Emken, Natalie: A coupled bulk-surface reaction-diffusion-advection model for cell polarization. 2016
Content
- Contents
- Introduction
- Biological preliminaries
- The mechanism of cell polarity
- The role of the cytoskeleton
- The Rho GTPases as key regulators in cell polarity
- Yeast as a model system for cell polarity
- Mathematical preliminaries
- Mathematics of reaction-diffusion-advection equations
- Conservation principles
- Diffusion and advection
- Initial and boundary conditions
- Systems of reaction-diffusion-advection equations
- Stability analysis
- Turing instability and pattern formation
- Traveling waves in reaction-diffusion equations
- Sobolev spaces and the weak formulations
- Coupled bulk-surface PDEs
- Numerical methods
- Triangulations and ansatz spaces
- Finite Elements and the Galerkin method
- Finite volume methods
- Time discretization
- Computational implementation
- The DUNE framework
- Numerical treatment of coupled bulk-surface problems
- Dual grid assembly
- The implementation of test problems
- Discussion
- A continuous reaction-diffusion-advection model for yeast cell polarization
- The reaction-diffusion system
- The reaction-diffusion-advection system
- Numerical simulations
- Polarization in the absence of actin-mediated transport
- Enhanced polarization by actin-mediated transport
- Actin-mediated transport in the absence of Bem1
- Actin-mediated transport in the absence of GDI
- Model comparison
- Discussion
- Derivation of a generic bulk-surface reaction-diffusion-advection system
- Model reduction
- Non-dimensionalization
- The generic coupled bulk-surface reaction-diffusion-advection system
- Linear stability analysis
- Discussion
- A stochastic approach to vesicular trafficking-mediated cell polarity
- Summary and outlook
- Chemical reactions
- Spherical harmonics
- Glossary
- Notation and symbols
- Bibliography