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

While performing biomolecular interaction analysis (BIA), scientistsoften use surface plasmon resonance (SPR) to measure rate constantsof the associated reactions. A mathematical model of a BIAcore^TM,a common SPR device, consists of a convection-diffusion equationin a channel with a reacting surface at the channel ceiling.Asymptotic and singular perturbation techniques are used toanalyse the concentration of the reacting species in two cases:when the reaction occurs much more slowly than diffusion, andwhen 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 physicallyrealizable cases. These expressions provide a direct way toestimate the rate constants from raw data.