Quantitative modeling and experimental verification of Förster resonant energy transfer in upconversion nanoparticle biosensors

Rare-earth-doped upconversion nanoparticles (UCNPs) have often been used in combination with fluorescent dyes for sensing applications. In these systems, sensing can be achieved through the modulation of Förster resonant energy transfer (FRET) between the dye and the UCNP. The effects of FRET in such cases are complex, as the extent to which FRET is experienced by the rare-earth ions is dependent on their position within the nanoparticle. Here, we develop an analytical model to accurately describe the effects of FRET for such a system. As a proof of principle, we verify our model by considering the case of a pH sensor comprised of fluorescein isothiocyanate and Tm3+-doped UCNPs. We extend our model to the case of core–shell UCNPs and discuss the design of an optimal FRET-based biosensor using UCNPs.