Estimating rate constants in a convection-diffusion system with a boundary reaction

While performing biomolecular interaction analysis (BIA), scientists often use surface plasmon resonance (SPR) to measure rate constants of the associated reactions. A mathematical model of a BIAcore(TM), a common SPR device, consists of a convection-diffusion equation in a channel with a reacting surface at the channel ceiling. Asymptotic and singular perturbation techniques are used to analyse the concentration of the reacting species in two cases: when the reaction occurs much more slowly than diffusion, and when the reaction occurs on the same time-scale as diffusion. Linear and nonlinear integral equations result from the analysis; explicit and asymptotic solutions are constructed for physically realizable cases. These expressions provide a direct way to estimate the rate constants from raw data.