相关论文: Mathematical models in biology
We introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion for modelling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or…
As the closest unicellular relatives of animals, choanoflagellates serve as useful model organisms for understanding the evolution of animal multicellularity. An important factor in animal evolution was the increasing ocean oxygen levels in…
Chemotaxis is a ubiquitous biological phenomenon in which cells detect a spatial gradient of chemoattractant, and then move towards the source. Here we present a position-dependent advection-diffusion model that quantitatively describes the…
Motivated by observations of the dynamics of {\it Myxococcus xanthus}, we present a self-interacting random walk model that describes the competition between chemokinesis and chemotaxis. Cells are constrained to move in one dimension, but…
Motile bacteria can migrate along chemical gradients in a process known as chemotaxis. When exposed to uniform environmental stress, Escherichia coli cells coordinate their chemotactic responses to form millimeter-sized condensates…
The purpose of this work is the study of \textit{chemotaxis} and how to model it through the equations of Keller-Segel. \textit{Chemotaxis} is a natural process which induces the organisms to direct their movement according to certain…
A connection is established between discrete stochastic model describing microscopic motion of fluctuating cells, and macroscopic equations describing dynamics of cellular density. Cells move towards chemical gradient (process called…
Bacteria track chemical gradients using a biased random walk, a process called chemotaxis. Experiments suggest that bacteria also communicate during this process. Using a mathematical model, we find that sufficiently strong communication…
Living cells are capable of interacting with their environments in a variety of ways, including cell signalling, adhesion, and directed motion. These behaviours are often mediated by receptor molecules embedded in the cell membrane, which…
Cell shape is determined by a balance of intrinsic properties of the cell as well as its mechanochemical environment. Inhomogeneous shape changes underly many morphogenetic events and involve spatial gradients in active cellular forces…
Biological cells are able to adapt their behaviour in response to environmental cues. Durotaxis is a phenomenon in which cells adjust their migration depending on the mechanical properties of a surrounding substrate. Although durotaxis has…
Many processes in biology involve both reactions and chemotaxis. However, to the best of our knowledge, the question of interaction between chemotaxis and reactions has not yet been addressed either analytically or numerically. We consider…
Endothelial cells are responsible for the formation of the capillary blood vessel network. We describe a system of endothelial cells by means of two-dimensional molecular dynamics simulations of point-like particles. Cells' motion is…
We discuss recent progress in the theoretical description of chemotaxis by coupling the diffusion equation of a chemical species to equations describing the motion of sensing microorganisms. In particular, we discuss models for…
During neurodevelopment, neuronal axons navigate through the extracellular environment, guided by various cues to establish connections with distant target cells. Among other factors, axon trajectories are influenced by heterogeneities in…
Chemotaxis in bacteria such as \textit{E.\ coli} is controlled by the slow methylation of chemoreceptors. As a consequence, intrinsic time and length scales of tens of seconds and hundreds of micrometers emerge, making the Keller--Segel…
Collective migration -- the directed, coordinated motion of many self-propelled agents -- is a fascinating emergent behavior exhibited by active matter that has key functional implications for biological systems. Extensive studies have…
It is of great biological interest to understand the molecular origins of chemotactic behavior of E. coli by developing population-level models based on the underlying signaling pathway dynamics. We derive macroscopic models for E.coli…
Flagellated bacteria, such as Escherichia coli, perform directed motion in gradients of concentration of attractants and repellents in a process called chemotaxis. The E. coli chemotaxis signaling pathway is a model for signal transduction,…
Background: Living cells of many types need to move in response to external stimuli in order to accomplish their functional tasks; these tasks range from wound healing to immune response to fertilization. While the directional motion is…