• Corpus ID: 252683258

Generation and motion of interfaces in a mass-conserving reaction-diffusion system

  title={Generation and motion of interfaces in a mass-conserving reaction-diffusion system},
  author={Pearson W. Miller and Daniel Fortunato and Matteo Novaga and Stanislav Y. Shvartsman and Cyrill B. Muratov},
Reaction-diffusion models with nonlocal constraints naturally arise as limiting cases of coupled bulk-surface models of intracellular signalling. In this paper, a minimal, mass-conserving model of cell-polarization on a curved membrane is analyzed in the limit of slow surface diffusion. Using the tools of formal asymptotics and calculus of variations, we study the characteristic wave-pinning behavior of this system on three dynamical timescales. On the short timescale, generation of an… 



Asymptotic and Bifurcation Analysis of Wave-Pinning in a Reaction-Diffusion Model for Cell Polarization

A bistable reaction-diffusion model for two interconverting chemical species that exhibits a phenomenon of wave-pinning is described and two ways in which the pinned solution can be lost depending on the details of the reaction kinetics are described: a saddle-node or a pitchfork bifurcation.

Symmetry breaking in a bulk–surface reaction–diffusion model for signalling networks

Signalling molecules play an important role for many cellular functions. We investigate here a general system of two membrane reaction–diffusion equations coupled to a diffusion equation inside the

Well-posedness and fast-diffusion limit for a bulk–surface reaction–diffusion system

We analyze a certain class of coupled bulk–surface reaction–drift–diffusion systems arising in the modeling of signalling networks in biological cells. The coupling is by a nonlinear Robin-type

Pattern forming systems coupling linear bulk diffusion to dynamically active membranes or cells

Some analytical and numerical results are presented for pattern formation properties associated with novel types of reaction–diffusion (RD) systems that involve the coupling of bulk diffusion in the

Stability analysis and simulations of coupled bulk-surface reaction–diffusion systems

New models for coupled systems of bulk-surface reaction–diffusion equations on stationary volumes are formulated and Robin-type boundary conditions seem to introduce a boundary layer coupling the bulk and surface dynamics.

Interfacial-curvature-driven coarsening in mass-conserved reaction-diffusion systems

Mass conservation in chemical species appears in a broad class of reaction-diffusion systems (RDs) and is known to bring about coarsening of the pattern in chemical concentration. Recent theoretical

A coupled bulk-surface model for cell polarisation.

Generation and propagation of interfaces for reaction-diffusion equations

Spatial homogenization and internal layers in a reaction-diffusion system

For a system of reaction-diusion equations of activator-inhibitor type, we show that solutions undergo at least three stages of dynamical behaviour when the activator diuses slowly and reacts fast,

A multiple scale pattern formation cascade in reaction-diffusion systems of activator-inhibitor type

A family of singular limits of reaction-diffusion systems of activator-inhibitor type in which stable stationary sharp-interface patterns may form is investigated. For concreteness, the analysis is