FLUID MECHANICS AND TRANSPORT PHENOMENA A pK Determination Method for Proteins from Titration Curves using Principle Component Analysis

Principal component analysis (PCA) technique is used for the precise determination of pK values from titration curves of amphoteric molecules, such as proteins and amino acids. A regression model is developed based on the effective charge of amphoteric molecules. Partial domain method, a new algorithm, is introduced to minimize or remove errors in extracted pK values from experimental (titration curve) data with hidden errors, such as sampling errors or experimental uncertainties. For the validation of our algorithm, 3 pK values are determined from the titration curves of glutamic acid and lysine. The extracted pKs are in exact agreement with the original pKs if partial domain method is used to obtain pKs from an exact (uncertainty free) titration curve. In addition, the effects of various uncertainty levels (1%, 2% and 3% noise) in the experimental titration curves are tested using both partial and full domain methods. Analytic results show that partial domain method is very effective in reducing the errors in extracted pKs especially at larger value of redundant number. Next, partial domain based PCA method is applied to extract 5 pKs from the experimental titration curve of hen egg-white lysozyme protein. These pK values are then used to simulate the isoelectric focusing of lysozyme protein in the presence of 25 biprotic ampholytes in a 2-D (two-dimensional) straight microchannel. The transient, as well as focused state behaviors of lysozyme protein are compared between original titration curve (20 pKs) and approximated titration curve (5 pKs) cases. Although there are minor differences at the early stages of focusing, the focusing time, position, and shapes of protein and ampholytes are identical at focused state. 2008 American Institute of Chemical Engineers AIChE J, 54: 2238–2249, 2008