Getting in shape and swimming: the role of cortical forces and membrane heterogeneity in eukaryotic cells

Abstract

Recent research has shown that motile cells can adapt their mode of propulsion to the mechanical properties of the environment in which they find themselves – crawling in some environments while swimming in others. The latter can involve movement by blebbing or other cyclic shape changes, and both highly-simplified and more realistic models of these modes have been studied previously. Herein we study swimming that is driven by membrane tension gradients that arise from flows in the actin cortex underlying the membrane, and does not involve imposed cyclic shape changes. Such gradients can lead to a number of different characteristic cell shapes, and our first objective is to understand how different distributions of membrane tension influence the shape of cells in an inviscid quiescent fluid. We then analyze the effects of spatial variation in other membrane properties, and how they interact with tension gradients to determine the shape. We also study the effect of fluid-cell interactions and show how tension leads to cell movement, how the balance between tension gradients and a variable bending modulus determine the shape and direction of movement, and how the efficiency of movement depends on the properties of the fluid and the distribution of tension and bending modulus in the membrane.

The Roles of Signaling in Cytoskeletal Changes, Random Movement, Direction-Sensing and Polarization of Eukaryotic Cells

“…This has been modeled and analyzed [28], and it was shown how characteristics of the protrusions, such as their height, affect the swimmer's speed and efficiency. In addition, it is also known that Dicty cells can swim for several cell lengths without shape changes [29], and it has been shown that they can do so by creating an axial tension gradient in the membrane [17].…”

“…It is thought that a gradient of cortical density and myo-II generates both the cortical flow and an axial pressure gradient in both morphologies, but what initiates the flow remains undetermined [168]. Computations reported in Wu et al [17] show that tension gradients in the cortex can generate large-scale flows sufficient to carry monomers anteriorly, and thus can provide another mechanism for polarization by segregating components via the flow.…”

“…In the first type cells generate a rearward flow of actin in the cortex, which leads to a reactive tension gradient in the membrane that propels the cell forward. This is called the tension- or friction-driven mode [ 17 ]. In the second type cells use actin-rich protrusions called pseudopodia at the leading edge, or by blebbing, in which cycles of extension of the front and retraction of the rear as shown in Figure 2 b are used.…”

“…Protrusions and other shape changes require forces that must be correctly orchestrated in space and time to produce net motion—those on cells in Figure 2 a are not, while those in Figure 2 b are—and to understand this orchestration one must couple the intracellular dynamics with the state of the surrounding fluid or ECM. Tension in and curvature of the membrane and cortex have emerged as important determinants in the orchestration, whether in the context of undirected cell movement, or in movement in response to environmental cues [ 17 ].…”

Eukaryotic cell dynamics from crawlers to swimmers

“…69,186,187 Computational results from a model using a free-energy-based description of the membrane shows that cells can swim under various combinations of tension gradient in the membrane and heterogeneity of the bending rigidity. 69 Moreover, the direction of migration depends on the balance between the cortical tension gradient and the variation of the bending rigidity. This provides an explanation of the observation that some cells move using a small cap in the front, while other cells move with the large bleb in front.…”