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The random motion of molecules in living cells has consistently been reported to deviate from standard Brownian motion, a behavior coined as ``anomalous diffusion''. Fluorescence Correlation Spectroscopy (FCS) is a powerful method to…

Quantitative Methods · Quantitative Biology 2024-07-18 Nathan Quiblier , Jan-Michael Rye , Pierre Leclerc , Henri Truong , Abdelkrim Hannou , Laurent Héliot , Hugues Berry

The nonlinear theory of anomalous diffusion is based on particle interactions giving an explicit microscopic description of diffusive processes leading to sub-, normal, or super-diffusion as a result competitive effects between attractive…

Statistical Mechanics · Physics 2016-01-20 Jean Pierre Boon , James F. Lutsko

The movement of molecules inside living cells is a fundamental feature of biological processes. The ability to both observe and analyse the details of molecular diffusion in vivo at the single molecule and single cell level can add…

Quantitative Methods · Quantitative Biology 2012-11-21 Alex Robson , Kevin Burrage , Mark Leake

Biophysical processes within living systems rely on encounters and interactions between molecules in complex environments such as cells. They are often described by anomalous diffusion transport. Recent advances in single-molecule…

Data Analysis, Statistics and Probability · Physics 2025-02-27 Solomon Asghar , Ran Ni , Giorgio Volpe

A ubiquitous observation in cell biology is that diffusion of macromolecules and organelles is anomalous, and a description simply based on the conventional diffusion equation with diffusion constants measured in dilute solution fails. This…

Soft Condensed Matter · Physics 2013-03-14 Felix Höfling , Thomas Franosch

Recent technological advances in cutting-edge ultrasensitive fluorescence microscopy have allowed single-molecule imaging experiments in living cells across all three domains of life to become commonplace. Single-molecule live-cell data is…

Biomolecules · Quantitative Biology 2015-04-15 Mark Leake

In this article we review classical and recent results in anomalous diffusion and provide mechanisms useful for the study of the fundamentals of certain processes, mainly in condensed matter physics, chemistry and biology. Emphasis will be…

Statistical Mechanics · Physics 2019-02-25 Fernando A. Oliveira , Rogelma M. S. Ferreira , Luciano C. Lapas , Mendeli H. Vainstein

It is well established that a wide variety of phenomena in cellular and molecular biology involve anomalous transport e.g. the statistics for the motility of cells and molecules are fractional and do not conform to the archetypes of simple…

Biological Physics · Physics 2023-10-17 Thomas A. Waigh , Nickolay Korabel

Anomalous diffusion occurs at very different scales in nature, from atomic systems to motions in cell organelles, biological tissues or ecology, and also in artificial materials, such as cement. Being able to accurately measure the…

Machine Learning · Computer Science 2021-08-09 Òscar Garibo i Orts , Miguel A. Garcia-March , J. Alberto Conejero

In a recent paper, Michael J. Saxton proposes to interpret as anomalous diffusion the occurrence of apparent transient sub-diffusive regimes in mean-squared displacements (MSD) plots, calculated from experimental trajectories of molecules…

Subcellular Processes · Quantitative Biology 2009-11-13 Nicolas Destainville , Aude Sauliere , Laurence Salome

Single-particle traces of the diffusive motion of molecules, cells, or animals are by-now routinely measured, similar to stochastic records of stock prices or weather data. Deciphering the stochastic mechanism behind the recorded dynamics…

Statistical Mechanics · Physics 2023-09-14 Henrik Seckler , Janusz Szwabinski , Ralf Metzler

Identifying subtle phenotypic variations in cellular images is critical for advancing biological research and accelerating drug discovery. These variations are often masked by the inherent cellular heterogeneity, making it challenging to…

Computer Vision and Pattern Recognition · Computer Science 2026-01-28 Anis Bourou , Biel Castaño Segade , Thomas Boyer , Valérie Mezger , Auguste Genovesio

We propose a computational method to simulate anomalous self-diffusion in a simple liquid. The method is based on a molecular dynamics simulation on which we impose the following two conditions: firstly, the inter-particle interaction is…

Statistical Mechanics · Physics 2010-04-07 Simon Standaert , Jan Ryckebusch , Lesley De Cruz

Building Virtual Cells that can accurately simulate cellular responses to perturbations is a long-standing goal in systems biology. A fundamental challenge is that high-throughput single-cell sequencing is destructive: the same cell cannot…

Machine Learning · Computer Science 2026-02-24 Xinyu Yuan , Xixian Liu , Ya Shi Zhang , Zuobai Zhang , Hongyu Guo , Jian Tang

The characterization of diffusion processes is a keystone in our understanding of a variety of physical phenomena. Many of these deviate from Brownian motion, giving rise to anomalous diffusion. Various theoretical models exists nowadays to…

Statistical Mechanics · Physics 2024-04-15 Gorka Muñoz-Gil , Guillem Guigó i Corominas , Maciej Lewenstein

A ubiquitous observation in crowded cell membranes is that molecular transport does not follow Fickian diffusion but exhibits subdiffusion. The microscopic origin of such a behaviour is not understood and highly debated. Here we discuss the…

Soft Condensed Matter · Physics 2011-02-15 Felix Höfling , Karl-Ulrich Bamberg , Thomas Franosch

Recent advances in molecular biology and fluorescence microscopy imaging have made possible the inference of the dynamics of single molecules in living cells. Such inference allows to determine the organization and function of the cell. The…

Applications · Statistics 2018-06-20 Vincent Briane , Charles Kervrann , Myriam Vimond

In cell membranes, proteins and lipids diffuse in a highly crowded and heterogeneous landscape, where aggregates and dense domains of proteins or lipids obstruct the path of diffusing molecules. In general, hindered motion gives rise to…

Soft Condensed Matter · Physics 2010-06-16 Margaret R. Horton , Felix Höfling , Joachim O. Rädler , Thomas Franosch

Cellular differentiation is governed by gene regulatory networks, the high-dimensional stochastic biochemical systems that determine the transcriptional landscape and mediate cellular responses to signals and perturbations. Although…

Molecular Networks · Quantitative Biology 2026-04-29 Suryanarayana Maddu , Victor Chardès , Michael J. Shelley

The plasma membrane of living cells is compartmentalized at multiple spatial scales ranging from the nano- to the meso-scale. This non-random organization is crucial for a large number of cellular functions. At the nanoscale, cell membranes…

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