5 papers
Elastic bilayer membranes under confinement -- Existence, regularity, and rigidity
Matthias Röger, Fabian Rupp
Motivated by applications to cell biology, we study the constrained minimization of the Helfrich energy among closed surfaces confined to a container. We show existence of minimize…
Interface behavior for the solutions of a mass conserving free boundary problem modeling cell polarization
Anna Logioti, Barbara Niethammer, Matthias Röger +1
We consider a parabolic non-local free boundary problem that has been derived as a limit of a bulk-surface reaction-diffusion system which models cell polarization. In previous pap…
A parabolic free boundary problem arising in a model of cell polarization
Anna Logioti, Barbara Niethammer, Matthias Röger +1
The amplification of an external signal is a key step in direction sensing of biological cells. We consider a simple model for the response to a time-depending signal, which was pr…
A bulk-surface reaction-diffusion system for cell polarization
Barbara Niethammer, Matthias Röger, Juan J. L. Velázquez
We propose a model for cell polarization as a response to an external signal which results in a system of PDEs for different variants of a protein on the cell surface and interior…
Global existence for a bulk/surface model for active-transport-induced polarisation in biological cells
Keith Anguige, Matthias Röger
We consider a coupled bulk/surface model for advection and diffusion of interacting chemical species in biological cells. Specifically, we consider a signalling protein that can ex…