Search

A refined electrochemical model accounting for intracellular calcium oscillations and their interrelations with oscillations of the potential difference across the membrane of the endoplasmic reticulum (ER) or other intracellular calcium stores is established. The ATP dependent uptake of Ca2+ from the cytosol into the ER, the Ca2+ release from the ER through channels following a calcium-induced calcium release mechanism, and a potential-dependent Ca2+ leak flux out of the ER are included in the model and described by plausible rate laws. The binding of calcium to specific proteins such as calmodulin is taken into account. The quasi-electroneutrality condition allows us to express the transmembrane potential in terms of the concentrations of cytosolic calcium and free binding sites on proteins, which are the two independent variables of the model. We include monovalent ions in the model, because they make up a considerable portion in the balance of electroneutrality. As the permeability of the endoplasmic membrane for these ions is much higher than that for calcium ions, we assume the former to be in Nernst equilibrium. A stability analysis of the steady-state solutions (which are unique or multiple depending on parameter values) is carried out and the Hopf bifurcation leading from stable steady states to self-sustained oscillations is analysed with the help of appropriate mathematical techniques. The oscillations obtained by numerical integration exhibit the typical spike-like shape found in experiments and reasonable values of frequency and amplitude. The model describes the process of switching between stationary and pulsatile regimes as well as changes in oscillation frequency upon parameter changes. It turns out that calcium oscillations can arise without a permanent influx of calcium into the cell, when a calcium-buffering system such as calmodulin is included.

A model is presented to simulate transverse lipid movement in the human erythrocyte membrane. The model is based on a system of differential equations describing the time-dependence of phospholipid redistribution and the steady state distribution between the inner and outer membrane monolayer. It takes into account several mechanisms of translocation: (i) ATP-dependent transport via the aminophospholipid translocase; (ii) protein-mediated facilitated and (iii) carrier independent transbilayer diffusion. A reasonable modelling of the known lipid asymmetry could only be achieved by introducing mechanism (iii). We have called this pathway the compensatory flux, which is proportional to the gradient of phospholipids between both membrane leaflets. Using realistic model parameters, the model allows the calculation of the transbilayer motion and distribution of endogenous phospholipids of the human erythrocyte membrane for several biologically relevant conditions. Moreover, the model can also be applied to experiments usually performed to assess phospholipid redistribution in biological membranes. Thus, it is possible to simulate transbilayer motion of exogenously added phospholipid analogues in erythrocyte membranes. Those experiments have been carried out here in parallel using spin labeled lipid analogues. The general application of this model to other membrane systems is outlined.

The mechanism of formation of supported lipid layers from phosphatidylcholine and phosphatidylserine vesicles in solution on polyelectrolyte multilayers was studied by a variety of experimental techniques. The interaction of zwitterionic and acidic lipid vesicles, as well as their mixtures, with polyelectrolyte supports was followed in real time by micro-gravimetry. The fabricated lipid–polyelectrolyte composite structures on top of multilayer coated colloidal particles were characterized by flow cytometry and imaging techniques. Lipid diffusion over the macroscopic scale was quantified by fluorescence recovery after photobleaching, and the diffusion was related to layer connectivity. The phospholipid–polyelectrolyte binding mechanism was investigated by infrared spectroscopy. A strong interaction of polyelectrolyte primary amino groups with phosphate and carboxyl groups of the phospholipids, leading to dehydration, was observed. Long-range electrostatic attraction was proven to be essential for vesicle spreading and rupture. Fusion of lipid patches into a homogeneous bilayer required lateral mobility of the lipids on the polyelectrolyte support. The binding of amino groups to the phosphate group of the zwitterionic lipids was too weak to induce vesicle spreading, but sufficient for strong adsorption. Only the mixture of phosphatidylcholine and phosphatidylserine resulted in the spontaneous formation of bilayers on polyelectrolyte multilayers. The adsorption of phospholipids onto multilayers displaying quarternary ammonium polymers produced a novel 3D lipid polyelectrolyte structure on colloidal particles.

Ionic concentrations in the close proximity of a carrier may be different from those in the bulk solution. An immediate layer in the solution in which this situation occurs is known as a diffusion layer. Such diffusion layers were calculated using general diffusion equations and postulating a membrane to be homogeneous in the plane with respect to its permeability. In contrast, the present mathematical model considers single-carrier mediated transport of ions across the membrane and their diffusion away from the carrier site into the electrolyte solution. In particular, the transport of Ca2+ ions is considered. The diffusion of electrolyte ions (Na+ and Cl-) and of Ca2+ ions is described by the Nernst-Planck electrodiffusion equation. The relation between the local electric potential and the ion concentrations is taken into account by the Poisson equation. The equations are solved numerically for radial symmetry by the relaxation method. The model predicts concentration and potential profiles in dependence of the flux rate of Ca2+ ions. It is shown that for fluxes mediated by a single carrier, a diffusion layer becomes significant if the flux is larger than 10(5) Ca2+ ions per second.

A metabolic osmotic model of red blood cells is presented which takes into account the main reaction steps of glycolysis and the passive and active fluxes of ions across the cell membrane. Cellular energy metabolism and osmotic behaviour are linked by the ATP consumption for the active transport of cations as well as by the osmotic action of the glycolytic intermediate 2,3-diphosphoglycerate (2,3-DPG). The model is based on a system of differential equations describing the metabolic reactions and transport processes. Further, two algebraic conditions for the osmotic equilibrium and the electroneutrality of the cell are considered. Using realistic system parameters the model allows the calculation of a great number of dependent variables, among them the cell volume, the concentrations of metabolites and ions and the transmembrane potential. Only stationary states are considered. The parameter dependence of important model variables is characterized by control coefficients. The main results are: (a) The volume of erythrocytes is mainly determined by the permeabilities of the leak fluxes of cations, the content of hemoglobin and the activity of the hexokinase-phosphofructokinase system of glycolysis; (b) Changes of volume affect the glycolytic rate mainly by changing the concentration of ATP which is a regulator of glycolysis; (c) A change in the membrane area may affect the other cell properties only if it is connected with variations of the number of active and leak sites of the membrane.

1. Permeative properties of the red blood cell membrane are utilized for an introduction of three osmotic states of the model cell with respect to equilibration of certain cell solution constituents across the membrane equilibration of water (W state), equilibration of water and chloride (C state), and equilibration of water, chloride and cations (D state). 2. The model cell introduced consists of the semipermeable membrane which separates the buffered external solution composed of water, univalent electrolyte, and sucrose from the internal hemoglobin and electrolyte solution. Three sets of equations each describing corresponding osmotic state are given. Certain physicochemical properties of the hemoglobin solution are taken into account. The inner pH is assumed to be established according to the chloride distribution across the membrane. 3. The volume and electric potential difference of the model cell are calculated for each osmotic state at different ratios of sucrose and electrolyte concentration of external solutions. Results are used for an analysis of general osmotic properties and lysis of red cells. 4. It is shown how cells are expected to behave if exposed to conditions with different osmotic pressure, composition of external solutions, or temperature. The importance of temperature effect and rate of performing osmotic experiments on the existence of the W state is pointed out. 5. Different experimental procedures which cause an increase in the membrane cation premeability are discussed in terms of the transition from the C to D state. It is indicated that after the membrane modification in the cases discussed osmotic accomodation of cells is governed by the net-chloride diffusion.