Computational Estimates of Membrane Flow and Tension Gradient in Motile Cells

Abstract

All parts of motile cells, including the plasma membrane, have to translocate in the direction of locomotion. Both directed intracellular membrane transport coupled with polarized endo- and exocytosis and fluid flow in the plane of the plasma membrane can contribute to this overall plasma membrane translocation. It remains unclear how strong a force is required to generate this flow. We numerically solve Stokes equations for the viscous membrane flow across a flat plasma membrane surface in the presence of transmembrane proteins attached to the cytoskeleton and find the membrane tension gradient associated with this flow. This gradient is sensitive to the size and density of the transmembrane proteins attached to the cytoskeleton and can become significant enough to slow down cell movement. We estimate the influence of intracellular membrane transport and actin growth and contraction on the tension gradient, and discuss possible ‘tank tread’ flow at ventral and dorsal surfaces.

Front-to-Rear Membrane Tension Gradient in Rapidly Moving Cells

“…Previous studies generally have mostly assumed, based on the fluid nature of the membrane and the lack of bulk membrane flow, that the tension distribution is homogenous during steady movement (8,19,21). However, recent theoretical studies suggest that steady-state gradients in the lateral tension can develop in the membranes of moving cells (9,10). The measurements presented here indeed show that measurable tension gradients exist in steadily moving keratocytes.…”

“…The lack of membrane flow in the cell frame of reference of motile cells implies that the tension gradient that develops in the membrane counterbalances the frictional drag on the membrane generated by the treadmilling cytoskeleton. The magnitude of the tension gradient is predicted to strongly depend on the density and distribution of the cytoskeleton-attached membrane anchors and adhesion complexes, and reasonable values of this density should lead to a considerable tension difference between the leading and trailing edges of motile cells (9,10). Here, we test these predictions experimentally by examining the membranetension distribution in fish epithelial keratocytes, which are notorious for their persistent and rapid movement (3,18,19).…”

“…During persistent cell movement, however, the plasma membrane undergoes a two-dimensional flow, and steady-state gradients in membrane tension could arise. Two recent studies (9,10) analyzed this situation theoretically and showed that the primary factor generating a steady-state gradient of membrane tension is an effective viscous friction associated with movement of the cell membrane relative to the actin cytoskeleton in motile cells. This friction is mainly due to transmembrane anchors and adhesion proteins that are bound to the actin network and treadmill rearward with it.…”

“…The movement of these cytoskeleton-attached membrane proteins within the viscous lipid bilayer generates frictional drag. The cumulative drag force increases steeply with the area fraction of the transmembrane cytoskeleton-attached anchors (9,10).…”

Water flow prediction for membranes using 3D simulations with detailed morphology

“…For many years, approximate analytical formulae (such as Kozeny-Carman model [7,8].) have been used to correlate the membrane morphology and the fluxes through it.…”