Membrane viscoplastic flow

Controllable Cell Deformation Using Acoustic Streaming for Membrane Permeability Modulation

Hydrodynamic force loading platforms for controllable cell mechanical deformation play an essential role in modern cell technologies. Current systems require assistance from specific microstructures thus limiting the controllability and flexibility in cell shape modulation, and studies on real-time 3D cell morphology analysis are still absent. This article presents a novel platform based on acoustic streaming generated from a gigahertz device for cell shape control and real-time cell deformation analysis. Details in cell deformation and the restoration process are thoroughly studied on the platform, and cell behavior control at the microscale is successfully achieved by tuning the treating time, intensity, and wave form of the streaming. The application of this platform in cell membrane permeability modulation and analysis is also exploited. Based on the membrane reorganization during cell deformation, the effects of deformation extent and deformation patterns on membrane permeability to micro- and macromolecules are revealed. This technology has shown its unique superiorities in cell mechanical manipulation such as high flexibility, high accuracy, and pure fluid force operation, indicating its promising prospect as a reliable tool for cell property study and drug therapy development.

Flow-Induced Damage to Blood Cells in Aortic Valve Stenosis

Valvular hemolysis and thrombosis are common complications associated with stenotic heart valves. This study aims to determine the extent to which hemodynamics induce such traumatic events. The viscous shear stress downstream of a severely calcified bioprosthetic valve was evaluated via in vitro 2D particle image velocimetry measurements. The blood cell membrane response to the measured stresses was then quantified using 3D immersed-boundary computational simulations. The shear stress level at the boundary layer of the jet flow formed downstream of the valve orifice was observed to reach a maximum of 1000-1700 dyn/cm(2), which was beyond the threshold values reported for platelet activation (100-1000 dyn/cm(2)) and within the range of thresholds reported for red blood cell (RBC) damage (1000-2000 dyn/cm(2)). Computational simulations demonstrated that the resultant tensions at the RBC membrane surface were unlikely to cause instant rupture, but likely to lead to membrane plastic failure. The resultant tensions at the platelet surface were also calculated and the potential damage was discussed. It was concluded that although shear-induced thrombotic trauma is very likely in stenotic heart valves, instant hemolysis is unlikely and the shear-induced damage to RBCs is mostly subhemolytic.

Mathematical modelling of peristaltic propulsion of viscoplastic bio-fluids

This article studies theoretically the transportation of rheological viscoplastic fluids through physiological vessels by continuous muscle contraction and relaxation, that is, peristalsis. Both cases of planar and cylindrical physiological vessels are considered. A mathematical model is developed under long wavelength and low Reynolds number approximations. Expressions for axial velocity in core region, axial velocity in plug flow region, volume flow rate and pressure gradient in non-dimensional form are obtained. A comparative study of velocity profiles, pressure distribution, friction force and mechanical efficiency for different viscoplastic liquids is conducted. The influence of width of plug flow region, shear rate strain index and yield stress index on the pressure distribution, friction force and mechanical efficiency is elaborated. The study is relevant to gastric fluid mechanics and also non-Newtonian biomimetic pump hazardous waste systems exploiting peristaltic mechanisms.

Lipid-based nanoparticles as pharmaceutical drug carriers: from concepts to clinic

In recent years, various nanotechnology platforms in the area of medical biology, including both diagnostics and therapy, have gained remarkable attention. Moreover, research and development of engineered multifunctional nanoparticles as pharmaceutical drug carriers have spurred exponential growth in applications to medicine in the last decade. Design principles of these nanoparticles, including nanoemulsions, dendrimers, nano-gold, liposomes, drug-carrier conjugates, antibody-drug complexes, and magnetic nanoparticles, are primarily based on unique assemblies of synthetic, natural, or biological components, including but not limited to synthetic polymers, metal ions, oils, and lipids as their building blocks. However, the potential success of these particles in the clinic relies on consideration of important parameters such as nanoparticle fabrication strategies, their physical properties, drug loading efficiencies, drug release potential, and, most importantly, minimum toxicity of the carrier itself. Among these, lipid-based nanoparticles bear the advantage of being the least toxic for in vivo applications, and significant progress has been made in the area of DNA/RNA and drug delivery using lipid-based nanoassemblies. In this review, we will primarily focus on the recent advances and updates on lipid-based nanoparticles for their projected applications in drug delivery. We begin with a review of current activities in the field of liposomes (the so-called honorary nanoparticles), and challenging issues of targeting and triggering will be discussed in detail. We will further describe nanoparticles derived from a novel class of amphipathic lipids called bolaamphiphiles with unique lipid assembly features that have been recently examined as drug/DNA delivery vehicles. Finally, an overview of an emerging novel class of particles (based on lipid components other than phospholipids), solid lipid nanoparticles and nanostructured lipid carriers will be presented. We conclude with a few examples of clinically successful formulations of currently available lipid-based nanoparticles.

Integral protein linkage and the bilayer-skeletal separation energy in red blood cells

Stabilization of the lipid bilayer membrane in red blood cells by its association with an underlying membrane-associated cytoskeleton has long been recognized as critical for proper red blood cell function. One of the principal connections between skeleton and bilayer is via linkages between band 3, the integral membrane protein that transports anions across the cell surface, and membrane skeletal elements including ankyrin, adducin, spectrin, and the junctional complex of the skeleton. Here, we use membrane tether formation coupled with fluorescent labeling of membrane components to examine the importance of band 3 in stabilizing the bilayer-skeletal association. In membranes from a patient deficient in band 3, the energy associated with the bilayer skeleton is approximately zero, whereas when band 3 is immobilized by ligation with the monoclonal antibody R10, the energy of association approximately doubles. Fluorescence images of tethers reveal that approximately 40% of the band 3 on the normal cell surface can be pulled into the tether, confirming a lateral segregation of membrane components during tether formation. These results validate a critical role for band 3 in stabilizing the bilayer-skeletal association in red cells.

The Cumulative and Sublethal Effects of Turbulence on Erythrocytes in a Stirred-Tank Model

Mechanical forces generated by prosthetic heart devices (artificial valves, artificial hearts, ventricular assist devices) have been known to cause damage and destruction of erythrocytes. Turbulent flow within such devices generates shear stresses and can induce cell damage. Current models of cell damage rate utilize only the power input per unit mass as a modeling parameter. A stirred-tank reactor provides for a more extensive characterization of turbulence through eddy scale calculations. Through a simplified model, turbulence can be characterized by evaluating the Kolmogorov microscale. Our analysis of erythrocyte rupture in a stirred tank reactor suggests that parameters such as eddy wavelength and eddy velocity may better characterize and model the turbulent damage. Further, hemolysis of red blood cells by turbulent effects has been shown to have a fixed rate for constant levels of power input. Damage inflicted on the remaining, intact erythrocytes (sublethal damage) was evaluated by exposure to turbulence followed by osmotic fragility (OF) testing. Logistic models were fit to the OF data indicating a significant osmotic sensitivity in the sublethal damaged population between control and turbulence-exposed cells (chi(2) test; p < 0.001). This susceptibility indicates a significant cell population more susceptible to destruction as a result of turbulent exposure. This work has therefore helped identify optimization parameters for evaluating cell damage potential when engineering cardiovascular prosthetic devices.

Viscoelasticity of the human red blood cell

We report here the first measurements of the complex modulus of the isolated red blood cell (RBC). Because the RBC is often larger than capillary diameter, important determinants of microcirculatory function are RBC deformability and its changes with pathologies, such as sickle cell disease and malaria. A functionalized ferrimagnetic microbead was attached to the membrane of healthy RBC and then subjected to an oscillatory magnetic field. The resulting torque caused cell deformation. From the oscillatory forcing and resulting bead motions, which were tracked optically, we computed elastic and frictional moduli, g′ and g‴, respectively, from 0.1 to 100 Hz. The g′ was nearly frequency independent and dominated the response at all but the highest frequencies measured. Over three frequency decades, g‴ increased as a power law with an exponent of 0.64, a result not predicted by any simple model. These data suggest that RBC relaxation times that have been reported previously, and any models that rest upon them, are artifactual; the artifact, we suggest, arises from forcing to an exponential fit data of limited temporal duration. A linear range of response was observed, but, as forcing amplitude increased, nonlinearities became clearly apparent. A finite element model suggests that membrane bending was localized to the vicinity of the bead and dominated membrane shear. While the mechanisms accounting for these RBC dynamics remain unclear, methods described here establish new avenues for the exploration of connections among the mechanical, chemical, and biological characteristics of the RBC in health and disease.

Biomechanics and biophysics of cancer cells

The past decade has seen substantial growth in research into how changes in the biomechanical and biophysical properties of cells and subcellular structures influence, and are influenced by, the onset and progression of human diseases. This paper presents an overview of the rapidly expanding, nascent field of research that deals with the biomechanics and biophysics of cancer cells. The review begins with some key observations on the biology of cancer cells and on the role of actin microfilaments, intermediate filaments and microtubule biopolymer cytoskeletal components in influencing cell mechanics, locomotion, differentiation and neoplastic transformation. In order to set the scene for mechanistic discussions of the connections among alterations to subcellular structures, attendant changes in cell deformability, cytoadherence, migration, invasion and tumor metastasis, a survey is presented of the various quantitative mechanical and physical assays to extract the elastic and viscoelastic deformability of cancer cells. Results available in the literature on cell mechanics for different types of cancer are then reviewed. Representative case studies are presented next to illustrate how chemically induced cytoskeletal changes, biomechanical responses and signals from the intracellular regions act in concert with the chemomechanical environment of the extracellular matrix and the molecular tumorigenic signaling pathways to effect malignant transformations. Results are presented to illustrate how changes to cytoskeletal architecture induced by cancer drugs and chemotherapy regimens can significantly influence cell mechanics and disease state. It is reasoned through experimental evidence that greater understanding of the mechanics of cancer cell deformability and its interactions with the extracellular physical, chemical and biological environments offers enormous potential for significant new developments in disease diagnostics, prophylactics, therapeutics and drug efficacy assays.

Role of membrane curvature in mechanoelectrical transduction: Ion carriers nonactin and valinomycin sense changes in integral bending energy

We describe the phenomenon of mechanoelectrical transduction in macroscopic lipid bilayer membranes modified by two cation-selective ionophores, valinomycin and nonactin. We found that bulging these membranes, while maintaining the membrane tension constant, produced a marked supralinear increase in specific carrier-mediated conductance. Analyses of the mechanisms involved in mechanoelectrical transduction induced by the imposition of a hydrostatic pressure gradient or by an amphipathic compound chlorpromazine reveal similar changes in the charge carrier motility and carrier reaction rates at the interface(s). Furthermore, the relative change in membrane conductance was independent of membrane diameter, but was directly proportional to the square of membrane curvature, thus relating the observed phenomena to the bilayer bending energy. Extrapolated to biological membranes, these findings indicate that ion transport in cells can be influenced simply by changing shape of the membrane, without a change in membrane tension.

Multiple membrane tethers probed by atomic force microscopy

Using the atomic force microscope to locally probe the cell membrane, we observed the formation of multiple tethers (thin nanotubes, each requiring a similar pulling force) as reproducible features within force profiles recorded on individual cells. Forces obtained with Chinese hamster ovary cells, a malignant human brain tumor cell line, and human endothelial cells (EA hy926) were found to be 28 +/- 10 pN, 29 +/- 9 pN, and 29 +/- 10 pN, respectively, independent of the nature of attachment to the cantilever. The rather large variation of the tether pulling forces measured at several locations on individual cells points to the existence of heterogeneity in the membrane properties of a morphologically homogeneous cell. Measurement of the summary lengths of the simultaneously extracted tethers provides a measure of the size of the available membrane reservoir through which co-existing tethers are associated. As expected, partial disruption of the actin cytoskeleton and removal of the hyaluronan backbone of the glycocalyx were observed to result in a marked decrease (30-50%) in the magnitude and a significant sharpening of the force distribution indicating reduced heterogeneity of membrane properties. Taken together, our results demonstrate the ability of the plasma membrane to locally produce multiple interdependent tethers-a process that could play an important role in the mechanical association of cells with their environment.

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.

Erythropoietin-induced rheological changes of rat erythrocytes

The effects of recombinant human erythropoietin (rhEPO) on red blood cell (RBC) rheological properties were investigated in rats. Rats received intramuscular injections of 150 U/kg/d rhEPO for 5 d, following which blood samples were obtained 1, 5 or 10 d later. RBC deformability was assessed by determining cell transit times through 5-microm micropores (CTA) and RBC shape recovery time constants via photometry, aggregation in plasma and dextran was measured by photometry and RBC electrophoretic mobility was determined in a cylindrical electrophoresis system. RBC aggregation was found to be significantly decreased on day 5 after rhEPO treatment (P < 0.05), yet was unchanged from control on days 1 and 10. Mean RBC micropore transit times remained unchanged, but the distributions of transit times were altered; compared with control, the 5th percentiles on both days 1 and 5 were decreased and the 95th percentile on day 1 was elevated. Electrophoretic mobility of RBCs in phosphate-buffered saline was significantly increased on day 5 after rhEPO treatment (P < 0.05), with mobility measurements in dextran 500 (MW = 500 kDa) solutions suggesting that the cells' surface properties related to the formation of a 'depletion layer' may be altered on day 1. These results indicate that the rheological behaviour of RBC as a consequence of rhEPO treatment are temporal and are affected by the presence of reticulocytes as well as by the average age of the circulating cells.

A membrane bending model of outer hair cell electromotility

We propose a new mechanism for outer hair cell electromotility based on electrically induced localized changes in the curvature of the plasma membrane (flexoelectricity). Electromechanical coupling in the cell's lateral wall is modeled in terms of linear constitutive equations for a flexoelectric membrane and then extended to nonlinear coupling based on the Langevin function. The Langevin function, which describes the fraction of dipoles aligned with an applied electric field, is shown to be capable of predicting the electromotility voltage displacement function. We calculate the electrical and mechanical contributions to the force balance and show that the model is consistent with experimentally measured values for electromechanical properties. The model rationalizes several experimental observations associated with outer hair cell electromotility and provides for constant surface area of the plasma membrane. The model accounts for the isometric force generated by the cell and explains the observation that the disruption of spectrin by diamide reduces force generation in the cell. We discuss the relation of this mechanism to other proposed models of outer hair cell electromotility. Our analysis suggests that rotation of membrane dipoles and the accompanying mechanical deformation may be the molecular mechanism of electromotility.

Accelerated interleaflet transport of phosphatidylcholine molecules in membranes under deformation

Biological membranes are lamellar structures composed of two leaflets capable of supporting different mechanical stresses. Stress differences between leaflets were generated during micromechanical experiments in which long thin tubes of lipid (tethers) were formed from the surfaces of giant phospholipid vesicles. A recent dynamic analysis of this experiment predicts the relaxation of local differences in leaflet stress by lateral slip between the leaflets. Differential stress may also relax by interleaflet transport of lipid molecules ("flip-flop"). In this report, we extend the former analysis to include interleaflet lipid transport. We show that transmembrane lipid flux will evidence itself as a linear increase in tether length with time after a step reduction in membrane tension. Multiple measurements were performed on 24 different vesicles composed of stearoyl-oleoyl-phosphatidylcholine plus 3% dinitrophenol-linked di-oleoyl-phosphatidylethanolamine. These tethers all exhibited a linear phase of growth with a mean value of the rate of interlayer permeation, cp = 0.009 s-1. This corresponds to a half-time of approximately 8 min for mechanically driven interleaflet transport. This value is found to be consistent with longer times obtained for chemically driven transport if the lipids cross the membrane via transient, localized defects in the bilayer.

Mechanically stimulated cytoskeleton rearrangement and cortical contraction in human neutrophils

A mechanical test with micropipets is used to characterize cytoskeleton rearrangement and contraction induced by mechanical stresses in human neutrophils. The yield shear resultant of the cell cortex is on the order of 0.06 to 0.09 mN.m-1. The measured yield shear resultant suggests that the neutrophil cortex is a weakly cross-linked structure. When a tether is pulled out from the cell surface, a polymer structure starts to fill it and spreads out from the cell body. The rate of advancement of the polymerization front is almost constant and, therefore, is not diffusion limited. The measured rate is much smaller than the one of spontaneous actin polymerization, suggesting that the limiting process is either the dissociation of actin monomers from their dimers with the capping proteins or the rate of formation of new nucleation sites or both. Polymerization is also observed after applying sufficient mechanical stresses on a small portion of the cell surface. The polymerization is followed by mass transfer from the cell into the prestressed region and later on by contraction of the main cell body. The pressure generating the flow is located in the prestressed region and most probably is a result of its "swelling" and contraction. The contraction of the main cell body is very similar (in its time dependence and magnitude) to the contraction during phagocytosis. The measured maximum cortical tension is on the order of 0.5 mN.m-1, which for a 3.5-microns diameter pipet corresponds to a maximum contraction force of 11 nN.

Role of lamellar membrane structure in tether formation from bilayer vesicles

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

Analysis of lateral diffusion from a spherical cell surface to a tubular projection

Cell surfaces are often heterogeneous with respect to the lateral distribution and mobility of membrane components. Because lateral mobility is related to membrane structure, measurement of a particular component's local diffusion coefficient within a distinct surface region provides useful information about the formation and maintenance of that region. Many structurally interesting cell surface features can be described as narrow tubular projections from the body of the cell. In a companion paper, we consider the thin "tethers" that can be mechanically drawn from the red blood cell membrane, and we measure the transport of fluorescent integral proteins from the surface of the cell body onto the tether. In this paper we present an analysis to describe the surface diffusion of membrane particles from a spherical shell onto a thin cylindrical process. Provision is made for different rates of diffusion within the two morphologically distinct regions. The relative role of each region in controlling the diffusive flux between regions is determined primarily by a single dimensionless parameter. This parameter incorporates the ratio of the two diffusion coefficients as well as the dimensions of each region. The analysis can be applied to a fluorescence photobleaching experiment in which the extended process is bleached. If the dimensions of the spherical cell body and the cylindrical extension are known, then the diffusion coefficients of both regions can be determined from the experimental fluorescence recovery curve.

Lateral mobility of integral proteins in red blood cell tethers

The red blood cell membrane is a complex material that exhibits both solid- and liquidlike behavior. It is distinguished from a simple lipid bilayer capsule by its mechanical properties, particularly its shear viscoelastic behavior and by the long-range mobility of integral proteins on the membrane surface. Subject to sufficiently large extension, the membrane loses its shear rigidity and flows as a two-dimensional fluid. These experiments examine the change in integral protein mobility that accompanies the mechanical phenomenon of extensional failure and liquidlike flow. A flow channel apparatus is used to create red cell tethers, hollow cylinders of greatly deformed membrane, up to 36-microns long. The diffusion of proteins within the surface of the membrane is measured by the technique of fluorescence redistribution after photobleaching (FRAP). Integral membrane proteins are labeled directly with a fluorescein dye (DTAF). Mobility in normal membrane is measured by photobleaching half of the cell and measuring the rate of fluorescence recovery. Protein mobility in tether membrane is calculated from the fluorescence recovery rate after the entire tether has been bleached. Fluorescence recovery rates for normal membrane indicate that more than half the labeled proteins are mobile with a diffusion coefficient of approximately 4 x 10(-11) cm2/s, in agreement with results from other studies. The diffusion coefficient for proteins in tether membrane is greater than 1.5 x 10(-9) cm2/s. This dramatic increase in diffusion coefficient indicates that extensional failure involves the uncoupling of the lipid bilayer from the membrane skeleton.

The structure and dynamics of patch-clamped membranes: a study using differential interference contrast light microscopy

We have developed techniques for micromanipulation under high power video microscopy. We have used these to study the structure and motion of patch-clamped membranes when driven by pressure steps. Patch-clamped membranes do not consist of just a membrane, but rather a plug of membrane-covered cytoplasm. There are organelles and vesicles within the cytoplasm in the pipette tip of both cell-attached and excised patches. The cytoplasm is capable of active contraction normal to the plane of the membrane. With suction applied before seal formation, vesicles may be swept from the cell surface by shear stress generated from the flow of saline over the cell surface. In this case, patch recordings are made from membrane that was not originally present under the tip. The vesicles may break, or fuse and break, to form the gigasealed patch. Patch membranes adhere strongly to the wall of the pipette so that at zero transmural pressure the membranes tend to be normal to the wall. With transmural pressure gradients, the membranes generally become spherical; the radius of curvature decreasing with increasing pressure. Some patches have nonuniform curvature demonstrating that forces normal to the membrane may be significant. Membranes often do not respond quickly to changes in pipette pressure, probably because viscoelastic cytoplasm reduces the rate of flow through the tip of the pipette. Inside-out patches may be peeled from the walls of the pipette, and even everted (with positive pressure), without losing the seal. This suggests that the gigaseal is a distributed property of the membrane-glass interface.

Erythrocyte rheology

Two main subjects of erythrocyte rheology, deformation and aggregation, are discussed in detail, on the basis of biochemical structure. The close relationship between the life span (or cell aging) and the rheology of individual erythrocytes is also briefly described. A currently important problem is emphasized, that is, the molecular aspect of the dynamic cytoskeletal structure and the mechanism of its regulation. This concerns not only the rheological function and the survival of circulating erythrocytes, but also the pathophysiology of abnormal erythrocytes.

Structure and deformation properties of red blood cells: concepts and quantitative methods

The lamellar configuration of the red cell membrane includes a (liquid) superficial bilayer of amphiphilic molecules supported by a (rigid) subsurface protein meshwork. Because of this composite structure, the red cell membrane exhibits very large resistance to changes in surface density or area with very low resistance to in-plane extension and bending deformations. The primary extrinsic factor in cell deformability is the surface area-to-volume ratio which establishes the minimum-caliber vessel into which a cell can deform (without rupture). Within the restriction provided by surface area and volume, the intrinsic properties of the membrane and cytoplasm determine the deformability characteristics of the red cell. Since the cytoplasm is liquid, the static rigidity of the cell is determined by membrane elastic constants. These include an elastic modulus for area compressibility in the range of 300-600 dyn/cm, an elastic modulus for in-plane extension or shear (at constant area) of 5-7 X 10(-3) dyn/cm, and a curvature or bending elastic modulus on the order of 10(-12) dyn.cm. Even though small, the surface rigidity of the cell membrane is sufficient to return the membrane capsule to a discoid shape after deformation by external forces. Viscous dissipation in the peripheral protein structure (cytoskeleton) dominates the dynamic response of the cell to extensional forces. Based on a time constant for recovery after extensional deformation on the order of 0.1 sec, the coefficient of surface viscosity is on the order of 10(-3) dyn.sec/cm. On the other hand, the dynamic resistance to folding of the cell appears to be limited by viscous dissipation in the cytoplasmic and external fluid phases. Dynamic rigidities for both extensional and folding deformations are important factors in the distribution of flow in the small microvessels. Although the red cell membrane normally behaves as a resilient viscoelastic shell, which recovers its conformation after deformation, structural relaxation and failure lead to break-up and fragmentation of the red cell. The levels of membrane extensional force which is two orders of magnitude less than the level of tension necessary to lyse vesicles by rapid area dilation. Each of the material properties ascribed to the red cell membrane plays an important role in the deformability and survivability of the red cell in the circulation over its several-month life span.

Cell surface energy and membrane associated actin in lymphocytes

We have shown previously that membrane associated actin correlates with the migratory abilities of lymphocytes during recirculation, and that cell surface energy correlates with the adhesiveness of lymphocytes to other cells. In this study, measurements of actin content and cell surface energy have been made for various lymphocyte subpopulations to examine the possibility that recirculation ability may be related to nonspecific adhesiveness. We have found that: both cell surface energy and actin content combine to provide a consistent explanation for the relative rates of recirculation of various lymphocyte subpopulations, and cell surface energies and actin contents vary independently in these lymphocyte subpopulations. Comparison of the actin contents and cell surface energies of metastatic and nonmetastatic lymphoma cell lines indicated that the differences in metastatic potential were more likely attributable to specific receptor-ligand interactions than to nonspecific adhesiveness. Cell surface energy and actin content are consistent with the greater adhesiveness of B cells than T cells to nylon wool, providing a physical basis for this common cell separation technique.

Myotendinous junctions of tonic muscle cells: structure and loading

Regions within frog semitendinosus muscle that are rich in tonic muscle cells were identified histochemically by myosin adenosine triphosphatase- and succinic dehydrogenase-staining procedures. Bundles of cells still attached to tendinous insertions were removed from those sites, prepared for electron microscopy and sectioned longitudinally through their myotendinous junctions. Tonic cells were identified by electron-microscopic criteria and their myotendinous junctions' morphology evaluated by morphometry. Although junctional components appear identical to those in twitch cells, the degree of membrane folding increases tonic junction area by a factor of 50.2 whereas twitch cells' junctional area is increased 22.2 times by folding relative to cells terminating as right circular cylinders. Calculations show that the tonic cell junction bears average loads of 3.4 X 10(3) N X m-2 during maximum force generation and that nearly all of the load is borne as shear stress at the junction. The junctions of twitch cells bear average loads of 1.6 X 10(4) N X m-2 during peak tension. The findings indicate that the magnitude of loading does not alone determine the degree of junctional membrane folding. Interpretation of the data in view of viscoelastic behavior of membranes indicates that duration of loading may be a functionally important correlate to degree of membrane folding at myotendinous junctions.

Effects of shape and size on red blood cell deformability: a static bending analysis

When flowing down a tapered tube, such as a narrow capillary, red blood cells (RBCs) are subject to deformation, the first event of which is folding in a pancake manner. The RBC deformability is reduced during cell ageing, a phenomenon that may reflect alterations in intracellular viscosity, membrane rigidity or RBC shape. Age related shape changes and their importance for increased RBC rigidity were theoretically analysed. The average empirically observed RBC profile is shown to offer little resistance to bending as compared to other, theoretically possible profiles of the same membrane area and RBC volume. Because of a decrease in projected area (diameter size), and therefore in pressure load, the pressure needed to initiate folding of an old RBC is between 20 and 55% higher than that required to fold a young one if, during RBC ageing, membrane area to cell volume ratio is constant as empirically observed. This difference exists whether the RBC is mathematically treated as a solid body or as a membrane shell.

Abnormal erythrocyte fragmentation and membrane deformability in paroxysmal nocturnal hemoglobinuria

Hemolysis in paroxysmal nocturnal hemoglobinuria (PNH) is considered to be a result of an intrinsic membrane defect. This defect may result in abnormal material properties of PNH erythrocytes. To examine this hypothesis, fragmentation failure, and membrane deformability were assessed in the absence of complement by micropipette techniques. Membrane viscosity was determined by observing relaxation of deformed cells. Results show a bimodal distribution of force for membrane failure, membrane viscoelasticity, and elastic shear modulus. One population requires significantly less force for fragmentation, mean 0.56 X 10(-6) dyne; has increased membrane viscosity, mean 0.205 X 10(-2) dyne sec/cm; and has decreased elastic shear modulus, mean 0.56 X 10(-2) dyne/cm. A second population resembles control with fragmentation force, mean 1.19 X 10(-6) dyne, control 1.05 X 10(-6) dyne; membrane viscosity, mean 0.112 X 10(-2) dyne/cm, control 0.102 X 10(-2) dyne sec/cm; elastic shear modulus, mean 0.70 X 10(-2) dyne/cm, control 0.78 X 10(-2) dyne/cm. The percent of cells with abnormal material properties corresponds to the percent of PNH III cells determined by complement lysis. Thus, the hemolysis attributed to an abnormal clone of erythrocytes in PNH is associated with an intrinsic membrane abnormality which predisposes to lysis.

Membrane stability

Rupture and buckling of artificial and biological membranes is an important part of many biological processes. In this review, we present some of the main experimental facts and their analysis. Recent theoretical work, in particular thin film models and nucleation mechanisms of membrane instability, are discussed in detail. Possible applications to membrane adhesion and fusion are pointed out. Attempts are made to explain biological phenomena and experimental results for biological membranes based on a rigorous physicochemical approach developed previously for thin films in colloid systems.

Viscous flow of cytoplasm and red cell membrane: membrane recovery and tether contraction

Several experiments have been designed to study the flow of membrane and measure its viscosity. In all cases, the viscous dissipation in the cytoplasm (i.e., hemoglobin) is assumed to be negligible in comparison to that in the membrane although this has not been shown analytically. Therefore, we analyze here the viscous flow or "dissipation" in membrane and hemoglobin for two particular experiments. One involves the recovery within a pipet of an aspirated portion of a membrane following the release of the aspiration pressure; the other involves the contraction of a membrane cylinder (tether) following a step change in the axial force acting on the tether. For the pipet -recovery experiment, our results indicate that the viscosity of hemoglobin must be 100 times larger before its dissipation compares to that in the membrane. For the tether-contraction experiment, hemoglobin viscosity must be 1000 to 10,000 times larger before it is significant. A preliminary result from a tether-contraction experiment gives a characteristic response time (approximately 10 sec) and a viscosity (approximately 10(-3) dyn X sec/cm) consistent with the analytical result that hemoglobin dissipation is negligible.

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.

Effects of abnormal cytoskeletal structure on erythrocyte membrane mechanical properties

Measurements of the mechanical properties of the erythrocyte membrane provide a direct assessment of the proper function of its structural components. To assess the effects of alterations in molecular structure on membrane mechanical properties, measurements have been performed on cells from six individuals whose membranes contain inherited, biochemically characterized structural defects. Because the contribution of the membrane skeleton to the mechanical behavior of the membrane is most evident in shear deformation, mechanical experiments were performed to measure the material constants which characterize the response of the membrane to shear force resultants. The surface elastic shear modulus characterizes the elastic response of the membrane; the yield shear resultant is the maximum shear force resultant which the membrane can support elastically; and the plastic viscosity coefficient characterizes the rate of membrane deformation when the elastic limit has been exceeded. Generally, it was found that when the molecular defect is found to occur in a region of the skeleton which is stress-supporting, the maximum elastic strength of the membrane is reduced. However, the magnitude of the reduction can be quite different for membranes having similar or even identical defects. In some cases the differences can be attributed to the removal of the most fragile cells of the population by the spleen, but other results indicate that the biochemical description of the defects may be incomplete. These results emphasize the need for further refinements both in the biochemical characterization of membrane skeleton structure and in the description and measurement of membrane mechanical properties.

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

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

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.

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

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

Surface viscosity measurements from large bilayer vesicle tether formation. I. Analysis

Recent observations indicate that it is possible to form tethers from large phospholipid vesicles. The process of tether formation is analyzed using a continuum mechanical approach to obtain the surface viscosity of the bilayer in terms of experimentally measurable parameters. The membrane is treated as a two-dimensional isotropic material which deforms a constant area. The constitutive equation relates the maximum surface shear resultant to the rate of deformation via the surface viscosity coefficient. The force which acts to increase the tether length is generated by fluid moving past the vesicle. The magnitude of the force is estimated from Stoke's drag equation. The analysis predicts that there is a critical force necessary to produce an increase in the tether length. A dimensionless tether growth parameter is defined, and its value is obtained as a function of the ratio of the applied force on the vesicle to the critical force. This relationship is independent of both the size of the vesicle and the radius of the tether. Knowing the force on the vesicle, the critical force, and the rate of tether growth, the surface viscosity can be calculated.

Red cell extensional recovery and the determination of membrane viscosity

A theory of membrane viscoelasticity developed by Evans and Hochmuth in 1976 is used to analyze the time-dependent recovery of an elongated cell. Before release, the elongated cell is the static equilibrium where external forces are balanced by membrane elastic force resultants. Upon release, the cell recovers its initial shape with a time-dependent exponential behavior characteristic of the viscoelastic solid model. It is shown that the model describes the time-dependent recovery process very well for a time constant in the range of 0.1-0.13 s. The time constant is the ratio membrane surface viscosity eta:membrane surface elasticity mu. Measurements for the shear modulus mu of 0.006 dyne/cm give a value for the surface viscosity of red cell membrane as a viscoelastic solid material of eta = mu tc = (6-8) X 10(-4) poise . cm.

The effects of suspending medium viscosity on erythrocyte deformation and haemolysis in vitro

Fresh adult human erythrocytes were suspended in isotonic pH adjusted solutions containing various concentrations of Dextran T.500. The cells were subjected to uniform hydrodynamic shear stress in a Ferranti Shirley Cone and Plate Viscosimeter. The amount of lysis incurred at any given combination of exposure parameters was markedly affected by the viscosity of the suspending medium. Optical diffraction patterns obtained whilst the cells were undergoing shear demonstrated that cellular deformation was also a function of viscosity. Consequently, the distorted shape of the stressed cell may play a crucial role in the haemolytic process.

Theoretical and experimental studies on viscoelastic properties of erythrocyte membrane

The deformation of a portion of erythrocyte during aspirational entry into a micropipette has been analyzed on the basis of a constant area deformation of an infinite plane membrane into a cylindrical tube. Consideration of the equilibrium of the membrane at the tip of the pipette has generated the relation between the aspirated length and the dimensionless time during deformational entry as well as during relaxation after the removal of aspiration pressure. Experimental studies on deformation and relaxation of normal human erythrocytes were performed with the use of micropipettes and a video dimension analyzer which allowed the continuous recording of the time-courses. The deformation consisted of an initial rapid phase with a membrane viscosity (range 0.6 x 10(-4) to 4 x 10(-4) dyn.s/cm) varying inversely with the degree of deformation and a later slow phase with a high membrane viscosity (mean 2.06 x 10(-2) dyn.s/cm) which was not correlated with the degree of deformation. The membrane viscosity of the recovery phase after 20 s of deformation (mean 5.44 x 10(-4) dyn.s/cm) was also independent of the degree of deformation. When determined after a short period of deformation (e.g., 2 s), however, membrane viscosity of the recovery phase became lower and agreed with that of the deformation phase. These results suggest that the rheological properties of the membrane can undergo dynamic changes depending on the extent and duration of deformation, reflecting molecular rearrangement in response to membrane strain.

Chromatin

The approximate shape of the chromatin subunit called the nucleosome is now known, but its internal architecture is not well understood. Recent studies reveal details of the organisation of DNA within the nucleosome, and show that the arginine-rich histones are essential to DNA folding. Nucleosomes or structures related to them seem to be present at points of DNA replication and transcription; interactions within and between nucleosomes are likely to play a critical part in these processes.

The immunoregulatory role of cholesterol and other lipids: a hypothesis

Membrane lipids play an important role in cellular responses to exogenous signals. In immunocompetent lymphocytes, marked changes in the concentrations of membrane lipids occur following cell-antigen interaction. These changes lead to an increase in membrane fluidity, thus facilitating the microaggregation of receptor-antigen complexes. This event constitutes the inductive signal for lymphocytes. Lipid profile alterations leading to increased concentration of membrane cholesterol, of polyunsaturated lipids, or of both, bring about a decrease in membrane fluidity. The latter interferes with receptor displacement preventing delivery of an inductive signal to the responding cell. Interference with microaggregation is readily brought about in interactions involving low affinity antigens, such as tumoral antigens. We postulate that in hyperlipidemic and hypercholesterolemic states there is decreased immune responsiveness to weak antigens due to the aformentioned lipid profile alterations in the membranes of immunocompetent cells. The manner in which an increase in the concentration of the lipids mentioned can lead to decreased immune responsiveness and hence to an increased incidence of malignancies in hyperlipidemic and hypercholesterolemic states is the hypothesis presented in this paper.

Decreased fluidity of red cell membrane lipids in abetalipoproteinemia

Acanthocytic red cells in patients with abetalipoproteinemia are morphologically similar to the red cells in spur cell anemia. Fluidity of membrane lipids is decreased in spur cells due to their excess cholesterol content. Acanthocyte membranes have an increased content of sphingomyelin and a decreased content of lecithin. To assess the effect of this abnormality of acanthocyte membrane lipid composition on membrane fluidity, we studied red cells from five patients with abetalipoproteinemia and four obligate heterozygote family members. Membrane fluidity was measured in terms of microviscosity ( eta) at 37 degrees C, assessed by means of the fluorescence polarization of 1,6-diphenyl-1,3,5-hexatriene. It was increased from 3.2+/-0.1 poise in normals to 4.01-4.14 poise in acanthocytes. This was associated with an increase in the sphingomyelin/lecithin ratio from 0.84+/-0.08 in normals in 1.45-1.61 in acanthocytes. The eta of acanthocyte membranes was not influenced by the degree of vitamin E deficiency. Similar changes in eta were observed in liposomes prepared from red cell lipids. Heterozygotes had normal sphingomyelin/lecithin ratios and normal values for eta. The flow activation energy for viscosity, a measure of the degree of order in the hydrophobic portion of the membrane, was decreased from 8.3 kcal/mole in normal red cells to 7.2 kcal/mole in acanthocytes, indicating that acanthocyte membrane lipids are more ordered. Variations in the sphingomyelin/lecithin mole ratio of liposomes prepared from brain sphingomyelin and egg lecithin with equimolar cholesterol caused similar changes in both eta and activation energy. The deformability of acanthocytes, assessed by means of filtration through 3-mum filters, was decreased. These studies indicate that the increased sphingomyelin/lecithin ratio of acanthocytes is responsible for their decreased membrane fluidity. As in spur cells and in red cells enriched with cholesterol in vitro, this decrease in membrane fluidity occurs coincidentally with an abnormality in cell contour and an impairment in cell deformability.

Elastic area compressibility modulus of red cell membrane

Micropipette measurements of isotropic tension vs. area expansion in pre-swollen single human red cells gave a value of 288 +/- 50 SD dyn/cm for the elastic, area compressibility modulus of the total membrane at 25 degrees C. This elastic constant, characterizing the resistance to area expansion or compression, is about 4 X 10(4) times greater than the elastic modulus for shear rigidity; therefore, in situations where deformation of the membrane does not require large isotropic tensions (e.g., in passage through normal capillaries), the membrane can be treated by a simple constitutive relation for a two-dimensionally, incompressible material (i.e. fixed area). The tension was found to be linear and reversible for the range of area changes observed (within the experimental system resolution of 10%). The maximum fractional area expansion required to produce lysis was uniformly distributed between 2 and 4% with 3% average and 0.7% SD. By heating the cells to 50 degrees C, it appears that the structural matrix (responsible for the shear rigidity and most of the strength in isotropic tension) is disrupted and primarily the lipid bilayer resists lysis. Therefore, the relative contributions of the structural matrix and lipid bilayer to the elastic, area compressibility could be estimated. The maximum isotropic tension at 25 degrees C is 10-12 dyn/cm and at 50 degrees C is between 3 and 4 dyn/cm. From this data, the respective compressibilities are estimated at 193 dyn/cm and 95 dyn/cm for structural network and bilayer. The latter value correlates well with data on in vitro, monolayer surface pressure versus area curves at oil-water interfaces.