Enumeration algorithm for determination of binding constants in capillary electrophoresis

With more accurate simulation models and more efficient algorithms becoming available, the binding constants of an affinity interaction can be obtained from much simpler experiments using capillary electrophoresis. With the enumeration algorithm, all possible combinations of the binding constant and the complex mobility in certain ranges that could result in the experimental migration time of an injected analyte are extracted from a 3-D surface, which depicts the migration times resulting from different values of the binding constant and the mobility of the complex formed between the interacting pair, to form a 2-D curve. When the experimental conditions are changed, the analyte migration time will also change. A new 2-D curve can be constructed from another 3-D surface on the basis of the pairs of binding constants and complex mobility values that could result in the new migration time. Because the true binding constant and complex mobility values have to be the same for both experimental conditions under the same temperature, there has to be a point where both 2-D curves will converge. The coordinates of the converging point give the values for a binding constant and a complex mobility that will fit all 2-D curves generated under certain experimental conditions. p-Nitrophenol is used as the analyte, beta-cyclodextrin is used as the additive, and a one-cell model is used to simulate affinity CE. The experimental conditions that can improve the accuracy of the binding constants are discussed.