Related papers: Cell migration: Beyond Brownian motion
An innovative extension of Geometric Brownian Motion model is developed by incorporating a weighting factor and a stochastic function modelled as a mixture of power and trigonometric functions. Simulations based on this Modified Brownian…
Recent single molecule experiments probing the passage process of a short single-stranded DNA (ssDNA) through a membrane channel (translocation) allow to measure the passage time distribution. Building on a recent modelling approach (D. K.…
Mathematical and computational models can assist in gaining an understanding of cell behavior at many levels of organization. Here, we review models in the literature that focus on eukaryotic cell motility at 3 size scales: intracellular…
The stochastic trajectories of molecules in living cells, as well as the dynamics in many other complex systems, often exhibit memory in their path over long periods of time. In addition, these systems can show dynamic heterogeneities due…
We introduce a model for stochastic transport on a one-dimensional substrate with particles assuming different conformations during their stepping cycles. These conformations correspond to different footprints on the substrate: in order to…
Based on symmetry consideration of migration and shape deformations, we formulate phenomenologically the dynamics of cell crawling in two dimensions. Forces are introduced to change the cell shape. The shape deformations induce migration of…
The mathematical formulation of the model for molecular movement of single motor proteins driven by cyclic biochemical reactions in an aqueous environment leads to a drifted Brownian motion characterized by coupled diffusion equations. In…
In this article we explore the phenomena of nonequilibrium stochastic process starting from the phenomenological Brownian motion. The essential points are described in terms of Einstein's theory of Brownian motion and then the theory…
The migration of living cells obeys usually the Einstein law of Brownian motion. While the latter is due to the thermal motion of surrounding matter, the cells locomotion is generally associated to their vitality. In the present paper the…
The dynamic interplay between collective cell movement and the various molecules involved in the accompanying cell signalling mechanisms plays a crucial role in many biological processes including normal tissue development and pathological…
In the absence of environmental cues, a migrating cell performs an isotropic random motion. Recently, the breaking of this isotropy has been observed when cells move in the presence of asymmetric adhesive patterns. However, up to now the…
We revisit the modeling framework introduced in [N. Loy and L. Preziosi: Bull. Math. Bio., 85, 2023] to describe the dynamics of cell orientation under cyclic stretch. We propose a reformulation based on the principles of Stochastic…
Amoeboid motion is a dynamic mode of cell motility essential for processes such as the immune response and wound healing. This review examines recent developments in the mathematical and computational modeling of amoeboid crawling, focusing…
Experiments of cell migration and chemotaxis assays have been classically performed in the so-called Boyden Chambers. A recent technology, xCELLigence Real Time Cell Analysis, is now allowing to monitor the cell migration in real time. This…
Long-term videomicroscopy and computer-aided statistical analysis were used to determine some characteristic parameters of in vitro cell motility and proliferation in three established cell lines derived from human glioblastoma tumors.…
The process of diffusion is the most elementary stochastic transport process. Brownian motion, the representative model of diffusion, played a important role in the advancement of scientific fields such as physics, chemistry, biology and…
In this work, we develop a stochastic multiscale model for glioma growth and invasion in the brain, incorporating the effects of therapeutic interventions. The model accounts for tumor cell migration influenced by brain tissue heterogeneity…
Brownian motion is a ubiquitous physical phenomenon across the sciences. After its discovery by Brown and intensive study since the first half of the 20th century, many different aspects of Brownian motion and stochastic processes in…
An individual-based model of stochastic branching is proposed and studied, in which point particles drift in $\bar{\mathds{R}}_{+}:=[0,+\infty)$ towards the origin (edge) with unit speed, where each of them splits into two particles that…
Collective cell migration plays a central role in tissue development, morphogenesis, wound repair and cancer progression. With the growing realization that physical forces mediate cell motility in development and physiology, a key…