Joint Estimation of Trajectory and Model Parameters for Single Particle Tracking of 3D Confined Diffusion Using the Double-Helix Point Spread Function

Single particle tracking plays a significant role in biophysics through its ability to reveal dynamic mechanisms and physical properties of biological macromolecules inside living cells. The motion of these molecules can often be modeled as a confined diffusion. The standard paradigm in the biophysics community is to first estimate the trajectory of a particle and then use a technique such as the Mean Square Displacement or the Maximum Likelihood Estimation (MLE) to determine model parameters. These approaches, however, ignore the fact that localization and parameter estimation problems are coupled. We have previously introduced a framework based on optimal estimation theory to simultaneously do localization and parameter estimation. Here we build upon that work by expanding it to include a recent advance in imaging three dimensional motion, namely the Double-Helix (DH) engineered Point Spread Function (PSF). The DH-PSF encodes the axial position of the particle directly into the 2D image acquired by the camera mounted to the microscope. Our approach uses Expectation Maximization (EM) and Sequential Monte Carlo (SMC) to handle the nonlinearities in the observation and motion models. In this paper, we also improve upon the computational complexity of this scheme, using a Gaussian Particle Filter and Backward Simulation Particle Smoother in the SMC elements of the algorithm. We compare our scheme through simulation to state of the art methods based on localization using Gaussian fitting followed by MLE of the model parameters. These results show that our method outperforms GF-MLE at the low signal intensity levels common to biophysical experiments. Copyright (C) 2021 The Authors.