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

2021 ◽  
Vol 154 (23) ◽  
pp. 234105
Author(s):  
Jakob Tómas Bullerjahn ◽  
Gerhard Hummer
Keyword(s):  
Maximum Likelihood ◽  
Particle Tracking ◽  
Single Particle ◽  
Diffusion Coefficients ◽  
Single Particle Tracking ◽  
Maximum Likelihood Estimates

scholarly journals An Estimation Algorithm for General Linear Single Particle Tracking Models with Time-Varying Parameters

Molecules ◽  
2021 ◽  
Vol 26 (4) ◽  
pp. 886
Author(s):  
Boris I. Godoy ◽  
Nicholas A. Vickers ◽  
Sean B. Andersson
Keyword(s):  
Particle Tracking ◽  
Single Particle ◽  
Estimation Algorithm ◽  
Single Particle Tracking ◽  
Maximum Likelihood Estimates ◽  
Parameter Estimates ◽  
Time Varying ◽  
Varying Parameters ◽  
Second Stage ◽  
Time Varying Parameters

Single Particle Tracking (SPT) is a powerful class of methods for studying the dynamics of biomolecules inside living cells. The techniques reveal the trajectories of individual particles, with a resolution well below the diffraction limit of light, and from them the parameters defining the motion model, such as diffusion coefficients and confinement lengths. Most existing algorithms assume these parameters are constant throughout an experiment. However, it has been demonstrated that they often vary with time as the tracked particles move through different regions in the cell or as conditions inside the cell change in response to stimuli. In this work, we propose an estimation algorithm to determine time-varying parameters of systems that discretely switch between different linear models of motion with Gaussian noise statistics, covering dynamics such as diffusion, directed motion, and Ornstein–Uhlenbeck dynamics. Our algorithm consists of three stages. In the first stage, we use a sliding window approach, combined with Expectation Maximization (EM) to determine maximum likelihood estimates of the parameters as a function of time. These results are only used to roughly estimate the number of model switches that occur in the data to guide the selection of algorithm parameters in the second stage. In the second stage, we use Change Detection (CD) techniques to identify where the models switch, taking advantage of the off-line nature of the analysis of SPT data to create non-causal algorithms with better precision than a purely causal approach. Finally, we apply EM to each set of data between the change points to determine final parameter estimates. We demonstrate our approach using experimental data generated in the lab under controlled conditions.

scholarly journals Extracting transition rates in single-particle tracking using analytical diffusion distribution analysis

2020 ◽  
Author(s):  
Jochem N.A. Vink ◽  
Stan J.J. Brouns ◽  
Johannes Hohlbein
Keyword(s):  
Dna Polymerase ◽  
Particle Tracking ◽  
Single Particle ◽  
Diffusion Coefficients ◽  
Dna Interaction ◽  
Single Particle Tracking ◽  
Distribution Analysis ◽  
Transition Rates ◽  
Chromosomal Dna

AbstractSingle-particle tracking is an important technique in the life sciences to understand the kinetics of biomolecules. Observed diffusion coefficients in vivo, for example, enable researchers to determine whether biomolecules are moving alone, as part of a larger complex or are bound to large cellular components such as the membrane or chromosomal DNA. A remaining challenge has been to retrieve quantitative kinetic models especially for molecules that rapidly interchange between different diffusional states. Here, we present analytic diffusion distribution analysis (anaDDA), a framework that allows extracting transition rates from distributions of observed diffusion coefficients. We show that theoretically predicted distributions accurately match simulated distributions and that anaDDA outperforms existing methods to retrieve kinetics especially in the fast regime of 0.1-10 transitions per imaging frame. AnaDDA does account for the effects of confinement and tracking window boundaries. Furthermore, we added the option to perform global fitting of data acquired at different frame times, to allow complex models with multiple states to be fitted confidently. Previously, we have started to develop anaDDA to investigate the target search of CRISPR-Cas complexes. In this work, we have optimized the algorithms and reanalysed experimental data of DNA polymerase I diffusing in live E. coli. We found that long-lived DNA interaction by DNA polymerase are more abundant upon DNA damage, suggesting roles in DNA repair. We further revealed and quantified fast DNA probing interactions that last shorter than 10 ms. AnaDDA pushes the boundaries of the timescale of interactions that can be probed with single-particle tracking and is a mathematically rigorous framework that can be further expanded to extract detailed information about the behaviour of biomolecules in living cells.

scholarly journals Information-Efficient, Off-Center Sampling Results in Improved Precision in 3D Single-Particle Tracking Microscopy

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 498
Author(s):  
Chen Zhang ◽  
Kevin Welsher
Keyword(s):  
Fisher Information ◽  
Particle Tracking ◽  
Single Particle ◽  
Biological Samples ◽  
Tracking System ◽  
Single Particle Tracking ◽  
Uniform Sampling ◽  
Single Dimension ◽  
3D Localization ◽  
Particle Localization

In this work, we present a 3D single-particle tracking system that can apply tailored sampling patterns to selectively extract photons that yield the most information for particle localization. We demonstrate that off-center sampling at locations predicted by Fisher information utilizes photons most efficiently. When performing localization in a single dimension, optimized off-center sampling patterns gave doubled precision compared to uniform sampling. A ~20% increase in precision compared to uniform sampling can be achieved when a similar off-center pattern is used in 3D localization. Here, we systematically investigated the photon efficiency of different emission patterns in a diffraction-limited system and achieved higher precision than uniform sampling. The ability to maximize information from the limited number of photons demonstrated here is critical for particle tracking applications in biological samples, where photons may be limited.

pH-Mediated nanoparticle dynamics in hydrogel nanocomposites

Soft Matter ◽  
2021 ◽  
Author(s):  
Katie A. Rose ◽  
Daeyeon Lee ◽  
Russell J. Composto
Keyword(s):  
Quantum Dot ◽  
Ethylene Glycol ◽  
Particle Tracking ◽  
Single Particle ◽  
Silica Particles ◽  
Single Particle Tracking ◽  
Poly Ethylene Glycol ◽  
Hydrogel Nanocomposites ◽  
Poly Ethylene ◽  
Nanoparticle Dynamics

The effect of static silica particles on the dynamics of quantum dot (QD) nanoparticles grafted with a poly(ethylene glycol) (PEG) brush in hydrogel nanocomposites is investigated using single particle tracking (SPT).

Adaptive optics enables three-dimensional single particle tracking at the sub-millisecond scale

2013 ◽  
Vol 102 (17) ◽  
pp. 173702 ◽  
Author(s):  
Manuel F. Juette ◽  
Felix E. Rivera-Molina ◽  
Derek K. Toomre ◽  
Joerg Bewersdorf
Keyword(s):  
Adaptive Optics ◽  
Particle Tracking ◽  
Single Particle ◽  
Three Dimensional ◽  
Single Particle Tracking
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