Related papers: A stochastic model for protrusion activity
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…
Cell migration often exhibits long-range temporal correlations and anomalous diffusion, even in the absence of external guidance cues such as chemical gradients or topographical constraints. These observations raise a fundamental question:…
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…
Motivated by the goal of understanding the evolution of populations undergoing selection, we consider branching Brownian motion in which particles independently move according to one-dimensional Brownian motion with drift, each particle may…
The dispersal of cells from an initially constrained location is a crucial aspect of many physiological phenomena ranging from morphogenesis to tumour spreading. In such processes, the way cell-cell interactions impact the motion of single…
Mathematical models describing the spatial spreading and invasion of populations of biological cells are often developed in a continuum modelling framework using reaction-diffusion equations. While continuum models based on linear diffusion…
Cell populations invade through a combination of proliferation and motility. Proliferation depends on the internal timing of cell division: how long cells take to complete the cell cycle. This timing varies substantially within (and across)…
Numerous physical models have been proposed to explain how cell motility emerges from internal activity, mostly focused on how crawling motion arises from internal processes. Here we offer a classification of self-propulsion mechanisms…
We present a deformation-dependent propulsion phenomenon for soft particles such as cells in microchannels. It is based on a broken time reversal symmetry generated by a fast forward and slow backward motion of a fluid which does not…
Cell-cell adhesion is one the most fundamental mechanisms regulating collective cell migration during tissue development, homeostasis and repair, allowing cell populations to self-organize and eventually form and maintain complex tissue…
Lattice-based random walk models are widely used to study populations of migrating cells with motility bias and proliferation. Crowding is typically represented by volume exclusion, where each lattice site can be occupied by at most one…
Modelling the transmission dynamics of an infectious disease is a complex task. Not only it is difficult to accurately model the inherent non-stationarity and heterogeneity of transmission, but it is nearly impossible to describe,…
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…
Cell polarization underlies many cellular processes, such as differentiation, migration, and budding. Many living cells, such as budding yeast and fission yeast, use cytoskeletal structures to actively transport proteins to one location on…
Self-activation coupled to a transport mechanism results in traveling waves that describe polymerization reactions, forest fires, tumor growth, and even the spread of epidemics. Diffusion is a simple and commonly used model of particle…
Collective cell migration is a multicellular phenomenon that arises in various biological contexts, including cancer and embryo development. "Collectiveness" can be promoted by cell-cell interactions such as co-attraction and contact…
Recent experiments suggest that the interplay between cells and the mechanics of their substrate gives rise to a diversity of morphological and migrational behaviors. Here, we develop a Cellular Potts Model of polarizing cells on a…
Density dependence is important in the ecology and evolution of microbial and cancer cells. Typically, we can only measure net growth rates, but the underlying density-dependent mechanisms that give rise to the observed dynamics can…
While it is commonly observed that the shape dynamics of mammalian cells can undergo large random fluctuations, theoretical models aiming at capturing cell mechanics often focus on the deterministic part of the motion. In this paper, we…
In this paper, we study a model of self-generated directional cell migration on viscoelastic substrates in the absence of apparent intrinsic polarity. This model, first proposed in \cite{Clark}, was observed numerically to manifest…