Effect of Cytoskeleton Elasticity on Amoeboid Swimming

Abstract

Recently, it has been reported that the cells of the immune system, as well as Dictyostelium amoebae, can swim in a bulk fluid by changing their shape repeatedly. We refer to this motion as amoeboid swimming. Here, we explore how the propulsion and the deformation of the cell emerge as an interplay between the active forces that the cell employs to activate the shape changes and the passive, viscoelastic response of the cell membrane, the cytoskeleton, and the surrounding environment. We introduce a model in which the cell is represented by an elastic capsule enclosing a viscous liquid. The motion of the cell is activated by time-dependent forces distributed along its surface. The model is solved numerically using the boundary integral formulation. The cell can swim in a fluid medium using cyclic deformations or strokes. We measure the swimming velocity of the cell as a function of the force amplitude, the stroke frequency, and the viscoelastic properties of the cell and the medium. We show that an increase in the shear modulus leads both to a regular slowdown of the swimming, which is more pronounced for more deflated swimmers, and to a tendency toward cell buckling. For a given stroke frequency, the swimming velocity shows a quadratic dependence on force amplitude for small forces, as expected, but saturates for large forces. We propose a scaling relationship for the dependence of swimming velocity on the relevant parameters that qualitatively reproduces the numerical results and allows us to define regimes in which the cell motility is dominated by elastic response or by the effective cortex viscosity. This leads to an estimate of the effective cortex viscosity of 10 Pa ⋅ s for which the two effects are comparable, which is close to that provided by several experiments.

Amoeboid swimming in a compliant channel

“…It will be interesting to investigate the impact of other parameters such as dimensionless active force and confinement on the swimming dynamics in future studies in order to explore full potential of the present model. Our earlier three dimensional studies on an amoeboid swimming [35,90] did not reveal any new interesting features as compared to the two dimensional studies [36,37]. Thus we performed two dimensional investigation in this article.…”

“…We consider viscosity of enclosing and suspending fluid to be equal for simplification. Our previous study [90] investigated effects of viscosity contrast on the swimming dynamics but did not divulge any new findings. The enclosing and suspending fluid and cell cortex act as a dashpots in parallel and are responsible for dissipation within the system.…”

Cell surface excess is essential for protrusions and motility in 3D matrix

“…It should also be noted that the majority of information about blebs has come from studies of cells spread on a solid 2D substrate or during artificially induced blebbing [65][66][67][68][69][70][71][72][73]. Moreover, for purposes such as the estimation of cortex thickness or modeling the biomechanical properties [73][74][75][76][77] it was often assumed that the membrane and actin cortex are two perfectly smooth concentric layers with uniform density. However, bearing in mind that the plasma membrane is essentially not stretchable, under this assumption the process of blebbing would not be possible because in order to develop one typical bleb with a radius of r=1 µm, an additional plasma membrane area of ~12 µm 2 is required.…”