Determination of bilayer membrane bending stiffness by tether formation from giant, thin-walled vesicles.

The curvature elastic modulus (bending stiffness) of stearoyloleoyl phosphatidylcholine (SOPC) bilayer membrane is determined from membrane tether formation experiments. R. E. Waugh and R. M. Hochmuth 1987. Biophys. J. 52:391-400) have shown that the radius of a bilayer cylinder (tether) is inversely related to the force supported along its axis. The coefficient that relates the axial force on the tether to the tether radius is the membrane bending stiffness. Thus, the bending stiffness can be calculated directly from measurements of the tether radius as a function of force. Giant (10-50-microns diam) thin-walled vesicles were aspirated into a micropipette and a tether was pulled out of the surface by gravitational forces on small glass beads that had adhered to the vesicle surface. Because the vesicle keeps constant surface area and volume, formation of the tether requires displacement of material from the projection of the vesicle in the pipette. Tethers can be made to grow longer or shorter or to maintain equilibrium by adjusting the aspiration pressure in the micropipette at constant tether force. The ratio of the change in the length of the tether to the change in the projection length is proportional to the ratio of the pipette radius to the tether radius. Thus, knowing the density and diameter of the glass beads and measuring the displacement of the projection as a function of tether length, independent determinations of the force on the tether and the tether radius were obtained. The bending stiffness for an SOPC bilayer obtained from these data is approximately 2.0 x 10(-12) dyn cm, for tether radii in the range of 20-100 nm.(ABSTRACT TRUNCATED AT 250 WORDS)     

Theoretical analysis of the effect of the transbilayer movement of phospholipid molecules on the dynamic behavior of a microtube pulled out of an aspirated vesicle

Observations over extended times of a lipid microtube (tether) formed from a lecithin vesicle have shown that under constant external loads the tether exhibits a continuous slow growth. It is considered that this growth is a consequence of the net transbilayer movement of phospholipid molecules in a direction which relieves the membrane strain resulting from the elastic deformation of the vesicle. The elastic deformation mode responsible for this effect is identified as the relative expansion of the two membrane layers reflecting the non-local contribution to membrane bending. An equation for the consequent rate of transbilayer movement of phospholipid molecules is derived. The dynamic behavior of the system is modeled by including frictional contributions due to interlayer slip and Stokes drag on the glass bead used to form the tether. The general numerical solution reveals a complex dependence of the tether growth rate on the system parameters and a continuous increase in the rate of tether growth at long times. Closed form expressions approximating the system behavior are derived and the conditions under which they can be applied are specified. Modeling the mechanically-driven lipid transport as a simple, stochastic, thermal process, allows the rate of lipid translocation to be related to the equilibrium transbilayer exchange rate of phospholipid molecules. Consideration of experimental results shows that the time constant for mechanically-driven translocation is shorter than the time for diffusion-driven translocation by approximately two orders of magnitude, indicating that lipid translocation is not a simple diffusive process. Received: 29 November 1996 / Revised version: 1 December 1997 / Accepted: 9 January 1998     

Vesicle production of heated and stressed erythrocytes.

Human erythrocytes develop vesicles by budding when heated to temperatures close to the thermal transition for spectrin. Regularly spaced strings of vesicles also develop if cells heated to 51--54 degrees C are pulled into unstable shapes by flow of liquid between cover slips. These strings of vesicles develop when cells which had attached to the glass are restrained in the flow by a long membrane-bound tether which maintains a connection with the attachment site on the glass. Breakup into regularly spaced vesicles suggests the breakup of a liquid-like cylinder by growth of Rayleigh instabilities. The ratio of length:diameter of the fragments of cylinder on which each disturbance grew ranged from 2.2 to 5.4 to 1 with a peak of 3.2, as measured from scanning electron micrographs. The upper limit of the range is slightly less than the ratio for the disturbance most likely to grow if surface tension and viscosity alone controlled the vesicle formation. Similar vesicle formation when the form-maintaining structures were weakened has been reported in other systems.     

Influence of thermally driven surface undulations on tethers formed from bilayer membranes

Tether formation is a powerful method to study the mechanical properties of soft lipid bilayer membranes. The force required to maintain a tether at a given length depends upon both membrane elastic properties and tension. In this report, we develop a theoretical analysis that considers the contribution of thermally driven surface undulations and the corresponding entropically driven tensions on the conformation of tethers formed from unaspirated lipid vesicles. In this model, thermal undulations of the vesicle surface provide the excess area required for tether formation. Energy minimization demonstrates the dependence of equilibrium tether conformation on membrane tension and provides an analytical relationship between tether force and radius. If the contributions of nonlocal bending are not considered, an analytical relationship between tether force and length can also be obtained. The predictions of the model are compared to recently reported experimental data, and a value for the initial vesicle tension is obtained. Since most analyses of tether formation from cells and unaspirated vesicles neglect the contributions of nonlocal bending, the appropriateness of this assumption is analyzed. The effect of surface microvesiculations on the tether force-length relation is also considered.     

Characteristics of a membrane reservoir buffering membrane tension.

When membrane-attached beads are pulled vertically by a laser tweezers, a membrane tube of constant diameter (tether) is formed. We found that the force on the bead (tether force) did not depend on tether length over a wide range of tether lengths, which indicates that a previously unidentified reservoir of membrane and not stretch of the plasma membrane provides the tether membrane. Plots of tether force vs. tether length have an initial phase, an elongation phase, and an exponential phase. During the major elongation phase, tether force is constant, buffered by the "membrane reservoir." Finally, there is an abrupt exponential rise in force that brings the tether out of the trap, indicating depletion of the membrane reservoir. In chick embryo fibroblasts and 3T3 fibroblasts, the maximum tether lengths that can be pulled at a velocity of 4 microm/s are 5.1 +/- 0. 3 and 5.0 +/- 0.2 microm, respectively. To examine the importance of the actin cytoskeleton, we treated cells with cytochalasin B or D and found that the tether lengths increased dramatically to 13.8 +/- 0.8 and 12.0 +/- 0.7 microm, respectively. Similarly, treatment of the cells with colchicine and nocodazole results in more than a twofold increase in tether length. We found that elevation of membrane tension (through osmotic pressure, a long-term elevation of tether force, or a number of transitory increases) increased reservoir size over the whole cell. Using a tracking system to hold tether force on the bead constant near its maximal length in the exponential phase, the rate of elongation of the tethers was measured as a function of tether force (membrane tension). The rate of elongation of tethers was linearly dependent on the tether force and reflected an increase in size of the reservoir. Increases in the reservoir caused by tension increases on one side of the cell caused increases in reservoir size on the other side of the cell. Thus, we suggest that cells maintain a plasma membrane reservoir to buffer against changes in membrane tension and that the reservoir is increased with membrane tension or disruption of the cytoskeleton.     

Deformation and flow of membrane into tethers extracted from neuronal growth cones.

Membrane tethers are extracted at constant velocity from neuronal growth cones using a force generated by a laser tweezers trap. A thermodynamic analysis shows that as the tether is extended, energy is stored in the tether as bending and adhesion energies and in the cell body as "nonlocal" bending. It is postulated that energy is dissipated by three viscous mechanisms including membrane flow, slip between the two monolayers that form the bilayer, and slip between membrane and cytoskeleton. The analysis predicts and the experiments show a linear relation between tether force and tether velocity. Calculations based on the analytical results and the experimental measurements of a tether radius of approximately 0.2 micron and a tether force at zero velocity of approximately 8 pN give a bending modulus for the tether of 2.7 x 10(-19) N.m and an extraordinarily small "apparent surface tension" in the growth cone of 0.003 mN/m, where the apparent surface tension is the sum of the far-field, in-plane tension and the energy of adhesion. Treatments with cytochalasin B and D, ethanol, and nocodazole affect the apparent surface tension but not bending. ATP depletion affects neither, whereas large concentrations of DMSO affect both. Under conditions of flow, data are presented to show that the dominant viscous mechanism comes from the slip that occurs when the membrane flows over the cytoskeleton. ATP depletion and the treatment with DMSO cause a dramatic drop in the effective viscosity. If it is postulated that the slip between membrane and cytoskeleton occurs in a film of water, then this water film has a mean thickness of only approximately 10 A.     

Mechanical properties of neuronal growth cone membranes studied by tether formation with laser optical tweezers.

Many cell phenomena involve major morphological changes, particularly in mitosis and the process of cell migration. For cells or neuronal growth cones to migrate, they must extend the leading edge of the plasma membrane as a lamellipodium or filopodium. During extension of filopodia, membrane must move across the surface creating shear and flow. Intracellular biochemical processes driving extension must work against the membrane mechanical properties, but the forces required to extend growth cones have not been measured. In this paper, laser optical tweezers and a nanometer-level analysis system were used to measure the neuronal growth cone membrane mechanical properties through the extension of filopodia-like tethers with IgG-coated beads. Although the probability of a bead attaching to the membrane was constant irrespective of treatment; the probability of forming a tether with a constant force increased dramatically with cytochalasin B or D and dimethylsulfoxide (DMSO). These are treatments that alter the organization of the actin cytoskeleton. The force required to hold a tether at zero velocity (F0) was greater than forces generated by single molecular motors, kinesin and myosin; and F0 decreased with cytochalasin B or D and DMSO in correlation with the changes in the probability of tether formation. The force of the tether on the bead increased linearly with the velocity of tether elongation. From the dependency of tether force on velocity of tether formation, we calculated a parameter related to membrane viscosity, which decreased with cytochalasin B or D, ATP depletion, nocodazole, and DMSO.(ABSTRACT TRUNCATED AT 250 WORDS)     

Extensional flow of erythrocyte membrane from cell body to elastic tether. II. Experiment.

This is the second of two papers on an analytical and experimental study of the flow of erythrocyte membrane. In the experiments discussed here, preswollen human erythrocytes are sphered by aspirating a portion of the cell membrane into a small micropipette; and long, thin, membrane filaments or tethers are steadily withdrawn from the cell at a point diametrically opposite to the point of aspiration. The aspirated portion of the membrane furnishes a reservoir of material that replaces the membrane as it flows as a liquid from the nearly spherical cell body to the cylindrical tether. The application of the principle of conservation of mass permits the tether radius Rt to be measured with the light microscope as the tether is formed and extended at a constant rate. The tether behaves as an elastic solid such that the tether radius decreases as the force or axial tension acting on the tether is increased. For the range of values for Rt is these experiments (100 A less than or equal to Rt less than or equal to 200 A), the slope of the tether-force, tether-radius line is -1.32 dyn/cm. The surface viscosity of the membrane as it flows from cell body to tether is 3 x 10(-3) dyn.s/cm. This viscosity is essentially constant for characteristic rates of deformation between 10 and 200 s-1.     

Membrane tether extraction from human umbilical vein endothelial cells and its implication in leukocyte rolling

During the rolling of human neutrophils on the endothelium, tethers (cylindrical membrane tubes) are likely extracted from the neutrophil. Tether extraction reduces the force imposed on the adhesive bond between the neutrophil and endothelium, thereby facilitating the rolling. However, whether tethers can be extracted from the endothelium is still unknown. Here, with the micropipette-aspiration technique, we show that tethers can be extracted from either suspended or attached human umbilical vein endothelial cells. We also show that a linear relationship between the pulling force and tether growth velocity exists and this relationship does not depend on the receptor type (used to impose point forces), tumor necrosis factor-alpha stimulation, or cell attachment state. With linear regression, we determined that the threshold force was 50 pN and the effective viscosity was 0.50 pN.s/microm. Therefore, tethers might be simultaneously extracted from the neutrophil and endothelial cell during the rolling and, more importantly, the endothelial cell might contribute much more to the total composite tether length than the neutrophil. Compared with tether extraction from the neutrophil alone, simultaneous tether extraction results in a larger increase in the lifetime of the adhesive bond, and thus further stabilizes the rolling of neutrophils under high physiological shear stresses.     

Nano- to microscale dynamics of P-selectin detachment from leukocyte interfaces. I. Membrane separation from the cytoskeleton

We have used a biomembrane force probe decorated with P-selectin to form point attachments with PSGL-1 receptors on a human neutrophil (PMN) in a calcium-containing medium and then to quantify the forces experienced by the attachment during retraction of the PMN at fixed speed. From first touch to final detachment, the typical force history exhibited the following sequence of events: i), an initial linear-elastic displacement of the PMN surface, ii), an abrupt crossover to viscoplastic flow that signaled membrane separation from the interior cytoskeleton and the beginning of a membrane tether, and iii), the final detachment from the probe tip by usually one precipitous step of P-selectin:PSGL-1 dissociation. In this first article I, we focus on the initial elastic response and its termination by membrane separation from the cytoskeleton, initiating tether formation. Quantifying membrane unbinding forces for rates of loading (force/time) in the elastic regime from 240 pN/s to 38,000 pN/s, we discovered that the force distributions agreed well with the theory for kinetically limited failure of a weak bond. The kinetic rate for membrane unbinding was found to increase as an exponential function of the pulling force, characterized by an e-fold scale in force of approximately 17 pN and a preexponential factor, or apparent unstressed off rate, of approximately 1/s. The rheological properties of tether growth subsequent to the membrane unbinding events are presented in a companion article II.     

Role of lamellar membrane structure in tether formation from bilayer vesicles.

A theoretical analysis is presented of the formation of membrane tethers from micropipette-aspirated phospholipid vesicles. In particular, it is taken into account that the phospholipid membrane is composed of two layers which are in contact but unconnected. The elastic energy of the bilayer is taken to be the sum of contributions from area expansivity, relative expansivity of the two monolayers, and bending. The vesicle is aspirated into a pipette and a constant point force is applied at the opposite side in the direction away from the pipette. The shape of the vesicle in approximated as a cylindrical projection into the pipette with a hemispherical cap, a spherical section, and a cylindrical tether with a hemispherical cap. The dimensions of the different regions of the vesicle are obtained by minimizing its elastic energy subject to the condition that the volume of the vesicle is fixed. The range of values for the parameters of the system is determined at which the existence of a tether is possible. Stability analysis is performed showing which of these configurations are stable. The importance of the relative expansion and compression of the constituent monolayers is established by recognizing that local bending energy by itself does not stabilize the vesicle geometry, and that in the limit as the relative expansivity modulus becomes infinitely large, a tether cannot be formed. Predictions are made for the functional relationships among experimentally observable quantities. In a companion report, the results of this analysis are applied to experimental measurements of tether formation, and used to calculate values for the membrane material coefficients.     

Double tether extraction from human neutrophils and its comparison with CD4+ T-lymphocytes

The initial arrest and subsequent rolling of a leukocyte on the vascular endothelium is believed to be facilitated by the extraction of tethers, which are narrow membranous tubes drawn from the leukocyte. Although single tether extraction from neutrophils has been studied thoroughly, the relationship between the tether force (F) and tether-growth velocity (U(t)) is still unknown for double tethers drawn from neutrophils. In this study, we have determined this relationship with the micropipette-aspiration technique. As a comparison, tether extraction from CD4+ T-lymphocytes was also studied. The threshold force and effective viscosity for single tether extraction from passive CD4+ T-lymphocytes were found to be 46 pN and 1.55 pN x s/microm, respectively. These values were modulated by stimulation with phorbol myristate acetate (PMA), but not interleukin-8 (IL-8). More importantly, for both types of leukocyte, the threshold force and effective viscosity for double tether extraction are about twice as large as those corresponding to single tether extraction. Neither IL-8 nor PMA stimulation had any effect on this correlation. These results indicate that double tethers are highly localized on cellular surfaces and independent of each other during the rolling process.     

Membrane tether formation from outer hair cells with optical tweezers

Optical tweezers were used to characterize the mechanical properties of the outer hair cell (OHC) plasma membrane by pulling tethers with 4.5-microm polystyrene beads. Tether formation force and tether force were measured in static and dynamic conditions. A greater force was required for tether formations from OHC lateral wall (499 +/- 152 pN) than from OHC basal end (142 +/- 49 pN). The difference in the force required to pull tethers is consistent with an extensive cytoskeletal framework associated with the lateral wall known as the cortical lattice. The apparent plasma membrane stiffness, estimated under the static conditions by measuring tether force at different tether length, was 3.71 pN/microm for OHC lateral wall and 4.57 pN/microm for OHC basal end. The effective membrane viscosity was measured by pulling tethers at different rates while continuously recording the tether force, and estimated in the range of 2.39 to 5.25 pN x s/microm. The viscous force most likely results from the viscous interactions between plasma membrane lipids and the OHC cortical lattice and/or integral membrane proteins. The information these studies provide on the mechanical properties of the OHC lateral wall is important for understanding the mechanism of OHC electromotility.     

Cell protrusions and tethers: a unified approach

Low pulling forces applied locally to cell surface membranes produce viscoelastic cell surface protrusions. As the force increases, the membrane can locally separate from the cytoskeleton and a tether forms. Tethers can grow to great lengths exceeding the cell diameter. The protrusion-to-tether transition is known as the crossover. Here we propose a unified approach to protrusions and tethers providing, to our knowledge, new insights into their biomechanics. We derive a necessary and sufficient condition for a crossover to occur, a formula for predicting the crossover time, conditions for a tether to establish a dynamic equilibrium (characterized by constant nonzero pulling force and tether extension rate), a general formula for the tether material after crossover, and a general modeling method for tether pulling experiments. We introduce two general protrusion parameters, the spring constant and effective viscosity, valid before and after crossover. Their first estimates for neutrophils are 50 pN μm⁻¹ and 9 pN s μm⁻¹, respectively. The tether elongation after crossover is described as elongation of a viscoelastic-like material with a nonlinearly decaying spring (NLDs-viscoelastic material). Our model correctly describes the results of the published protrusion and tether pulling experiments, suggesting that it is universally applicable to such experiments.     

Extensional flow of erythrocyte membrane from cell body to elastic tether. I. Analysis.

This is the first of two papers on an analytical and experimental study of the flow of the erythrocyte membrane. In the experiment to be discussed in detail in the second paper, preswollen human erythrocytes are sphered by aspirating a portion of the cell membrane into a small micropipette; and long, thin, membrane filaments or "tethers" are steadily withdrawn from the cell at a point diametrically opposite to the point of aspiration. The aspirated portion of the membrane furnished a "reservoir" of material that replaces the membrane as it flows as a liquid from the nearly spherical cell body to the cylindrical tether. In this paper we show that an application of the principle of conservation of mass permits the tether radius (approximately 200 A or less) to be measured with the light microscope as the tether is formed and extended at a constant rate. A static analysis of the axisymmetric cell deformation and tether formation process reveals that the tether radius is uniquely determined by the isotropic tension in the membrane and the elastic constitutive (material) behavior of the tether itself. A dynamic analysis of the extensional flow process reveals that the tether radius must decrease as the velocity of the tether is increased and that the decrease depends on both the viscosity of the membrane and the elasticity of the tether. The analysis also shows that these two factors (membrane viscosity and tether elasticity) are readily decomposed and determined separately when flow experiments are performed at different isotropic tensions.     

Direct observation of membrane tethers formed during neutrophil attachment to platelets or P-selectin under physiological flow

Adhesion and subsequent aggregation between neutrophils and platelets is dependent upon the initial binding of P-selectin on activated platelets to P-selectin glycoprotein ligand 1 (PSGL-1) on the microvilli of neutrophils. High speed, high resolution videomicroscopy of flowing neutrophils interacting with spread platelets demonstrated that thin membrane tethers were pulled from neutrophils in 32 +/- 4% of the interactions. After capture by spread platelets, neutrophil membrane tethers (length of 5.9 +/- 4.1 microm, n = 63) were pulled at an average rate of 6-40 microm/s as the wall shear rate was increased from 100-250 s(-1). The average tether lifetime decreased significantly (P < 0.001) from 630 to 133 ms as the shear rate was increased from 100 s(-1) (F(bond) = 86 pN) to 250 s(-1) (F(bond) = 172 pN), which is consistent with P-selectin/PSGL-1 bond dynamics under stress. Tether formation was blocked by antibodies against P-selectin or PSGL-1, but not by anti-CD18 antibodies. During neutrophil rolling on P-selectin at 150 s(-1), thin membrane tethers were also pulled from the neutrophils. The characteristic jerking motion of the neutrophil coexisted with tether growth (8.9 +/- 8.8 microm long), whereas tether breakage (average lifetime of 3.79 +/- 3.32 s) caused an acute jump in the rolling velocity, proving multiple bonding in the cell surface and the tether surface contact area. Extremely long membrane tethers (>40 microm) were sometimes pulled, which detached in a flow-dependent mechanism of microparticle formation. Membrane tethers were also formed when neutrophils were perfused over platelet monolayers. These results are the first visualization of the often hypothesized tethers that shield the P-selectin/PSGL-1 bond from force loading to regulate neutrophil rolling during inflammation and thrombosis.     

Distinct membrane mechanical properties of human mesenchymal stem cells determined using laser optical tweezers

The therapeutic efficacy of mesenchymal stem cells (MSCs) in tissue engineering and regenerative medicine is determined by their unique biological, mechanical, and physicochemical characteristics, which are yet to be fully explored. Cell membrane mechanics, for example, has been shown to critically influence MSC differentiation. In this study, we used laser optical tweezers to measure the membrane mechanics of human MSCs and terminally differentiated fibroblasts by extracting tethers from the outer cell membrane. The average tether lengths were 10.6+/-1.1 microm (hMSC) and 3.0+/-0.5 microm (fibroblasts). The tether extraction force did not increase during tether formation, which suggests existence of a membrane reservoir intended to buffer membrane tension fluctuations. Cytoskeleton disruption resulted in a fourfold tether length increase in fibroblasts but had no effect in hMSCs, indicating weak association between the cell membrane and hMSC actin cytoskeleton. Cholesterol depletion, known to decrease lipid bilayer stiffness, caused an increase in the tether length both in fibroblasts and hMSCs, as does the treatment of cells with DMSO. We postulate that whereas fibroblasts use both the membrane rigidity and membrane-cytoskeleton association to regulate their membrane reservoir, hMSC cytoskeleton has only a minor impact on stem cell membrane mechanics.     

Mechanics of tether formation in liposomes

It is well-known that a "tether" may be drawn out from a pressurized liposome by means of a suitably applied radial-outward force applied locally to the lipid bilayer. The tether is a narrow, uniform cylindrical tube, which joins the main vesicle in a short "transition region." A first-order energy analysis establishes the broad relationship between the force F needed to draw the tether, the radius R0 of the tether, the bending-stiffness constant B for the lipid bilayer and the membrane tension T in the pressurized liposome. The aim of the present paper is to study in detail the "transition region" between the tether and the main vesicle, by means of a careful application of the engineering theory of axisymmetric shell structures. It turns out that the well-known textbook "thin-shell" theory is inadequate for this purpose, because the tether is evidently an example of a thick-walled shell; and a novel ingredient of the present study is the introduction of elastic constitutive relations that are appropriate to the thick-shell situation. The governing equations are set up in dimensionless form, and are solved by means of a "shooting" technique, starting with a single disposable parameter at a point on the meridian in the tether, which can be adjusted until the boundary conditions at the far "equator" of the main vessel are satisfied. It turns out that the "transition region" between the tether and the main vessel is well characterized by only a few parameters, while the tether and main vessel themselves are described by very simple equations. Introduction of the thick-shell constitutive relation makes little difference to the conformation of and stress-resultants in, the main vessel; but it makes a great deal of difference in the tether itself Indeed, a kind of phase-change appears to take place in the "transition region" between these two zones of the liposome.     

Tether extrusion from red blood cells: integral proteins unbinding from cytoskeleton

We investigate the mechanical strength of adhesion and the dynamics of detachment of the membrane from the cytoskeleton of red blood cells (RBCs). Using hydrodynamical flows, we extract membrane tethers from RBCs locally attached to the tip of a microneedle. We monitor their extrusion and retraction dynamics versus flow velocity (i.e., extrusion force) over successive extrusion-retraction cycles. Membrane tether extrusion is carried out on healthy RBCs and ATP-depleted or -inhibited RBCs. For healthy RBCs, extrusion is slow, constant in velocity, and reproducible through several extrusion-retraction cycles. For ATP-depleted or -inhibited cells, extrusion dynamics exhibit an aging phenomenon through extrusion-retraction cycles: because the extruded membrane is not able to retract properly onto the cell body, each subsequent extrusion exhibits a loss of resistance to tether growth over the tether length extruded at the previous cycle. In contrast, the additionally extruded tether length follows healthy dynamics. The extrusion velocity L depends on the extrusion force f according to a nonlinear fashion. We interpret this result with a model that includes the dynamical feature of membrane-cytoskeleton association. Tether extrusion leads to a radial membrane flow from the cell body toward the tether. In a distal permeation regime, the flow passes through the integral proteins bound to the cytoskeleton without affecting their binding dynamics. In a proximal sliding regime, where membrane radial velocity is higher, integral proteins can be torn out, leading to the sliding of the membrane over the cytoskeleton. Extrusion dynamics are governed by the more dissipative permeation regime: this leads to an increase of the membrane tension and a narrowing of the tether, which explains the power law behavior of L(f). Our main result is that ATP is necessary for the extruded membrane to retract onto the cell body. Under ATP depletion or inhibition conditions, the aging of the RBC after extrusion is interpreted as a perturbation of membrane-cytoskeleton linkage dynamics.     

Temperature dependence of the yield shear resultant and the plastic viscosity coefficient of erythrocyte membrane. Implications about molecular events during membrane failure.

Structural failure of the erythrocyte membrane in shear deformation occurs when the maximum shear resultant (force/length) exceeds a critical value, the yield shear resultant. When the yield shear resultant is exceeded, the membrane flows with a rate of deformation characterized by the plastic viscosity coefficient. The temperature dependence of the yield shear resultant and the plastic viscosity coefficient have been measured over the temperature range 10-40 degrees C. Over this range the yield shear resultant does not change significantly (+/- 15%), but the plastic viscosity coefficient changes exponentially from a value of 1.3 X 10(-2) surface poise (dyn s/cm) at 10 degrees C to a value of 6.2 X 10(-4) surface poise (SP) at 40 degrees C. The different temperature dependence of these two parameters is not surprising, inasmuch as they characterize different molecular events. The yield shear resultant depends on the number and strength of intermolecular connections within the membrane skeleton, whereas the plastic viscosity depends on the frictional interactions between molecular segments as they move past one another in the flowing surface. From the temperature dependence of the plastic viscosity, a temperature-viscosity coefficient, E, can be calculated: eta p = constant X exp(--E/RT). This quantity (E) is related to the probability that a molecular segment can "jump" to its next location in the flowing network. The temperature-viscosity coefficient for erythrocyte membrane above the elastic limit is calculated to be 18 kcal/mol, which is similar to coefficients for other polymeric materials.