Taxis equations for amoeboid cells. (English) Zbl 1148.92003
Summary: 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 [R. Erban and H. G. Othmer, SIAM J. Appl. Math. 65, No. 2, 361–391 (2004; Zbl 1073.35116), Multiscale Model. Simul. 3, No. 2, 362–394 (2005; Zbl 1073.35205)]. 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.
MSC:
| 92C17 | Cell movement (chemotaxis, etc.) |
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
| 35B05 | Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs |
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
Keywords:
amoeboid cells; microscopic models; direction sensing; aggregation; chemotaxis equation; velocity jump processReferences:
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