Method for simultaneous localization and parameter estimation in particle tracking experiments

Ashley, Trevor T.; Andersson, Sean B.

doi:10.1103/physreve.92.052707

Cited by 30 publications

(30 citation statements)

References 42 publications

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“…To demonstrate, we fixed the background rate N bgd = 10 and the peak signal intensity G = 100, representing a strong but not atypical signal in actual SPT experiments [1], [4]. A typical image is shown in Fig.…”

Section: A Demonstrationmentioning

confidence: 99%

Simultaneous Localization and Parameter Estimation for Single Particle Tracking via Sigma Points based EM

Lin

Andersson

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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Single Particle Tracking (SPT) is a powerful class of tools for analyzing the dynamics of individual biological macromolecules moving inside living cells. The acquired data is typically in the form of a sequence of camera images that are then post-processed to reveal details about the motion. In this work, we develop an algorithm for jointly estimating both particle trajectory and motion model parameters from the data. Our approach uses Expectation Maximization (EM) combined with an Unscented Kalman filter (UKF) and an Unscented Rauch-Tung-Striebel smoother (URTSS), allowing us to use an accurate, nonlinear model of the observations acquired by the camera. Due to the shot noise characteristics of the photon generation process, this model uses a Poisson distribution to capture the measurement noise inherent in imaging. In order to apply a UKF, we first must transform the measurements into a model with additive Gaussian noise. We consider two approaches, one based on variance stabilizing transformations (where we compare the Anscombe and Freeman-Tukey transforms) and one on a Gaussian approximation to the Poisson distribution. Through simulations, we demonstrate efficacy of the approach and explore the differences among these measurement transformations.

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Section: A Demonstrationmentioning

confidence: 99%

Simultaneous Localization and Parameter Estimation for Single Particle Tracking via Sigma Points based EM

Lin

Andersson

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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“…In this section, we present the construction of empirical estimators that serve to recover physical properties from parametric [37,41,87] and non-parametric statistics [4]. Retrieving statistical parameters of a diffusion process from one-dimensional time series statistics have been studied using Bayesian inference in [30,65].…”

Section: Empirical Estimation Of the Drift And Diffusion Tensor Of A mentioning

confidence: 99%

Statistical methods for large ensemble of super-resolution stochastic single particle trajectories

Hozé¹,

Holcman

2017

Preprint

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Following recent progresses in super-resolution microscopy obtained in the last decade, massive amount of redundant single stochastic trajectories are now available for statistical analysis. Flows of trajectories of molecules or proteins are sampling the cell membrane or its interior at a very high time and space resolution. Several statistical analysis were developed to extract information contained in these data, such as the biophysical parameters of the underlying stochastic motion to reveal the cellular organization. These trajectories can further reveal hidden subcellular organization. We present here the statistical analysis of these trajectories based on the classical Langevin equation, which serves as a model of trajectories. Parametric and non-parametric estimators are constructed by discretizing the stochastic equations and they allow recovering tethering forces, diffusion tensor or membrane organization from measured trajectories, that differ from physical ones by a localization noise. Modeling, data analysis and automatic detection algorithms serve extracting novel biophysical features such as potential wells and other sub-structures, such as rings at an unprecedented spatiotemporal resolution. It is also possible to reconstruct the surface membrane of a biological cell from the statistics of projected random trajectories.

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“…This procedure was presented in [23] where it was described in the context of tracking fluorescent particles using widefield fluorescence measurements; code is available at an online repository [26]. The approach is general and can be applied to a wide variety of measurement techniques; in the remainder of this section we describe its use in the current setting where confocal measurements are used.…”

Section: Data Analysis: Particle Trajectory and Motion Model Estimationmentioning

confidence: 99%

“…In Sec. 3 we describe its application in the context of the confocal measurements used in our reactive tracker; further details on SMC-EM, including validation of estimation accuracy can be found in [23].…”

Section: Introductionmentioning

confidence: 99%

Tracking single fluorescent particles in three dimensions via extremum seeking

Ashley¹,

Gan²,

Pan³

et al. 2016

Biomed. Opt. Express

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The ability to track single fluorescent particles in three-dimensions with subdiffraction limit precision as well as sub-millisecond temporal resolution has enabled the understanding of many biophysical phenomena at the nanometer scale. While there are several techniques for achieving this, most require complicated experimental setups that are expensive to implement. These methods can offer superb performance but their complexity may be overwhelming to the end-user whose aim is only to understand the feature being imaged. In this work, we describe a method for tracking a single fluorescent particle using a standard confocal or multi-photon microscope configuration. It relies only on the assumption that the relative position of the measurement point and the particle can be actuated and that the point spread function has a global maximum that coincides with the particle's position. The method uses intensity feedback to calculate real-time position commands that "seek" the extremum of the point spread function as the particle moves through its environment. We demonstrate the method by tracking a diffusing quantum dot in a hydrogel on a standard epifluorescent confocal microscope.

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Method for simultaneous localization and parameter estimation in particle tracking experiments

Cited by 30 publications

References 42 publications

Simultaneous Localization and Parameter Estimation for Single Particle Tracking via Sigma Points based EM

Simultaneous Localization and Parameter Estimation for Single Particle Tracking via Sigma Points based EM

Statistical methods for large ensemble of super-resolution stochastic single particle trajectories

Tracking single fluorescent particles in three dimensions via extremum seeking

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