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.     

Cyclic loading on the red cell membrane in a shear flow: a possible cause of hemolysis

The fluid force acting on single human red cells in a high shear flow was analyzed. A two-dimensional elliptical microcapsule as a model of the deformed red cells was adopted to numerically calculate the distributions of the shear forces on both sides of the cell membrane. It is theoretically shown that the cell membrane undergoes an unsteady cyclic loading under the rotational motion around the interior. The mechanism leading to blood cell trauma is examined by repeatedly loading the continuously moving cell membrane.     

Shear breakage of nylon membrane microcapsules in a turbine reactor

The breakage of nylon membrane microcapsules is proposed as a new method to study and quantify shear effects in biological systems. A critique of this method shows that a narrower particle size distribution may be an important improvement in the breakage study as well as breakage control in many bioreactor and biotechnological applications. In a turbine reactor, it was shown that the primary process which determines the microcapsule breakage is the shear effect. The breakage kinetics are first order with regard to the microcapsule concentration. The breakage kinetic constant was ob served to be dependent on the temperature and the particle size, and proportional to the average shear rate and the third power of the turbine angular velocity. Decrease of the breakage kinetic constant with temperature can be explained by a decrease of fluid viscosity and a change in nylon membrane properties. An increase in the breakage kinetic constant with the microcapsule diameter can be due to a lowering of internal pressure and a reduction of the membrane resistance with size. Proportionality between the breakage kinetic constant and the shear rate shows that shear is the main process which leads to microcapsule breakage. The additional intervention in the shear rate expression of the turbine angular speed in the form of the turbine and particle velocities, results in the dependence of the breakage kinetic constant on the third power of the angular velocity.     

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.     

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.     

Wrinkling and thermal conductivity of one graphene sheet under shear

Tersoff-potential - based molecular dynamics method is used to simulate wrinkling deformation of one graphene sheet under shear, and the obtained deformation is compared with analytical solutions of macro-membrane. Furthermore, thermal conductivity of the wrinkled graphene at different temperatures is calculated. It is found that (1) the wrinkling deformation of graphene sheet under shear is close to the analytical solutions of macro-membrane under shear, which implies that the solutions of macro-membrane are applicable to predict the wrinkling deformation of graphene sheets under shear; (2) the more serious the wrinkling of the graphene under shear is, the stronger the phonon scattering is and, therefore, the lower the thermal conductivity of the wrinkled graphene is; (3) within the temperature range of 400–700 K, the thermal conductivity of graphene sheet decreases with increase in temperature.     

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.     

Computational Analysis of Dynamic Interaction of Two Red Blood Cells in a Capillary

The dynamic interaction of two red blood cells (RBCs) in a capillary is investigated computationally by the two-fluid model, including their deformable motion and interaction. For characterization of the deformation, the RBC membrane is treated as a curved two-dimensional shell with finite thickness by the shell model, and allowed to undergo the stretching strain and bending deformation. Moreover, a Morse potential is adopted to model the intercellular interaction for the aggregation behavior, which is characterized as the weak attraction at far distance and strong repulsion at near distance. For validation of the present technique, the dynamic interaction of two RBCs in static blood plasma is simulated firstly, where the RBCs aggregate slowly until a balanced configuration is achieved between the deformation and aggregation forces. The balanced configuration is in good agreement with the results reported previously. Three important effects on the dynamic behavior of RBCs are then analyzed, and they are the initial RBC shape, RBC deformability, and the intercellular interaction strength. It is found that the RBC is less deformed into a well-known parachute shape when the initial RBC shape is larger. Similarly, if the elastic shear modulus and bending stiffness of RBC membrane increase, the RBC resistance to deformation becomes higher, such that the RBC is less deformed. The simulation results also demonstrate that the RBC deformability strongly depends on the intercellular interaction strength. The RBCs deform more easily as the intercellular interaction strength increases.     

Simulation of a Single Red Blood Cell Flowing Through a Microvessel Stenosis Using Dissipative Particle Dynamics

The motion and deformation of a single red blood cell flowing through a microvessel stenosis was investigated employing dissipative particle dynamics (DPD) method. The numerical model considers plasma, cytoplasm, the RBC membrane and the microvessel walls, in which a three dimensional coarse-grained spring network model of RBC’s membrane was used to simulate the deformation of the RBC. The suspending plasma was modelled as an incompressible Newtonian fluid and the vessel walls were regarded as rigid body. The body force exerted on the free DPD particles was used to drive the flow. A modified bounce-back boundary condition was enforced on the membrane to guarantee the impenetrability. Adhesion of the cell to the stenosis vessel surface was mediated by the interactions between receptors and ligands. Firstly, the motion of a single RBC in a microfluidic channel was simulated and the results were found in agreement with the experimental data cited by [1]. Then the mechanical behavior of the RBC in the microvessel stenosis was studied. The effects of the bending rigidity of membrane, the size of the stenosis and the driven body force on the deformation and motion of red blood cell were discussed.     

In vitro synthesis and properties of pectin/Acetobacter xylinus cellulose composites

Pectin and cellulose are major components of most primary cell walls, yet little is known about the way in which they interact either during assembly or in subsequent functional performance of the wall. As a mimic of cell wall assembly, we studied the formation of molecular composites formed by deposition of cellulose from Acetobacter xylinus into pectin/calcium systems, and the molecular, architectural and mechanical properties of the composites obtained. The formation of interpenetrating cellulose/pectin composite networks (as envisaged in current models for primary cell walls) required a pre-existing, but not too strong, pectin network. For pectin either in solution or strongly networked, phase separation from cellulose occurred, providing two physical models for the formation of middle lamellae. Composite networks showed no evidence of direct molecular interaction between the components, but pectin networks became more aggregated following deposition of cellulose into them. The shear strength under small deformation conditions for cellulose/pectin composites was very similar to that of cellulose alone. In contrast, under uniaxial tension, extensibility was greatly increased and stiffness decreased. These major changes were due to the effect of pectin on cellulose network architecture at deposition, as they were maintained upon removal of the pectin component. These results show that the presence and physical state of pectin at the time of cellulose deposition in muro may be a significant determinant of subsequent extensibility without compromising strength.     

A Theoretical Study of Single-Cell Electroporation in a Microchannel

Electroporation of a single cell in a microchannel was studied. The effects of electrical (e.g., strength of the electric pulse) and geometrical (e.g., microchannel height, electrode size and position) parameters on cell membrane permeabilization were investigated. The electrodes were assumed to be embedded in the walls of the microchannel; the cell was suspended between these two electrodes. By keeping the electric pulse constant, increasing the microchannel height reduces the number and the radius of the biggest nanopores, as well as the electroporated area of the cell membrane. If the width of the electrodes is bigger than the cell diameter, the transmembrane potential will be centralized and have a sinusoidal distribution around the cell if nanopores are not generated. As the width of the electrode decreases and becomes smaller than the cell diameter, the local transmembrane potential decreases; in the nonelectroporative area, the transmembrane potential distribution deviates from the sinusoidal behavior; the induced transmembrane potential also concentrates around the poles of the cell membrane (the nearest points of the cell membrane to the electrodes). During cell membrane permeabilization, the biggest nanopores are initially created at the poles and then the nanopore population expands toward the equator. The number of the created nanopores reaches its maximal value within a few microseconds; further presence of the electric pulse may not influence the number and location of the created nanopores anymore but will develop the generated nanopores. Strengthening the electric pulse intensifies the size and number of the created nanopores as well as the electroporated area on the cell membrane.     

A computational study of leukocyte adhesion and its effect on flow pattern in microvessels

Three-dimensional computational modeling and simulation are presented on the adhesive rolling of deformable leukocytes over a P-selectin coated surface in parabolic shear flow in microchannels. The computational model is based on the immersed boundary method for cell deformation and Monte Carlo simulation for receptor/ligand interaction. The simulations are continued for at least 1 s of leukocyte rolling during which the instantaneous quantities such as cell deformation index, cell/substrate contact area, and fluid drag remain statistically stationary. The characteristic ‘stop-and-go’ motion of rolling leukocytes, and the ‘tear-drop’ shape of adherent leukocytes as observed in experiments are reproduced by the simulations. We first consider the role of cell deformation and cell concentration on rolling characteristics. We observe that compliant cells roll slower and more stably than rigid cells. Our simulations agree with previous in vivo observation that the hydrodynamic interactions between nearby leukocytes affect cell rolling, and that the rolling velocity decreases inversely with the separation distance, irrespective of cell deformability. We also find that cell deformation decreases, and the cells roll more stably with reduced velocity fluctuation, as the cell concentration is increased. However, the effect of nearby cells on the rolling characteristics is found to be more significant for rigid cells than compliant cells. We then address the effect of cell deformability and rolling velocity on the flow resistance due to, and the fluid drag on, adherent leukocytes. While several earlier computational works have addressed this problem, two key features of leukocyte adhesion, such as cell deformation and rolling, were often neglected. Our results suggest that neglecting cell deformability and rolling velocity may significantly overpredict the flow resistance and drag force. Increasing the cell concentration is shown to increase the flow resistance and reduce the fluid drag. The reduced drag then results in slower and more stable rolling of the leukocytes with longer pause time and shorter step distance. But the increase/decrease in the flow resistance/fluid drag due to the increase in the cell concentration is observed to be more significant in case of rigid cells than compliant cells.     

Influence of domain orientation on the mechanical properties of regenerated cellulose fibers

The determination of the crystal orientation of regenerated cellulose fibers produced under different drawing regimes is presented. Orientation is determined by using wide-angle X-ray diffraction from a synchrotron source and by measuring the azimuthal width of equatorial reflections. The orientation parameter theta is then determined to compare fiber samples. By using a 500 nm beam size, clear differences between the crystal orientations of the skin and the core of the fibers are reported for a range of differently processed fibers for the first time. These results are shown to have implications for the mechanical properties of regenerated cellulose fibers. By applying tensile deformation to fiber bundles it is shown that the most misoriented samples undergo rapid decreases in the orientation parameter, which is an indication of crystal reorientation. However, the more highly oriented fibers undergo little reorientation. An average shear modulus for these fibers is determined by placing the data on a master curve and fitting with a model equation. By using another model for the fibers of low orientation and the shear modulus from the master curve analysis, it is shown that the deformation of less oriented fibers is dominated by shear between crystals, whereas the more oriented filaments are likely to undergo more significant chain deformation. By using a new model for fibers of low orientation, a parameter ksigma is introduced that gives the proportion of the fiber stress that is due to crystal shear. Systematic differences between this parameter for fibers of increasing initial orientation are reported. Moreover it is shown that the fibers of initially lower average orientation are governed by uniform strain, in agreement with the new model, whereas more highly oriented fibers deform under uniform stress. Furthermore, the model that we propose for misoriented domains and the use of a new factor dictating the proportion of shear stress may have general applications in materials engineering.     

Roles of Cellulose and Xyloglucan in Determining the Mechanical Properties of Primary Plant Cell Walls

The primary cell walls of growing and fleshy plant tissue mostly share a common set of molecular components, cellulose, xyloglucan (XyG), and pectin, that are required for both inherent strength and the ability to respond to cell expansion during growth. To probe molecular mechanisms underlying material properties, cell walls and analog composites from Acetobacter xylinus have been measured under small deformation and uniaxial extension conditions as a function of molecular composition. Small deformation oscillatory rheology shows a common frequency response for homogenized native cell walls, their sequential extraction residues, and bacterial cellulose alone. This behavior is characteristic of structuring via entanglement of cellulosic rods and is more important than cross-linking with XyG in determining shear moduli. Compared with cellulose alone, composites with XyG have lower stiffness and greater extensibility in uniaxial tension, despite being highly cross-linked at the molecular level. It is proposed that this is due to domains of cross-linked cellulose behaving as mechanical elements, whereas cellulose alone behaves as a mat of individual fibrils. The implication from this work is that XyG/cellulose networks provide a balance of extensibility and strength required by primary cell walls, which is not achievable with cellulose alone.     

Theoretical model and experimental study of red blood cell (RBC) deformation in microchannels

The motion and deformation of red blood cells (RBCs) flowing in a microchannel were studied using a theoretical model and a novel automated rheoscope. The theoretical model was developed to predict the cells deformation under shear as a function of the cells geometry and mechanical properties. Fluid dynamics and membrane mechanics are incorporated, calculating the traction and deformation in an iterative manner. The model was utilized to evaluate the effect of different biophysical parameters, such as: inner cell viscosity, membrane shear modulus and surface to volume ratio on deformation measurements. The experimental system enables the measurement of individual RBCs velocity and their deformation at defined planes within the microchannel. Good agreement was observed between the simulation results, the rheoscope measurements and published ektacytometry results. The theoretical model results imply that such deformability measuring techniques are weakly influenced by changes in the inner viscosity of the cell or the ambient fluid viscosity. However, these measurements are highly sensitive to RBC shear modulus. The shear modulus, estimated by the model and the rheoscope measurements, falls between the values obtained by micropipette aspiration and laser trapping. The study demonstrates the integration of a theoretical model with a microfabricated device in order to achieve a better understanding of RBC mechanics and their measurement using microfluidic shear assays. The system and the model have the potential of serving as quantitative clinical tools for diagnosing deformability disorders in RBCs.     

Temperature dependence of the viscoelastic recovery of red cell membrane.

The time-dependent recovery of an elongated red cell is studied as a function of temperature. Before release, the elongated cell is in static equilibrium where external forces are balanced by surface elastic force resultants. Upon release, the cell recovers its initial shape with a time-dependent exponential behavior characteristic of a viscoelastic solid material undergoing large ("finite") deformation. The recovery process is characterized by a time constant, tc, that decreases from approximately 0.27 s at 6 degrees C to 0.06 s at 37 degrees C. From this measurement of the time constant and an independent measurement of the shear modulus of surface elasticity for red cell membrane, the value for the membrane surface viscosity as a function of temperature can be calculated.     

The effect of compliance on wall shear in casts of a human aortic bifurcation

Rigid and compliant casts of a human aortic bifurcation were subjected to physiologically realistic pulsatile fluid flows. At a number of sites near the wall in the approximate median plane of the bifurcation of these models, fluid velocity was measured with a laser Doppler velocimeter, and wall motion (in the case of the compliant cast) was determined with a Reticon linescan camera. The velocity and wall motion data were combined to estimate the instantaneous shear rates at the cast wall. Analysis showed that at the outer walls the cast compliance reduced shear rates, while at the walls of the flow divider the shear rate was increased.     

Influence of cell deformation on leukocyte rolling adhesion in shear flow

Blood cell interaction with vascular endothelium is important in microcirculation, where rolling adhesion of circulating leukocytes along the surface of endothelial cells is a prerequisite for leukocyte emigration under flow conditions. HL-60 cell rolling adhesion to surface-immobilized P-selectin in shear flow was investigated using a side-view flow chamber, which permitted measurements of cell deformation and cell-substrate contact length as well as cell rolling velocity. A two-dimensional model was developed based on the assumption that fluid energy input to a rolling cell was essentially distributed into two parts: cytoplasmic viscous dissipation, and energy needed to break adhesion bonds between the rolling cell and its substrate. The flow fields of extracellular fluid and intracellular cytoplasm were solved using finite element methods with a deformable cell membrane represented by an elastic ring. The adhesion energy loss was calculated based on receptor-ligand kinetics equations. It was found that, as a result of shear-flow-induced cell deformation, cell-substrate contact area under high wall shear stresses (20 dyn/cm2) could be as much as twice of that under low stresses (0.5 dyn/cm2). An increase in contact area may cause more energy dissipation to both adhesion bonds and viscous cytoplasm, whereas the fluid energy input may decrease due to the flattened cell shape. Our model predicts that leukocyte rolling velocity will reach a plateau as shear stress increases, which agrees with both in vivo and in vitro experimental observations.     

The mechanical properties and molecular dynamics of plant cell wall polysaccharides studied by Fourier-transform infrared spectroscopy

Polarized one- and two-dimensional infrared spectra were obtained from the epidermis of onion (Allium cepa) under hydrated and mechanically stressed conditions. By Fourier-transform infrared microspectroscopy, the orientation of macromolecules in single cell walls was determined. Cellulose and pectin exhibited little orientation in native epidermal cell walls, but when a mechanical stress was placed on the tissue these molecules showed distinct reorientation as the cells were elongated. When the stress was removed the tissue recovered slightly, but a relatively large plastic deformation remained. The plastic deformation was confirmed in microscopic images by retention of some elongation of cells within the tissue and by residual molecular orientation in the infrared spectra of the cell wall. Two-dimensional infrared spectroscopy was used to determine the nature of the interaction between the polysaccharide networks during deformation. The results provide evidence that cellulose and xyloglucan associate while pectin creates an independent network that exhibits different reorientation rates in the wet onion cell walls. The pectin chains respond faster to oscillation than the more rigid cellulose.