Related papers: Cell migration: Beyond Brownian motion
A simple model is proposed that describes the various morphodynamic principles of migrating cells from polar to amoeboidal motions. The model equation is derived using competing internal cellular compass variables and symmetries of the…
A dynamical treatment of Markovian diffusion is presented and several applications discussed. The stochastic interpretation of quantum mechanics is considered within this framework. A model for Brownian movement which includes second order…
Cell migration is often accompanied by collisions with other cells, which can lead to cessation of movement, repolarization, and migration away from the contact site - a process termed contact inhibition of locomotion (CIL). During CIL, the…
Binding and unbinding of ligands to specific sites of a macromolecule are one of the most elementary molecular interactions inside the cell that embody the computational processes of biological regulations. The interaction between…
This paper is a review of the recent progresses on the branching brownian motion seen from its left-most particule. We describe in particular the recent works by Arguin-Bovier-Kistler and A\"id\'ekon-Berestycki-Brunet-Shi. This is the text…
This paper theoretically analyzes a phenomenological stochastic model for bacterial growth. This model comprises cell division and the linear growth of cells, where growth rates and cell cycles are drawn from lognormal distributions. We…
Cell proliferation and cell movement are fundamentally stochastic processes which lead to variability in the growth and spatial structure of cell populations in many biological settings, such as cell invasion, wound healing, and tumour…
We provide a new, concise proof of weak existence and uniqueness of solutions to the stochastic differential equation for the multidimensional skew Brownian motion. We also present an application to Brownian particles with skew-elastic…
Nucleic acids and proteins are not only biologically important polymers: They have recently been recognized as novel functional materials surpassing in many aspects the conventional ones. Although Herculean efforts have been undertaken to…
I review theoretical treatments of diffusion in crowded (i.~e., non-dilute) solutions of globular macromolecules. The focus is on the classical statistico-mechanical literature, much of which dates to before 1990. Classes of theoretical…
Cell biomechanics involve a great number of complex phenomena that are fundamental to the evolution of life itself and other associated processes, ranging from the very early stages of embryo-genesis to the maintenance of damaged structures…
Although understanding the collective migration of cells, such as that seen in epithelial sheets, is essential for understanding diseases such as metastatic cancer, this motion is not yet as well characterized as individual cell migration.…
Cell movement has essential functions in development, immunity and cancer. Various cell migration patterns have been reported and a general rule has recently emerged, the so-called UCSP (Universal Coupling between cell Speed and cell…
Molecular motion through pores plays a crucial role in various natural and industrial processes. One of the most fascinating features of biological channel-facilitated transport is a stochastic gating process, when the channels dynamically…
We revisit the one-dimensional stochastic model of Lubensky and Nelson [Biophys. J 77, 1824 (1999)] for the electrically driven translocation of polynucleotides through alpha-hemolysin pores. We show that the model correctly describes two…
These notes provide a review of basic stochastic population models including branching processes and models of population genetics. Measure-valued population models including superprocesses and Fleming-Viot processes are also introduced…
This paper explores stochastic modeling approaches to elucidate the intricate dynamics of stock prices and volatility in financial markets. Beginning with an overview of Brownian motion and its historical significance in finance, we delve…
Long cell protrusions, which are effectively one-dimensional, are highly dynamic subcellular structures. Length of many such protrusions keep fluctuating about the mean value even in the the steady state. We develop here a stochastic model…
This review is an introduction to theoretical models and mathematical calculations for biological evolution, aimed at physicists. The methods in the field are naturally very similar to those used in statistical physics, although the…
The capability of cells to form surface extensions to non-locally probe the surrounding environment plays a key role in cell migration. The existing mathematical models for migration of cell populations driven by this non-local form of…