Optical Response of Magnetic Fluorescent Microspheres Used for Force Spectroscopy in the Evanescent Field

Abstract

Force spectroscopy based on magnetic tweezers is a powerful technique for manipulating single biomolecules and studying their interactions. The resolution in magnetic probe displacement, however, needs to be commensurate with molecular sizes. To achieve the desirable sensitivity in tracking displacements of the magnetic probe, some recent approaches have combined magnetic tweezers with total internal reflection fluorescence microscopy. In this situation, a typical force probe is a polymer microsphere containing two types of optically active components: a pure absorber (magnetic nanoparticles for providing the pulling force) and a luminophore (semiconducting nanoparticles or organic dyes for fluorescent imaging). To assess the system's capability fully with regard to tracking the position of the force probe with subnanometer accuracy, we developed a body-of-revolution formulation of the method of auxiliary sources (BOR-MAS) to simulate the absorption, scattering, and fluorescence of microscopic spheres in an evanescent electromagnetic field. The theoretical formulation uses the axial symmetry of the system to reduce the dimensionality of the modeling problem and produces excellent agreement with the reported experimental data on forward scattering intensity. Using the BOR-MAS numerical model, we investigated the probe detection sensitivity for a high numerical aperture objective. The analysis of both backscattering and fluorescence observation modes shows that the total intensity of the bead image decays exponentially with the distance from the surface (or the length of a biomolecule). Our investigations demonstrate that the decay lengths of observable optical power are smaller than the penetration depth of the unperturbed excitation evanescent wave. In addition, our numerical modeling results illustrate that the expected sensitivity for the decay length changes with the angle of incidence, tracking the theoretical penetration depth for a two-media model, and is sensitive to the bead size. The BOR-MAS methodology developed in this work for near-field modeling of bead-tracking experiments fully describes the fundamental photonic response of microscopic BOR probes at the subwavelength level and can be used for future improvements in the design of these probes or in the setup of bead-tracking experiments.