Joint Estimation of Trajectory and Motion Model Parameters in Three-Dimensional Single Particle Tracking using the Double-Helix Point Spread Function

Abstract

Single particle tracking (SPT) is a powerful tool for studying and analyzing dynamic mechanisms of biomolecules. Our approach to analyzing SPT data uses a generic Expectation Maximization (EM)-based framework for simultaneous localization refinement and parameter estimation. This approach has benefits in terms of estimation accuracy across a wide range of signal to noise levels. When observing a particle of interest moving in three-dimensions, the acquired data is typically a sequence of images of a 2-D slice of the point spread function (PSF) determined by the relative position of the focal plane and the particle. Unlike the standard PSF, which has only one bright spot in the image plane, the Double-Helix point spread function (DH-PSF) forms two bright spots. As the particle moves along the optical axis, these spots rotate, thereby encoding the axial position of the particle. In this work, we extend our EM-based scheme to handle the DH-PSF. Our method begins with the segmented images, using the camera data directly to jointly estimate particle locations and motion model parameters. We consider two representative methods in our framework: one uses a direct sequential importance resampling (SIR) based particle filter (PF) and particle smoother (PS), the other uses the alternative Gaussian particle filter (aGPF) and the backward-simulation particle smoother (BSPS). The aGPF/BSPS is less general but has significantly less computational load when compared to the PF/PS. Using extensive simulation studies, we demonstrate that both methods produce reliable estimates of both particle position and model parameters. In future work, we plan to consider the additional influence of readout noise determined by specific camera sensors.