Quantitative Analysis of Single Particle Trajectories: Mean Maximal Excursion Method

Tejedor, Vincent; Bénichou, Olivier; Voituriez, Raphaël; Jungmann, Ralf; Simmel, Friedrich C.; Selhuber‐Unkel, Christine; Oddershede, Lene B.; Metzler, Ralf

doi:10.1016/j.bpj.2009.12.4282

Cited by 200 publications

(217 citation statements)

References 41 publications

Supporting

Mentioning

207

Contrasting

Order By: Relevance

“…There is a long history of methods that seek to go beyond the MSD to characterize dynamics (29,30), particularly since the advent of single-molecule tracking experiments. Recent innovations include comparing exchange and persistence time distributions to detect glassy behavior (31), p-variation (32), the mean maximal excursion method for anomalous diffusion (33), and the diffusivity distribution (34). However, these methods focus on distributions of extents of changes (e.g., distances traveled) and their scaling with time.…”

Section: Discussionmentioning

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.

112

115

View full text Add to dashboard Cite

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...

show abstract

Section: Discussionmentioning

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.

112

115

View full text Add to dashboard Cite

show abstract

“…There are three main mechanisms leading to subdiffusion, as underlined section A : random walk on a fractal medium, random walk with long waiting times (CTRW), or random walk with long range correlations such as Fractional Brownian Motion (FBM). Which of these possibilities best describes transport in crowded environments such as the cellular medium is however still unclear (see He et al (2008), Bancaud et al (2009), Szymanski andWeiss (2009) or Tejedor et al (2010) for various opinions on the subject). Lomholt et al (2007) explore the effect of a crowded environment with subdiffusion r 2 (t) ∝ t α (0 < α < 1) caused by waiting times distributed as p(t) ∼ τ α /t 1+α .…”

Section: Crowding Effectsmentioning

confidence: 99%

Intermittent search strategies

et al. 2011

View full text Add to dashboard Cite

This review examines intermittent target search strategies, which combine phases of slow motion, allowing the searcher to detect the target, and phases of fast motion during which targets cannot be detected. We first show that intermittent search strategies are actually widely observed at various scales. At the macroscopic scale, this is for example the case of animals looking for food ; at the microscopic scale, intermittent transport patterns are involved in reaction pathway of DNA binding proteins as well as in intracellular transport. Second, we introduce generic stochastic models, which show that intermittent strategies are efficient strategies, which enable to minimize the search time. This suggests that the intrinsic efficiency of intermittent search strategies could justify their frequent observation in nature. Last, beyond these modeling aspects, we propose that intermittent strategies could be used also in a broader context to design and accelerate search processes.

show abstract

“…in the exact relation between the second and the higher even central moments of the PDF) may in principle solve the problem [16]. However, the limited amount of available information is not enough to produce a distinguishable PDF (an example is shown in the Supplementary Material), and moreover no analytical form is known for the percolation PDF.…”

mentioning

confidence: 99%

Test for Determining a Subdiffusive Model in Ergodic Systems from Single Trajectories

2013

View full text Add to dashboard Cite

Experiments on particles' motion in living cells show that it is often subdiffusive. This subdiffusion may be due to trapping, percolation-like structures, or viscoelatic behavior of the medium. While the models based on trapping (leading to continuous-time random walks) can easily be distinguished from the rest by testing their non-ergodicity, the latter two cases are harder to distinguish. We propose a statistical test for distinguishing between these two based on the space-filling properties of trajectories, and prove its feasibility and specificity using synthetic data. We moreover present a flow-chart for making a decision on a type of subdiffusion for a broader class of models.Experiments on particles' motion in living cells aimed on understanding molecular crowding [1][2][3][4] have unveiled that diffusion in such environments is often anomalous, i.e. the mean squared displacement (MSD) does not grow proportionally to time, x 2 (t) ∝ t , but follows a slower patternwith 0 < α < 1 (subdiffusion), and the nature of this anomaly has to be understood. Anomalous diffusion is not only apparent in biological systems, but is found in complex systems ranging from amorphous semiconductors [5], goeology [6], to turbulent systems [7]. There are several mathematical models leading to subdiffusion, corresponding to different physical assumptions about the structure and energy landscape of the system in which the subdiffusive motion takes place. Since one is mostly interested in the actual microscopic structure of the system, an important task is working out tests which allow for distinguishing between different models giving the same prediction for the MSD. The three most popular models which might be pertinent to explaining subdiffusion in cells are:(i) continuous time random walk (CTRW), a mathematical model which is physically realized in systems with traps, i.e. binding sites of different energetic depths, a case pertinent to energetic disorder, (ii) diffusion on fractal structures, as exemplified by percolation, a situation pertinent to structural disorder, and (iii) fractional Brownian motion [8] (fBm), a Gaussian process with stationary increments which satisfies the following statistical properties: the process is symmetric, i.e x H (t) = 0 where x H (0) = 0, and the MSD scales as x 2 H (t) ∼ t 2H where H is the Hurst exponent. Note that H < 1/2 leads to subdiffusion, while H = 1/2 recovers Brownian motion. fBm physically corresponding to systems with predominating slow modes of motion and is realized in viscoelastic media as exemplified by polymers and polymer networks, where disorder does not play a leading role.Lastly, one has to discuss (iv) the time-dependent diffusion coefficient (TDDC) model -normal diffusion with a time-dependent diffusion coefficient, which is used to fit experimental results from, for example, FRAP (fluorescence recovery after photobleaching) experiments [9]. This model corresponds e.g. to a situation when the step rate is explicitly time-dependent, and does not have a clear physical ...

show abstract

Quantitative Analysis of Single Particle Trajectories: Mean Maximal Excursion Method

Cited by 200 publications

References 41 publications

Distribution of directional change as a signature of complex dynamics

Distribution of directional change as a signature of complex dynamics

Intermittent search strategies

Test for Determining a Subdiffusive Model in Ergodic Systems from Single Trajectories

Contact Info

Product

Resources

About