we have to increase [H+] (lower
pH) to add the proton
so the pKa of the residue
decreases from 4 to ~2
e.g. a glutamate with a high pKa
this glutamate is partly buried &
forms no favorable interactions with
other residues
this is very unfavorable for the
charged form (compared with being
in water)
this shifts the equilibrium in favor of
the neutral form
so it will be protonated even at low
[H+] (i.e. high pH) or does not want
to be deprotonated
so the pKa of the residue increases
from 4.4 to ~6
Simple rules for guessing pKa shifts
remember: a pKa is just the ∆G for deprotonation
acidic residues
(asp & glu)
COOH ↔ COO– + H3O+
if charged form is unhappy:
deprotonation is more
difficult so pKa shifts up
if charged form is happy:
deprotonation is easier
so pKa shifts down
basic residues
(arg, lys & his)
NH3+ ↔ NH2 + H3O+
if charged form is unhappy:
deprotonation is easier
so pKa shifts down
if charged form is happy:
deprotonation is more
difficult so pKa shifts up
Reasons for interest in pKas [1]
enzyme activity is pH dependent
many catalytic steps involve addition or removal of
protons
the rates of these steps will depend on the pH and the
pKas of the residues involved
enzymes have optimal pHs
(sometimes loss of activity at
non-optimal pHs is due to
unfolding of the enzyme)
(Pace et al. Biochemistry 2: 2564 (1990)
Reasons for interest in pKas [2]
protein stability is pH dependent
if the pKa of a residue is different in the folded state from
its value in the unfolded state, the protein’s stability will
depend on pH
∆G unfold
–
pH
For most proteins the folded state is
only 1-5 kCal/mol more favored
than the unfolded state. A typical
ionic interaction is around 2-5
kCal/mol. So a single ionic
interaction can determine whether
or not a protein will fold.
Reasons for interest in pKas [3]
a protonation equilibrium can be thought of as a very simple
ligand-binding reaction (with the ligand being H+)
knowing the pKa of a protein residue and the protein’s
structure...
we can start to determine the relative importance of different
factors, e.g.:
1. desolvation effects
2. charge-charge interactions
3. protein dielectric properties
From the change in pKa, one can determine the free energy (∆G)
associated with the reaction:
The standard free energy of dissociation (HA ↔ H+ + A-) is given by:
∆G° = -RT ln([H+] [A-]/[HA]) = -RT ln Ka = 2.303 RT pKa (standard state) -------(1)
Actual free energy of ionization: ∆Gioniz= ∆G° + RT ln ([H+] [A-] / [HA]) ----(2)
Suppose the ionization reaction is coupled to some other interaction: e.g. binding of a
proton to A - changes the interaction of A- with some other group in the molecule.
∆Gtotal = ∆Gioniz + ∆Ginter = ∆G° + ∆Ginter + RT ln ([H+] [A-] / [HA]) ------(3)
At equillibrium ∆Gtotal = 0. The H+ concentration at which the acid is half ionized is:
(H+)1/2 = e -(∆G° + ∆Ginter )/RT -----------(4)
The apparent pKa’ is: pKa’ = -log (H+)1/2 = (∆G° + ∆Ginter ) / 2.303 RT ---------(5)
For a model system without coupling: pKa = ∆G° / 2.303 RT
----------(6)
Therefore, from the difference in the two pKa values, the interaction energy can be
calculated as ∆Ginter = 2.303 RT (pKa’ – pKa) --------------(7)
pKa analysis by NMR
The side chain 1H, 13C or 15N chemical shift changes with ionization. Usually the
largest change occurs closest to the site of protonation / deprotonation.
Monitor the chemical shift change as a function of pH. Fit to modified Hill Equation:
δHA + δA- x 10pH-pKa
δobs =
δHA is the chemical shift in the acidic pH limit
δA- is the chemical shift in the basic pH limit
1+ 10pH-pKa
8.0-8.8 ppm
2
4
Ionization of Histidine
6.8-7.2 ppm
1
C2H proton appears at higher frequency than
most other protons and is sensitive to the
protonation of the ring.
3
C2HC4H
H
+H3 N
C
COO-
H
C
H
+
4
C
H N
1
C
C2
CαH CβH
0
10
H
Raise pH
N3 H
H
ppm
10
0
Titration of the C2H of Histidine
1
Shift measured with multiple 1D
spectra starting with pH 1.0 and
moving through to pH 9. The
chemical shift change of the proton
on C2 reflects the protonation state
of N1
50% of
complete
change
Chemical
Shift
Change
∆δ (ppm)
pKa = 5.2
0
1
3
5
7
9 11pH
Observation of Histidine Residues in Proteins by Means of Nuclear Magnetic
Resonance Spectroscopy. (Markley J., Acc Chem Res. 8, 1975, 70-80)
4 histidines which could
be monitored and have their
pKa’s measured.
Chemical shift change of C2H
and C4H monitored as a
function of pH using 1D NMR
H1 = His105
H2 = His119
H3 = His12
H4 = His48
C2H titration
Measure pKa of each histidine
pKa
C4H titration
His105
6.7
His119
6.2
His12
5.8
His48 is more complex,
sudden discontinuity in the
curve.
There is a conformational change affecting
this peak so that at some pHs two peaks were
observed. H4a and H4b were acid and base
stable forms.
Found that 200mM Na+CH3COOhelped to stabilize the protein.
Can then determine that the pKa
of C2H is 6.31.
Repeat titrations in the presence
of an inhibitor.
His105
in this case, cytidine-3’monophosphate (3’-CMP)
His48
O
N
O
OPO3 -
His12
His119
HOCH2
NH2
OH
His48 and His105 are unchanged
His12 and His119 curved are shifted
downfield.
His119 changes from 6.2 to 8.0
His 12 changes from 5.8 to 7.4
Why downfield??
Both His12 and His119 are protonated in the enzymeinhibitor complex. The proton is protected from exchange
by the presence of the inhibitor. Need to go to higher pH
to remove it.
NH2
HOCH 2
O
N
O
OPO3 -
OH
pKa values of acidic residues of hen and turkey lysozymes by two
dimensional 1H NMR (Bartik, K. et.al. Biophys J., 66, 1994, 1180-1184)
pH=
1.1
pH=
5.9
Both enzymes have identical activity profile as a function
of pH as indicated by identical pKa values of the residues
in the active site.
2D DQFCOSY
Protein is positively charged (pI = 11) between pH 1 to pH 7 (titration range). This
results in an overall decrease in the stability of the positively charged histidine
residues and increase in the stability of the negatively charged Asp and Glu
residues. Therefore, a decrease in the pKa values is observed for these residues
from their standard values.
pKa values of the conserved residues at the active site (Glu35 and Asp52) is higher
than rest of the residues due to the hydrophobic nature of the active site cleft and
interaction between Glu 35 and Asp52.
Direct Measurement of the Aspartic Acid 26 pKa for Reduced E. Coli
Thioredoxin by 13C NMR (J. Dyson et al., Biochemistry, 35, 1996, 1-6.)
pH
O H
H
C—C—N—C—CH
H—C—H
C
O
O-
Two dimensional HCACO spectrum of thioredoxin at pH 8.52.
pKa determined using modified 2D HCACO experiment that detects coupling between
13CO of a carboxyl group and the adjacent 13CβH or 13CγH.
O H
H
C—C—N—C—CH
H—C—H
C
O
O-
The carboxyl group of Asp 26 is buried in a
hydrophobic environment that elevates its pKa value
to 7.3-7.5 from a standard value of 4.0.
Ionization of Asp26 also affected by two Cysteine
thiol groups ionizing at the active site.
Plot of chemical shift as a function of pH