One-dimensional approach to study kinetics of reversible binding of protein on capillary walls

We introduce a method for kinetic characterization of reversible binding of protein onto the inner capillary wall. In essence, a short plug of the protein solution is propagated through the capillary by pressure, and the protein is detected at the distal capillary end. The signal versus time profile is fitted with a numerical model which uses the rate constants of adsorption, kad, and desorption, kde, as fitting parameters. The values of kad and kde which result in the best fit are considered to be the sought ones. We first used COMSOL multiphysics software to develop a numerical model with two-dimensional (2D) equations of mass transfer. Although 2D models in general can describe experiments more accurately than one-dimensional (1D) models, computing 2D models takes much more time (many hours to find two parameters: kad and kde). We used the fact that the capillary is narrow and long to develop a simplified model with 1D equations of mass transfer. Our comparison of the 1D and 2D models showed that the errors of the 1D approximation were less than 5%, whereas the computation of the 1D model was 100 times faster. We finally used the 1D approach to study kinetics of reversible binding of conalbumin to the uncoated fused-silica capillary walls. We determined kad, kde, and a diffusion coefficient, D. The obtained value of D is in excellent agreement with literature data which suggests that the values of kad and kde (for which there are no literature data) are also calculated correctly. Our approach for finding kad and kde will facilitate quantitative characterization of protein adsorption on capillary walls as well as properties of passivating materials used for capillary coating.