Lymphocyte culture supernatants prevent sickling of red blood cells

Metabisulphate-treated red blood cells from sickle-cell patients were protected from sickling by exposure to supernatants from cultures of phytohemagglutinin-stimulated normal human lymphocytes. Such supernatants, when not thus stimulated, afforded no protection.     

Single cell laser light scattering spectroscopy in a flow cell: Repeated sickling of sickle red blood cells

We performed dynamic laser light scattering measurements of hemoglobin aggregates in single, sickle erythrocytes. Sickle erythrocytes were attached to the poly-(l-lysine)-coated surface of a flow cell. They were exposed to several oxygenation-deoxygenation cycles by repeatedly changing the flowing solution. The rate of cycling was found to be a determining factor for the formation of irreversible morphologic alterations as well as irreversible hemoglobin aggregates. In slow cycling, the sickle erythrocytes took an irreversible, irregular, rounded shape, and hemoglobin aggregates were observed even in the oxygenated state after 20 cycles. In the fast cycling, however, these changes did not take place even after 60 cycles.     

Membrane components in the red cells of patients with sickle cell anemia Relationship to cell aging and to irreversibility of sickling

Cholesterol, phospholipid and sialic acid were measured in red cells from patients with sickle cell anemia to determine whether the cells had abnormal concentrations of these components and whether the amounts of these compounds differed in irreversibly sickled cells as compared to non-irreversibly sickled cells. Sickle cells had significantly higher levels of both lipids than similar populations of normal cells, however, comparisons to populations of young control cells showed that the differences were generally not significant. Sialic acid levels in sickle cells were not significantly different from normal cells. Irreversibly sickled cells had lower lipid and sialic acid concentrations than those not irreversibly sickled, but the differences were either not significant or did not occur when compared to young control cells. The studies show that the increased lipid concentrations in the membrane of sickle cells are not abnormal but are related to cell age and that the decrease in membrane components in irreversibly sickled cells is no greater than would be predicted for similarly aged populations of cells.     

Effect of sickling on dimyristoylphosphatidylcholine-induced vesiculation in sickle red blood cells

To study the effect of sickling on dimyristoylphosphatidylcholine (DMPC)-induced vesiculation, sickle (SS) red blood cells were incubated with sonicated suspensions of DMPC under either room air or nitrogen. Like normal red cells, when sickle cells were incubated with DMPC under oxygenated conditions, incorporation of DMPC into the erythrocyte membrane occurred, followed by echinocytic shape transformation and subsequent release of membrane vesicles. On the other hand, when SS cells were induced to sickle by deoxygenation, DMPC-induced vesiculation of these cells was dramatically reduced. However, upon reoxygenation, release of vesicles from these sickle erythrocytes occurred immediately. When SS cells were incubated under hypertonic (500 mosM) and deoxygenated conditions (where hemoglobin polymerization occurs but red cells do not show the typical sickle morphology), a similar decrease in the extent of vesiculation was observed. Experiments with radiolabelled lipid vesicles indicated that incorporation of DMPC into erythrocyte membranes occurred in all cases and therefore was not the limiting factor in the reduction of vesiculation in deoxygenated SS cells. Taken together, these results indicate that cellular viscosity and membrane rigidity, both of which are influenced by hemoglobin polymerization, are two important factors in process of vesicle release from sickle erythrocytes.     

Mathematical model of a cell size checkpoint

How cells regulate their size from one generation to the next has remained an enigma for decades. Recently, a molecular mechanism that links cell size and cell cycle was proposed in fission yeast. This mechanism involves changes in the spatial cellular distribution of two proteins, Pom1 and Cdr2, as the cell grows. Pom1 inhibits Cdr2 while Cdr2 promotes the G2 → M transition. Cdr2 is localized in the middle cell region (midcell) whereas the concentration of Pom1 is highest at the cell tips and declines towards the midcell. In short cells, Pom1 efficiently inhibits Cdr2. However, as cells grow, the Pom1 concentration at midcell decreases such that Cdr2 becomes activated at some critical size. In this study, the chemistry of Pom1 and Cdr2 was modeled using a deterministic reaction-diffusion-convection system interacting with a deterministic model describing microtubule dynamics. Simulations mimicked experimental data from wild-type (WT) fission yeast growing at normal and reduced rates; they also mimicked the behavior of a Pom1 overexpression mutant and WT yeast exposed to a microtubule depolymerizing drug. A mechanism linking cell size and cell cycle, involving the downstream action of Cdr2 on Wee1 phosphorylation, is proposed.     

Membrane components in the red cells of patients with sickle cell anemia. Relationship to cell aging and to irreversibility of sickling

Cholesterol, phospholipid and sialic acid were measured in red cells from patients with sickle cell anemia to determine whether the cells had abnormal concentrations of these components and whether the amounts of these compounds differed in irreversibly sickled cells as compared to non-irreversibly sickled cells. Sickle cells had significantly higher levels of both lipids than similar populations of normal cells, however, comparisons to populations of young control cells showed that the differences were generally not significant. Sialic acid levels in sickle cells were not significantly different from normal cells. Irreversibly sickled cells had lower lipid and sialic acid concentrations than those not irreversibly sickled, but the differences were either not significant or did not occur when compared to young control cells. The studies show that the increased lipid concentrations in the membrane of sickle cells are not abnormal but are related to cell age and that the decrease in membrane components in irreversibly sickled cells is no greater than would be predicted for similarly aged populations of cells.     

Mathematical model for contact inhibited cell division

We present a mathematical model for cell growth, which takes into account cell-cell interactions and leads to non-exponential inhibited growth of number of cells. The resulting difference equation is solved and extended to a differential equation which turns out to be of a non-linear diffusion type.     

Osmotic fragility model for red cell populations

A model that predicts the osmotic fragility curve of a red cell population is developed by relating the critical osmotic pressure to the size distribution of the cells, determined by resistive pulse spectroscopy. Two of the parameters involved, namely the normalized osmotic volume correction, B, and the swelling index, k, are previously determined from the experimental average properties of the population. From these values the critical volume of the cell is obtained, and is shown to be 6-12% larger than the first spherical volume, obtained from an independent experiment. A new parameter, n, a measure of the surface area distribution of the cells, is incorporated through a simple function that relates the critical volume to the size of the cells, and is theoretically shown to be linked to parameters k and B. The model is used to fit and interpret fragility data obtained in this laboratory for normal and sickle cell samples. From the values of n obtained for normal samples, the model predicts an essentially constant surface-to-volume ratio within an individual's cell population. For sickle cell samples, instead, the value of index n is negative, thereby supporting an increase in excess surface area as cell size decreases. Both findings are in agreement with direct observations reported in the literature. It is concluded that this set of parameters may be used to develop an index classification of blood disorders.     

Mathematical model for the cancer stem cell hypothesis

Recent research on the origin of brain cancer has implicated a subpopulation of self-renewing brain cancer stem cells for malignant tumour growth. Various genes that regulate self-renewal in normal stem cells are also found in cancer stem cells. This implies that cancers can occur because of mutations in normal stem cells and early progenitor cells. A predictive mathematical model based on the cell compartment method is presented here to pose and validate non-intuitive scenarios proposed through the neural cancer stem cell hypothesis. The growths of abnormal (stem and early progenitor) cells from their normal counterparts are ascribed with separate mutation probabilities. Stem cell mutations are found to be more significant for the development of cancer than a similar mutation in the early progenitor cells. The model also predicts that, as previously hypothesized, repeated insult to mature cells increases the formation of abnormal progeny, and hence the risk of cancer.     

A statistical model for red blood cell survival

A statistical model for the survival time of red blood cells (RBCs) with a continuous distribution of cell lifespans is presented. The underlying distribution of RBC lifespans is derived from a probability density function with a bathtub-shaped hazard curve, and accounts for death of RBCs due to senescence (age-dependent increasing hazard rate) and random destruction (constant hazard), as well as for death due to initial or delayed failures and neocytolysis (equivalent to early red cell mortality). The model yields survival times similar to those of previously published studies of RBC survival and is easily amenable to inclusion of drug effects and haemolytic disorders.     

A multiscale model for red blood cell mechanics

The objective of this article is the derivation of a continuum model for mechanics of red blood cells via multiscale analysis. On the microscopic level, we consider realistic discrete models in terms of energy functionals defined on networks/lattices. Using concepts of Γ-convergence, convergence results as well as explicit homogenisation formulae are derived. Based on a characterisation via energy functionals, appropriate macroscopic stress–strain relationships (constitutive equations) can be determined. Further, mechanical moduli of the derived macroscopic continuum model are directly related to microscopic moduli. As a test case we consider optical tweezers experiments, one of the most common experiments to study mechanical properties of cells. Our simulations of the derived continuum model are based on finite element methods and account explicitly for membrane mechanics and its coupling with bulk mechanics. Since the discretisation of the continuum model can be chosen freely, rather than it is given by the topology of the microscopic cytoskeletal network, the approach allows a significant reduction of computational efforts. Our approach is highly flexible and can be generalised to many other cell models, also including biochemical control.     

Static equilibrium configurations of a model red blood cell

Summary The membrane of the red blood cell is modeled as a fluid shell which resists bending and changes in area. The differential equations governing the mechanical equilibrium of such a membrane are derived and axisymmetric solutions are obtained numerically.     

Identification and function of transmembrane glycoproteins--the red cell model

Transmembrane glycoproteins in the red cell membrane traverse the plasma membrane, have their carbohydrate moieties on the extracellular surface, are sialyated (except for band 3) and are tethered to the membrane cytoskeleton proteins on the cytoplasmic surface. This linkage between the transmembrane proteins and the skeletal membrane proteins provides a two-way communication between the extracellular surface and the interior of the red cell; i.e., a transmembrane effect can be initiated from either side. These interactions are discussed in this review, including the example of sickle cell anemia in which the membrane bound hemoglobin may exert a transmembrane effect to change the conformation or distribution of transmembrane glycoproteins and and hence the extracellular surface receptors. This, in turn, may explain why sickle cells adhere to endothelium in vitro. Although the RBC transmembrane sialoglycoproteins may function in communication, regulation of cell shape, and adhesion, uncertainties exist regarding many of their functions. To study these sialoglycoproteins, we have developed a double staining technique (Dzandu et al., 1984) that differentially stains human RBC membrane sialoglycoproteins and asialoproteins in SDS-polyacrylamide gels. This should aid in elucidating the conformational structure and function of transmembrane glycoproteins.     

A solid-liquid composite model of the red cell membrane

Summary Direct mechanical experiments and analyses support the view that the red cell membrane is a composite with a solid structural matrix, which can behave as either a viscoelastic or viscoplastic material.     

Mathematical model of excitation-contraction in a uterine smooth muscle cell

Uterine contractility is generated by contractions of myometrial smooth muscle cells (SMCs) that compose most of the myometrial layer of the uterine wall. Calcium ion (Ca²⁺) entry into the cell can be initiated by depolarization of the cell membrane. The increase in the free Ca²⁺ concentration within the cell initiates a chain of reactions, which lead to formation of cross bridges between actin and myosin filaments, and thereby the cell contracts. During contraction the SMC shortens while it exerts forces on neighboring cells. A mathematical model of myometrial SMC contraction has been developed to study this process of excitation and contraction. The model can be used to describe the intracellular Ca²⁺ concentration and stress produced by the cell in response to depolarization of the cell membrane. The model accounts for the operation of three Ca²⁺ control mechanisms: voltage-operated Ca²⁺ channels, Ca²⁺ pumps, and Na⁺/Ca²⁺ exchangers. The processes of myosin light chain (MLC) phosphorylation and stress production are accounted for using the cross-bridge model of Hai and Murphy (Am J Physiol Cell Physiol 254: C99–C106, 1988) and are coupled to the Ca²⁺ concentration through the rate constant of myosin phosphorylation. Measurements of Ca²⁺, MLC phosphorylation, and force in contracting cells were used to set the model parameters and test its ability to predict the cell response to stimulation. The model has been used to reproduce results of voltage-clamp experiments performed in myometrial cells of pregnant rats as well as the results of simultaneous measurements of MLC phosphorylation and force production in human nonpregnant myometrial cells. cellular calcium control mechanisms; myometrial contractions; myosin light chain phosphorylation