The random walk's guide to anomalous diffusion: a fractional dynamics approach

Perillo

et al. 2016

Biophysical Journal

Whereas important discoveries made by single-particle tracking have changed our view of the plasma membrane organization and motor protein dynamics in the past three decades, experimental studies of intracellular processes using singleparticle tracking are rather scarce because of the lack of three-dimensional (3D) tracking capacity. In this study we use a newly developed 3D single-particle tracking method termed TSUNAMI (Tracking of Single particles Using Nonlinear And Multiplexed Illumination) to investigate epidermal growth factor receptor (EGFR) trafficking dynamics in live cells at 16/43 nm (xy/z) spatial resolution, with track duration ranging from 2 to 10 min and vertical tracking depth up to tens of microns. To analyze the long 3D trajectories generated by the TSUNAMI microscope, we developed a trajectory analysis algorithm, which reaches 81% segment classification accuracy in control experiments (termed simulated movement experiments). When analyzing 95 EGF-stimulated EGFR trajectories acquired in live skin cancer cells, we find that these trajectories can be separated into three groups-immobilization (24.2%), membrane diffusion only (51.6%), and transport from membrane to cytoplasm (24.2%). When EGFRs are membrane-bound, they show an interchange of Brownian diffusion and confined diffusion. When EGFRs are internalized, transitions from confined diffusion to directed diffusion and from directed diffusion back to confined diffusion are clearly seen. This observation agrees well with the model of clathrin-mediated endocytosis.

Section: Challenges In Molecular Trajectory Analysismentioning

confidence: 99%

Segmentation of 3D Trajectories Acquired by TSUNAMI Microscope: An Application to EGFR Trafficking

Perillo

et al. 2016

Biophysical Journal

Magnetic Resonance Imaging

“…In this case, the MSD as a function of t, is characterized by a power law: MSD(t)∝t v (where v is the dynamic exponent of the transport process, or scaling index) which characterizes anomalous diffusion (AD) processes. The case vN1 describes superdiffusive, while vb1 describes subdiffusive processes [9,10]. In this scenario, AD or nonGaussian diffusion methods may, in principle, provide more or different microstructural information which couldn't be obtained using conventional diffusion methods based on Gaussian diffusion.…”

Section: Magnetic Resonance Imaging XXX (2012) Xxx-xxxmentioning

confidence: 99%

“…The approach utilizes the theory of the Continuous Time Random Walk (CTRW) [10] as an effective approach to describe the features of non normal, or anomalous diffusion [9,10].…”

Section: Magnetic Resonance Imaging XXX (2012) Xxx-xxxmentioning

confidence: 99%

See 1 more Smart Citation

Spatio-temporal anomalous diffusion imaging: results in controlled phantoms and in excised human meningiomas

Capuani

Palombo

Gabrielli³

et al. 2013

Recently, we measured two anomalous diffusion (AD) parameters: the spatial and the temporal AD indices, called γ and α, respectively, by using spectroscopic pulse gradient field methods. We showed that γ quantifies pseudo-superdiffusion processes, while α quantifies subdiffusion processes. Here, we propose γ and α maps obtained in a controlled heterogeneous phantom, comprised of packed micro-beads in water and in excised human meningiomas. In few words, α maps represent the multi-scale spatial distribution of the disorder degree in the system, while γ maps are influenced by local internal gradients, thus highlighting the interface between compartments characterized by different magnetic susceptibility. γ maps were already obtained by means of AD stretched exponential imaging and α-type maps have been recently achieved for fixed rat brain with the aim of highlighting the fractal dimension of specific brain regions. However, to our knowledge, the maps representative of the spatial distribution of α and γ obtained on the same controlled sample and in the same excised tissue have never been compared. Moreover, we show here, for the first time, that α maps are representative of the spatial distribution of the disorder degree of the system. In a first phase, γ and α maps of controlled phantom characterized by an ordered and a disordered rearrangement of packed micro-beads of different sizes in water and by different magnetic susceptibility (Δχ) between beads and water were obtained. In a second phase, we investigated excised human meningiomas of different consistency. Results reported here, obtained at 9.4 T, show that α and γ maps are characterized by a different image contrast. Indeed, unlike γ maps, α maps are insensible to (Δχ) and they are sensible to the disorder degree of the microstructural rearrangement. These observations strongly suggest that AD indices α and γ reflect some additional microstructural information which cannot be obtained using conventional diffusion methods based on Gaussian diffusion. Moreover, α and γ maps obtained in excised meningiomas seem to provide more microstructural details above those obtained with conventional DTI analysis, which could be used to improve the classification of meningiomas based on their consistency.

Journal of Theoretical Biology

“…Aranson et al [1997] perform such an argument mathematically in a slightly different fitness landscape to ours. By analogy to pinning in anomalous diffusion [Bouchaud andGeorges, 1990, Ralf Metzler andJoseph Klafter, 2000], if there is some maximum to the time the population can spend at fit sites then a rescaling of the mutation rate will recover standard mutation-drift dynamics.…”

Section: Two Competing Typesmentioning

confidence: 99%

The role of weak selection and high mutation rates in nearly neutral evolution

Lawson

2009

International audienceNeutral dynamics occur in evolution if all types are ‘effectively equal' in their reproductive success, where the definition of ‘effectively equal' depends on the population size and the details of mutations. Empirically observed neutral genetic evolution in extremely large clonal populations can only be explained under current models if selection is completely absent. Such models typically consider the case where population dynamics occurs on a different timescale to evolution. However, this assumption is invalid when mutations are not rare in a whole population. We show that this has important consequences for the occurrence of neutral evolution in clonal populations. In highly connected type spaces, neutral dynamics can occur for all population sizes despite significant selective differences, via the forming of effectively neutral networks connecting rare neutral types. Biological implications include an explanation for the high diversity of rare types that survive in large clonal populations, and a theoretical justification for the use of neutral null models