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

The datasets store both motion and observation information of a single fluorescent sub-diffraction limit-sized particle moving in a three-dimensional confined environment. The confined motion is following a nonlinear model driven by non-Gaussian noise, the observation is formed by engineered Double-helix (DH) point spread function (PSF) and captured by scientific complementary metal-oxide semiconductor (sCMOS) camera. Based on our prior computationally efficient application of Sequential Monte Carlo - Expectation Maximization (SMC-EM), we extended it to handle the DH-PSF for encoding the three-dimensional position of the particle in two-dimensional image plane of the camera. We focus on studying the datasets at low signal and low signal-to-background ratio (SBR). Based on the datasets across different SBR and confinement lengths, a quantitative comparison is conducted to show 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.

Methods
All datasets were simulated using Python 3.8. The camera type considered in this work is the scientific complementary metal-oxide semiconductor (sCMOS) where both shot noise and the pixel-dependent readout noise are common noise sources. The motion of a single fluorescent particle was generated at a time step of 1 ms. The camera was assumed to take images at a rate of 10 Hz with a shutter period of 10 ms. Motion blur is considered for all data simulation. The 10 pixelated images during the shutter period were accumulated to generate a single camera image. (See the Usage Notes for details).