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 to perform a linear fit on mean-square-displacement curves. However, this strategy is suboptimal and prone to errors. Recently, it was shown that the increments between observed positions provide a good estimate for the diffusion coefficient  . Here, we construct a likelihood function based on the statistics of the position increments. The corresponding maximum likelihoodestimator for the global diffusion coefficient of multiple trajectories can be efficiently evaluated in \mathcal{O extend the model to mixtures of subpopulations differing in their diffusion coefficients, which we estimate by using the expectation-maximization algorithm. This formulation naturally leads to a probabilistic assignment of trajectories to subpopulations. We employ the theory to analyze experimental tracking data that cannot be explained with a single diffusion coefficient. We test how well a dataset conforms to the assumptions of a diffusion model and determine the optimal number of subpopulations with the help of a quality factor of known analytical distribution. To facilitate use by practitioners, we provide a data analysis script .
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 to perform a linear fit on mean-square-displacement curves. However, this strategy is suboptimal and prone to errors. Recently, it was shown that the increments between observed positions provide a good estimate for the diffusion coefficient , and their statistics are well-suited for likelihood-based analysis methods . Here, we revisit the problem of extracting diffusion coefficients from single-particle tracking experiments subject to static and dynamic noise using the principle of maximum likelihood. Taking advantage of an efficient real-space formulation, we extend the model to mixtures of subpopulations differing in their diffusion coefficients, which we estimate with the help of the expectation-maximization algorithm. This formulation naturally leads to a probabilistic assignment of trajectories to subpopulations. We employ the theory to analyze experimental tracking data that cannot be explained with a single diffusion coefficient. We test how well a dataset conforms to the assumptions of a diffusion model and determine the optimal number of subpopulations with the help of a quality factor of known analytical distribution. To facilitate use by practitioners, we provide a fast open-source implementation of the theory for the efficient analysis of multiple trajectories in arbitrary dimensions simultaneously .
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, and their statistics are well-suited for likelihood-based analysis methods
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construct a likelihood function based on the statistics of the position increments. The corresponding maximum likelihoodestimator for the global diffusion coefficient of multiple trajectories can be efficiently evaluated in \mathcal{O
revisit the problem of extracting diffusion coefficients from single-particle tracking experiments subject to static and dynamic noise using the principle of maximum likelihood. Taking advantage of an efficient real-space formulation, we
R
by using the
with the help of the
R
data analysis script
fast open-source implementation of the theory for the efficient analysis of multiple trajectories in arbitrary dimensions simultaneously