Passive mechanical behavior of human neutrophils: power-law fluid.

The mechanical behavior of the neutrophil plays an important role in both the microcirculation and the immune system. Several laboratories in the past have developed mechanical models to describe different aspects of neutrophil deformability. In this study, the passive mechanical properties of normal human neutrophils have been further characterized. The cellular mechanical properties were assessed by single cell micropipette aspiration at fixed aspiration pressures. A numerical simulation was developed to interpret the experiments in terms of cell mechanical properties based on the Newtonian liquid drop model (Yeung and Evans, Biophys. J., 56: 139-149, 1989). The cytoplasmic viscosity was determined as a function of the ratio of the initial cell size to the pipette radius, the cortical tension, aspiration pressure, and the whole cell aspiration time. The cortical tension of passive neutrophils was measured to be about 2.7 x 10(-5) N/m. The apparent viscosity of neutrophil cytoplasm was found to depend on aspiration pressure, and ranged from approximately 500 Pa.s at an aspiration pressure of 98 Pa (1.0 cm H2O) to approximately 50 Pa.s at 882 Pa (9.0 cm H2O) when tested with a 4.0-micron pipette. These data provide the first documentation that the neutrophil cytoplasm exhibits non-Newtonian behavior. To further characterize the non-Newtonian behavior of human neutrophils, a mean shear rate gamma m was estimated based on the numerical simulation. The apparent cytoplasmic viscosity appears to decrease as the mean shear rate increases. The dependence of cytoplasmic viscosity on the mean shear rate can be approximated as a power-law relationship described by mu = mu c(gamma m/gamma c)-b, where mu is the cytoplasmic viscosity, gamma m is the mean shear rate, mu c is the characteristic viscosity at characteristic shear rate gamma c, and b is a material coefficient. When gamma c was set to 1 s-1, the material coefficients for passive neutrophils were determined to be mu c = 130 +/- 23 Pa.s and b = 0.52 +/- 0.09 for normal neutrophils. The power-law approximation has a remarkable ability to reconcile discrepancies among published values of the cytoplasmic viscosity measured using different techniques, even though these values differ by nearly two orders of magnitude. Thus, the power-law fluid model is a promising candidate for describing the passive mechanical behavior of human neutrophils in large deformation. It can also account for some discrepancies between cellular behavior in single-cell micromechanical experiments and predictions based on the assumption that the cytoplasm is a simple Newtonian fluid.     

Cell cycle-dependence of HL-60 cell deformability.

In this study, the role of cytoskeleton in HL-60 deformability during the cell cycle was investigated. G1, S, and G2/M cell fractions were separated by centrifugal elutriation. Cell deformability was evaluated by pipette aspiration. Tested at the same aspiration pressures, S cells were found to be less deformable than G1 cells. Moreover, HL-60 cells exhibited power-law fluid behavior: mu = mu c(gamma m/ gamma c)-b, where mu is cytoplasmic viscosity, gamma m is mean shear rate, mu c is the characteristic viscosity at the characteristic shear rate gamma c, and b is a material constant. At a given shear rate, S cells (mu c = 276 +/- 14 Pa.s, b = 0.51 +/- 0.03) were more viscous than G1 cells (mu c = 197 +/- 25, b = 0.53 +/- 0.02). To evaluate the relative importance of different cytoskeletal components in these cell cycle-dependent properties, HL-60 cells were treated with 30 microM dihydrocytochalasin B (DHB) to disrupt F-actin or 100 microM colchicine to collapse microtubules. DHB dramatically softened both G1 and S cells, which reduced the material constants mu c by approximately 65% and b by 20-30%. Colchicine had a limited effect on G1 cells but significantly reduced mu c of S cells (approximately 25%). Thus, F-actin plays the predominate role in determining cell mechanical properties, but disruption of microtubules may also influence the behavior of proliferating cells in a cell cycle-dependent fashion.     

The behavior of human neutrophils during flow through capillary pores

The passage times of individual human neutrophils through single capillary-sized pores in polycarbonate membranes were measured with the resistive pulse technique, and results were compared to those obtained from the micropipette aspiration of entire cells. Pore transit measurement serves as a useful means to screen populations of cells, and allows for protocols that measure time dependent changes to the population. Neutrophils exhibited a highly linear pressure/flow rate relationship at aspiration pressures from 200 Pa to 1,500 Pa in both the pore and pipette systems. Cellular viscosity, as determined by the method of Hochmuth and Needham, was 89.0 Pa.s for the pore systems and 134.9 Pa.s for the pipette systems. These results are in general agreement with recent values of neutrophil viscosity published in the literature. Extrapolation of the observed linear flow response revealed an apparent minimum pressure for whole cell aspiration significantly above the threshold pressure predicted by Evans' liquid drop model. However, whole cell aspiration was achieved in both the pore and pipette systems at pressures below this extrapolated minimum, although the calculated cellular viscosity was greatly increased. The implications of these two regimes of cell deformation is unclear. This behavior could be explained by shear thinning of the material in the cell body. However the origin of this phenomenon may be in the cortical region of the cell, which exhibits an elastic tension that may be deformation rate dependent.     

Passive mechanical behavior of human neutrophils: effects of colchicine and paclitaxel.

The role of microtubules in determining the mechanical rigidity of neutrophils was assessed. Neutrophils were treated with colchicine to disrupt microtubules, or with paclitaxel to promote formation of microtubules. Paclitaxel caused an increase in the number of microtubules in the cells as assessed by immunofluorescence, but it had no effect on the presence or organization of actin filaments or on cellular mechanical properties. Colchicine at concentrations <1.0 microM caused disruption of microtubular structures, but had little effect on either F-actin or on cellular mechanical properties. Higher concentrations of colchicine disrupted microtubular structure, but also caused increased actin polymerization and increases in cell rigidity. Treatment with 10 microM colchicine increased F-actin content by 17%, the characteristic cellular viscosity by 30%, the dependence of viscosity on shear rate by 10%, and the cortical tension by 18%. At 100 microM colchicine the corresponding increases were F-actin, 25%; characteristic viscosity, 50%; dependence of viscosity on shear rate, 20%; and cortical tension, 21%. These results indicate that microtubules have little influence on the mechanical properties of neutrophils, and that increases in cellular rigidity caused by high concentrations of colchicine are due to a secondary effect that triggers actin polymerization. This study supports the conclusion that actin filaments are the primary structural determinants of neutrophil mechanical properties.     

Baseline mechanical characterization of J774 macrophages

Macrophage cell lines like J774 cells are ideal model systems for establishing the biophysical foundations of autonomous deformation and motility of immune cells. To aid comparative studies on these and other types of motile cells, we report measurements of the cortical tension and cytoplasmic viscosity of J774 macrophages using micropipette aspiration. Passive J774 cells cultured in suspension exhibited a cortical resting tension of ∼0.14 mN/m and a viscosity (at room temperature) of 0.93 kPa·s. Both values are about one order of magnitude higher than the respective values obtained for human neutrophils, lending support to the hypothesis that a tight balance between cortical tension and cytoplasmic viscosity is a physical prerequisite for eukaryotic cell motility. The relatively large stiffness of passive J774 cells contrasts with their capacity for a more than fivefold increase in apparent surface area during active deformation in phagocytosis. Scanning electron micrographs show how microscopic membrane wrinkles are smoothed out and recruited into the apparent surface area during phagocytosis of large targets.     

A modified micropipette aspiration technique and its application to tether formation from human neutrophils

Tether formation, which is mechanically characterized by its threshold force and effective viscosity, is involved in neutrophil emigration from blood circulation. Using the micropipette aspiration technique, which was improved by quantitative contact control and computerized data analysis, we extracted tethers from human neutrophils treated with IL-8, PMA, or cytochalasin D. We found that both IL-8 and PMA elevated the threshold force to about twice as large as the value for passive neutrophils. All these treatments decreased the effective viscosity dramatically (approximately 80%). With a novel method, the residual cortical tension of the cytochalasin-D-treated non-spherical neutrophils was measured to be approximately 8.8 pN/microm.     

The mechanics of neutrophils: synthetic modeling of three experiments

Much experimental data exist on the mechanical properties of neutrophils, but so far, they have mostly been approached within the framework of liquid droplet models. This has two main drawbacks: 1), It treats the cytoplasm as a single phase when in reality, it is a composite of cytosol and cytoskeleton; and 2), It does not address the problem of active neutrophil deformation and force generation. To fill these lacunae, we develop here a comprehensive continuum-mechanical paradigm of the neutrophil that includes proper treatment of the membrane, cytosol, and cytoskeleton components. We further introduce two models of active force production: a cytoskeletal swelling force and a polymerization force. Armed with these tools, we present computer simulations of three classic experiments: the passive aspiration of a neutrophil into a micropipette, the active extension of a pseudopod by a neutrophil exposed to a local stimulus, and the crawling of a neutrophil inside a micropipette toward a chemoattractant against a varying counterpressure. Principal results include: 1), Membrane cortical tension is a global property of the neutrophil that is affected by local area-increasing shape changes. We argue that there exists an area dilation viscosity caused by the work of unfurling membrane-storing wrinkles and that this viscosity is responsible for much of the regulation of neutrophil deformation. 2), If there is no swelling force of the cytoskeleton, then it must be endowed with a strong cohesive elasticity to prevent phase separation from the cytosol during vigorous suction into a capillary tube. 3), We find that both swelling and polymerization force models are able to provide a unifying fit to the experimental data for the three experiments. However, force production required in the polymerization model is beyond what is expected from a simple short-range Brownian ratchet model. 4), It appears that, in the crawling of neutrophils or other amoeboid cells inside a micropipette, measurement of velocity versus counterpressure curves could provide a determination of whether cytoskeleton-to-cytoskeleton interactions (such as swelling) or cytoskeleton-to-membrane interactions (such as polymerization force) are predominantly responsible for active protrusion.     

Viscosity of passive human neutrophils undergoing small deformations.

At issue is the type of constitutive equation that can be used to describe all possible types of deformation of the neutrophil. Here a neutrophil undergoing small deformations is studied by aspirating it into a glass pipet with a diameter that is only slightly smaller than the diameter of the spherically shaped cell. After being held in the pipet for at least seven seconds, the cell is rapidly expelled and allowed to recover its undeformed, spherical shape. The recovery takes approximately 15 s. An analysis of the recovery process that treats the cell as a simple Newtonian liquid drop with a constant cortical (surface) tension gives a value of 3.3 x 10(-5) cm/s for the ratio of the cortical tension to cytoplasmic viscosity. This value is about twice as large as a previously published value obtained with the same model from studies of large deformations of neutrophils. This discrepancy indicates that the cytoplasmic viscosity decreases as the amount of deformation decreases. An extrapolated value for the cytoplasmic viscosity at zero deformation is approximately 600 poise when a value for the cortical tension of 0.024 dyn/cm is assumed. Clearly the neutrophil does not behave like a simple Newtonian liquid drop in that small deformations are inherently different from large deformations. More complex models consisting either of two or more fluids or multiple shells must be developed. The complex structure inside the neutrophil is shown in scanning electron micrographs of osmotically burst cells and cells whose membrane has been dissolved away.     

Effect of temperature on tether extraction, surface protrusion, and cortical tension of human neutrophils

Neutrophil rolling on endothelial cells, the initial stage of its migrational journey to a site of inflammation, is facilitated by tether extraction and surface protrusion. Both phenomena have been studied extensively at room temperature, which is considerably lower than human body temperature. It is known that temperature greatly affects cellular mechanical properties such as viscosity. Therefore, we carried out tether extraction, surface protrusion, and cortical tension experiments at 37 degrees C with the micropipette aspiration technique. The experimental temperature was elevated using a custom-designed microscope chamber for the micropipette aspiration technique. To evaluate the constant temperature assumption in our experiments, the temperature distribution in the whole chamber was computed with finite element simulation. Our simulation results showed that temperature variation around the location where our experiments were performed was less than 0.2 degrees C. For tether extraction at 37 degrees C, the threshold force required to pull a tether (40 pN) was not statistically different from the value at room temperature (51 pN), whereas the effective viscosity (0.75 pN.s/microm) decreased significantly from the value at room temperature (1.5 pN.s/microm). Surface protrusion, which was modeled as a linear deformation, had a slightly smaller spring constant at 37 degrees C (40 pN/microm) than it did at room temperature (56 pN/microm). However, the cortical tension at 37 degrees C (5.7+/-2.2 pN/microm) was substantially smaller than that at room temperature (23+/-8 pN/microm). These data clearly suggest that neutrophils roll differently at body temperature than they do at room temperature by having distinct mechanical responses to shear stress of blood flow.     

Aspiration of human neutrophils: effects of shear thinning and cortical dissipation.

It is generally accepted that the human neutrophil can be mechanically represented as a droplet of polymeric fluid enclosed by some sort of thin slippery viscoelastic cortex. Many questions remain however about the detailed rheology and chemistry of the interior fluid and the cortex. To address these quantitative issues, we have used a finite element method to simulate the dynamics of neutrophils during micropipet aspiration using various plausible assumptions. The results were then systematically compared with aspiration experiments conducted at eight different combinations of pipet size and pressure. Models in which the cytoplasm was represented by a simple Newtonian fluid (i.e., models without shear thinning) were grossly incapable of accounting for the effects of pressure on the general time scale of neutrophil aspiration. Likewise, models in which the cortex was purely elastic (i.e., models without surface viscosity) were unable to explain the effects of pipet size on the general aspiration rate. Such models also failed to explain the rapid acceleration of the aspiration rate during the final phase of aspiration nor could they account for the geometry of the neutrophil during various phases of aspiration. Thus, our results indicate that a minimal mechanical model of the neutrophil needs to incorporate both shear thinning and surface viscosity to remain valid over a reasonable range of conditions. At low shear rates, the surface dilatation viscosity of the neutrophil was found to be on the order of 100 poise-cm, whereas the viscosity of the interior cytoplasm was on the order of 1000 poise. Both the surface viscosity and the interior viscosity seem to decrease in a similar fashion when the shear rate exceeds approximately 0.05 s(-1). Unfortunately, even models with both surface viscosity and shear thinning studied are still not sufficient to fully explain all the features of neutrophil aspiration. In particular, the very high rate of aspiration during the initial moments after ramping of pressure remains mysterious.     

Cytoplasmic rheology of passive neutrophils.

The rheological properties of leukocytes are important to their effectiveness in the microcirculation. Previous studies based on in vitro data from micropipette experiments suggest that a Maxwell fluid bounded by a cortical shell with persistent tension is a realistic model for non-activated neutrophils in both the rapid and slow deformation phases. However, various viscoelastic coefficients have been obtained depending on the degree of cell deformation. In the present paper it is demonstrated that the cytoplasmic apparent viscosity and elasticity vary continuously, depending on the degree of deformation. These apparent variations are due to the inhomogeneous nature of the neutrophil internal structure. It is shown that the nucleus is much stiffer than the cytoplasm. The composite structure of the cell results in the deformation-dependent properties.     

Effect of colchicine on viscoelastic properties of neutrophils

The effect of colchicine (15-60 micrograms/ml) on the viscoelastic properties of human neutrophils was studied by the micropipette technique. The small deformation of the neutrophil in response to a step aspiration pressure was analyzed by using a three-element model in which an elastic element, K1, is in parallel with a Maxwell element composed of another elastic element, K2, in series with a viscous element, mu. Colchicine treatment of neutrophils caused decreases in K2 and mu without affecting K1. The results indicate that the integrity of the microtubules plays a significant role in providing the viscoelastic resistance (as represented by the Maxwell element in the model) of neutrophils to deforming stress.     

Passive deformation analysis of human leukocytes

The following analysis presents an experimental and theoretical study of the passive viscoelastic behavior of human leukocytes. Individual neutrophils in EDTA were observed both during their partial aspiration into a small micropipette and after expulsion from a large micropipette where the cell had been totally aspirated and deformed into a sausage shape. To analyze the data, a passive model of leukocyte rheology has been developed consisting of a cortical shell containing a Maxwell fluid which describes the average properties of the cell cytoplasm. The cortical shell represents a crosslinked actin layer near the surface of the cell and is assumed to be under pre-stressed tension. This model can reproduce the results of experiments using micropipette for both short-time small deformation and slow recovery data after large deformation. In addition, a finite element scheme has been established for the same model which shows close agreement with the analytical solution.     

Alteration of red cell membrane viscoelasticity by heat treatment: effect on cell deformability and suspension viscosity

The membrane shear elastic modulus (mu) and the time constant for extensional shape recovery (tc) were measured for normal, control human red blood cells (RBC) and for RBC heat treated (HT) at 48 degrees C. Three separate methods for the measurement of mu were compared (two used a micropipette and one employed a flow channel), and the membrane viscosity (n) was calculated from the relation n = mu. tc. The deformability of HT and control cells was evaluated using micropipette techniques, and the bulk viscosity of RBC suspensions at 40% hematocrit was measured. The shear elastic modulus, or "membrane rigidity", was more than doubled by heat treatment, although both the absolute value for mu and the estimate of the increase induced by heat treatment varied depending on the method of measurement. Heat treatment caused smaller increases in membrane viscosity and in membrane bending resistance, and only minimal changes in cell geometry. The deformability of HT cells was reduced: 1) the pressure required for cell entry (Pe) into 3 micrometers pipettes was increased, on average, by 170%; 2) at an aspiration pressure (Pa) exceeding Pe, longer times were required for cell entry into the same pipettes. However, when Pa was scaled relative to the mean entry pressure for a given sample (i.e, Pa/Pe), entry times were similar for control and HT cells. Bulk viscosity of HT RBC suspensions was elevated by approximately 12% on average (shear rates 75 to 1500 inverse seconds). These findings suggest that alteration of RBC membrane mechanical properties, similar to those induced by heat treatment, would most affect the in vivo circulation in regions where vessel dimensions are smaller than cellular diameters.     

Cortical shell-liquid core model for passive flow of liquid-like spherical cells into micropipets.

Many nonadherent cells exist as spheres in suspension and when sucked into pipets, deform continuously like liquids within the fixed surface area limitation of a plasma membrane envelope. After release, these cells eventually recover their spherical form. Consequently, pipet aspiration test provides a useful method to assay the apparent viscosity of such cells. For this purpose, we have analyzed the inertialess flow of a liquid-like model cell into a tube at constant suction pressure. The cell is modeled as a uniform liquid core encapsulated by a distinct cortical shell. The method of analysis employs a variational approach that minimizes errors in boundary conditions defined by the equations of motion for the cortical shell where the trial functions are exact solutions for the flow field inside the liquid core. For the particular case of an anisotropic liquid cortex with persistent tension, we have determined universal predictions for flow rate scaled by the ratio of excess pressure (above the threshold established by the cortical tension) and core viscosity which is the reciprocal of the dynamic resistance to entry. The results depend on pipet to cell size ratio and a parameter that characterizes the ratio of viscous flow resistance in the cortex to that inside the cytoplasmic core. The rate of entry increases markedly as the pipet size approaches the outer segment diameter of the cell. Viscous dissipation in the cortex strongly influences the entry flow resistance for small tube sizes but has little effect for large tubes. This indicates that with sufficient experimental resolution, measurement of cell entry flow with different-size pipets could establish both the cortex to cell dissipation ratio as well as the apparent viscosity of the cytoplasmic core.     

Leukocyte rolling on P-selectin: a three-dimensional numerical study of the effect of cytoplasmic viscosity

Rolling leukocytes deform and show a large area of contact with endothelium under physiological flow conditions. We studied the effect of cytoplasmic viscosity on leukocyte rolling using our three-dimensional numerical algorithm that treats leukocyte as a compound droplet in which the core phase (nucleus) and the shell phase (cytoplasm) are viscoelastic fluids. The algorithm includes the mechanical properties of the cell cortex by cortical tension and considers leukocyte microvilli that deform viscoelastically and form viscous tethers at supercritical force. Stochastic binding kinetics describes binding of adhesion molecules. The leukocyte cytoplasmic viscosity plays a critical role in leukocyte rolling on an adhesive substrate. High-viscosity cells are characterized by high mean rolling velocities, increased temporal fluctuations in the instantaneous velocity, and a high probability for detachment from the substrate. A decrease in the rolling velocity, drag, and torque with the formation of a large, flat contact area in low-viscosity cells leads to a dramatic decrease in the bond force and stable rolling. Using values of viscosity consistent with step aspiration studies of human neutrophils (5-30 Pa·s), our computational model predicts the velocities and shape changes of rolling leukocytes as observed in vitro and in vivo.     

Influence of preparative procedures on the membrane viscoelasticity of human red cell ghosts

The effects of systematic variations in the preparative procedures on the membrane viscoelastic properties of resealed human red blood cell ghosts have been investigated. Ghosts, prepared by hypotonic lysis at 0 degrees C and resealing at 37 degrees C, were subjected to: measurement of the time constant for extensional recovery (tc); measurement of the membrane shear elastic modulus (mu) via three separate techniques; determination of the membrane viscosity (eta m) via a cone-plate Rheoscope. Membrane viscosity was also determined as eta m = mu X tc. Compared to intact cells, ghosts had shorter tc, regardless of their residual hemoglobin concentration (up to 21.6 g/dl). However, prolonged exposure to hypotonic media did increase their recovery time toward the intact cell value. The shear elastic modulus, as judged by micropipette aspiration of membrane tongues (mu p), was similar for all ghosts and intact cells. This result, taken with the tc data, indicates that ghosts have reduced membrane viscosity. Rheoscopic analysis also showed that eta m was reduced for ghosts, with the degree of reduction (approx. 50%) agreeing well with that estimated by the product mu p X tc. However, flow channel and pipette elongation estimates indicated that the ghost membrane elastic modulus was somewhat elevated compared to intact cells. We conclude that: ghosts have reduced membrane viscosity; ghosts have membrane rigidities close to intact cells, except possibly when the membrane is subjected to very large strains; the reduction in eta m is not directly related to the loss of hemoglobin; prolonged exposure of ghosts to low-ionic strength media increases the membrane viscosity toward its initial cellular level. These data indicate that the mechanical characteristics of ghost membranes can be varied by changing the methods of preparation and thus have potential application to further studies of the structural determinants of red cell membrane viscoelasticity.     

Micropipette aspiration on the outer hair cell lateral wall

The mechanical properties of the lateral wall of the guinea pig cochlear outer hair cell were studied using the micropipette aspiration technique. A fire-polished micropipette with an inner diameter of approximately 4 microm was brought into contact with the lateral wall and negative pressure was applied. The resulting deformation of the lateral wall was recorded on videotape and subjected to morphometric analysis. The relation between the length of the aspirated portion of the cell and aspiration pressure is characterized by the stiffness parameter, K(s) = 1.07 +/- 0.24 (SD) dyn/cm (n = 14). Values of K(s) do not correlate with the original cell length, which ranges from 29 to 74 microm. Theoretical analysis based on elastic shell theory applied to the experimental data yields an estimate of the effective elastic shear modulus, mu = 15.4 +/- 3.3 dyn/cm. These data were obtained at subcritical aspiration pressures, typically less than 10 cm H2O. After reaching a critical (vesiculation) pressure, the cytoplasmic membrane appeared to separate from the underlying structures, a vesicle with a length of 10-20 microm was formed, and the cytoplasmic membrane resealed. This vesiculation process was repeated until a cell-specific limit was reached and no more vesicles were formed. Over 20 vesicles were formed from the longest cells in the experiment.     

Is the surface area of the red cell membrane skeleton locally conserved?

The incompressibility of the lipid bilayer keeps the total surface area of the red cell membrane constant. Local conservation of membrane surface area requires that each surface element of the membrane skeleton keeps its area when its aspect ratio is changed. A change in area would require a flow of lipids past the intrinsic proteins to which the skeleton is anchored. in fast red cell deformations, there is no time for such a flow. Consequently, the bilayer provides for local area conservation. In quasistatic deformations, the extent of local change in surface area is the smaller the larger the isotropic modulus of the skeleton in relation to the shear modulus. Estimates indicate: (a) the velocity of relative flow between lipid and intrinsic proteins is proportional to the gradient in normal tension within the skeleton and inversely proportional to the viscosity of the bilayer; (b) lateral diffusion of lipids is much slower than this flow; (c) membrane tanktreading at frequencies prevailing in vivo as well as the release of a membrane tongue from a micropipette are fast deformations; and (d) the slow phase in micropipette aspiration may be dominated by a local change in skeleton surface.     

Force relaxation and permanent deformation of erythrocyte membrane.

Force relaxation and permanent deformation processes in erythrocyte membrane were investigated with two techniques: micropipette aspiration of a portion of a flaccid cell, and extension of a whole cell between two micropipettes. In both experiments, at surface extension ratios less than 3:1, the extent of residual membrane deformation is negligible when the time of extension is less than several minutes. However, extensions maintained longer result in significant force relaxation and permanent deformation. The magnitude of the permanent deformation is proportional to the total time period of extension and the level of the applied force. Based on these observations, a nonlinear constitutive relation for surface deformation is postulated that serially couples a hyperelastic membrane component to a linear viscous process. In contrast with the viscous dissipation of energy as heat that occurs in rapid extension of a viscoelastic solid, or in plastic flow of a material above yield, the viscous process in this case represents dissipation produced by permanent molecular reorganization through relaxation of structural membrane components. Data from these experiments determine a characteristic time constant for force relaxation, tau, which is the ratio of a surface viscosity, eta to the elastic shear modulus, mu. Because it was found that the concentration of albumin in the cell suspension strongly mediates the rate of force relaxation, values for tau of 10.1, 40.0, 62.8, and 120.7 min are measured at albumin concentrations of 0.0, 0.01, 0.1, and 1.% by weight in grams, respectively. The surface viscosity, eta, is calculated from the product of tau and mu. For albumin concentrations of 0.0, 0.01, 0.1, and 1% by weight in grams, eta is equal to 3.6, 14.8, 25.6, and 51.9 dyn s/cm, respectively.