Examination of the origin, variation, and proper use of expressions for the estimation of association constants by capillary electrophoresis

Over the last several decades a variety of techniques have been developed to determine apparent equilibrium constants for molecular association in solution (e.g., to micelles, proteins, cyclodextrins, antibiotics, etc.). The relationships describing binding isotherms appear in several forms and have been given several different names. It is well known that most of these expressions are closely related and that some may be more advantageous than others for experimental or statistical reasons. In the case of electrophoresis, association constants are calculated from the relationship between ligand concentration and the measured electrophoretic mobility of the solute. This relationship has appeared in many forms that have been used numerous times at least since 1951. Recently they have reappeared in identical or slightly rearranged versions in several capillary electrophoresis (CE) studies. Some of these methods require the measurement of the electrophoretic mobility of the solute-ligand complex, a value that often cannot be accurately measured. Some systems require correction or normalization procedures in order to negate any changes in solute mobility that are not due to binding. The relationship between the various expressions that can be used to calculate binding constants with CE is shown. The advantages, limitations and proper use of the various approaches are discussed. Examples are given for both achiral and chiral analytes.