Multiple surface reactions in arrays with applications to optical biosensors

We analyze surface-volume reactions in the context of optical biosensors with arrays of reacting zones. For arrays having zones with the same rate constants, we consider a two-dimensional reacting zone boundary definition and quantify ligand depletion with the effective Damköhler number. We use asymptotics to obtain ligand depletion results for the one-dimensional case, and also compute results for the circular reacting zone case. For arrays having zones with different rate constants, depletion effects cannot be expressed as the product of time-dependent and space-dependent terms, and we propose two effective rate constant equations for this case.