  Surface plasmon resonance (SPR) chips are widely used to measure association
and dissociation rates for the binding kinetics between two species of
chemicals, e.g., cell receptors and ligands. It is commonly assumed that
ligands are spatially well mixed in the SPR region, and hence a mean-field rate
equation description is appropriate. This approximation however ignores the
spatial fluctuations as well as temporal correlations induced by multiple local
rebinding events, which become prominent for slow diffusion rates and high
binding affinities. We report detailed Monte Carlo simulations of ligand
binding kinetics in an SPR cell subject to laminar flow. We extract the binding
and dissociation rates by means of the techniques frequently employed in
experimental analysis that are motivated by the mean-field approximation. We
find major discrepancies in a wide parameter regime between the thus extracted
rates and the known input simulation values. These results underscore the
crucial quantitative importance of spatio-temporal correlations in binary
reaction kinetics in SPR cell geometries, and demonstrate the failure of a
mean-field analysis of SPR cells in the regime of high Damk\"ohler number Da >
0.1, where the spatio-temporal correlations due to diffusive transport and
ligand-receptor rebinding events dominate the dynamics of SPR systems.
