The Mathematical Institute, University of Oxford, Eprints Archive

From Individual to Collective Behavior of Unicellular Organisms: Recent Results and Open Problems

Xue, Chuan and Othmer, H. G. and Erban, R. (2009) From Individual to Collective Behavior of Unicellular Organisms: Recent Results and Open Problems. Not specified . (Submitted)

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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.

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:833
Deposited By:Dr M. Stoll
Deposited On:08 Oct 2009 17:23
Last Modified:08 Oct 2009 17:23

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