Measurement of the Elastic Modulus for Red Cell Membrane Using a Fluid Mechanical Technique

Red cells which adhere to a surface in a parallel plate flow channel are stretched when acted on by a fluid shear stress. Three types of stretching are studied: whole cell stretching, the stretching of a red cell evagination, and tether (long, thin membrane process) stretching. In addition, the stretching of a large scale model cell attached to a surface is studied in a Couette flow channel. The results indicate that the uniaxial stretching of red cell membrane can be described by a linear stress-strain relationship. Simple theories developed from free body diagrams permit the calculation of a value for the modulus of elasticity of cell membrane in each of the three experiments. In all cases the value for the modulus is on the order of 10⁴ dyn/cm² for an assumed membrane thickness of 0.01 μm. It was also observed that red cell tethers steadily increase in length when the fluid shear stress is greater than approximately 1.5 dyn/cm² and tether lengths in excess of 200 μm have been achieved. Tethers appear to possess both fluid and elastic properties.     

Dynamic shear stress in parallel-plate flow chambers

An in vitro model using a parallel-plate fluid flow chamber is supposed to simulate in vivo fluid shear stresses on various cell types exposed to dynamic fluid flow in their physiological environment. The metabolic response of cells in vitro is associated with the wall shear stress. However, parallel-plate flow chambers have not been characterized for dynamic fluid flow experiments. We use a dimensionless ratio h / lambda(v), in determining the exact magnitude of the dynamic wall shear stress, with its oscillating components scaled by a shear factor T. It is shown that, in order to expose cells to predictable levels of dynamic fluid shear stress, two conditions have to be met: (1) h / lambda(v) < 2, where h is the distance between the plates and lambda(v) is the viscous penetration depth; and (2) f(0) < f(c) / m, where the critical frequency f(c) is the upper threshold for this flow regime, m is the highest harmonic mode of the flow, and f(0) is the fundamental frequency of fluid flow.     

An elastic network model based on the structure of the red blood cell membrane skeleton.

A finite element network model has been developed to predict the macroscopic elastic shear modulus and the area expansion modulus of the red blood cell (RBC) membrane skeleton on the basis of its microstructure. The topological organization of connections between spectrin molecules is represented by the edges of a random Delaunay triangulation, and the elasticity of an individual spectrin molecule is represented by the spring constant, K, for a linear spring element. The model network is subjected to deformations by prescribing nodal displacements on the boundary. The positions of internal nodes are computed by the finite element program. The average response of the network is used to compute the shear modulus (mu) and area expansion modulus (kappa) for the corresponding effective continuum. For networks with a moderate degree of randomness, this model predicts mu/K = 0.45 and kappa/K = 0.90 in small deformations. These results are consistent with previous computational models and experimental estimates of the ratio mu/kappa. This model also predicts that the elastic moduli vary by 20% or more in networks with varying degrees of randomness. In large deformations, mu increases as a cubic function of the extension ratio lambda 1, with mu/K = 0.62 when lambda 1 = 1.5.     

Mammalian cell damage in a novel membrane bioreactor

The experimental study has assessed a novel membrane bioreactor for mammalian cell culture. In the absence of a gas phase, the key features of cell damage associated with laminar and turbulent flow have been identified. The bioreactor employs a dimpled membrane in order to enhance transverse mixing in a narrow channel, but a fall in viable cell density has been observed at Reynolds numbers above Re = 83. In the laminar flow regime wall shear is the critical mechanism and an accurate calculation of shear rate in a complex channel has been achieved using the Reynolds analogy. Flow generating a wall shear rate in excess of 3000 s(-1) has been shown to cause damage. Power dissipation measurements have been used to distinguish between laminar and turbulent flow and also to predict Kolmogorov eddy lengths. An additional turbulent bulk stress damage mechanism at higher Reynolds numbers (Re > 250) results in a very rapid fall in viable cell density.     

Influence of sickle hemoglobin polymerization and membrane properties on deformability of sickle erythrocytes in the microcirculation.

The rheological properties of normal erythrocytes appear to be largely determined by those of the red cell membrane. In sickle cell disease, the intracellular polymerization of sickle hemoglobin upon deoxygenation leads to a marked increase in intracellular viscosity and elastic stiffness as well as having indirect effects on the cell membrane. To estimate the components of abnormal cell rheology due to the polymerization process and that due to the membrane abnormalities, we have developed a simple mathematical model of whole cell deformability in narrow vessels. This model uses hydrodynamic lubrication theory to describe the pulsatile flow in the gap between a cell and the vessel wall. The interior of the cell is modeled as a Voigt viscoelastic solid with parameters for the viscous and elastic moduli, while the membrane is assigned an elastic shear modulus. In response to an oscillatory fluid shear stress, the cell--modeled as a cylinder of constant volume and surface area--undergoes a conical deformation which may be calculated. We use published values of normal and sickle cell membrane elastic modulus and of sickle hemoglobin viscous and elastic moduli as a function of oxygen saturation, to estimate normalized tip displacement, d/ho, and relative hydrodynamic resistance, Rr, as a function of polymer fraction of hemoglobin for sickle erythrocytes. These results show the transition from membrane to internal polymer dominance of deformability as oxygen saturation is lowered. More detailed experimental data, including those at other oscillatory frequencies and for cells with higher concentrations of hemoglobin S, are needed to apply fully this approach to understanding the deformability of sickle erythrocytes in the microcirculation. The model should be useful for reconciling the vast and disparate sets of data available on the abnormal properties of sickle cell hemoglobin and sickle erythrocyte membranes, the two main factors that lead to pathology in patients with this disease.     

Differential membrane potential and ion current responses to different types of shear stress in vascular endothelial cells

Vascular endothelial cells (ECs) distinguish among and respond differently to different types of fluid mechanical shear stress. Elucidating the mechanisms governing this differential responsiveness is the key to understanding why early atherosclerotic lesions localize preferentially in arterial regions exposed to low and/or oscillatory flow. An early and very rapid endothelial response to flow is the activation of flow-sensitive K⁺ and Cl^– channels that respectively hyperpolarize and depolarize the cell membrane and regulate several important endothelial responses to flow. We have used whole cell current- and voltage-clamp techniques to demonstrate that flow-sensitive hyperpolarizing and depolarizing currents respond differently to different types of shear stress in cultured bovine aortic ECs. A steady shear stress level of 10 dyn/cm² activated both currents leading to rapid membrane hyperpolarization that was subsequently reversed to depolarization. In contrast, a steady shear stress of 1 dyn/cm² only activated the hyperpolarizing current. A purely oscillatory shear stress of 0 ± 10 dyn/cm² with an oscillation frequency of either 1 or 0.2 Hz activated the hyperpolarizing current but only minimally the depolarizing current, whereas a 5-Hz oscillation activated neither current. These results demonstrate for the first time that flow-activated ion currents exhibit different sensitivities to shear stress magnitude and oscillation frequency. We propose that flow-sensitive ion channels constitute components of an integrated mechanosensing system that, through the aggregate effect of ion channel activation on cell membrane potential, enables ECs to distinguish among different types of flow. ion channels; atherosclerosis; mechanotransduction     

Erythrocyte membranes alteration in a shear stress measured by fluorescence anisotropy.

An experimental setup has been designed to allow fluorescence anisotropy measurements on labeled cell membranes under shear stress. An important change is observed when increasing the shear stress and varying the experimental parameters indicates that a decrease in membrane cohesion leads to a subsequent increase in the membrane alteration under shear stress. A model has been developed that shows, in agreement with experiment, that the effect observed is mainly the result of the alteration of the membrane, elongation, and orientation with respect to the fluid flow, which can be estimated.     

Viscoelastic properties of proteoglycan subunits and aggregates in varying solution concentrations

Using a cone-on-plate mechanical spectrometer, we have measured the linear and non-linear rheological properties of cartilage proteoglycan solutions at concentrations similar to those found in situ. Solutions of bovine nasal cartilage proteoglycan subunits (22S) and aggregates (79S) were studied at concentrations ranging from 10 to 50 mg ml-1. We determined: (1) the complex viscoelastic shear modulus G (omega) under small amplitude (0.02 radians) oscillatory excitation at frequencies (omega) ranging from 1.0 to 20.0 Hz, (2) the non-linear shear rate (gamma) dependent apparent viscosity napp (gamma) in continuous shear, and (3) the non-linear shear rate dependent primary normal stress difference sigma 1 (gamma) in continuous shear. Both the apparent viscosity and normal stress difference were measured over four decades of shear rates ranging from 0.25 to 250 s-1. Analysis of the experimental results were performed using a variety of materially objective non-linear viscoelastic constitutive laws. We found that the non-linear, four-coefficient Oldroyd rate-type model was most effective for describing the measured flow characteristics of proteoglycan subunit and aggregate solutions. Values of the relaxation time lambda 1, retardation time lambda 2, zero shear viscosity no, and nonlinear viscosity parameter muo were computed for the aggregate and subunit solutions at all of the solute concentrations used. The four independent material coefficients showed marked dependence on the two different molecular conformations, i.e. aggregate or subunit, of proteoglycans in solution.     

Erythrocyte membranes alteration in a shear stress measured by fluorescence anisotropy

An experimental setup has been designed to allow fluorescence anisotropy measurements on labeled cell membranes under shear stress. An important change is observed when increasing the shear stress and varying the experimental parameters indicates that a decrease in membrane cohesion leads to a subsequent increase in the membrane alteration under shear stress. A model has been developed that shows, in agreement with experiment, that the effect observed is mainly the result of the alteration of the membrane, elongation, and orientation with respect to the fluid flow, which can be estimated.     

Differential effects of pulsatile versus steady flow on coronary endothelial membrane potential

Steady shear stress stimulates transient hyperpolarization coupled to calcium-sensitive potassium (KCa) channels and sustained depolarization linked to chloride-selective channels. Physiological flow is pulsatile not static, and whereas in vivo data suggest phasic shear stress may preferentially activate KCa channels, its differential effects on both currents remain largely unknown. To determine this interaction, coronary endothelial cells were cultured in glass capillary flow tubes, loaded with the voltage-sensitive dye bis-(1,3-dibutylbarbituric acid)trimethine oxonol, and exposed to constant or pulsatile shear stress. The latter was generated by a custom servoperfusion system employing physiological pressure and flow waveforms. Steady shear induced a sustained depolarization inhibited by the Cl- channel blocker DIDS. Even after exposure to steady flow, subsequent transition to pulsatile shear stress further stimulated DIDS-sensitive depolarization. DIDS pretreatment "unmasked" a pulsatile flow-induced hyperpolarization of which magnitude was further enhanced by nifedipine, which augments epoxygenase synthesis. Pulse-shear hyperpolarization was fully blocked by KCa channel inhibition (charybdotoxin + apamin), although these agents had no influence on membrane potential altered by steady flow. Thus KCa-dependent hyperpolarization is preferentially stimulated by pulsatile over steady flow, whereas both can stimulate Cl--dependent depolarization. This supports studies showing greater potency of pulsatile flow for triggering KCa-dependent vasorelaxation.     

Nanoliter scale microbioreactor array for quantitative cell biology

A nanoliter scale microbioreactor array was designed for multiplexed quantitative cell biology. An addressable 8 x 8 array of three nanoliter chambers was demonstrated for observing the serum response of HeLa human cancer cells in 64 parallel cultures. The individual culture unit was designed with a "C" shaped ring that effectively decoupled the central cell growth regions from the outer fluid transport channels. The chamber layout mimics physiological tissue conditions by implementing an outer channel for convective "blood" flow that feeds cells through diffusion into the low shear "interstitial" space. The 2 microm opening at the base of the "C" ring established a differential fluidic resistance up to 3 orders of magnitude greater than the fluid transport channel within a single mold microfluidic device. Three-dimensional (3D) finite element simulation were used to predict fluid transport properties based on chamber dimensions and verified experimentally. The microbioreactor array provided a continuous flow culture environment with a Peclet number (0.02) and shear stress (0.01 Pa) that approximated in vivo tissue conditions without limiting mass transport (10 s nutrient turnover). This microfluidic design overcomes the major problems encountered in multiplexing nanoliter culture environments by enabling uniform cell loading, eliminating shear, and pressure stresses on cultured cells, providing stable control of fluidic addressing, and permitting continuous on-chip optical monitoring.     

Effect of hydroperoxides on red blood cell membrane mechanical properties

We investigate the effect of oxidative stress on red blood cell membrane mechanical properties in vitro using detailed analysis of the membrane thermal fluctuation spectrum. Two different oxidants, the cytosol-soluble hydrogen peroxide and the membrane-soluble cumene hydroperoxide, are used, and their effects on the membrane bending elastic modulus, surface tension, strength of confinement due to the membrane skeleton, and 2D shear elastic modulus are measured. We find that both oxidants alter significantly the membrane elastic properties, but their effects differ qualitatively and quantitatively. While hydrogen peroxide mainly affects the elasticity of the membrane protein skeleton (increasing the membrane shear modulus), cumene hydroperoxide has an impact on both membrane skeleton and lipid bilayer mechanical properties, as can be seen from the increased values of the shear and bending elastic moduli. The biologically important implication of these results is that the effects of oxidative stress on the biophysical properties, and hence the physiological functions, of the cell membrane depend on the nature of the oxidative agent. Thermal fluctuation spectroscopy provides a means of characterizing these different effects, potentially in a clinical milieu.     

Vascular endothelial wound closure under shear stress: role of membrane fluidity and flow-sensitive ion channels.

Sufficiently rapid healing of vascular endothelium following injury is essential for preventing further pathological complications. Recent work suggests that fluid dynamic shear stress regulates endothelial cell (EC) wound closure. Changes in membrane fluidity and activation of flow-sensitive ion channels are among the most rapid endothelial responses to flow and are thought to play an important role in EC responsiveness to shear stress. The goal of the present study was to probe the role of these responses in bovine aortic EC (BAEC) wound closure under shear stress. BAEC monolayers were mechanically wounded and subsequently subjected to either "high" (19 dyn/cm(2)) or "low" (3 dyn/cm(2)) levels of steady shear stress. Image analysis was used to quantify cell migration and spreading under both flow and static control conditions. Our results demonstrate that, under static conditions, BAECs along both wound edges migrate at similar velocities to cover the wounded area. Low shear stress leads to significantly lower BAEC migration velocities, whereas high shear stress results in cells along the upstream edge of the wound migrating significantly more rapidly than those downstream. The data also show that reducing BAEC membrane fluidity by enriching the cell membrane with exogenous cholesterol significantly slows down both cell spreading and migration under flow and hence retards wound closure. Blocking flow-sensitive K and Cl channels reduces cell spreading under flow but has no impact on cell migration. These findings provide evidence that membrane fluidity and flow-sensitive ion channels play distinct roles in regulating EC wound closure under flow.     

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.     

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.     

Local measurements of viscoelastic parameters of adherent cell surfaces by magnetic bead microrheometry.

A magnetic bead microrheometer has been designed which allows the generation of forces up to 10(4) pN on 4.5 micron paramagnetic beads. It is applied to measure local viscoelastic properties of the surface of adhering fibroblasts. Creep response and relaxation curves evoked by tangential force pulses of 500-2500 pN (and approximately 1 s duration) on the magnetic beads fixed to the integrin receptors of the cell membrane are recorded by particle tracking. Linear three-phasic creep responses consisting of an elastic deflection, a stress relaxation, and a viscous flow are established. The viscoelastic response curves are analyzed in terms of a series arrangement of a dashpot and a Voigt body, which allows characterization of the viscoelastic behavior of the adhering cell surface in terms of three parameters: an effective elastic constant, a viscosity, and a relaxation time. The displacement field generated by the local tangential forces on the cell surface is visualized by observing the induced motion of assemblies of nonmagnetic colloidal probes fixed to the membrane. It is found that the displacement field decays rapidly with the distance from the magnetic bead. A cutoff radius of Rc approximately 7 micron of the screened elastic field is established. Partial penetration of the shear field into the cytoplasm is established by observing the induced deflection of intracellular compartments. The cell membrane was modeled as a thin elastic plate of shear modulus mu * coupled to a viscoelastic layer, which is fixed to a solid support on the opposite side; the former accounts for the membrane/actin cortex, and the latter for the contribution of the cytoskeleton to the deformation of the cell envelope. It is characterized by the coupling constant chi characterizing the elasticity of the cytoskeleton. The coupling constant chi and the surface shear modulus mu * are obtained from the measured displacements of the magnetic and nonmagnetic beads. By analyzing the experimental data in terms of this model a surface shear modulus of mu * approximately 2 . 10(-3) Pa m to 4 . 10(-3) Pa m is found. By assuming an approximate plate thickness of 0.1 micron one estimates an average bulk shear modulus of mu approximately (2 / 4) . 10(-4) Pa, which is in reasonable agreement with data obtained by atomic force microscopy. The viscosity of the dashpot is related to the apparent viscosity of the cytoplasm, which is obtained by assuming that the top membrane is coupled to the bottom (fixed) membrane by a viscous medium. By application of the theory of diffusion of membrane proteins in supported membranes we find a coefficient of friction of bc approximately 2 . 10(9) Pa s/m corresponding to a cytoplasmic viscosity of 2 . 10(3) Pa s.     

Red blood cell deformation in shear flow. Effects of internal and external phase viscosity and of in vivo aging.

Shear deformation of young and old human red blood cells was examined over a range of shear stresses and suspending phase viscosities (eta o) using a cone-plate Rheoscope. The internal viscosities (eta i) of these cell types differ, and further changes in internal viscosity were induced by alteration of suspension osmolality and hence cell volume. For low suspending viscosities (0.0555 or 0.111 P) old cells tended to tumble in shear flow, whereas young cells achieved stable orientation and deformed. Changes in osmolality, at these external viscosities, altered the percentage of cells deforming, and for each cell type threshold osmolalities (Osm-50) were determined where 50% of cells deformed. The threshold osmolalities were higher for younger cells than for older cells, but the internal viscosities of the two cell types were similar at their respective Osm-50. Threshold osmolalities were also higher for the higher external viscosity, but the ratio of internal to external viscosities (i.e., eta i/eta o) was nearly constant for both external viscosities. Deformation of stably oriented cells increased with increasing shear stress and approached a value limited by cell surface area and volume. For isotonic media, over a wide range of external viscosities and shear stresses, deformation was greater for younger cells than for older cells. However, deformation vs. shear stress data for the two cell types became nearly coincident if young cells were osmotically shrunk to have their internal viscosity close to that for old cells. Increases in external viscosity, at constant shear stress, caused greater deformation for all cells. This effect of external viscosity was not equal for young and old cells; the ratio of old/young cell deformation increased with increasing eta o. However, if deformation was plotted as a function of the ratio lambda = eta i/eta o, at constant shear stress, young and old cell data followed similar paths. Thus the ratio lambda is a major determinant of cell deformation as well as a critical factor affecting stable orientation in shear flow.     

The fluid shear stress distribution on the membrane of leukocytes in the microcirculation

Recent in-vivo and in-vitro evidence indicates that fluid shear stress on the membrane of leukocytes has a powerful control over several aspects of their cell function. This evidence raises a question about the magnitude of the fluid shear stress on leukocytes in the circulation. The flow of plasma on the surface of a leukocyte at a very low Reynolds number is governed by the Stokes equation for the motion of a Newtonian fluid. We numerically estimated the distribution of fluid shear stress on a leukocyte membrane in a microvessel for the cases when the leukocyte is freely suspended, as well as rolling along or attached to a microvessel wall. The results indicate that the fluid shear stress distribution on the leukocyte membrane is nonuniform with a sharp increase when the leukocyte makes membrane attachment to the microvessel wall. In a microvessel (10 microns diameter), the fluid shear stress on the membrane of a freely suspended leukocyte (8 microns diameter) is estimated to be several times larger than the wall shear stress exerted by the undisturbed Poiseuille flow, and increases on an adherent leukocyte up to ten times. High temporal stress gradients are present in freely suspended leukocytes in shear flow due to cell rotation, which are proportional to the local shear rate. In comparison, the temporal stress gradients are reduced on the membrane of leukocytes that are rolling or firmly adhered to the endothelium. High temporal gradients of shear stress are also present on the endothelial wall. At a plasma viscosity of 1 cPoise, the peak shear stresses for suspended and adherent leukocytes are of the order of 10 dyn/cm2 and 100 dyn/cm2, respectively.