Slow-equilibration approximation in studying kinetics of protein adsorption on capillary walls

Adsorption of proteins on inner capillary walls affects the quality of capillary electrophoresis (CE) analyses. Coating the capillary surface with an anti-adhesive layer is a method typically used to suppress protein adsorption. The successful development of methods for prevention of protein adsorption requires quantitative characterization of the surface ability to adsorb and desorb a protein. It can be done by determining kinetic rate constants of adsorption, kad, and desorption, kdes. We have recently developed a pattern-based method for determination of kad and kdes for protein interaction with a capillary wall. The protein is moved through the capillary in a CE instrument by pressure and a temporal pattern of protein propagation through the detector is recorded. The experimental pattern is fitted with a numerical solution of the protein mass transfer to find kad and kdes. The fitting procedure is not "transparent" and can be complicated. In the present work, we obtained approximate analytical solutions of the protein mass transfer equations in the case of slow-equilibration during adsorption and desorption of the protein. These analytical solutions allow us to introduce a fitting-free parameter based method for determination of kad and kdes. It uses simple explicit expressions for kad and kdes in terms of experimental characteristics easily measured in capillaries. We tested the accuracy of the method by applying it to signals simulated with numerical solutions of protein mass-transfer equations. For the slow equilibration approximation the accuracy of kad and kdes was better than 12%.