Taxis equations for amoeboid cells

Radek Erban, Hans G. Othmer

Research output: Contribution to journalArticlepeer-review

47 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)847-885
Number of pages39
JournalJournal of Mathematical Biology
Issue number6
StatePublished - Jun 2007


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


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