Computational Analysis of Amoeboid Swimming at Low Reynolds Number

TL;DR

This paper models amoeboid swimming at low Reynolds number using complex analysis, providing insights into how cell shape and protrusions influence swimming behavior, which can inform the design of artificial microswimmers.

Contribution

It introduces a 2D complex analysis-based model for amoeboid swimming, analyzing the effects of cell shape and protrusions on swimming efficiency at low Reynolds number.

Findings

Cell shape and protrusion geometry significantly affect swimming performance.

The Schwarz-Christoffel transformation effectively models cell protrusions.

Results can guide the design of bio-inspired microswimmers.

Abstract

Recent experimental work has shown that eukaryotic cells can swim in a fluid as well as crawl on a substrate. We investigate the swimming behavior of Dictyostelium discoideum amoebae who swim by initiating traveling protrusions at the front that propagate rearward. In our model we prescribe the velocity at the surface of the swimming cell, and use techniques of complex analysis to develop 2D models that enable us to study the fluid-cell interaction. Shapes that approximate the protrusions used by Dictyostelium discoideum can be generated via the Schwarz-Christoffel transformation, and the boundary- value problem that results for swimmers in the Stokes flow regime is then reduced to an integral equation on the boundary of the unit disk. We analyze the swimming characteristics of several varieties of swimming Dictyostelium discoideum amoebae, and discuss how the slenderness of the cell body and the shapes of the protrusion effect the swimming of these cells. The results may provide guidance in designing low Reynolds number swimming models.