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Article

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

1
Department of Mechanical Engineering, Boston University, Boston, MA 02215, USA
2
Division of Systems Engineering, Boston University, Boston, MA 02215, USA
*
Author to whom correspondence should be addressed.
Academic Editor: Francesco Simone Ruggeri
Molecules 2021, 26(4), 886; https://doi.org/10.3390/molecules26040886
Received: 22 January 2021 / Revised: 4 February 2021 / Accepted: 4 February 2021 / Published: 8 February 2021
(This article belongs to the Special Issue Single-Molecule: From Physics to Biology)
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. View Full-Text
Keywords: single particle tracking; single molecule biophysics; fluorescence single particle tracking; single molecule biophysics; fluorescence
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MDPI and ACS Style

Godoy, B.I.; Vickers, N.A.; Andersson, S.B. An Estimation Algorithm for General Linear Single Particle Tracking Models with Time-Varying Parameters. Molecules 2021, 26, 886. https://doi.org/10.3390/molecules26040886

AMA Style

Godoy BI, Vickers NA, Andersson SB. An Estimation Algorithm for General Linear Single Particle Tracking Models with Time-Varying Parameters. Molecules. 2021; 26(4):886. https://doi.org/10.3390/molecules26040886

Chicago/Turabian Style

Godoy, Boris I., Nicholas A. Vickers, and Sean B. Andersson. 2021. "An Estimation Algorithm for General Linear Single Particle Tracking Models with Time-Varying Parameters" Molecules 26, no. 4: 886. https://doi.org/10.3390/molecules26040886

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