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.     

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 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.     

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.     

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.     

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.     

Mathematical model of stabilization of circadian rhythm in cell energy metabolism

A mathematical model for circadian self-oscillation in the carbohydrate branch of energy metabolism (CEM) was analysed. The self-oscillations are due to the reciprocal regulation of the activities of 6-phosphofructokinase and fructose-1,6-bisphosphatase by fructose-1,6-bisphosphate. The circadian period was shown to be insensitive to metabolic disturbances because of the presence in CEM of negative feedback mechanisms regulating the activities of the key enzymes 6-phosphofructokinase, fructose-1,6-bisphosphatase, pyruvate kinase and phosphoenolpyruvate carboxykinase. It has been also shown that such mechanisms are largely synergistic in their action.     

Mathematical model of interphase cell death. Biophysical justification and generalization

The authors propose a biophysical justification of a radiation-induced injury and interphase death of cells. The injury to certain units of the microtrabecular network and cytoskeleton is considered to be a primary biological effect of radiation on cells. The role of these structural changes in the development of the specific radiation response is discussed. It is found possible to describe formally, by the defined parameters of the proposed model, the survival curves for not only interphase but also reproductive cell death.     

Simple model can explain self-inhibition of red cell anion exchange.

Ion translocation in red cell anion exchange is assumed to occur by means of an alternating access mechanism, in which a critical binding site for the transported ion alternates between two conformational states, each accessible from only one side of the membrane. If this alternating site is located within the transport protein at some distance from one or both surfaces of the membrane, an access channel is required to connect the alternating site to the adjacent bulk solution. This automatically leads to inhibition of transport at high concentrations of the transported ion because release of the ion from the alternating site can occur only via unoccupied channel sites.     

Mathematical model of two pathways of light perception by the photoreceptor cell

On the basis of the concept postulating polyfunctional role of rhodopsin in the photoreceptor cell excitation a mathematical model of two pathways of excitation was formulated. One pathway involves the appearance of Ca2+ ions in the cell, which block the sodium channels. The second one results in cGMP splitting which also brings about the blocking of sodium channels. A change in the concentration of acting agents and development of cell excitation under illumination was calculated. The calcium branch is shown to be rapid and direct, but of a low sensitivity. The cGMP branch is a slow one but has a high intensification coefficient. The action time of the calcium branch does not depend on illumination, while the time of cGMP branch decreases with the illumination rise and is in an inverse proportion to the square root of the flash intensity. Under repeated illumination the amplitude of calcium response decreases, and its time remains constant. In cGMP branch the time of the response to the second flash decreases. The amplitude of the second response depends on the intensity of the first flash, it can be smaller or larger than the amplitude of the first response.