Measuring pKa

A compound's pKa is a fundamental parameter that influences its solubility, membrane permeability, and protein binding and thus its ADME properties. Knowing the pKa of a compound can help with rational design and formulation. Because of its importance the FDA now requires new drug applications to report the compound's pKa. NMR is one of the ways to measure pKas and in this post I'll describe how its done.

The pKa of a functional group is the pH at which that group is half protonated and half dissociated. Since protonation alters charge, the signals in an NMR spectrum are affected by the protonation state. If we record spectra at a series of pHs we should see the peaks of nuclei near the protonation site move. The figure below shows a series of ¹H spectra recorded at different pHs using a sample of nicotine in phosphate buffer. As the pH is increased from 1.85 at the top of the figure, to 9.56 at the bottom, all the peaks move upfield. Only the aromatic region is shown for clarity, but the aliphatic peaks also move as the pH is changed.

The stack plot above suggests that the rate at which the peaks move is not consistent. If the chemical shifts of the peaks are measured and plotted against pH we can see that at certain pHs, e.g. pH 3.5, the change in chemical shift is more rapid than at other pHs. In this case the data appears to show two sigmoidal curves, a large one centered around pH 3.5 and a smaller one at pH 8. By fitting the data we can obtain the inflection point of both sigmoidal curves which corresponds to the pKa. In this case fitting gave pKas of 3.4 and 8.2.

Looking at the structure of nicotine we can see that there are two nitrogens which could be protonated, one on the aliphatic ring and the other on the aromatic ring. The pKas derived by fitting the data in the graph above were obtained from the aromatic resonances and we can assume that the pKa corresponding to the largest change in chemical shift (pKa=3.4) was due to protonation of the aromatic nitrogen, while the smaller chemical shift change (pKa=8.2) was due to protonation of the more distant aliphatic nitrogen.

This is supported by the movement of the aliphatic resonances (not shown) which show the greatest change around pH 8.2 and a smaller one at 3.4. This is one of the advantages of using NMR to measure pKas. The atomic specificity of NMR provides information on the sites of protonation that other techniques cannot.

To obtain the most accurate and precise pKa measurements one should consider a few experimental points.

• Use a physiological aqueous buffer, or something as close to physiological as possible. Phosphate buffer is best for NMR as it does not introduce additional peaks to the NMR spectrum.

• Measure the pH after dissolving your compound. Often dissolving your compound will change the pH slightly.

• Do not add D₂O to the buffer. Adding deuterium to a buffer changes the pH measurement. Empirical corrections are available but their applicability is dubious.

• For the NMR lock signal use a sealed capillary tube filled with a deuterated solvent. The capillary can be placed inside a 5mm NMR tube. The deuterated solvent should be chosen so that its peaks do not overlap those of your compound.

• Measure chemical shifts to at least three decimal places.

• If possible use multiple peaks to obtain pKas. Peaks can be fitted separately and the derived pKas averaged, or multiple peaks can be fitted simultaneously to a single pKa.

Acknowledgments
Thanks to Gisela Andrea Camacho-Hernandez from the Taylor lab for use of her data.