Recent research has shown that motile cells can adapt their mode ofpropulsion to the mechanical properties of the environment in which they findthemselves - crawling in some environments while swimming in others. The lattercan involve movement by blebbing or other cyclic shape changes, and bothhighly-simplified and more realistic models of these modes have been studiedpreviously. Herein we study swimming that is driven by membrane tensiongradients that arise from flows in the actin cortex underlying the membrane,and does not involve imposed cyclic shape changes. Such gradients can lead to anumber of different characteristic cell shapes, and our first objective is tounderstand how different distributions of membrane tension influence the shapeof cells in a quiescent fluid. We then analyze the effects of spatial variationin other membrane properties, and how they interact with tension gradients todetermine the shape. We also study the effect of fluid-cell interactions andshow how tension leads to cell movement, how the balance between tensiongradients and a variable bending modulus determine the shape and direction ofmovement, and how the efficiency of movement depends on the properties of thefluid and the distribution of tension and bending modulus in the membrane.
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