Maximum likelihood estimates of diffusion coefficients from single-particle tracking experiments

Single-molecule localization microscopy allows practitioners to locate and track labeled molecules in biological systems. When extracting diffusion coefficients from the resulting trajectories, it is common practice perform a linear fit on mean-squared-displacement curves. However, this strategy suboptimal prone errors. Recently, was shown that increments between observed positions provide good estimate for coefficient, their statistics are well-suited likelihood-based analysis methods. Here, we revisit problem of single-particle tracking experiments subject static noise dynamic motion blur using principle maximum likelihood. Taking advantage an efficient real-space formulation, extend model mixtures subpopulations differing coefficients, which with help expectation–maximization algorithm. This formulation naturally leads probabilistic assignment trajectories subpopulations. We employ theory analyze experimental data cannot be explained single coefficient. test how well dataset conforms assumptions determine optimal number quality factor known analytical distribution. To facilitate use by practitioners, fast open-source implementation multiple arbitrary dimensions simultaneously.