Abstract
The collective movements of unicellular organisms such as bacteria or amoeboid (crawling) cells are often modeled by partial differential equations (PDEs) that describe the time evolution of cell density. In particular, chemotaxis equations have been used to model the movement towards various kinds of extracellular cues. Well-developed analytical and numerical methods for analyzing the time-dependent and time-independent properties of solutions make this approach attractive. However, these models are often based on phenomenological descriptions of cell fluxes with no direct correspondence to individual cell processes such signal transduction and cell movement. This leads to the question of how to justify these macroscopic PDEs from microscopic descriptions of cells, and how to relate the macroscopic quantities in these PDEs to individual-level parameters. Here we summarize recent progress on this question in the context of bacterial and amoeboid chemotaxis, and formulate several open problems.
| Original language | English (US) |
|---|---|
| Title of host publication | AIP Conference Proceedings |
| Publisher | AIP Publishing |
| Pages | 3-14 |
| Number of pages | 12 |
| ISBN (Print) | 9780735407046 |
| DOIs | |
| State | Published - Sep 23 2009 |
| Externally published | Yes |
Bibliographical note
KAUST Repository Item: Exported on 2020-10-01Acknowledged KAUST grant number(s): KUK-Cl-013-04
Acknowledgements: This research was supported in part by NSF Grant DMS # 0817529 and NIH Grant 02911123 (HGO), by the Mathematical Biosciences Institute via a post-doctoral fellowship (CX) and by Somerville College, University of Oxford (RE). This publication is based on work supported by Award No. KUK-Cl-013-04, made by King Abdullah University of Science and Technology (KAUST) (RE).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.