Cellular diffusion processes in singularly perturbed domains
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909246183964672 |
|---|---|
| author | Bressloff, Paul C |
| author_facet | Bressloff, Paul C |
| contents | There are many processes in cell biology that can be modeled in terms of particles diffusing in a two-dimensional (2D) or three-dimensional (3D) bounded domain $Ω\subset \R^d$ containing a set of small subdomains or interior compartments $\calU_j$, $j=1,\ldots,N$ (singularly-perturbed diffusion problems). The domain $Ω$ could represent the cell membrane, the cell cytoplasm, the cell nucleus or the extracellular volume, while an individual compartment could represent a synapse, a membrane protein cluster, a biological condensate, or a quorum sensing bacterial cell. In this review we use a combination of matched asymptotic analysis and Green's function methods to solve a general type of singular boundary value problems (BVP) in 2D and 3D, in which an inhomogeneous Robin condition is imposed on each interior boundary $\partial \calU_j$. This allows us to incorporate a variety of previous studies of singularly perturbed diffusion problems into a single mathematical modeling framework. We mainly focus on steady-state solutions and the approach to steady-state, but also highlight some of the current challenges in dealing with time-dependent solutions and randomly switching processes |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_05747 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cellular diffusion processes in singularly perturbed domains Bressloff, Paul C Analysis of PDEs Quantitative Methods There are many processes in cell biology that can be modeled in terms of particles diffusing in a two-dimensional (2D) or three-dimensional (3D) bounded domain $Ω\subset \R^d$ containing a set of small subdomains or interior compartments $\calU_j$, $j=1,\ldots,N$ (singularly-perturbed diffusion problems). The domain $Ω$ could represent the cell membrane, the cell cytoplasm, the cell nucleus or the extracellular volume, while an individual compartment could represent a synapse, a membrane protein cluster, a biological condensate, or a quorum sensing bacterial cell. In this review we use a combination of matched asymptotic analysis and Green's function methods to solve a general type of singular boundary value problems (BVP) in 2D and 3D, in which an inhomogeneous Robin condition is imposed on each interior boundary $\partial \calU_j$. This allows us to incorporate a variety of previous studies of singularly perturbed diffusion problems into a single mathematical modeling framework. We mainly focus on steady-state solutions and the approach to steady-state, but also highlight some of the current challenges in dealing with time-dependent solutions and randomly switching processes |
| title | Cellular diffusion processes in singularly perturbed domains |
| topic | Analysis of PDEs Quantitative Methods |
| url | https://arxiv.org/abs/2407.05747 |