 Cells are able to sense shallow chemical gradients, which can direct their growth or guide them towards mates. These gradients are amplified within cells through intracellular mechanisms and are transmitted via surface-bound membrane receptors. To accurately model the dynamics of these gradients, we developed a hybrid numerical asymptotic method combining matched asymptotic analysis with numerical inverse Laplace transforms. This allowed us to quickly and accurately solve the parabolic exterior problem describing the diffusive fluxes to receptors. We found that equilibration occurs over long-time scales, suggesting that steady-state quantities may not be reliable for localization at practical biological time scales. Furthermore, we observed that directional information was encoded primarily in early arrivals to the receptors, while equilibrium quantities informed on source distance. Finally, we demonstrated that complex receptor configurations could be replaced by a uniform effective condition, even when the cell adopted the angular direction of the first impact. This article was authored by Alan E. Lindsay, Andrew J. Bernoff and Adrian Navarro Hernandez. We are article.tv, links in the description below.