Maximum likelihood estimates of diffusion coefficients from single-particle tracking experiments
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866909226249486336 |
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| author | Bullerjahn, Jakob Tómas Hummer, Gerhard |
| author_facet | Bullerjahn, Jakob Tómas Hummer, Gerhard |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_09955 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Maximum likelihood estimates of diffusion coefficients from single-particle tracking experiments Bullerjahn, Jakob Tómas Hummer, Gerhard Biological Physics Statistical Mechanics Quantitative Methods 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. |
| title | Maximum likelihood estimates of diffusion coefficients from single-particle tracking experiments |
| topic | Biological Physics Statistical Mechanics Quantitative Methods |
| url | https://arxiv.org/abs/2011.09955 |