Computational analysis of amoeboid swimming at low Reynolds number

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.

Progress and perspectives in signal transduction, actin dynamics, and movement at the cell and tissue level: lessons fromDictyostelium

“…As is shown in figure 8, swimming by extending protrusions is mostly asymmetric in that they alternate sides, and thus the motion is not rotation-free and the trajectory of a swimming cell is snake-like rather than along a straight line. These characteristics of several varieties of swimming Dd amoebae have been reproduced with a computational model [65], and compared with the data described above. The computational model enables one to study how the slenderness of the cell body and the shapes of the protrusion affect the swimming of these cells, and to predict the power consumption and the efficiency of the different varieties.…”

“…Thus there is no clear evidence that the cell is rotating around its symmetry axis, and as a result a two-dimensional model developed in [65] is a reasonable simplification of a threedimensional swimming cell. As is shown in figure 8, swimming by extending protrusions is mostly asymmetric in that they alternate sides, and thus the motion is not rotation-free and the trajectory of a swimming cell is snake-like rather than along a straight line.…”

The performance of discrete models of low reynolds number swimmers

“…This has units of 1/force. When the volume changes are small several conclusions can be reached analytically [42,41]. Since a swimming stroke is a closed path in the v 1 − v 3 plane or equivalently, a closed path in the a 1 − a 3 plane, we find the following relation between the differential displacementdx and the differential controls (da 1 , da 3 ) from (24)…”

Optimal Strokes of Low Reynolds Number Linked-Sphere Swimmers

“…In addition, the numerical scheme presented here can be applied to more advanced LRN swimming systems. For example, it can be applied for general 2D and 3D swimmers, when the swimmer shapes can be represented by conformal mappings or spherical harmonics [35,58,57,56].…”