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)     

Membrane tethers formed from blood cells with available area and determination of their adhesion energy

Fundamental to all mammalian cells is the adherence of the lipid bilayer membrane to the underlying membrane associated cytoskeleton. To investigate this adhesion, we physically detach the lipid membrane from the cell by mechanically forming membrane tethers. For the most part these have been tethers formed from either neutrophils or red cells. Here we do a simple thermodynamic analysis of the tether formation process using the entire cell, including tether, as the control volume. For a neutrophil, we show that the total adhesion energy per unit area between lipid membrane and cytoskeleton depends on the square of the tether force. For a flaccid red cell, we show that the total adhesion energy minus the tension in the spectrin cytoskeleton depends also on the square of the tether force. Finally, we discuss briefly the viscous flow of membrane. Using published data we calculate and compare values for the various adhesion energies and viscosities.     

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.     

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.     

Membrane tether formation from blebbing cells

Membrane tension has been proposed to be important in regulating cell functions such as endocytosis and cell motility. The apparent membrane tension has been calculated from tether forces measured with laser tweezers. Both membrane-cytoskeleton adhesion and membrane tension contribute to the tether force. Separation of the plasma membrane from the cytoskeleton occurs in membrane blebs, which could remove the membrane-cytoskeleton adhesion term. In renal epithelial cells, tether forces are significantly lower on blebs than on membranes that are supported by cytoskeleton. Furthermore, the tether forces are equal on apical and basolateral blebs. In contrast, tether forces from membranes supported by the cytoskeleton are greater in apical than in basolateral regions, which is consistent with the greater apparent cytoskeletal density in the apical region. We suggest that the tether force on blebs primarily contains only the membrane tension term and that the membrane tension may be uniform over the cell surface. Additional support for this hypothesis comes from observations of melanoma cells that spontaneously bleb. In melanoma cells, tether forces on blebs are proportional to the radius of the bleb, and as large blebs form, there are spikes in the tether force in other cell regions. We suggest that an internal osmotic pressure inflates the blebs, and the pressure calculated from the Law of Laplace is similar to independent measurements of intracellular pressures. When the membrane tension term is subtracted from the apparent membrane tension over the cytoskeleton, the membrane-cytoskeleton adhesion term can be estimated. In both cell systems, membrane-cytoskeleton adhesion was the major factor in generating the tether force.     

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.     

Internal forces, tension and energy density in tethered cellular membranes

We analyze tethered cellular membranes by considering the membrane resultants, tension and densities of two modes of energy, bending and adhesion. These characteristics are determined based on a computational (finite-difference) analysis of membrane shape. We analyze the relative contribution and distribution of the membrane characteristics in four typical zones of the membrane surface. Using an axisymmetric model, we found that the meridional and circumferential components of the resultant are different near the tether body and they converge to the value of membrane tension farther from the tether. At the beginning of the area of membrane detachment from the cytoskeleton, the density of bending energy is on the same order of magnitude as membrane tension (resultant). Away from the tether, the bending energy density quickly decreases and becomes of the same order as that of the adhesion energy in the membrane-cytoskeleton attachment area. In that area, both modes of energy are significantly smaller than the membrane tension. We also consider the effect of the membrane bending modulus on the distribution of the membrane characteristics. An increase in the bending modulus results in changing the length and position on the membrane surface of zone 1 characterized by significant evolution of the resultant components. It also results in shortening zone 2 that covers the rest of the area of membrane detachment. The obtained results can help in a better interpretation of the measurements of membrane mechanical properties as well as in analyses of proteins and channels in curved membranes.     

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.     

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.     

Nano- to microscale dynamics of P-selectin detachment from leukocyte interfaces. II. Tether flow terminated by P-selectin dissociation from PSGL-1

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 most often by one precipitous step of P-selectin:PSGL-1 dissociation. Analyzing the initial elastic response and membrane unbinding from the cytoskeleton in our companion article I, we focus in this article on the regime of tether extrusion that nearly always occurred before release of the extracellular adhesion bond at pulling speeds > or =1 microm/s. The force during tether growth appeared to approach a plateau at long times. Examined over a large range of pulling speeds up to 150 microm/s, the plateau force exhibited a significant shear thinning as indicated by a weak power-law dependence on pulling speed, f(infinity) = 60 pN(nu(pull)/microm/s)(0.25). Using this shear-thinning response to describe the viscous element in a nonlinear Maxwell-like fluid model, we show that a weak serial-elastic component with a stiffness of approximately 0.07 pN/nm provides good agreement with the time course of the tether force approach to the plateau under constant pulling speed.     

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)     

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.     

Modulation of cellular mechanics during osteogenic differentiation of human mesenchymal stem cells

Recognition of the growing role of human mesenchymal stem cells (hMSC) in tissue engineering and regenerative medicine requires a thorough understanding of intracellular biochemical and biophysical processes that may direct the cell's commitment to a particular lineage. In this study, we characterized the distinct biomechanical properties of hMSCs, including the average Young's modulus determined by atomic force microscopy (3.2 +/- 1.4 kPa for hMSC vs. 1.7 +/- 1.0 kPa for fully differentiated osteoblasts), and the average membrane tether length measured with laser optical tweezers (10.6 +/- 1.1 microm for stem cells, and 4.0 +/- 1.1 microm for osteoblasts). These differences in cell elasticity and membrane mechanics result primarily from differential actin cytoskeleton organization in these two cell types, whereas microtubules did not appear to affect the cellular mechanics. The membrane-cytoskeleton linker proteins may contribute to a stronger interaction of the plasma membrane with F-actins and shorter membrane tether length in osteoblasts than in stem cells. Actin depolymerization or ATP depletion caused a two- to threefold increase in the membrane tether length in osteoblasts, but had essentially no effect on the stem-cell membrane tethers. Actin remodeling in the course of a 10-day osteogenic differentiation of hMSC mediates the temporally correlated dynamical changes in cell elasticity and membrane mechanics. For example, after a 10-day culture in osteogenic medium, hMSC mechanical characteristics were comparable to those of mature bone cells. Based on quantitative characterization of the actin cytoskeleton remodeling during osteodifferentiation, we postulate that the actin cytoskeleton plays a pivotal role in determining the hMSC mechanical properties and modulation of cellular mechanics at the early stage of stem-cell osteodifferentiation.     

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.     

Cell Membrane Tethers Generate Mechanical Force in Response to Electrical Stimulation

Living cells maintain a huge transmembrane electric field across their membranes. This electric field exerts a force on the membrane because the membrane surfaces are highly charged. We have measured electromechanical force generation by cell membranes using optically trapped beads to detach the plasma membrane from the cytoskeleton and form long thin cylinders (tethers). Hyperpolarizing potentials increased and depolarizing potentials decreased the force required to pull a tether. The membrane tether force in response to sinusoidal voltage signals was a function of holding potential, tether diameter, and tether length. Membrane electromechanical force production can occur at speeds exceeding those of ATP-based protein motors. By harnessing the energy in the transmembrane electric field, cell membranes may contribute to processes as diverse as outer hair cell electromotility, ion channel gating, and transport.     

Hypotonic Challenge of Endothelial Cells Increases Membrane Stiffness with No Effect on Tether Force

Regulation of cell volume is a fundamental property of all mammalian cells. Multiple signaling pathways are known to be activated by cell swelling and to contribute to cell volume homeostasis. Although cell mechanics and membrane tension have been proposed to couple cell swelling to signaling pathways, the impact of swelling on cellular biomechanics and membrane tension have yet to be fully elucidated. In this study, we use atomic force microscopy under isotonic and hypotonic conditions to measure mechanical properties of endothelial membranes including membrane stiffness, which reflects the stiffness of the submembrane cytoskeleton complex, and the force required for membrane tether formation, reflecting membrane tension and membrane-cytoskeleton attachment. We find that hypotonic swelling results in significant stiffening of the endothelial membrane without a change in membrane tension/membrane-cytoskeleton attachment. Furthermore, depolymerization of F-actin, which, as expected, results in a dramatic decrease in the cellular elastic modulus of both the membrane and the deeper cytoskeleton, indicating a collapse of the cytoskeleton scaffold, does not abrogate swelling-induced stiffening of the membrane. Instead, this swelling-induced stiffening of the membrane is enhanced. We propose that the membrane stiffening should be attributed to an increase in hydrostatic pressure that results from an influx of solutes and water into the cells. Most importantly, our results suggest that increased hydrostatic pressure, rather than changes in membrane tension, could be responsible for activating volume-sensitive mechanisms in hypotonically swollen cells.     

Stereocilia membrane deformation: implications for the gating spring and mechanotransduction channel

In hair cells, although mechanotransduction channels have been localized to tips of shorter stereocilia of the mechanically sensitive hair bundle, little is known about how force is transmitted to the channel. Here, we use a biophysical model of the membrane-channel complex to analyze the nature of the gating spring compliance and channel arrangement. We use a triangulated surface model and Monte Carlo simulation to compute the deformation of the membrane under the action of tip link force. We show that depending on the gating spring stiffness, the compliant component of the gating spring arises from either the membrane alone or a combination of the membrane and a tether that connects the channel to the actin cytoskeleton. If a bundle is characterized by relatively soft gating springs, such as those of the bullfrog sacculus, the need for membrane reinforcement by channel tethering then depends on membrane parameters. With stiffer gating springs, such as those from rat outer hair cells, the channel must be tethered for all biophysically realistic parameters of the membrane. We compute the membrane forces (resultants), which depend on membrane tension, bending modulus, and curvature, and show that they can determine the fate of the channel.     

Phosphatidylinositol 4,5-bisphosphate functions as a second messenger that regulates cytoskeleton-plasma membrane adhesion

Binding interactions between the plasma membrane and the cytoskeleton define cell functions such as cell shape, formation of cell processes, cell movement, and endocytosis. Here we use optical tweezers tether force measurements and show that plasma membrane phosphatidylinositol 4,5-bisphosphate (PIP2) acts as a second messenger that regulates the adhesion energy between the cytoskeleton and the plasma membrane. Receptor stimuli that hydrolyze PIP2 lowered adhesion energy, a process that could be mimicked by expressing PH domains that sequester PIP2 or by targeting a 5'-PIP2-phosphatase to the plasma membrane to selectively lower plasma membrane PIP2 concentration. Our study suggests that plasma membrane PIP2 controls dynamic membrane functions and cell shape by locally increasing and decreasing the adhesion between the actin-based cortical cytoskeleton and the plasma membrane.     

Energy of dissociation of lipid bilayer from the membrane skeleton of red blood cells

The association between the lipid bilayer and the membrane skeleton is important to cell function. In red blood cells, defects in this association can lead to various forms of hemolytic anemia. Although proteins involved in this association have been well characterized biochemically, the physical strength of this association is only beginning to be studied. Formation of a small cylindrical strand of membrane material (tether) from the membrane involves separation of the lipid bilayer from the membrane skeleton. By measuring the force required to form a tether, and knowing the contribution to the force due to the deformation of a lipid bilayer, it is possible to calculate the additional contribution to the work of tether formation due to the separation of membrane skeleton from the lipid bilayer. In the present study, we measured the tethering force during tether formation using a microcantilever (a thin, flexible glass fiber) as a force transducer. Numerical calculations of the red cell contour were performed to examine how the shape of the contour affects the calculation of tether radius, and subsequently separation work per unit area W(sk) and bending stiffness k(c). At high aspiration pressure and small external force, the red cell contour can be accurately modeled as a sphere, but at low aspiration pressure and large external force, the contour deviates from a sphere and may affect the calculation. Based on an energy balance and numerical calculations of the cell contour, values of the membrane bending stiffness k(c) = 2.0 x 10(-19) Nm and the separation work per unit area W(sk) = 0.06 mJ/m2 were obtained.     

Modeling the mechanics of tethers pulled from the cochlear outer hair cell membrane

Cell membrane tethers are formed naturally (e.g., in leukocyte rolling) and experimentally to probe membrane properties. In cochlear outer hair cells, the plasma membrane is part of the trilayer lateral wall, where the membrane is attached to the cytoskeleton by a system of radial pillars. The mechanics of these cells is important to the sound amplification and frequency selectivity of the ear. We present a modeling study to simulate the membrane deflection, bending, and interaction with the cytoskeleton in the outer hair cell tether pulling experiment. In our analysis, three regions of the membrane are considered: the body of a cylindrical tether, the area where the membrane is attached and interacts with the cytoskeleton, and the transition region between the two. By using a computational method, we found the shape of the membrane in all three regions over a range of tether lengths and forces observed in experiments. We also analyze the effects of biophysical properties of the membrane, including the bending modulus and the forces of the membrane adhesion to the cytoskeleton. The model's results provide a better understanding of the mechanics of tethers pulled from cell membranes.