Segregation into separate rouleaux of erythrocytes from different species. Evidence against the agglomerin hypothesis of rouleaux formation.

Erythrocytes from one species were labelled with fluorescein isothiocyanate and mixed with unlabelled erythrocytes from another species. Albumin polymers were added to generate rouleaux. The species of origin of erythrocytes in rouleaux was determined by fluorescence microscopy. Erythrocytes from different species segregated into independent rouleaux. However, fluorescent and non-fluorescent erythrocytes from one individual were mixed randomly in rouleaux. These results confirm, using a novel experimental approach, previous observations of Sewchand & Canham [(1976) Can. J. Physiol. Pharmacol. 54, 437-442]. Since rouleaugenic agents are not species-specific, under the 'agglomerin' hypothesis of rouleau formation they would be expected to form bridges between cells from different species. It follows that either the agglomerin hypothesis is incorrect, or additional species-specific surface components are involved in the aggregation of agglomerin-cross-bridged cells.     

Kinetics of rouleau formation. I. A mass action approach with geometric features.

In the presence of certain macromolecules, such as fibrinogen, immunoglobulin, dextran, and polylysine, erythrocytes tend to aggregate and form cylindrical clusters called "rouleaux" in which cells resemble coins in a stack. The aggregates may remain cylindrical or they may branch, forming tree, and networklike structures. Using the law of mass action and notions from polymer chemistry, we derive expressions describing the kinetics of the early phase of aggregation. Our models generalize work initiated by Ponder in 1927 who used the Smoluchowski equation to predict the concentration of rouleaux of different sizes. There are two novel features to our generalization. First, we allow erythrocytes that collide near the end of a stack of cells to move to the end of the cylinder and elongate it. Second, we incorporate geometric information into our models and describe the kinetics of branched rouleau formation. From our models we can predict the concentration of rouleaux with n cells and b branches, the mean number of cells per rouleau, the mean number of branches per rouleau, and the average length of a branch. Comparisons are made with the available experimental data.     

Thixotropic properties of whole blood from healthy human subjects

The steady state non-Newtonian viscosity of whole human blood has been widely studied as a function of the shear rate; and used to characterize the blood in various pathological disorders. In our previous studies, we demonstrated that blood is a thixotropic fluid. Its time-dependency and shear rate dependency of rheological behavior can be represented by an equation developed by Huang. Parameters of the equation can be used for the characterization of an individual's blood. They provide information, such as the kinetic rate constant of breakdown of RBC rouleaux to individual erythrocytes and the relative amount of rouleau formation in the dynamic equilibrium between rouleaux and individual erythrocytes. In this communication, the thixotropic parameters from blood samples of fifteen apparently healthy human subjects were investigated. When compared to the use of apparent viscosity values for the correlation with a pathological disorder, thixotropic parameters are preferable. The mean values of thixotropic parameters obtained from apparently healthy human subjects provide a base for comparison with the same parameters as obtained from blood samples of patients with certain pathological disorders involving the circulation.     

Rouleau formation of erythrocytes: A dynamical model

A model is presented for the nonBrownian motion of living erythrocytes suspended in their own plasma as observed by Rowlands et al. On the basis of this model, the formation of rouleaux (contractile fibrils among interacting erythrocytes) can be described in terms of an organization of the molecules (mainly fibrinogen) present in blood plasma; this organization is sustained by the nonlinear propagation of electric vibrations generated by red blood cells (coherent electric vibrations of the Fröhlich type).A number of peculiar experimental features otherwise unexplained can also be taken into account in the framework of the model.     

Lysophosphatidic acid and human erythrocyte aggregation

The effect of lysophosphatidic acid (LPA) on the shape and aggregation of human erythrocytes in autologous plasma was studied. The morphology of erythrocytes and their aggregates were studied by light microscopy. It is shown that the addition of plasma with a high LPA content to erythrocytes leads to a change of their shape: discocytes are transformed into echinocytes. There is practically no aggregation of erythrocytes in the form of rouleaux. At the same time, there is observed a strong aggregation of echinocytes. This is accompanied by the formation of microvesicles. The addition of normal blood plasma to echinocytes restores their shape and aggregation of red blood cells in the form of rouleaux. A possible mechanism of action of lysophosphatidic acid on erythrocytes is discussed.     

Effects of shear rate on rouleau formation in simple shear flow

A kinetic equation for rouleau formation in a simple shear flow is derived, based on several assumptions. These are (a) colliding rouleaux stick to one another with a certain probability to form a single rouleau; (b) simultaneous collisions between more than two rouleaux are negligible; (c) rouleaux are broken by a viscous force exerted by the suspending fluid on the surfaces of rouleaux; (d) when a rouleau is broken by viscous forces, only two fragments are formed. Based on a simple mathematical model, collision rate, sticking probability and degradation rate are obtained as functions of applied shear rate. From the solution of the kinetic equation, the average size of rouleaux is obtained as a function of time with shear rate as a parameter. It is shown that the average size of rouleaux increases monotonically with increasing time and tends to an equilibrium size. The average size of rouleaux in a dynamical equilibrium decreases monotonically with increasing shear rate and tends to one cell as shear rate approaches infinity. It is also found that the initial rate of rouleau formation increases with increasing shear rate at very low shear rate, but this trend is reversed at higher shear rates. The theoretical results are compared quantitatively with experimental data.     

Kinetics of rouleau formation. II. Reversible reactions.

Red blood cells aggregate face-to-face to form long, cylindrical, straight chains and sometimes branched structures called rouleaux. Here we extend a kinetic model developed by R. W. Samsel and A. S. Perelson (1982, Biophys. J. 37:493-514) to include both the formation and dissociation of rouleaux. We examine thermodynamic constraints on the rate constants of the model imposed by the principle of detailed balance. Incorporation of reverse reactions allows us to compute mean sizes of rouleaux and straight chain segments within rouleaux, as functions of time and at equilibrium. Using the Flory - Stockmayer method from polymer chemistry, we obtain a closed-form solution for the size distribution of straight chain segments within rouleaux at any point in the evolution of the reaction. The predictions of our theory compare favorably with data collected by D. Kernick , A.W.L. Jay , S. Rowlands , and L. Skibo (1973, Can. J. Physiol. Pharmacol. 51:690-699) on the kinetics of rouleau formation. When rouleaux grow large, they may contain rings or loops and take on the appearance of a network. We demonstrate the importance of including the kinetics of ring closure in the development of realistic models of rouleaux formation.     

Electro-orientation of ellipsoidal erythrocytes. Theory and experiment.

The frequency-dependent orientation of human and llama erythrocytes suspended in isotonic solutions and subjected to linearly polarized electric fields is examined. Human erythrocytes may be represented as oblate spheroids (3.9:3.9:1.1 microns) with two distinguishable orientations, while the llama cells are approximated as ellipsoids with three distinct axes (4.0:2.0:1.1 microns). Under appropriate experimental conditions, both orientations of the human cells and all three orientations of the llama cells are observed. A theoretical cell model which accounts for the membrane as a thin confocal layer of ideal capacitance is used to predict the orientational spectra. The predicted spectra compare favorably in frequency range and orientational sequence with experimental data. Estimates for cell internal conductivity and permittivity are obtained by adjusting the values of these important parameters to achieve the closet fit of the theoretical curves to the data. By the use of this method, the internal conductivity of llama erythrocytes is estimated to be 0.26 S/m (+/- 20%), while the effective internal dielectric constant and conductivity of Euglena gracilis are estimated to be 120 (+/- 10%) and 0.43 S/m (+/- 20%), respectively.     

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.     

Erythrocytes-the 'house elves' of photodynamic therapy.

Photodynamic therapy (PDT) and fluorescence diagnosis (FD) are being developed for a number of clinical applications. Since fluorophores and photosensitising drugs are usually given systemically their effect on blood elements are of significant importance. Photodynamic effects on erythrocytes occur naturally in patients with erythropoietic protoporphyria (EPP). Exposure to small fluences, as obtained by the erythrocytes when they pass capillaries in the skin, leads to transfer of the photosensitiser protoporphyrin IX (PP IX), from EPP erythrocytes to endothelial cells. Thus, the erythrocytes are partly protected while the endothelial cells suffer photodamage. During photodynamic therapy in vivo erythrocytes are regularly photosensitised. This side effect is partly intended but mostly unwanted, and a summary of this topic is given. Furthermore, the effect of UV-A on erythrocytes that is accompanied with the formation of bilirubin is reviewed. Erythrocytes serve as convenient model cells for experimental research. Such use of erythrocytes to screen new photosensitisers may be of limited value. A combination of photohaemolysis and haemoglobin oxygenation may become the basis for an assay for in vitro phototoxicity. Erythrocytes from birds are good model cells for exploration of physiological and molecular mechanisms involved in PDT. A potential mechanism of PDT induced behaviour resembling apoptosis in erythrocytes is provided.PDT for sterilisation of erythrocyte concentrates has a potential for medical use. Photodynamic effects on the erythrocytes themselves should be avoided. This is realised by choosing a virus-selective photosensitiser, low fluences and treatment of the concentrates with agents like dipyridamole and antioxidants. Future aspects of applications of photosensitisation of red blood cells are discussed.     

Rheology of Human Blood, near and at Zero Flow: Effects of Temperature and Hematocrit Level

Static normal human blood possesses a distinctive yield stress. When the yield stress is exceeded, the same blood has a stress-shear rate function under creeping flow conditions closely following Casson's model, which implies reversible aggregation of red cells in rouleaux and flow dominated by movement of rouleaux. The yield stress is essentially independent of temperature and its cube root varies linearly with hematocrit value. The dynamic rheological properties in the creeping flow range are such that the relative viscosity of blood to water is almost independent of temperature. Questions raised by these data are discussed, including red cell aggregation promoted by elements in the plasma.     

Inhibition and acceleration of erythrocyte aggregation induced by small macromolecules

The aggregation (especially the 'rouleau' formation) of human erythrocytes induced by polysaccharide and polyglutamic acid was quantitatively examined by using a low-shear rheoscope combined with a television image analyzer and a computer. (1) The morphological characteristics of rouleaux induced by these macromolecules are presented. (2) Polysaccharides with high molecular weights of 70 400 and 494 000 and poly(glutamic acids) with weights of 50 000 and 66 000 formed the rouleaux (then the three-dimensional aggregates). But polysaccharides with the low molecular weights of 10 300 and 42 500 and poly(glutamic acids) with weights of 8000 and 20 000 did not. The dependences of the velocity of rouleau formation on the macromolecule concentration and on the shear rate are shown. (3) The erythrocyte aggregation induced by high-molecular-weight polysaccharides was inhibited by low-molecular-weight polysaccharides and glucose, but was not affected by low-molecular-weight poly(glutamic acids). (4) The aggregation induced by high-molecular-weight poly(glutamic acids) was inhibited by poly(glutamic acid) with a molecular weight of 8000, but was accelerated by that of 20 000. The poly(glutamic acid)-induced aggregation was not affected by low-molecular-weight polysaccharides. (5) The stereochemical structure-dependent interaction (or the mode of bridging) of macromolecules with erythrocytes was stressed for the mechanism of erythrocyte aggregation.     

Mechanisms of successive modes of erythrocyte stability and instability in the presence of various polymers

Upon examination in real time of the adhesion of human erythrocytes by observing cells suspended by ultrasonic radiation force in solutions of dextran, polylysine, and polyethylene glycol, it was reported earlier that concave-ended cell pairs and rouleaux are seen in low (0.5-2.0% w/v) concentrations of Dextran T500. At concentrations of 5-7%, dextran spherical cell doublets and convex-ended cell agglutinates are formed. When adhesion occurs in polylysine (MW 14,000) or in polyethylene glycol (MW 8,000) only spherical cell doublets or convex-ended cell clumps occur. The final cell movement completing the formation of these adhesion products takes place over time scales of the order of 1s. In this work, quantitative consideration is given to the extent to which repulsion between adhesion-inducing macromolecules associated with the glycocalyx and those free in solution can influence adhesion through a phase separation effect. It is shown for cells in dextran and in polylysine that the forces associated with this repulsion are of the same order of magnitude as the electrostatic interactions between cells.     

Effects of hemolysate concentration, ionic strength and cytochrome b5 concentration on the rate of methemoglobin reduction in hemolysates of human erythrocytes.

An assay for determining the rate of methemoglobin reduction in hemolysates of human erythrocytes has been developed. The rates obtained by this assay, when corrected for dilution, are comparable to those obtained with intact cells. Increased ionic strength inhibits the reaction, whereas EDTA increases the rate of reduction. The rate with NADPH as electron donor is 65-70% of the rate with NADH. Added cytochrome b5 stimulates the reaction. The assay has been used to examine erythrocytes from two methemoglobinemic sisters and their asymptomatic mother. Hemolysates of the two patients have both decreased dichlorophenolindophenol reductase activity and decreased ability to reduce methemoglobin. Hemolysates from the heterozygous mother have intermediate dichlorophenolindophenol reductase activity and intermediate methemoglobin reduction ability. The data presented in this paper indicate that the concentrations of cytochrome b5 and cytochrome b5 reductase determine the rate of methemoglobin reduction in hemolysates.     

Electrophoretic mobility of human erythrocytes. On the applicability of the charged layer model.

The limitations of previous linear electrokinetic theories are discussed. A special model of the surface charge distribution, based on the minimum condition of the interfacial electrostatic free energy, is introduced. The model describes the electrophoretic mobility, taking into account the electroosmotic flow through the surface macromolecular layer and the surface conductivity. This nonlinear electrophoretic theory describes experimental data obtained with human erythrocytes. Numerical results for an uniformly distributed space charge are also presented.     

Mechanisms of successive modes of erythrocyte stability and instability in the presence of various polymers

Upon examination in real time of the adhesion of human erythrocytes by observing cells suspended by ultrasonic radiation force in solutions of dextran, polylysine, and polyethylene glycol, it was reported earlier that concave-ended cell pairs and rouleaux are seen in low (0.5–2.0% w/v) concentrations of Dextran T500. At concentrations of 5–7%, dextran spherical cell doublets and convex-ended cell agglutinates are formed. When adhesion occurs in polylysine (MW 14,000) or in polyethylene glycol (MW 8,000) only spherical cell doublets or convex-ended cell clumps occur. The final cell movement completing the formation of these adhesion products takes place over time scales of the order of 1s. In this work, quantitative consideration is given to the extent to which repulsion between adhesion-inducing macromolecules associated with the glycocalyx and those free in solution can influence adhesion through a phase separation effect. It is shown for cells in dextran and in polylysine that the forces associated with this repulsion are of the same order of magnitude as the electrostatic interactions between cells.     

The erythrocyte sedimentation rates: some model experiments

In order to obtain a better understanding of the erythrocyte sedimentation rate (ESR), several models are presented. The first directs attention to the importance of geometrical models to represent the structure of mixtures. Here it is our intention to understand the effect of the structure on the packing of red blood cells. In this part of the study, "Cheerios" (trademark General Mills) are used as a macroscopic model. It is interesting that a random sampling of "Cheerios" has the same volume distribution curve that is found for erythrocytes with a Coulter Sizing Apparatus. In order to examine the effect of rouleaux formation, the "Cheerios" are stacked one on top of another and then glued. Rouleaux of 2,3,4,5, 7 and 10 discs were used. In order to examine a more realistic biological model, the experiments of Dintenfass were used. These investigations were performed in a split-capillary photo viscometer using whole blood from patients with a variety of diseases. The novel part of this research is the fact that the work was performed at 1g and at near zero gravity in the space shuttle "Discovery." The size of the aggregates and/or rouleaux clearly showed a dependence upon the gravity of the experiment. The purpose of this model was to examine the condition of self-similarity and fractal behavior. Calculations are reported which clearly indicate that there is general agreement in the magnitude of the fractal dimension from the "Cheerios" model, the "Discovery" experiment with those determined with the automatic sedimentimeter. The final aspect of this work examines the surface texture of the sedimention tube. A series of tubes were designed with "roughened" interiors. A comparison of the sedimentation rates clearly indicates a more rapid settling in "roughened" tubes than in ones with a smooth interior surface.     

Mechanisms of successive modes of erythrocyte stability and instability in the presence of various polymers

Upon examination in real time of the adhesion of human erythrocytes by observing cells suspended by ultrasonic radiation force in solutions of dextran, polylysine, and polyethylene glycol, it was reported earlier that concave-ended cell pairs and rouleaux are seen in low (0.5–2.0% w/v) concentrations of Dextran T500. At concentrations of 5–7%, dextran spherical cell doublets and convex-ended cell agglutinates are formed. When adhesion occurs in polylysine (MW 14,000) or in polyethylene glycol (MW 8,000) only spherical cell doublets or convex-ended cell clumps occur. The final cell movement completing the formation of these adhesion products takes place over time scales of the order of 1s. In this work, quantitative consideration is given to the extent to which repulsion between adhesion-inducing macromolecules associated with the glycocalyx and those free in solution can influence adhesion through a phase separation effect. It is shown for cells in dextran and in polylysine that the forces associated with this repulsion are of the same order of magnitude as the electrostatic interactions between cells.     

Kinetics of linear rouleaux formation studied by visual monitoring of red cell dynamic organization

Red blood cells (RBCs) in the presence of plasma proteins or other macromolecules may form aggregates, normally in rouleaux formations, which are dispersed with increasing blood flow. Experimental observations have suggested that the spontaneous aggregation process involves the formation of linear rouleaux (FLR) followed by formation of branched rouleaux networks. Theoretical models for the spontaneous rouleaux formation were formulated, taking into consideration that FLR may involve both "polymerization," i.e., interaction between two single RBCs (e + e) and the addition of a single RBC to the end of an existing rouleau (e + r), as well as "condensation" between two rouleaux by end-to-end addition (r + r). The present study was undertaken to experimentally examine the theoretical models and their assumptions, by visual monitoring of the spontaneous FLR (from singly dispersed RBC) in plasma, in a narrow gap flow chamber. The results validate the theoretical model, showing that FLR involves both polymerization and condensation, and that the kinetic constants for the above three types of intercellular interactions are the same, i.e., k(ee) = k(er) = k(rr) = k, and for all tested hematocrits (0.625-6%) k < 0.13 +/- 0.03 s(-1).     

Frequency domain impedance measurements of erythrocytes. Constant phase angle impedance characteristics and a phase transition.

We report measurements of the electrical impedance of human erythrocytes in the frequency range from 1 Hz to 10 MHz, and for temperatures from 4 to 40 degrees C. In order to achieve high sensitivity in this frequency range, we embedded the cells in the pores of a filter, which constrains the current to pass through the cells in the pores. Based on the geometry of the cells embedded in the filter a circuit model is proposed for the cell-filter saline system. A constant phase angle (CPA) element, i.e., an impedance of the form Z = A/(j omega)alpha, where A is a constant, j = square root of -1, omega is angular frequency, and 0 less than alpha less than 1 has been used to describe the ac response of the interface between the cell surface and the electrolyte solution, i.e., the electrical double layer. The CPA and other elements of the circuit model are determined by a complex nonlinear least squares (CNLS) fit, which simultaneously fits the real and imaginary parts of the experimental data to the circuit model. The specific membrane capacitance is determined to be 0.901 +/- 0.036 microF/cm2, and the specific cytoplasm conductivity to be 0.413 +/- 0.031 S/m at 26 degrees C. The temperature dependence of the cytoplasm conductivity, membrane capacitance, and CPA element has been obtained. The membrane capacitance increases markedly at approximately 37 degrees C, which suggests a phase transition in the cell membrane.