Related papers: Biomembranes report
A stochastic walker model is proposed to describe the chemotactic guidance of growth cones, i.e. the tips of developing neurites. The model accounts for the influence of both attractive and repulsive chemical cues, which are emitted by the…
Biological cells can exchange messages through soluble molecules or membrane-bound receptors. In particular in the latter case, the interaction is usually located in specific regions of the interacting cells and may depend on or induce…
Many mathematical models for biological phenomena, such as the spread of diseases, are based on reaction-diffusion equations for densities of interacting cell populations. We present a consistent derivation of reaction-diffusion equations…
We introduce a phase field approach for diffusion inside and outside a closed cell with damping and with source terms at the interface. The method is compared to exact solutions (where possible) and the more traditional finite element…
A practical introduction to stochastic modelling of reaction-diffusion processes is presented. No prior knowledge of stochastic simulations is assumed. The methods are explained using illustrative examples. The article starts with the…
A new approach to computing the equilibria and steady-states of biomolecular systems modelled by bond graphs is presented. The approach is illustrated using a model of a biomolecular cycle representing a membrane transporter and a model of…
A hybrid stochastic individual-based model of proliferating cells with chemotaxis is presented. The model is expressed by a branching diffusion process coupled to a partial differential equation describing concentration of a chemotactic…
In this article we highlight chemotaxis (cellular movement) as a rich source of potential engineering applications and computational models, highlighting current research and possible future work. We first give a brief description of the…
Free boundaries of biofilms advancing on surfaces evolve according to conservation laws coupled with systems of partial differential equations for velocities, pressures and chemicals affecting cell behavior. Thin film approximations lead to…
We consider a system of reaction-diffusion equations including chemotaxis terms and coming out of the modeling of multiple sclerosis. The global existence of strong solutions to this system in any dimension is proved, and it is also shown…
This paper concerns a model for tumor cell migration through the surrounding extracellular matrix by considering mass balance phenomena involving the chemical interactions produced on the cell surface. The well-posedness of this model is…
We study a chemotaxis-consumption mechanism, in which some chemical signal and cells density interact each other. In order to control the concentration of such a population, sources involving gradient nonlinearities, which introduce a…
In this paper we develop a field-theoretic description for run and tumble chemotaxis, based on a density functional description of crystalline materials modified to capture orientational ordering. We show that this framework, with its…
We investigate the (reduced) Keller-Segel equations modeling chemotaxis of bio-organisms. We present a formal derivation and partial rigorous results of the blowup dynamics of solution of these equations describing the chemotactic…
Stochastic reaction-diffusion processes may be presented in terms of integrable quantum chains and can be used to describe various biological and chemical systems. Exploiting the integrability of the models one finds in some cases good…
Population dynamics and in particular microbial population dynamics, though they are complex but also intrinsically discrete and random, are conventionally represented as deterministic differential equations systems. We propose to revisit…
Chemotaxis refers to the directed movement of cells in response to a chemical signal called chemoattractant. A crucial point in the mathematical modeling of chemotactic processes is the correct description of the chemotactic sensitivity and…
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…
This paper deals with the micro-macro derivation of virus models coupled with a reaction diffusion models that generates the dynamics in space of the virus particles. The first part of the presentation focuses, starting from [5, 6] on a…
We introduce a simulation strategy to consistently couple continuum biomembrane dynamics to the motion of discrete biological macromolecules residing within or on the membrane. The methodology is used to study the diffusion of integral…