Modeling Fluorescence Collection from Single Molecules in Liquid Microspheres

Abstract

Optimization of molecular detection efficiencies is of central importance in analytical applications involving single molecule detection.1 In addition to limitations imposed on the fraction of molecules which can be detected by the average signal-to-noise ratio, experimental factors such as excitation inhomogeneity and molecular diffusion conspire to further limit "molecular detectability." Recent single molecule detection experiments in microdroplets suggest that such experimental limitations can be significantly reduced primarily because the molecule cannot diffuse away from the excitation volume. However, unlike fluorescence detection from bulk streams where the fluorescence intensity is isotropic in space, the large refractive index change at the surface of microdroplets implies that the fluorescence intensity collected by a lens will be strongly dependent on the position of the molecule within the droplet. In addition, the same refractive index discontinuity at the droplet surface produces a complicated excitation intensity distribution within the droplet as a result of interference between refracted and totally-internally-reflected rays. Thus, issues such as whether molecules near the surface of the sphere can "hide" from the detector as a result of total internal reflection of emission near the droplet surface, or poor excitation efficiency due to the molecule being located in a "shadow" region of the droplet will have a potential effect on molecular detection efficiencies. These questions are nontrivial to address in a quantitative way. Here we discuss development of numerical tools for modeling the fluorescence collected from a single molecule within a microdroplet as a function of position, orientation, and detection geometry based on the semiclassical electrodynamics formalism developed by Chew2 for light scattering in dielectric microspheres. In addition we also examine effects of excitation inhomogeneity within the sphere, molecular diffusion, and transition rate modification in order to obtain a realistic model of molecular detection efficiencies in microdroplets.