Estimation of motility parameters from trajectory data

Vestergaard, Christian; Pedersen, Jonas Nyvold; Mortensen, Kim I.; Flyvbjerg, Henrik

doi:10.1140/epjst/e2015-02452-5

Cited by 36 publications

(63 citation statements)

References 55 publications

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“…In particular, a conceptually important question often raised within this context is if one can reliably extract information about the ensemble-averaged properties of random processes from single-trajectory data [46]. Considerable theoretical progress has been achieved, for instance, in finding the way to get the ensemble-averaged diffusion coefficient from a single Brownian trajectory, which task amounts to seeking properly defined functionals of the trajectory which possess an ergodic property (see, e.g., [43][44][45][46][48][49][50][51][52][53][54][55][56] for a general overview).One of such functionals used in single-trajectory analysis is the time-averaged mean squared displacement (MSD) (see, e.g., [39, 43-47])…”

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confidence: 99%

Power spectral density of a single Brownian trajectory: what one can and cannot learn from it

et al. 2018

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The power spectral density (PSD) of any time-dependent stochastic process X t is a meaningful feature of its spectral content. In its text-book definition, the PSD is the Fourier transform of the covariance function of X t over an infinitely large observation time T, that is, it is defined as an ensemble-averaged property taken in the limit  ¥ T . A legitimate question is what information on the PSD can be reliably obtained from single-trajectory experiments, if one goes beyond the standard definition and analyzes the PSD of a single trajectory recorded for a finite observation time T. In quest for this answer, for a d-dimensional Brownian motion (BM) we calculate the probability density function of a single-trajectory PSD for arbitrary frequency f, finite observation time T and arbitrary number k of projections of the trajectory on different axes. We show analytically that the scaling exponent for the frequency-dependence of the PSD specific to an ensemble of BM trajectories can be already obtained from a single trajectory, while the numerical amplitude in the relation between the ensemble-averaged and single-trajectory PSDs is a fluctuating property which varies from realization to realization. The distribution of this amplitude is calculated exactly and is discussed in detail. Our results are confirmed by numerical simulations and single-particle tracking experiments, with remarkably good agreement. In addition we consider a truncated Wiener representation of BM, and the case of a discrete-time lattice random walk. We highlight some differences in the behavior of a single-trajectory PSD for BM and for the two latter situations. The framework developed herein will allow for meaningful physical analysis of experimental stochastic trajectories.

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confidence: 99%

Power spectral density of a single Brownian trajectory: what one can and cannot learn from it

et al. 2018

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“…To analyze the motility data from single molecules, initially, we assumed the simplest possible model: normal, free diffusion in the two dimensions of the cell membrane. Thus, we determined the diffusion coefficient for individual molecules along each coordinate axis using the near-optimal covariance-based estimator 26,27 (black points, Figure 3a Consequently, we could not reject the hypothesis that all molecules diffuse identically and that the observed variation simply is due to finite statistics ( Figure 3a,b). Comparison, of experimental and theoretical power-spectra for displacements 26,27 , however, demonstrated that this did not explain our data The MSDs deviated systematically from the straight line expected from normal, free diffusion of AQP3 in the plasma membrane ( Figure 3g).…”

Section: Spt-palm Reveals Confined Diffusion Of Aqp3-meos3 In the Plamentioning

confidence: 98%

Regulation of Plasma Membrane Nanodomains of the Water Channel Aquaporin-3 Revealed by Fixed and Live Photoactivated Localization Microscopy

et al. 2018

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Several aquaporins (AQP) water channels are short-term regulated by the messenger cyclic adenosine monophosphate (cAMP), including AQP3. Bulk measurements show that cAMP can change diffusive properties of AQP3, however, it remains unknown how elevated cAMP affects AQP3 organization at the nanoscale. Here we analyzed AQP3 nano-organization following cAMPstimulation using photoactivated localization microscopy (PALM) of fixed cells combined with pair correlation analysis. Moreover, in live cells we combined PALM acquisitions of single fluorophores with single particle tracking (spt-PALM).These analyses revealed that AQP3 tend to cluster and that the diffusive mobility is confined to nano-domains with radii of ~150 nm. This domain size increases by ~30 % upon elevation of cAMP, which, however, is not accompanied by a significant increase in the confined diffusion coefficient. This regulation of AQP3 organization at the nanoscale may be important for understanding the mechanisms of water AQP3-mediated water transport across plasma membranes.

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“…The motion blur has even more effect on fast moving particles, as the particle observed position is the result of integration over longer areas. Including motion blur in the MSD leads to the following estimate for MSD [88] ⟨ρ n ⟩ = 2Dn∆t + 2(σ 2 − 2RD∆t).…”

Section: Comparison With Classical Single Particle Trajectories Analysismentioning

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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Estimation of motility parameters from trajectory data

Cited by 36 publications

References 55 publications

Power spectral density of a single Brownian trajectory: what one can and cannot learn from it

Power spectral density of a single Brownian trajectory: what one can and cannot learn from it

Regulation of Plasma Membrane Nanodomains of the Water Channel Aquaporin-3 Revealed by Fixed and Live Photoactivated Localization Microscopy

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

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