Shape memory of human red blood cells

The human red cell can be deformed by external forces but returns to the biconcave resting shape after removal of the forces. If after such shape excursions the rim is always formed by the same part of the membrane, the cell is said to have a memory of its biconcave shape. If the rim can form anywhere on the membrane, the cell would have no shape memory. The shape memory was probed by an experiment called go-and-stop. Locations on the membrane were marked by spontaneously adhering latex spheres. Shape excursions were induced by shear flow. In virtually all red cells, a shape memory was found. After stop of flow and during the return of the latex spheres to the original location, the red cell shape was biconcave. The return occurred by a tank-tread motion of the membrane. The memory could not be eliminated by deforming the red cells in shear flow up to 4 h at room temperature as well as at 37 degrees C. It is suggested that 1). the characteristic time of stress relaxation is >80 min and 2). red cells in vivo also have a shape memory.     

Tank-tread frequency of the red cell membrane: dependence on the viscosity of the suspending medium

Single human red cells were suspended in media with viscosities ranging from 12.9 to 109 mPa s and subjected to shear flow ranging from 1/s to 290/s in a rheoscope. This is a transparent cone-plate chamber adapted to a microscope. The motion of the membrane around red cells oriented in a steady-state fashion in the shear field (tank-tread motion) was videotaped. The projected length and width of the cells as well as the frequency of tank-tread motion were measured. One-thousand eight-hundred seventy-three cells of three blood donors were evaluated. The frequency increased with the mean shear rate in an almost linear fashion. The slope of this dependence increased weakly with the viscosity of the suspending medium. No correlation was found between the frequency and four morphological red cell parameters: the projected length and width of the cells as well as the ratio and the square root of the product of these quantities. The energy dissipation within the red cell membrane was estimated based on the measured parameters and compared to the energy dissipation in the undisturbed shear flow. At constant mean shear rate the rise of the energy dissipation with viscosity is slower whereas at constant viscosity the rise with the shear rate is steeper than in the undisturbed shear flow. A fit of the data collected in this work to a theoretical red cell model might allow one to determine intrinsic mechanical constants in the low deformation regime.     

On the energy dissipation in a tank-treading human red blood cell.

The energy dissipation in the membrane (ED mem) and in the cytoplasm (ED cyt) of tank-treading human red blood cells is estimated. The tank-tread motion of the membrane occurs when the cells in a sheared suspension assume a steady-state of orientation (Fischer et al., 1978, Science [Wash. D. C.], 202:894). The kinematic data used are from red cells suspended either in a dextran-saline solution at a low hematocrit, or in plasma at a hematocrit of 45%. The viscosities of the cytoplasm and the membrane are taken from the literature. The cell in dextran was subjected to seven different shear rates. Both ED mem and ED cyt showed a strong increase with shear rate. Their ratio, however, was always of the order of 1. From this value and the value which was given by Hochmuth et al. (1979, Biophys. J., 26:101) for a shape recovery of a red cell, it is concluded that the range of ED mem/ED cyt for all possible geometries is 1-100.     

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.     

Blood as a near-"ideal" emulsion: a retrospective on the concept of the red cell as a fluid drop, its implications for the structure of the red cell membrane

Although the question whether the red cell is fluid or solid has been discussed since 17th century, it was the author's measurement of the relative viscosity of blood in 1960's that supplied the first direct evidence that the red cell interior is fluid. Furthermore, through his application of the equations of Taylor and, later, Oldroyd, to this problem, it became evident that, for the red cell to exhibit fluid-drop-like behavior, the membrane must also be fluid. This led to his concept of the red cell membrane as a complex two-phase structure (lipoprotein micelles and two-dimensional protein networks) which was similar to the one accepted nearly a decade later. The requirements of the theory of ideal emulsions that the shear stress be transmitted into the cell interior via low viscosity membrane, are met in the later work of other investigators using the concept of a tank-treading membrane having viscoelastic properties. This paper reviews the original work of the author which led to the development of an equation for the relative viscosity of blood as a function of volume concentration, C: nr = (1 - TkC)-2.5, valid at shear rates above 180 sec-1, in which T is the Taylor factor which gives a measure of fluidity of the red cell, and k is a plasma trapping factor. Both T and k increase with increasing rigidity of the red cell. Finally, the effect of the membrane viewed as a complex two-phase fluid, on the rheology of the red cell is discussed.     

Thermoelasticity of red blood cell membrane.

The elastic properties of the human red blood cell membrane have been measured as functions of temperature. The area compressibility modulus and the elastic shear modulus, which together characterize the surface elastic behavior of the membrane, have been measured over the temperature range of 2-50 degrees C with micropipette aspiration of flaccid and osmotically swollen red cells. In addition, the fractional increase in membrane surface area from 2-50 degrees C has been measured to give a value for the thermal area expansivity. The value of the elastic shear modulus at 25 degrees C was measured to be 6.6 X 10(-3) dyne/cm. The change in the elastic shear modulus with temperature was -6 X 10(-5) dyne/cm degrees C. Fractional forces were shown to be only on the order of 10-15%. The area compressibility modulus at 25 degrees C was measured to be 450 dyne/cm. The change in the area compressibility modulus with temperature was -6 dyne/cm degrees C. The thermal area expansivity for red cell membrane was measured to be 1.2 X 10(-3)/degrees C. With this data and thermoelastic relations the heat of expansion is determined to be 110-200 ergs/cm2; the heat of extension is 2 X 10(-2) ergs/cm2 for unit extension of the red cell membrane. The heat of expansion is of the order anticipated for a lipid bilayer idealized as twice the behavior of a monolayer at an oil-water interface. The observation that the heat of extension is positive demonstrates that the entropy of the material increases with extension, and that the dominant mechanism of elastic energy storage is energetic. Assuming that the red cell membrane shear rigidity is associated with "spectrin," unit extension of the membrane increases the configurational entropy of spectrin by 500 cal/mol.     

The stress-free shape of the red blood cell membrane.

The two main proposals found in the literature for the stress-free shape of the red cell membrane are (a) the bioconcave shape and (b) the sphere of the same surface area. These possibilities are evaluated in this paper using theoretical modeling of equilibrium membrane shapes according to Zarda et al. (1977. J. Biomech. 10:211-221) and by comparison to experiments on red cells whose membrane shear modulus has been increased by treatment with diamide. Neither proposal is found to be compatible with all the experimental behaviour of native red cells. Neither proposal is found to be compatible with all the experimental behaviour of native red cells. To account for this discrepancy we propose that either the shear modulus of the native membrane is dependent on the membrane strain or that the bending stiffness is higher than estimated by Evans (1980. Biophys. J. 30:265-286). These studies suggest that the bioconcave disk is the more likely possibility for the stress-free shape.     

Microfiltration of recombinant yeast cells using a rotating disk dynamic filtration system

To develop a highly efficient cell harvest step under time constraint, a novel rotating disk dynamic filtration system was studied on the laboratory scale (0.147-ft.(2) nylon membrane) for concentrating recombinant yeast cells containing an intracellular product. The existing cross-flow microfiltration method yielded pseudo-steady state flux values below 25 LMH (L/m(2). h) even at low membrane loadings (10 L/ft.(2)). By creating high shear rates (up to 120,000(-1)) on the membrane surface using a rotating solid disk, this dynamic filter has demonstrated dramatically improved performance, presumably due to minimal cake buildup and reduced membrane fouling. Among the many factors investigated, disk rotating speed, which determines shear rates and flow patterns, was found to be the most important adjustable parameter. Our experimental results have shown that the flux increases with disk rotating speed, increases with transmembrane pressure at higher cell concentrations, and can be sustained at high levels under constant flux mode. At a certain membrane loading level, there was a critical speed below which it behaved similarly to a flat sheet system with equivalent shear. Average flux greater than 200 LMH has been demonstrated at 37-L/ft.(2) loading at maximum speed to complete sixfold concentration and 15-volume diafiltration for less than 100 min. An order of magnitude improvement over the crossflow microfiltration control was projected for large scale production. This superior performance, however, would be achieved at the expense of additional power input and heat dissipation, especially when cell concentration reaches above 80 g dry cell weight (DCW)/L. Although a positive linear relationship between power input and dynamic flux at a certain concentration factor has been established, high cell density associated with high viscosity impacted adversely on effective average shear rates and, eventually, severe membrane fouling, rather than cake formation, would limit the performance of this novel system. (c) 1995 John Wiley & Sons, Inc.     

Aggregation and disaggregation of red blood cells

The aggregation of red blood cells may be analyzed as an interaction of an adhesive surface energy and the elastic stored energy which results from deformation of the cell. The adhesive surface energy is the work required to separate a unit adhered area and is the resultant of adhesive forces due to the bridging molecules that bind the cells together and the electrostatic repulsion due to surface charge. The elastic strain energy in the case of the red blood is associated with the membrane elasticity only since the interior of the cell is liquid. The membrane elasticity is due both to bending stiffness and shear. The area expansion is small and may be neglected. These assumptions allow realistic computation of red cell shapes in rouleaux. The disaggregation of rouleaux requires an external force which must overcome the adhesive energy and also supply additional elastic energy of deformation. Depending on the geometry, the initial effect of elastic energy may tend to aid disaggregation. In a shear flow, the stresses on a suspended rouleau alternately tend to compress and to disaggregate the cells if they are free to rotate. This introduces a time dependence so that viscous effects due to the viscosity of the cell membrane, the cell cytoplasm and the external fluid may play a role in determining whether disaggregation proceeds to completion or not.     

Measurement of the erythrocyte orientation in a flow by spin labeling

When a suspension of erythrocytes labeled in their membrane with a fatty acid paramagnetic molecule is allowed to flow in a flat quartz sample cell, the recorded electron paramagnetic spectra change as a function of the orientation of the cell in the magnetic field. This indicates that the red cells are themselves oriented in the flow. Such spectral variations have been reproduced by a numerical simulation procedure, which allowed us to quantify the proportion of oriented red blood cells by measuring the amplitude of some characteristic lines on the experimental spectra. Orientation rates were then measured as a function of various rheological parameters, such as shear rate, hematocrit and viscosity of the suspending medium. The kinetics of the disorientation process was determined by stopping the flow.     

Prosthetic heart valves' mechanical loading of red blood cells in patients with hereditary membrane defects

Implantable cardiovascular devices such as prosthetic heart valves (PHVs) are widely applied clinical tools. Upon implantation, the patient can suffer from anemia as a result of red cell destruction and hemolysis can be more relevant whenever the patient is also affected by red cell disorders in which erythrocytes are more susceptible to mechanical stress such as hereditary spherocytosis (HS) and hereditary elliptocytosis (HE). Considering the typical morphological alterations observed in HS and HE, a study of the influence of cell geometry on the distribution of the shear stress on red cells in biological fluids was carried out. A numerical simulation of the loading caused by Reynolds shear stresses on a prolate spheroid was performed, with the ellipticity of the particle as the independent parameter. The average shear stress on a particle in the blood stream was found to depend on the particle's geometry, besides the stress field produced by the prosthetic device. The relevance of an increasing particle ellipticity on the global load is discussed. The model was applied to erythrocytes from implanted patients with HE or HS, enabling to explain the occurrence of moderate or severe anemia, respectively. The clinical data support the relevance of the proposed global parameter as erythrocyte trauma predictor with regard to the fluid dynamics of artificial organs.     

Membrane stress and internal pressure in a red blood cell freely suspended in a shear flow.

Presented is an algorithm for the approximate calculation of the membrane stress distribution and the internal pressure of a steadily tank-treading red cell. The algorithm is based on an idealized ellipsoidal model of the tank-treading cell (Keller, S.R., and R. Skalak, 1982, J. Fluid Mech., 120:27-47) joined with experimental observations of projected length, width, and tank-treading frequency. The results are inexact because the membrane shape and velocity are assumed a priori, rather than being determined via appropriate material constitutive relations for the membrane; these results are, nevertheless, believed to be approximately correct, and show that internal pressure builds up slowly as cell elongation increases, rising more rapidly as the deformed cell approaches the limiting geometry of a prolate ellipsoid. The maximum shear stress resultant in the membrane was found to be below but approaching the yield point range at the highest shear rate applied.     

Cross bonding and stiffening of the red cell membrane

Cross bonding and stiffening of the human red cell membrane was studied using treatments with SH, amino, and carboxyl reagents, oxidizing and denaturing treatments and acidification. Membrane cross bonding was initiated when, after red cell treatment, opposite areas of the cytoplasmic face of the red cell membrane were brought into contact by cell shrinking. Membrane cross bonding was detected by light microscopy when this contact persisted upon swelling the cells in a hypotonic medium. Membrane stiffening was recorded as a decrease in elongation of red cells in the shear field of a viscous dextran solution. No correlation was found between membrane cross bonding and membrane stiffening. The results are explained by the existence of two modifications of spectrin, type I causing solely membrane stiffening, type II causing membrane cross bonding as well as membrane stiffening. The amino and carboxyl reagents caused only type I modification. The other treatments caused both types of modification although with varying proportions. The results support the previously suggested mechanism of membrane cross bonding which involves a rearrangement of spectrin similar to denaturation by heat or urea, a decrease in associations within the membrane skeletal network, and a lateral aggregation of membrane proteins. These changes are proposed to occur by the type II modification. The data further substantiate the membrane stiffening effect of inter- and intra-molecular cross linking of spectrin which is identified with the type I modification. Finally, hypotheses are presented concerning the mechanism of membrane stiffening due to type II modifications of spectrin.     

The bulk rheology of close-packed red blood cells in shear flow

A theoretical analysis is made of the dynamical behavior and bulk rheology of close-packed red blood cell suspensions subjected to simple shear flow. The model for the polyhedral cell shapes and tank-treading membrane motion developed in the companion paper (1) is used. The flow in the thin lubricating plasma layers between cells is analyzed taking into account the mechanical properties of the membrane at the corner regions of sharp membrane curvature. This leads to predictions for the apparent viscosity as a function of hematocrit and shear rate. Good agreement with experimental results is obtained at moderate and high shear rates (above 20 s-1). At lower shear rates, a rapid rise in apparent viscosity has been found experimentally, and the mechanisms leading to this behavior are examined.     

Intraerythrocytic parasites and red cell deformability: Plasmodium berghei and Babesia microti

In the studies reported here, we examined the effects of two intraerythrocytic parasites (Plasmodium berghei and Babesia microti) on the deformability of their host red cells. Red cell deformability was assessed by three criteria: 1) the prevalence of tank-treading (the tank-tread-like movement of the red cell membrane around its cytoplasmic contents), 2) elongation under fluid shear stress (the steady-state length: width ratio), and 3) the time required for the red cell to reduce its steady-state elongation by 63.2% after the abrupt release of the shear stress (the characteristic shape-recovery time). Trophozoite-stage parasites of both species reduced the prevalence of tank-treading. Ring- and trophozoite-stage parasites of both species reduced steady-state elongation, and ring-stage P. berghei prolonged the shape-recovery time. These results suggest that altered red cell deformability is a common feature of infection with intraerythrocytic parasites.     

Prehemolytic effects of hydrogen peroxide and t-butylhydroperoxide on selected red cell properties

To provide further understanding of how oxidative damage affects red cell membrane function, the effects of low levels of two different types of oxidants on selected red cell properties have been studied. Hydrogen peroxide (H2O2), an example of a water soluble oxidant, and t-butylhydroperoxide (tBHP), a hydrophobic hydroperoxide, were compared with respect to their effects on membrane permeability, membrane mechanical properties and binding of autologous serum antibodies to the cell surface. Whereas H2O2 treatment resulted in a dose-dependent increase in membrane permeability to potassium that was evident after one hour of oxidant exposure, cells treated with tBHP at doses up to 5 mumol/ml cells showed no immediate change in cation permeability. H2O2 also caused a marked decrease in membrane deformability, whereas tBHP-treated cells showed minimal loss of deformability. However, tBHP treatment did result in a dose-dependent increase in the susceptibility of the membrane to fragmentation under high shear stress. With exclusion of treated samples that bound excess rabbit anti-spectrin antibody, indicating exposure of intracellular components, neither agent promoted the binding of autologous serum antibody in amounts comparable to that found in vivo on high density or some pathologic red cells. Taken together, the results suggest that tBHP and H2O2 cause damage to human red cells by distinct oxidative mechanisms which do not lead directly to substantive generation of binding sites for autologous serum antibodies.     

Effects of inherited membrane abnormalities on the viscoelastic properties of erythrocyte membrane.

Several workers have identified molecular abnormalities associated with inherited blood disorders. The present work examines how these alterations in molecular structure affect the viscoelastic properties of the red blood cell membrane. Changes in the membrane shear modulus, the membrane viscosity, and the apparent membrane bending stiffness were observed in cells of eight patients having a variety of disorders: Two had reductions in the number of high-affinity ankyrin binding sites, two had abnormalities associated with the protein band 4.1, and six were known to be deficient in spectrin. The data suggest that the membrane shear modulus is proportional to the density of spectrin on the membrane and support the view that spectrin is primarily responsible for membrane shear elasticity. Although membranes having abnormalities associated with the function of ankyrin or band 4.1 exhibited reduced elasticity, the degree of mechanical dysfunction was quantitatively inconsistent with the extent of the molecular abnormality. This indicates that these skeletal components do not play a primary role in determining membrane shear elasticity. The membrane viscosity was reduced in seven of the eight patients studied. The reduction in viscosity was usually greater than the reduction in shear modulus, but the degree of reduction in viscosity was variable and did not correlate well with the degree of molecular abnormality.     

Interaction between bending and tension forces in bilayer membranes.

A theoretical analysis is presented of the bending mechanics of a membrane consisting of two tightly-coupled leaflets, each of which shears and bends readily but strongly resists area changes. Structures of this type have been proposed to model biological membranes such as red blood cell membrane. It is shown that when such a membrane is bent, anisotropic components of resultant membrane tension (shear stresses) are induced, even when the tension in each leaflet is isotropic. The induced shear stresses increase as the square of the membrane curvature, and become significant for moderate curvatures (when the radius of curvature is much larger than the distance between the leaflets). This effect has implications for the analysis of shape and deformation of freely suspended and flowing red blood cells.     

The influence of red cell mechanical properties on flow through single capillary-sized pores

The resistive pulse technique was used to study the influence of specific mechanical properties of the red cell on its ability to enter and flow through single capillary-sized pores with diameters of 3.6, 5.0 and 6.3 micron and lengths of 11 micron. A two-fold increase in membrane shear elasticity resulted in a 40 percent increase in the cell's transit time through a 3.6 micron pore but produced no change in transit time through a 6.3 micron pore. A two-fold increase in membrane shear viscosity produced a 40 percent increase in transit time through the 3.6 micron pore and small but significant increases in transit times through the larger pores. Osmotically dehydrated cells showed no increase in transit time through a 6.3 micron pore, but showed increases in transit times of 50 to 70 percent through 5.0 and 3.6 micron pores. Dense red cells showed increased transit times through both 5.0 micron and 6.0 micron pores. These results indicate that for cells with normal geometric properties, the membrane's shear viscosity and elasticity only influence the cell's transit through pores of 5 micron or less in diameter. However, alterations in the cell's geometric properties can extend the influence of membrane shear properties to larger diameter pores.     

Red blood cell orientation in orbit C = 0.

Two modes of behavior of single human red cells in a shear field have been described. It is known that in low viscosity media and at shear rates less than 20 s-1, the cells rotate with a periodically varying angular velocity, in accord with the theory of Jeffery (1922) for oblate spheroids. In media of viscosity greater than approximately 5 mPa s and sufficiently high shear rates, the cells align themselves at a constant angle to the direction of flow with the membrane undergoing tank-tread motion. Also, in low viscosity media, as the shear rate is increased, more and more cells lie in the plane of shear, undergoing spin with their axes of symmetry aligned with the vorticity axis of the shear field in an orbit "C = 0" (Goldsmith and Marlow, 1972). We have explored this latter phenomenon using two experimental methods. First, the erythrocytes were observed in the rheoscope and their diameters measured. Forward light scattering patterns were correlated with the red cell orientation mode. Light flux variations after flow onset or stop were measured, and the characteristic times of erythrocyte orientation and disorientation were assessed. The characteristic time of erythrocyte orientation in Orbit C = 0 is proportional to the inverse of the shear rate. The corresponding coefficient of proportionality depends on the suspending medium viscosity eta o. The disorientation time tau D, after flow has been stopped, is such that the ratio tau D/eta o is independent of the initial applied shear stress. However, tau D is much shorter than one would expect if pure Brownian motion were involved. The proportion of erythrocytes in orbit C = 0 was also measured. It was found that this proportion is a function of both the shear rate and eta o. At low values of eta o, the proportion increases with increasing shear rate and then reaches a plateau. For higher values of eta o (5 to 10 mPa s), the proportion of RBC in orbit C = 0 is a decreasing function of the shear stress. A critical transition between orbit C = 0 and parallel alignment was observed at high values of eta o, when the shear stress is on the order of 1 N/m2. Finally, the effect of altering membrane viscoelastic properties (by heat or diamide treatment) was tested. The proportion of oriented cells is a steep decreasing function of red cell rigidity.