Expectation maximization based framework for joint localization and parameter estimation in single particle tracking from segmented images - Simulation Data

The datasets contain simulated Single Particle Tracking (SPT) data consisting of sequences of camera images of a single fluorescent sub-diffraction limit-sized particle undergoing two-dimensional diffusion. We simulated a variety of experimental conditions, including different Signal-to-Background Ratios (SBRs), two different camera types, different diffusion speeds, and two different settings for motion blur. SPT is a class of experimental methods and data analysis techniques for exploring the motion of individual biological macromolecules. Typical estimation algorithms split the problem into two parts: first localize the particle at each data point to generate a trajectory and then estimate model parameters from that trajectory. We have recently introduced a class of algorithms for jointly estimating both trajectory and model parameters. In this study, we used the data to perform quantitative comparisons between two variants of our approach, one relying on a Sequential Monte Carlo methods combined with Expectation Maximization (SMC-EM) that is applicable to a very broad set of motion and observation models, and one that replaces the SMC elements with methods based on the Unscented Kalman Filter (UKF) to improve upon the computational complexity. We also compared our methods to two current standards in the field. The first uses Gaussian Fitting to localize the particle, following by a Mean Square Displacement (GF-MSD) analysis to determine model parameters while the other replaces MSD with Maximum Likelihood Estimation (GF-MLE). The main results of our study indicate that our EM-based schemes significantly outperform the existing algorithms at low SBR while at high SBR, GF-MLE performs equally well but at a lower computational cost.

Methods
All datasets were simulated using MATLAB (MathWorks, Natick, MA). Two camera types were considered: (1) An ideal camera with Poisson distributed shot noise but no readout noise; (2) A camera with both shot noise and the pixel-dependent readout noise that is common to scientific complementary metal-oxide semiconductor (sCMOS) cameras. For each run, the diffusive motion of a single particle was generated at a time step of 1 ms. At each time step, a pixelated image was generated by integrating a standard Gaussian model of the Point Spread Function (PSF) of the microscope over each of the pixels in the camera image. The cameras were assumed to take images at a rate of 10 Hz with a shutter period of 10 ms. For data that included motion blur, the 10 pixelated images in the shutter period were accumulated to generate a single camera image. For data that ignored motion blur, only the first pixelated image was used. In each case, both background and camera readout noise were included based on the model of the camera being considered. Datasets were generated at a range of SBRs and diffusion coefficients (see Usage Notes for details).