相关论文: Coarsening dynamics of chemotactic aggregates
Cellular aggregates play a significant role in the evolution of biological systems such as tumor growth, tissue spreading, wound healing, and biofilm formation. Analysis of such biological systems, in principle, includes examining the…
Active particles with their characteristic feature of self-propulsion are regarded as the simplest models for motility in living systems. The accumulation of active particles in low activity regions has led to the general belief that…
Many eukaryotic cells chemotax, sensing and following chemical gradients. However, experiments have shown that even under conditions when single cells cannot chemotax, small clusters may still follow a gradient. This behavior has been…
We analyze the existence, linear stability, and slow dynamics of localized 1D spike patterns for a Keller--Segel model of chemotaxis that includes the effect of logistic growth of the cellular population. Our analysis of localized patterns…
New model equations are derived for dynamics of self-aggregation of finite-size particles. Differences from standard Debye-Huckel and Keller-Segel models are: the mobility of particles depends on the configuration of their neighbors and…
The large scale behaviour of a population of cells that grow and interact through the concentration field of the chemicals they secrete is studied using dynamical renormalization group methods. The combination of the effective long-range…
This paper aims to develop numerical approximations of the Keller--Segel equations that mimic at the discrete level the lower bounds and the energy law of the continuous problem. We solve these equations for two unknowns: the organism (or…
How can repulsive and attractive forces, acting on a conservative system, create stable traveling patterns or branching instabilities? We have proposed to study this question in the framework of the hyperbolic Keller-Segel system with…
Flux-limited Keller-Segel (FLKS) model has been recently derived from kinetic transport models for bacterial chemotaxis and shown to represent better the collective movement observed experimentally. Recently, associated to the kinetic…
Colonies of bacteria grown on thin agar plate exhibit fractal patterns as a result of adaptation to their environments. The bacterial colony pattern formation is regulated crucially by chemotaxis, the movement of cells along a chemical…
We present a simple model that describes the motion of a single chemotactic cell exposed to a traveling wave of the chemoattractant. The model incorporates two types of responses to stimulation by the chemoattractant, i.e., change in…
In this paper we investigate pattern formation in Keller--Segel chemotaxis models over a multi--dimensional bounded domain subject to homogeneous Neumann boundary conditions. It is shown that the positive homogeneous steady state loses its…
Chemotaxis describes the intricate interplay of cellular motion in response to a chemical signal. We here consider the case of slab geometry which models chemotactic motion between two infinite membranes. Like previous works, we are…
Motivated by experimental observations in 3D/organoid cultures derived from glioblastoma, we develop a mathematical model where tumour aggregate formation is obtained as the result of nutrient-limited cell proliferation coupled with…
This paper is concerned with a parabolic-elliptic Keller-Segel system where both diffusive and chemotactic coefficients (motility functions) depend on the chemical signal density. This system was originally proposed by Keller and Segel in…
This paper investigates the formation of time--periodic and stable patterns of a two--competing--species Keller--Segel chemotaxis model with a focus on the effect of cellular growth. We carry out rigorous Hopf bifurcation analysis to obtain…
As motivated by studies of cellular motility driven by spatiotemporal chemotactic gradients in microdevices, we develop a framework for constructing approximate analytical solutions for the location, speed and cellular densities for cell…
We present a generalized Keller-Segel model where an arbitrary number of chemical compounds react, some of which are produced by a species, and one of which is a chemoattractant for the species. To investigate the stability of homogeneous…
Aggregation of animal cells in culture comprises a series of motility, collision and adhesion processes of basic relevance for tissue engineering, bioseparations, oncology research and \textit{in vitro} drug testing. In the present paper, a…
Aerotaxis is the particular form of chemotaxis in which oxygen plays the role of both the attractant and the repellent. Aerotaxis occurs without methylation adaptation, and it leads to fast and complete aggregation toward the most favorable…