16 papers · ranked by Valyu relevance
Jakub Spiechowicz, Jerzy Łuczka
We reveal the mechanism of subdiffusion which emerges in a straightforward, one dimensional classical nonequilibrium dynamics of a Brownian ratchet driven by both a time-periodic force and Gaussian white noise. In a tailored parameter set for which the deterministic counterpart is in a non-chaotic regime, subdiffusion…
Toby Kay, Luca Giuggioli
We derive, through subordination techniques, a generalized Feynman-Kac equation in the form of a time fractional Schrödinger equation. We relate such equation to a functional which we name the subordinated local time. We demonstrate through a stochastic treatment how this generalized Feynman-Kac equation describes…
Tadeusz Kosztołowicz, Mohammad Reza Rahimi Tabar
Superdiffusion is usually defined as a random walk process of a molecule, in which the time evolution of the mean-squared displacement, $σ2$, of the molecule is a power function of time, $σ2(t)∼t(2/γ)$, with $γ\in(1,2)$. An equation with a Riesz-type fractional derivative of the order $γ$ with respect to a spatial…
Tadeusz Kosztołowicz, Aldona Dutkiewicz, Katarzyna D. Lewandowska
Normal and anomalous diffusion processes are characterized by the time evolution of the mean square displacement of a diffusing molecule $σ2(t)$. When $σ2(t)$ is a power function of time, the process is described by a fractional subdiffusion, fractional superdiffusion or normal diffusion equation. However, for other…
S. Girst, V. Hable, G. A. Drexler, C. Greubel + 4 more
'M. Haum' 'A. A. Friedl' 'G. Dollinger'] The mobility of damaged chromatin regions in the nucleus may affect the probability of mis-repair. In this work, live-cell observation and distance tracking of GFP-tagged DNA damage response protein MDC1 was used to study the random-walk behaviour of chromatin domains containing…
Anna S. Bodrova, Aleksei V. Chechkin, Andrey G. Cherstvy, Hadiseh Safdari + 2 more
'Hadiseh Safdari' 'Igor M. Sokolov' 'Ralf Metzler'] It is quite generally assumed that the overdamped Langevin equation provides a quantitative description of the dynamics of a classical Brownian particle in the long time limit. We establish and investigate a paradigm anomalous diffusion process governed by an…
Eugene B. Postnikov, Anastasia I. Lavrova, Dmitry E. Postnov, Cecília R. Santos + 2 more
'Cecília R. Santos' 'Telma Quintela' 'Isabel Goncalves'] The mechanisms of transport of substances in the brain parenchyma have been a hot topic in scientific discussion in the past decade. This discussion was triggered by the proposed glymphatic hypothesis, which assumes a directed flow of cerebral fluid within the…
Yu-Jo Chai, Ching-Ya Cheng, Yi-Hung Liao, Chih-Hsiang Lin + 1 more
'Chia-Lung Hsieh'] Cholesterol plays a unique role in the regulation of membrane organization and dynamics by modulating the membrane phase transition at the nanoscale. Unfortunately, due to their small sizes and dynamic nature, the effects of cholesterol-mediated membrane nanodomains on membrane dynamics remain…
Christopher N. Angstmann, Bruce I. Henry
A standard reaction-diffusion equation consists of two additive terms, a diffusion term and a reaction rate term. The latter term is obtained directly from a reaction rate equation which is itself derived from known reaction kinetics, together with modelling assumptions such as the law of mass action for well-mixed…
Hugues Berry, Hédi A. Soula
Experimental measurements of the mobility of macromolecules, especially proteins, in cells and their membranes consistently report transient subdiffusion with possibly position-dependent-non-homogeneous-properties. However, the spatiotemporal dynamics of protein mobility when transient subdiffusion is restricted to a…
Stephen Smith, Claudia Cianci, Ramon Grima
It is now well established that cell interiors are significantly crowded by macromolecules, which impede diffusion and enhance binding rates. However, it is not fully appreciated that levels of crowding are heterogeneous, and can vary substantially between subcellular regions. In this article, starting from a…
Aleksander Stanislavsky, Aleksander Weron
The Laplace distribution of random processes was observed in numerous situations that include glasses, colloidal suspensions, live cells, and firm growth. Its origin is not so trivial as in the case of Gaussian distribution, supported by the central limit theorem. Sums of Laplace distributed random variables are not…
Xi Chen, Jianhong Kang, Ceji Fu, Wenchang Tan + 1 more
sparks and waves play important roles in calcium release and calcium propagation during the excitation-contraction (EC) coupling process in cardiac myocytes. Although the classical Fick’s law is widely used to model sparks and waves in cardiac myocytes, it fails to reasonably explain the full-width at half…
Carson Ingo, Yi Sui, Yufen Chen, Todd B. Parrish + 2 more
'Itamar Ronen'] In this paper, we provide a context for the modeling approaches that have been developed to describe non-Gaussian diffusion behavior, which is ubiquitous in diffusion weighted magnetic resonance imaging of water in biological tissue. Subsequently, we focus on the formalism of the continuous time random…
Marco Palombo, Andrea Barbetta, Cesare Cametti, Gabriele Favero + 2 more
'Silvia Capuani' 'Georgios Bokias'] Considering the current development of new nanostructured and complex materials and gels, it is critical to develop a sub-micro-scale sensitivity tool to quantify experimentally new parameters describing sub-microstructured porous systems. Diffusion NMR, based on the measurement of…
Cyril Favard
The fluorescence recovery after photobleaching (FRAP) technique has been used for decades to measure movements of molecules in two-dimension (2D). Data obtained by FRAP experiments in cell plasma membranes are assumed to be described through a means of two parameters, a diffusion coefficient, D (as defined in a pure…