Hydrodynamic narrowing of tubes extruded from cells

Abstract

We discuss the pulling force f required to extrude a lipid tube from a living cell as a function of the extrusion velocity L . The main feature is membrane friction on the cytoskeleton. As recently observed for neutrophils, the tether force exhibits a ''shear thinning'' response over a large range of pulling velocities, which was previously interpreted by assuming viscoelastic flows of the sliding membrane. Here, we propose an alternative explanation based on purely Newtonian flow: The diameter of the tether decreases concomitantly with the increase of the membrane tension in the lipid tube. The pulling force is found to vary as L 1/3 , which is consistent with reported experimental data for various types of cells.cytoskeleton ͉ dynamics ͉ membrane tethers M any cellular processes [such as intracellular trafficking (1) or intercellular organelle transport (2)] involve the formation of thin tubular structures known as tethers. Membranous tails also are observed to be left by migrating cells in culture dishes (3). Tethers can be extracted from synthetic vesicles or living cells by the application of an external point force [using a fluid drag (4, 5) or pipette-tweezer system (6, 7)]. In the case of living cells, where the lipidic membrane is coupled to a cytoskeleton, tethers can be used as membrane sensors to measure the membrane-cytoskeleton adhesion energy W 0 (8-12).Our aim here is to describe the formation of a tether and to derive the required pulling force as a function of the extrusion velocity. Pulling a tube from a cell membrane implies a surface flow of lipid from the cell body to the tether through the membranecytoskeleton binders. This viscous drag gives rise to an increase of the membrane tension in the tube and a decrease of its radius. Statics of ExtrusionWe follow the thermodynamic analysis of tether formation proposed by Waugh and coworkers (7,13,14), Evans and Yeung (15), and Derényi and coworkers (16) for lipidic bilayers and extended to cell membranes by Sheetz and coworkers (10, 12). As shown in Fig. 1, the cell is usually held by micropipette suction (pressure Ϫ⌬P) that sets the membrane tension of the cell : 2 Ӎ R p ⌬P, where R p is the radius of the micropipette. The length of the tongue in the pipette is L p . Another case of experimental interest is found when cells are spread onto an adhesive surface, which ensures that the membrane tension remains weak or constant during the time course of the experiment. The tube is then either extruded by pulling out a small bead adhering to the membrane via micromanipulation if the cell is firmly adhered or, more simply, by applying a hydrodynamic flow over the cell in case of a discrete and sparse adhesion site. The length of the tube is L, the membrane tension of the tube is t , and its radius is r t . We want to relate r t and t to , the tension of the cell body, and to W 0 , the adhesion energy of the membrane to the cytoskeleton. The pulling force f 0 is deduced from the following four equations. The distribution of areas:2 r t dL ϭ 2 R p dL p...

The effect of cellular cholesterol on membrane-cytoskeleton adhesion

“…There are different theories for the analysis of the function F(V t ), including power law (Brochard-Wyart et al, 2006;Evans et al, 2005;Heinrich et al, 2005) and linear relationship . In our experimental regime, the linear relationship F=F 0 +2 eff V t worked well.…”

“…tether force) needed to pull a tether from the membrane at a constant velocity V t is measured and then the dependence of F on V t is analyzed (Brochard-Wyart et al, 2006;Evans et al, 2005;Hochmuth et al, 1996). In most cases this dependence is accurately described by the relationship F=F 0 +2 eff V t , which is used to evaluate the membrane surface viscosity eff and the threshold pulling force F 0 .…”

Dynamical organization of the cytoskeletal cortex probed by micropipette aspiration

“…Only the contractile tension γ myo ð∼5 mN∕mÞ, which is also controlled by myosin and actin density, is relevant. PM linkers (26): ηðLÞ ∼ η b ð1 þ L∕R p Þ, where the effective membrane friction η b includes friction with the pipette walls. The value η b ¼ 130 Pa s∕μm evaluated in SI Text predicts a bare membrane velocity consistent with our observations (∼μm∕s for ΔP ¼ 1 kPa).…”

Processivity and collectivity of biomolecular motors extracting membrane nanotubes

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“…[9][10][11][12][13][14][15] remarkably fall into the viscosity range η m 10 −10 -10 −9 Pa m s. This is within the dominance of the tip force, because of the artificiality of PC membranes rather than the processivity of the motors. In contrast, biological membranes are more viscous (η m 10 −8 Pa m s [20,21]) and hence susceptible to the drag exerted by stem motors. For instance, tubulation in a neuron (η m 10 −8 Pa m s [20]) by kinesins (P 100 at, say, ρ = 500 μm −2 ) falls into the stem regime.…”