Rheological behaviors of bovine blood forming artificial rouleaux

A purpose of the present study is to make an artificial rouleau of bovine red blood cells which is not capable of rouleau formation under physiological condition. Rheological behaviors of bovine blood forming artificial rouleaux were examined. The modification of cell surface by enzyme trypsin induced rouleau formation, whereas the modification of cell surface by neuraminidase did not cause any aggregate formation. The drastic elevation of the fibrinogen content in bovine red blood cells suspension also brought about the formation of rouleau. The value of dynamic rigidity modulus G' of bovine red blood cells in saline solution containing high concentration of fibrinogen is somewhat smaller than that of trypsin treated bovine red blood cells in plasma. The value of G' of trypsin treated bovine red blood cells in plasma first increased to a maximum value and then decreased with the time. It is supposed that the removal of macro-molecules from the cell surface facilitates the mutual approach of cells and causes the formation of rouleau which seems to be the same as that of human and horse bloods.     

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.     

Aggregation of human red blood cells after moderate heat treatment

The aggregation behaviour of normal and heat treated (48.4 degrees C, 48.8 degrees C, 49.5 degrees C) red blood cells (RBCs) suspended in dextran-saline solutions (Dx 70, Dx 173) was investigated by a laser light reflectometric method over a wide range of bridging energies. The characteristic times of rouleau formation were found to be increased after RBC heat treatment. The disaggregation shear stress is not significantly different between normal RBCs and heat treated RBCs. The loss of cell deformability is nevertheless shown to improve slightly the dissociation efficiency of the flowing liquid in a shear flow resulting in a small reduction of the disaggregation shear rate after heat treatment. Heat treatment is also shown to alter the structure of RBC network at equilibrium. These results indicate that heat induced alterations of erythrocytes only affects the mechanical properties of the cell membrane without significant changes in the macromolecular bridging energy.     

Equilibrium shapes of erythrocytes in rouleau formation

A well known physiological property of erythrocytes is that they can aggregate and form a rouleau. We present a theoretical analysis of erythrocyte shapes in a long rouleau composed of cells with identical sizes. The study is based on the area difference elasticity model of lipid membranes, and takes into consideration the adhesion of curved axisymmetric membranes. The analysis predicts that the erythrocytes in the rouleau can have either a discoid or a cup-like shape. These shapes are analogous to the discoid and stomatocyte shapes of free erythrocytes. The transitions between the discoid and cup-like shapes in the rouleau are characterized. The occurrence of these transitions depends on three model parameters: the cell relative volume, the preferred difference between the areas of the membrane bilayer leaflets, and the strength of the adhesion between the membranes. The cup-like shapes are favored at small relative volumes and small preferred area differences, and the discoid shapes are favored at large values of these parameters. Increased adhesion strength enlarges the contact area between the cells, flattens the cells, and consequently promotes the discoid shapes.     

Anomalous diffusion of erythrocytes in the presence of polyvinylpyrrolidone

The diffusion coefficient of erythrocytes was measured using quasi-elastic light-scattering (QELS) techniques. The cells were suspended in phosphate-buffered saline solutions with and without a macromolecule, polyvinylpyrrolidone (PVP[360]). In the presence of the PVP(360) an anomalously high diffusion coefficient was measured for metabolizing cells with a normal transmembrane potential. The results are in agreement with experiments on rouleau formation by red blood cells and are supportive of the hypothesis of a long-range coherent interaction between metabolically active biological cells.     

Modes of rouleaux formation of human red blood cells in polyvinylpyrrolidone and dextran solutions

The mechanics by which normal human erythrocytes join on a plastic cover slip into two cell doublets and larger aggregates of rouleaux were studied microscopically. Polyvinylpyrrolidone (PVP-360) or dextran (DX-70 or DX-110) were used as the rouleau agents. The minimum concentration of the rouleau-inducing agents required to form doublets was 1 g/L for PVP-360 and 5 g/L for the DXs. Three modes of interaction were observed in Ringer's solution with PVP or DX, cresting and flipping (involving no intercellular sliding) and a sliding mode of doublet formation (involving less gravitational work and less cellular deformation). The sliding mechanism occurred in suspensions with the lower concentrations of the rouleau agent but was also observed when geometric constraints prevented the nonsliding interaction of larger groups of cells in the higher concentrations of the rouleau agent. The technique provides a sensitive index for studying the combined effect of cellular flexibility and intercellular adhesion. Significant changes were observed for reduced membrane surface charge or reduced ionic calcium.     

Membrane tethers formed from blood cells with available area and determination of their adhesion energy

Fundamental to all mammalian cells is the adherence of the lipid bilayer membrane to the underlying membrane associated cytoskeleton. To investigate this adhesion, we physically detach the lipid membrane from the cell by mechanically forming membrane tethers. For the most part these have been tethers formed from either neutrophils or red cells. Here we do a simple thermodynamic analysis of the tether formation process using the entire cell, including tether, as the control volume. For a neutrophil, we show that the total adhesion energy per unit area between lipid membrane and cytoskeleton depends on the square of the tether force. For a flaccid red cell, we show that the total adhesion energy minus the tension in the spectrin cytoskeleton depends also on the square of the tether force. Finally, we discuss briefly the viscous flow of membrane. Using published data we calculate and compare values for the various adhesion energies and viscosities.     

Minimum energy analysis of membrane deformation applied to pipet aspiration and surface adhesion of red blood cells.

An experimental procedure is demonstrated which can be used to determine the interfacial free energy density for red cell membrane adhesion and membrane elastic properties. The experiment involves micropipet aspiration of a flaccid red blood cell and manipulation of the cell proximal to a surface where adhesion occurs. A minimum free energy method is developed to model the equilibrium contour of unsupported membrane regions and to evaluate the partial derivatives of the total free energy, which correspond to the micropipet suction force and the interfacial free energy density of adhesion. It is shown that the bending elasticity of the red cell membrane does not contribute significantly to the pressure required to aspirate a flaccid red cell. Based on experimental evidence, the upper bound for the bending or curvature elastic modulus of the red cell membranes is 10-12 ergs (dyn-cm). Analysis of the adhesion experiment shows that interfacial free energy densities for red cell adhesion can be measured from a lower limit of 10-4 ergs/cm2 to an upper limit established by the membrane tension for lysis of 5-10 ergs/cm2.     

Strain Energy Function of Red Blood Cell Membranes

The several widely different values of the elastic modulus of the human red blood cell membrane which have been reported in the literature are incorporated into a single strain energy function consisting of two terms. One term gives the small stresses and low elastic modulus which is observed when the red cell membrane is deformed at constant area. The second term contributes a large isotropic stress dependent on the change of area. The strain energy function is applied to the process of sphering of red blood cells in a hypotonic solution. It is shown that a nearly perfect sphere can result even though the red blood cell membrane is homogeneous in all areas of the cell. Results pertinent to sieving and micropipette experiments are also explored.     

Factors involved in cell adhesion to vascular endothelium

The adhesion of blood cells to endothelium can be studied in vitro using human endothelial cells in culture. This experimental model and radiometric techniques provide us with a simple system to quantify the adhesion of blood cells to endothelium. Normal human granulocytes isolated by density gradient adhere to normal endothelial cells in a proportion of 25%. Human promyelocytic cells (HL 60) induced by retinoic acid into mature cells adhere as well as normal granulocytes while the noninduced adhere poorly to endothelium. A small percentage of normal red cells attach to endothelial cells while red cells from patients with sickle cell anemia or diabetes mellitus have a significantly increased adhesion to endothelial cells (P greater than 0.001). This adhesion is statistically correlated with the extent and severity of vascular complications in diabetes mellitus (P less than 0.05). The addition of fibrinogen significantly increased (P less than 0.01) the adhesion of normal red cells, red cells from patients with sickle cell anemia or diabetes mellitus while gamma-globulins did not modify adhesion. Fibronectin potentiated the adhesion of normal red cells.     

Free energy potential for aggregation of erythrocytes and phosphatidylcholine/phosphatidylserine vesicles in Dextran (36,500 MW) solutions and in plasma.

The free energy potential (affinity) for aggregation of human red blood cells and lipid vesicles in Dextran solutions and blood plasma has been quantitated by measuring to what extent a vesicle is encapsulated by the red cell surface. The free energy reduction per unit area of contact formation (affinity) was computed from the observation of the fractional extent of encapsulation at equilibrium with the use of a relation based on the elastic compliance of the red cell membrane as it is deformed to adhere to the vesicle surface. Micromanipulation methods were used to select and transfer single lipid vesicles (2-3 X 10(-4) cm diameter) from a chamber that contained the vesicle suspension to a separate chamber on the microscope stage that contained red cells in an EDTA buffer with Dextran or whole plasma. The vesicle and a red cell were maneuvered into close proximity and contact allowed to take place without forcing the cells together. To evaluate the effects of surface charge density and steric interactions on aggregation, vesicles were made from mixtures of egg phosphatidylcholine (PC) and bovine phosphatidylserine (PS) over a range of mole ratios (PC/PS)from (1:0) to (1:1); the vesicles were formed by rehydration in buffer. The Dextran solutions were made with a sharp-cut fraction of 36,500 MW in a concentration range of 0-10% by weight in grams (wt/wt).(ABSTRACT TRUNCATED AT 250 WORDS)     

Red blood cell aggregation and dissociation in shear flows simulated by lattice Boltzmann method

In this paper we develop a lattice Boltzmann algorithm to simulate red blood cell (RBC) behavior in shear flows. The immersed boundary method is employed to incorporate the fluid-membrane interaction between the flow field and deformable cells. The cell membrane is treated as a neo-Hookean viscoelastic material and a Morse potential is adopted to model the intercellular interaction. Utilizing the available mechanical properties of RBCs, multiple cells have been studied in shear flows using a two-dimensional approximation. These cells aggregate and form a rouleau under the action of intercellular interaction. The equilibrium configuration is related to the interaction strength. The end cells exhibit concave shapes under weak interaction and convex shapes under strong interaction. In shear flows, such a rouleau-like aggregate will rotate or be separated, depending on the relative strengths of the intercellular interaction and hydrodynamic viscous forces. These behaviors are qualitatively similar to experimental observations and show the potential of this numerical scheme for future studies of blood flow in microvessels.     

The equilibrium size distribution of rouleaux.

Rouleaux are formed by the aggregation of red blood cells in the presence of macromolecules that bridge the membranes of adherent erythrocytes. We compute the size and degree of branching of rouleaux for macroscopic systems in thermal equilibrium in the absence of fluid flow. Using techniques from statistical mechanics, analytical expressions are derived for (a) the average number of rouleaux consisting of n cells and having m branch points; (b) the average number of cells per rouleau; (c) the average number of branch points per rouleau; and (d) the number of rouleaux with n cells, n = 1, 2, ..., in a system containing a total of N cells. We also present the results of numerical evaluations to establish the validity of asymptotic expressions that simplify our formal analytic results.     

Analysis of adhesion of large vesicles to surfaces.

An experimental procedure that can be used to measure the interfacial free energy density for the adhesion of membranes of large vesicles to other surfaces is outlined and analyzed. The approach can be used for both large phospholipid bilayer vesicles and red blood cells when the membrane force resultants are dominated by isotropic tension. The large vesicle or red cell is aspirated by a micropipet with sufficient suction pressure to form a spherical segment outside the pipet. The vesicle is then brought into close proximity of the surface to be tested and, the suction pressure reduced to permit adhesion, and the new equilibrium configuration is established. The mechanical analysis of the equilibrium shape provides the interfacial free energy density for the surface affinity. With this approach, the measurable range of membrane surface affinity is 10(-4)-3 erg/cm2 for large phospholipid bilayer vesicles and 10(-2)-10 erg/cm2 for red blood cells.     

Fibrinogen-induced erythrocyte aggregation: erythrocyte-binding site in the fibrinogen molecule

The effect of fibrinogen and fibrinogen-derived products on the velocity of rouleau formation of human erythrocytes was quantitatively examined with a rheoscope combined with a video-camera, an image analyzer and a computer. (i) The velocity of rouleau formation by naturally occurring low-molecular-weight fibrinogen of 305 kDa and by desialylated fibrinogen was the same as that by native fibrinogen of 340 kDa. (ii) Concerning fibrinogen degradation products by plasmin, the velocity of rouleau formation decreased upon going from fibrinogen greater than fragment X greater than fragment Y (the ratio of molar concentration of fibrinogen, fragment X and fragment Y for giving a certain velocity of rouleau formation was approx. 1:2:5). The effect of fragments X and Y on the fibrinogen-induced rouleau formation was additive. (iii) Fragments D and E could not induce rouleau formation and did not affect the fibrinogen-, fragment X- and fragment Y-induced rouleau formation. (iv) Fibrinopeptides A and B and artificial tetrapeptides (Gly-Pro-Arg-Pro and Gly-His-Arg-Pro) did not affect the fibrinogen-induced rouleau formation. (v) The possible erythrocyte-binding site in fibrinogen molecule for leading to rouleaux was proposed to be in A alpha-chain (probably, around residues No. 207-303) near the terminal domain of the trinodular structure of fibrinogen.     

Phenomenon of pili formation in Yersinia enterocolitica

In Y. enterocolitica strain, serovar 0:10, the capacity for the formation of pili inducing the mannose-resistant hemagglutination (MRHA) of formolated sheep red blood cells was due to the presence of plasmid pYE10. MRHA-inducing pili differed serologically from Y. pestis and Y. tuberculosis adhesion pili. Plasmid pYE10 was immobilized for transfer to cells of Escherichia coli strain HB101 (rec A) by means of pRP 4. The expression of MRHA-inducing pili in the new host the rec A-independent character of the synthesis. Y. enterocolitica cells containing pYE10 agglutinated in tissue-culture media with 10% of serum added at 37 degrees C.     

Fibrinogen inhibits red cell adhesion to glass

Studies of human erythrocyte adhesion to glass have demonstrated consistently greater adhesion with serum-containing media than with a comparable concentration of plasma. This serum-plasma difference is explained by the adhesion-inhibiting property of plasma fibrinogen. The fibrinogen effect is probably mediated through its firm binding to glass, since no adsorption onto the red cell surface could be demonstrated. The ability of more red cells to adhere to a foreign surface after plasma coagulation (the formation of serum from plasma) may be significant in the red cell surface interactions necessary for the formation of a fibrin-red cell thrombus.     

Monitoring of erythrocyte aggregate morphology under flow by computerized image analysis

The morphology of red blood cell (RBC) aggregates was studied by direct visualization of RBC aggregation at different flow conditions in a computerized image analyzer. The aggregate morphology is expressed by an Aggregate Shape Parameter (ASP), defined as the ratio of the aggregate projected area to its square perimeter. Aggregation was induced by either dextran-70 (m.w. 70,000) or dextran-500 (m.w. 500,000), and compared to that in plasma. It was found that the aggregate morphology is a characteristic of the aggregating agent-in dextran-500, the RBC form rouleau aggregates as in plasma, while in dextran-70, they form clusters. In each system, while maintaining the overall typical morphology, the ASP decreases (i.e., the aggregate becomes longer) as the aggregate size is increased. The distribution of the ASP as a function of the aggregate size remains unchanged when the aggregate size is changed by modulation of the dextran concentration or the shear stress. Stretching of a rouleau aggregate by application of shear stress is reflected by a corresponding change in the ASP. It is suggested that the ASP is a characteristic of intercellular interactions. A theoretical model is proposed for evaluation of the deviation of aggregate shape from that of rouleau structure.     

Affinity of red blood cell membrane for particle surfaces measured by the extent of particle encapsulation.

An experimental technique and a simple analysis are presented that can be used to quantitate the affinity of red blood cell membrane for surfaces of small beads or microsomal particles up to 3 micrometers Diam. The technique is demonstrated with an example of dextran-mediated adhesion of small spherical red cell fragments to normal red blood cells. Cells and particles are positioned for contact by manipulation with glass micropipets. The mechanical equilibrium of the adhesive contact is represented by the variational expression that the decrease in interfacial free energy due to a virtual increase in contact area is balanced by the increase in elastic energy of the membrane due to virtual deformation. The surface affinity is the reduction in free energy per unit area of the interface associated with the formation of adhesive contact. From numerical computations of equilibrium configurations, the surface affinity is derived as a function of the fractional extent of particle encapsulation. The range of surface affinities for which the results are applicable is increased over previous techniques to several times the value of the elastic shear modulus. It is shown that bending rigidity of the membrane has little effect on the analytical results for particles 1--3 micrometers Diam and that results are essentially the same for both cup- and disk-shaped red cells. A simple analytical model is shown to give a good approximation for surface affinity (normalized by the elastic shear modulus) as a function of the fractional extent of particle encapsulation. The model predicts that a particle would be almost completely vacuolized for surface affinities greater than or equal to 10 times the elastic shear modulus. Based on an elastic shear modulus of 6.6 x 10(-3) dyn/cm, the range for the red cell-particle surface affinity as measured by this technique is from approximately 7 x 10(-4) to 7 x 10(-2) erg/cm2. Also, an approximate relation is derived for the level of surface affinity necessary to produce particle vacuolization by a phospholipid bilayer surface which possesses bending rigidity and a fixed tension.