Journal of Mathematical Biology

, Volume 54, Issue 6, pp 847–885 | Cite as

Taxis equations for amoeboid cells

  • Radek Erban
  • Hans G. Othmer


The classical macroscopic chemotaxis equations have previously been derived from an individual-based description of the tactic response of cells that use a “run-and-tumble” strategy in response to environmental cues [17,18]. Here we derive macroscopic equations for the more complex type of behavioral response characteristic of crawling cells, which detect a signal, extract directional information from a scalar concentration field, and change their motile behavior accordingly. We present several models of increasing complexity for which the derivation of population-level equations is possible, and we show how experimentally measured statistics can be obtained from the transport equation formalism. We also show that amoeboid cells that do not adapt to constant signals can still aggregate in steady gradients, but not in response to periodic waves. This is in contrast to the case of cells that use a “run-and-tumble” strategy, where adaptation is essential.


Amoeboid cells Microscopic models Direction sensing Aggregation Chemotaxis equation Velocity jump process 

Mathematics Subject Classification (2000)

35Q80 60J15 65U05 92B05 35B05 92C17 


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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Mathematical InstituteUniversity of OxfordOxfordUK
  2. 2.School of MathematicsUniversity of MinnesotaMinneapolisUSA

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