Modes of correlated angular motion in live cells across three distinct time scales

Harrison, Andrew; Kenwright, David A.; Waigh, Thomas A.; Woodman, Philip; Allan, Viki

doi:10.1088/1478-3975/10/3/036002

Cited by 38 publications

(38 citation statements)

References 26 publications

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“…These features are illustrated by our analysis of colloidal suspensions: Pðθ; ΔÞ clearly shows the transition from unconfined to confined dynamics with packing fraction, and it yields insights into the time scales for particles to escape their neighbors and mix. One recent study of lipid droplets in live cells did examine direction of motion but characterized it through the time correlation function for relative angles (16), which is an ensemble average. Although it has been shown that the velocity autocorrelation can yield information about subtle features, such as anharmonicity (30), in general, averaging obscures the heterogeneity in a population and the self-similarity of the motion.…”

Section: Discussionmentioning

confidence: 99%

“…A deeper understanding of the structure of Pðθ; ΔÞ for this system requires exploration of microscopic models with explicit molecular features, which is beyond the scope of the present study. Rather, the key point is that the relative angle distribution reveals directional correlations and self-similarity that are not evident in the MSD (or measures of angular correlation that are averages) (16), and these features can be used to further constrain models of transport.…”

Section: Application To Experimental Datamentioning

confidence: 99%

See 1 more Smart Citation

Distribution of directional change as a signature of complex dynamics

Burov¹,

Tabei²,

Huynh³

et al. 2013

Proc. Natl. Acad. Sci. U.S.A.

120

123

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Analyses of random walks traditionally use the mean square displacement (MSD) as an order parameter characterizing dynamics. We show that the distribution of relative angles of motion between successive time intervals of random walks in two or more dimensions provides information about stochastic processes beyond the MSD. We illustrate the behavior of this measure for common models and apply it to experimental particle tracking data. For a colloidal system, the distribution of relative angles reports sensitively on caging as the density varies. For transport mediated by molecular motors on filament networks in vitro and in vivo, we discover self-similar properties that cannot be described by existing models and discuss possible scenarios that can lead to the elucidated statistical features.random walks | angular correlation | cytoskeleton C omplex dynamics often emerge from ensembles of interacting constituents. Trajectories that are obtained by tracking individual constituents contain information beyond the evolution of ensemble properties, and these data can thus reveal new mechanistic features of the system studied. Examples cut across disciplines and include quantum dots (1), colloidal beads (2), features in cells (3, 4), fish in schools (5), birds in flocks (6), and primates in social groups (7,8). These data (individual trajectories) demand theoretical frameworks for characterizing and interpreting them.The standard reporter for different forms of motion is the mean square displacement (MSD)where brackets and overlines denote ensemble and time averages, respectively. In simple Brownian motion (9), the MSD grows linearly with the separation in time between two observation points (the lag time, Δ) and does not depend on the amount of data included in averages (the measurement time, T)-i.e., there is ergodicity. Anomalous (i.e., non-Brownian) dynamics can arise from correlations in the walk steps. Correlations in the step sizes [e.g., as in fractional Brownian motion (FBM)] (10) give rise to nonlinear scaling of the MSD with lag time, retaining ergodicity (11). By contrast, a power-law distribution of dwell times [e.g., as in a continuous time random walk (CTRW)] (12) is associated with linear scaling with lag time but nonergodicity (13, 14). The two types of correlations can exist together (4, 15). Despite the success of the MSD as an order parameter for dynamics, it is essentially a 1D measure. We expect random walks in two and more dimensions to contain information beyond the MSD, and various alternative analyses have been suggested (16) (Conclusions). In this paper, we introduce a statistical measure of such information. Specifically, we consider the relative angle, which quantifies the direction of motion over successive time intervals. We show that different models of stochastic processes give rise to different distributions of relative angles and how the intervals can be varied to probe contributing time scales. We apply our order parameter to 2D experimental data obtained for mesoscopic systems. We ex...

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Section: Discussionmentioning

confidence: 99%

Section: Application To Experimental Datamentioning

confidence: 99%

Distribution of directional change as a signature of complex dynamics

Burov¹,

Tabei²,

Huynh³

et al. 2013

Proc. Natl. Acad. Sci. U.S.A.

120

123

View full text Add to dashboard Cite

show abstract

“…However, anomalous transport regimes can also be readily enforced. This model provides a principal framework to explain the origin of β = 1.3±0.1 for α = 0.4 in Robert et al (2010), and also the origin of β ≈ 1.74 in Harrison et al (2013), where the passive subdiffusion of lipid droplets with α ≈ 0.58 is changed to superdiffusion induced and assisted by molecular motors.…”

Section: Introductionmentioning

confidence: 88%

“…It is essentially larger than 2α = 0.8. Also another experiment by Harrison et al (2013) yielded β ≈ 1.74 for the active transport with More realistic biochemical cycle for one motor head (left) and the minimal two-state model of cycling (right) that includes a binding potential change due to a change of the charge state of the motor. Spatial dependence of the transition rates on the coordinate along a periodic polar background of microtubule provides an allosteric mechanism of the mechano-chemical coupling.…”

Section: Introductionmentioning

confidence: 99%

Perfect anomalous transport of subdiffusive cargos by molecular motors in viscoelastic cytosol

Goychuk

2019

Biosystems

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Multiple experiments show that various submicron particles such as magnetosomes, RNA messengers, viruses, and even much smaller nanoparticles such as globular proteins diffuse anomalously slow in viscoelastic cytosol of living cells. Hence, their sufficiently fast directional transport by molecular motors such as kinesins is crucial for the cell operation. It has been shown recently that the traditional flashing Brownian ratchet models of molecular motors are capable to describe both normal and anomalous transport of such subdiffusing cargos by molecular motors with a very high efficiency. This work elucidates further an important role of mechanochemical coupling in such an anomalous transport. It shows a natural emergence of a perfect subdiffusive ratchet regime due to allosteric effects, where the random rotations of a "catalytic wheel" at the heart of the motor operation become perfectly synchronized with the random stepping of a heavily loaded motor, so that only one ATP molecule is consumed on average at each motor step along microtubule. However, the number of rotations made by the catalytic engine and the traveling distance both scale sublinearly in time. Nevertheless, this anomalous transport can be very fast in absolute terms. arXiv:1809.08032v3 [physics.bio-ph] 9 Nov 2018

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“…To measure the turning times of the vesicles, an angular threshold method was used in conjunction with a distance threshold. In a set of N points, there will be N − 2 angles characterizing the direction of the path and for three arbitrary data points, i, i + 1 and i + 2, the angle deviation of the path was calculated by [19]:…”

Section: Experimental Methods and Analysis Of Trajectoriesmentioning

confidence: 99%

Memory effects and Lévy walk dynamics in intracellular transport of cargoes

et al. 2018

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We demonstrate the phenomenon of cumulative inertia in intracellular transport involving multiple motor proteins in human epithelial cells by measuring the empirical survival probability of cargoes on microtubules and their detachment rates. We found the longer a cargo moves along a microtubule, the less likely it detaches from it. As a result, the movement of cargoes is non-Markovian and involves a memory. We observe memory effects on the scale of up to 2 seconds. We provide a theoretical link between the measured detachment rate and the super-diffusive Lévy walk-like cargo movement.

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Modes of correlated angular motion in live cells across three distinct time scales

Cited by 38 publications

References 26 publications

Distribution of directional change as a signature of complex dynamics

Distribution of directional change as a signature of complex dynamics

Perfect anomalous transport of subdiffusive cargos by molecular motors in viscoelastic cytosol

Memory effects and Lévy walk dynamics in intracellular transport of cargoes

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