Membrane tension feedback on shape and motility of eukaryotic cells

Abstract

In the framework of a phase field model of a single cell crawling on a substrate, we investigate how the properties of the cell membrane affect the shape and motility of the cell. Since the membrane influences the cell dynamics on multiple levels and provides a nontrivial feedback, we consider the following fundamental interactions: (i) the reduction of the actin polymerization rate by membrane tension; (ii) area conservation of the cell's two-dimensional cross-section vs. conservation of its circumference (i.e. membrane inextensibility); and (iii) the contribution from the membrane's bending energy to the shape and integrity of the cell. As in experiments, we investigate two pertinent observables -the cell's velocity and its aspect ratio. We find that the most important effect is the feedback of membrane tension on the actin polymerization. Bending rigidity has only minor effects, visible mostly in dynamic reshaping events, as exemplified by collisions of the cell with an obstacle.

Cell Membranes Resist Flow

“…Fluorescently tagged transmembrane proteins typically diffuse freely in both artificial bilayers and in intact cells, albeit with a 10-100 fold lower diffusion coefficient in cells (Kusumi et al, 2005). Together these results, each consistent with the fluid mosaic model (Singer and Nicolson, 1972), led to the widespread belief that two-dimensional (2D) flow of lipids in cells mediates rapid intracellular equilibration of membrane tension (Basu et al, 2016; Diz-Muñoz et al, 2013; Fogelson and Mogilner, 2014; Gauthier et al, 2012; Gauthier et al, 2011; Houk et al, 2012; Huse, 2017; Keren et al, 2008; Keren, 2011; Kozlov and Mogilner, 2007; Lieber et al, 2015; Morris and Homann, 2001; Mueller et al, 2017; Mueller et al, 2017; Ofer et al, 2011; Pontes et al, 2017; Saha et al, 2018; Schweitzer et al, 2014; Sens and Plastino, 2015; Watanabe et al, 2013; Winkler et al, 2016), providing a long-range signaling mechanism analogous to the rapid propagation of electrical signals in neurons (Keren, 2011). Some studies have contemplated the possibility of tension gradients in rapidly migrating cells (Basu et al, 2016; Fogelson and Mogilner, 2014; Lieber et al, 2015; Schweitzer et al, 2014), but in these studies the role of membrane-cytoskeleton friction was assumed to be a modest perturbation on the essentially fluid nature of the membrane.…”

Computational approaches to substrate-based cell motility

“…We hence anticipate that they will have an increasing role in the design of biomedical assays for cell sorting, manipulation and analysis, both on structured substrates and in narrow channels or constrictions. 38 Equally successful was the phase-field approach applied to multiple migrating cells. [151][152][153] It was able to reproduce many experimentally observed effects, including inelastic scattering of colliding cells and 'activation' of nonmotile cells by moving cells owing to steric interactions 153 and the emergence of coherently moving or rotating cell clusters, 152,153 as well as the formation of tissue-like stationary clusters.…”

“…While being flexible enough to allow deformation and motion, the membrane is endowed with surface tension and rigidity, which, in turn, also provides a highly nontrivial feedback on cell migration. 23,[36][37][38] For example, membrane tension influences the polymerisation rates of the actin network 12,39 and is involved in the localisation of regulatory elements, e.g., growth factors and actin-related protein (Arp2/3) complexes. 40 As the membrane is very thin (of the order of 4-8 nm compared with typical cell sizes of 20 μm), it is very tempting and intuitive to mathematically describe the membrane as an infinitely thin line, which represents the so-called sharp interface limit (cf.…”

“…It was found 38 that the most important effect is the membrane's counteracting force on actin polymerisation. In contrast, bending rigidity has only minor effects on the shape and migration speed, and is relevant only in reshaping events.…”

“…In contrast, bending rigidity has only minor effects on the shape and migration speed, and is relevant only in reshaping events. 38 The phase-field approach can also be applied to cells exhibiting ameboidal motility, such as neutrophils or the social ameba D. discoideum. 132 The motility mechanism for these cells is not due to tightly controlled actin ratcheting close to the membrane, but rather relies on spontaneous actin polymerisation waves regulated by certain nucleators.…”