Three-dimensional localization refinement and motion model parameter estimation for confined single particle tracking under low-light conditions.

Confined diffusion is an important model for describing the motion of biological macromolecules moving in the crowded, three-dimensional environment of the cell. In this work we build upon the technique known as sequential Monte Carlo - expectation maximization (SMC-EM) to simultaneously localize the particle and estimate the motion model parameters from single particle tracking data. We extend SMC-EM to handle the double-helix point spread function (DH-PSF) for encoding the three-dimensional position of the particle in the two-dimensional image plane of the camera. SMC-EM can handle a wide range of camera models and here we assume the data was acquired using a scientific CMOS (sCMOS) camera. The sensitivity and speed of these cameras make them well suited for SPT, though the pixel-dependent nature of the camera noise presents a challenge for analysis. We focus on the low signal setting and compare our method through simulation to more standard approaches that use the paradigm of localize-then-estimate. To localize the particle under the standard paradigm, we use both a Gaussian fit and a maximum likelihood estimator (MLE) that accounts for both the DH-PSF and the pixel-dependent noise of the camera. Model estimation is then carried out either by fitting the model to the mean squared displacement (MSD) curve, or through an optimal estimation approach. Our results indicate that in the low signal regime, the SMC-EM approach outperforms the other methods while at higher signal-to-background levels, SMC-EM and the MLE-based methods perform equally well and both are significantly better than fitting to the MSD. In addition our results indicate that at smaller confinement lengths where the nonlinearities dominate the motion model, the SMC-EM approach is superior to the alternative approaches.