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

Stability Analysis of a Bulk–Surface Reaction Model for Membrane Protein Clustering

(2020) Lucas M. Stolerman et al.   BULLETIN OF MATHEMATICAL BIOLOGY

A bulk-surface reaction-diffusion system for cell polarization

(2020) Barbara Niethammer et al.   INTERFACES AND FREE BOUNDARIES

Localised signalling compartments in 2D coupled by a bulk diffusion field: Quorum sensing and synchronous oscillations in the well-mixed limit

(2020) SARAFA A. IYANIWURA et al.   EUROPEAN JOURNAL OF APPLIED MATHEMATICS

Global existence, uniqueness and stability for nonlinear dissipative bulk-interface interaction systems

(2020) Karoline Disser   JOURNAL OF DIFFERENTIAL EQUATIONS

Pattern formation in a coupled membrane-bulk reaction-diffusion model for intracellular polarization and oscillations

(2020) Frédéric Paquin-Lefebvre et al.   JOURNAL OF THEORETICAL BIOLOGY

Spherical Caps in Cell Polarization

(2018) Rocky Diegmiller et al.   BIOPHYSICAL JOURNAL

Spots, traps, and patches: asymptotic analysis of localized solutions to some linear and nonlinear diffusive systems

(2018) M J Ward   NONLINEARITY

A coupled bulk-surface model for cell polarisation

(2018) D. Cusseddu et al.   JOURNAL OF THEORETICAL BIOLOGY

The nonlinear eigenvalue problem

(2017) Stefan Güttel et al.   ACTA NUMERICA

The bulk-surface finite element method for reaction–diffusion systems on stationary volumes

(2016) Anotida Madzvamuse et al.   FINITE ELEMENTS IN ANALYSIS AND DESIGN

An Asymptotic Analysis of a 2-D Model of Dynamically Active Compartments Coupled by Bulk Diffusion

(2016) J. Gou et al.   JOURNAL OF NONLINEAR SCIENCE

Oscillation helps to get division right

(2016) David J. Sherratt   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

Explicitly Solvable Nonlocal Eigenvalue Problems and the Stability of Localized Stripes in Reaction-Diffusion Systems

(2016) I. Moyles et al.   STUDIES IN APPLIED MATHEMATICS

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

(2015) A. Madzvamuse et al.   PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES

Individual-Based Model for Quorum Sensing with Background Flow

(2014) Hannes Uecke et al.   BULLETIN OF MATHEMATICAL BIOLOGY

Membrane Binding of MinE Allows for a Comprehensive Description of Min-Protein Pattern Formation

(2013) Mike Bonny et al.   PLoS Computational Biology

Approximating the dynamics of communicating cells in a diffusive medium by ODEs—homogenization with localization

(2012) Johannes Müller et al.   JOURNAL OF MATHEMATICAL BIOLOGY

Oscillatory Dynamics of Cdc42 GTPase in the Control of Polarized Growth

(2012) M. Das et al.   SCIENCE

Highly Canalized MinD Transfer and MinE Sequestration Explain the Origin of Robust MinCDE-Protein Dynamics

(2012) Jacob Halatek et al.   Cell Reports

Turing instabilities in a mathematical model for signaling networks

(2011) Andreas Rätz et al.   JOURNAL OF MATHEMATICAL BIOLOGY

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

(2011) Yoichiro Mori et al.   SIAM JOURNAL ON APPLIED MATHEMATICS

A Comparison of Mathematical Models for Polarization of Single Eukaryotic Cells in Response to Guided Cues

(2011) Alexandra Jilkine et al.   PLoS Computational Biology

The Onset of Collective Behavior in Social Amoebae

(2010) T. Gregor et al.   SCIENCE