Strategy for NSAID administration to aspirin-intolerant asthmatics in combination with PGE2 analogue: a theoretical approach.

Aspirin-induced asthma (AIA) is a severe inflammatory disease, which affects aspirin-intolerant patients after ingestion of aspirin or other non-steroidal anti-inflammatory drugs (NSAIDs). In this article, a mathematical model describing arachidonic acid metabolism and its interaction with NSAIDs, is used to study the strategy for safe managing of NSAIDs to AIA patients. Three different AIA patient populations are taken into consideration. First, the values of aspirin and ibuprofen limiting doses that might induce symptoms of AIA are calculated and compared to experimentally observed threshold doses to enlighten which AIA patient population is susceptible to aspirin and ibuprofen. Second, the methodology of NSAID administration is studied on AIA populations susceptible to aspirin and ibuprofen by using 1,000 mg dose of aspirin and 200 or 400 mg dose of ibuprofen followed by PGE(2) analogue dosing. Our model results show that successive doses of PGE(2) analogue applied at appropriate time after aspirin or ibuprofen ingestion would enable administration of both NSAIDs to AIA patients. PGE(2) analogue doses and the corresponding times of their applications are calculated. The model is also used to estimate the duration of symptoms of AIA for different aspirin and ibuprofen doses.

Role of expression of prostaglandin synthases 1 and 2 and leukotriene C4 synthase in aspirin-intolerant asthma: a theoretical study.

Altered expressions of the key enzymes in arachidonic acid (AA) metabolism, prostaglandin synthase 1 and 2 and cysteinyl leukotriene C(4) synthase, are of importance in understanding aspirin-induced asthma. We propose a mathematical model of AA metabolism and its interaction with non-steroidal anti-inflammatory drugs (NSAIDs). Model simulations depict the impact of modified expressions of the above enzymes on the time dependent synthesis of cysteinyl leukotrienes and anti-inflammatory prostaglandins before and during NSAID exposure in different model states describing healthy humans as well as aspirin-tolerant and -intolerant asthmatics. The results are compared and evaluated with experimental data taken from the literature. Our results identify the decreased expression of prostaglandin H synthase 1 and increased expression of leukotriene C(4) synthase as the key elements in AA metabolism that contribute to increased leukotriene C(4) and decreased anti-inflammatory prostaglandins after NSAID dosing in aspirin-intolerant patients. On the other hand, the decreased expression of prostaglandin H synthase 2 implies permanently increased leukotriene C(4) and lowers the sensitivity to increased drug doses. The model is used for identification of susceptible patient populations for aspirin and ibuprofen, and for identification of critical aspirin doses that might induce bronchoconstriction.

Complex calcium oscillations and the role of mitochondria and cytosolic proteins.

Intracellular calcium oscillations, which are oscillatory changes of cytosolic calcium concentration in response to agonist stimulation, are experimentally well observed in various living cells. Simple calcium oscillations represent the most common pattern and many mathematical models have been published to describe this type of oscillation. On the other hand, relatively few theoretical studies have been proposed to give an explanation of complex intracellular calcium oscillations, such as bursting and chaos. In this paper, we develop a new possible mechanism for complex calcium oscillations based on the interplay between three calcium stores in the cell: the endoplasmic reticulum (ER), mitochondria and cytosolic proteins. The majority ( approximately 80%) of calcium released from the ER is first very quickly sequestered by mitochondria. Afterwards, a much slower release of calcium from the mitochondria serves as the calcium supply for the intermediate calcium exchanges between the ER and the cytosolic proteins causing bursting calcium oscillations. Depending on the permeability of the ER channels and on the kinetic properties of calcium binding to the cytosolic proteins, different patterns of complex calcium oscillations appear. With our model, we are able to explain simple calcium oscillations, bursting and chaos. Chaos is also observed for calcium oscillations in the bursting mode.

Mitochondria as an important factor in the maintenance of constant amplitudes of cytosolic calcium oscillations.

Theoretical models of intracellular calcium oscillations have hitherto focused on the endoplasmic reticulum (ER) as an internal calcium store. These models reproduced the large variability in oscillation frequency observed experimentally. In the present contribution, we extend our earlier model [Marhl et al., Biophys. Chem., 63 (1997) 221] by including, in addition to the ER, mitochondria as calcium stores. Simple plausible rate laws are used for the calcium uptake into, and release from, the mitochondria. It is demonstrated with the help of this extended model that mitochondria are likely to act in favour of frequency encoding by enabling the maintenance of fairly constant amplitudes over wide ranges of frequency.

Mitochondria as an important factor in the maintenance of constant amplitudes of cytosolic calcium oscillations.

Theoretical models of intracellular calcium oscillations have hitherto focused on the endoplasmic reticulum (ER) as an internal calcium store. These models reproduced the large variability in oscillation frequency observed experimentally. In the present contribution, we extend our earlier model [Marhl et al., Biophys. Chem., 63 (1997) 221] by including, in addition to the ER, mitochondria as calcium stores. Simple plausible rate laws are used for the calcium uptake into, and release from, the mitochondria. It is demonstrated with the help of this extended model that mitochondria are likely to act in favour of frequency encoding by enabling the maintenance of fairly constant amplitudes over wide ranges of frequency.

Modelling of phospholipid translocation in the erythrocyte membrane: a combined kinetic and thermodynamic approach.

A mathematical model for the dynamics of transbilayer movements of lipids in the erythrocyte plasma membrane is presented. It takes into account an active carrier which mediates the ATP-dependent translocation of phosphatidylserine and phosphatidylethanolamine from the outer to the cytoplasmic leaflet of the membrane and passive fluxes of these lipids as well as of phosphatidylcholine, sphingomyelin and cholesterol between both layers. It is assumed that the passive fluxes are driven by concentration gradients of the lipids and by mechanical forces which result from area limitation for lipid occupation in both leaflets. Compared with a previous mathematical treatment of lipid translocation processes in the erythrocyte membrane the present model is much closer to realistic conditions, e.g. concerning the number of lipid species involved. Furthermore, the use of linear flux-force relationships as known from irreversible thermodynamics allows a simpler treatment of the passive fluxes than before and provides a relevant framework to study the coupling between the various processes. The model allows to simulate the time dependent changes of lipid concentrations which take place after activation or inhibition of ATP-dependent translocation. Using realistic parameter values it explains in quantitative terms the stationary asymmetric distribution of lipids under in vivo conditions. Using principles of metabolic control analysis we are able to quantify the role of the various active and passive processes in determining the asymmetric distribution for each lipid species.

Modeling the interrelations between the calcium oscillations and ER membrane potential oscillations.

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.

Low pH induced shape changes and vesiculation of human erythrocytes.

Shape changes and vesiculation were induced in intact human erythrocytes by gradually decreasing pH in the cell suspension. A sequence of different shapes preceding vesiculation was documented, i.e. discocytes, stomatocytes, and stomatoacantocytes. The final state was characterized by spherical mother cells and vesicles released. Low pH-induced vesiculation was also studied in the presence of stomatocytogenic or echinocytogenic compounds. The action of stomatocytogenic compounds was inhibitory, and echinocytogenic compounds had no effect on low pH-induced vesiculation. Vesiculation induced by low pH was studied also in isotonic solutions of different sucrose/salt composition. It was concluded that (i) low intracellular pH is responsible for cell shape transformations as well as for release of vesicles, (ii) at temperature 37 degrees C the intracellular pH value which induces the release of vesicles is 5.4, and (iii) the sequence of typical shape changes preceding vesiculation does not include echinocytes. The results are discussed on the basis of the layered membrane model of the shape formation and shape transformations of the human erythrocyte, and additionally considering the partial detachment of the membrane skeleton from the bilayer part of the membrane.

Diffusion layer caused by local ionic transmembrane fluxes.

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.

Mathematical modelling of lipid transbilayer movement in the human erythrocyte plasma membrane.

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.

Microspectroscopy of red blood cells.

Spectroscopic techniques have been widely employed to analyze properties of macromolecules and dynamics of intracellular events on bulk preparations of cells. The development of computer controlled microspectrophotometers has made possible the study of the same events in single cells, often providing significant and unexpected results. This paper briefly reviews experimental works carried out in our laboratories on single red blood cells. Microspectrophotometric techniques were applied which make use of the fact that ligand binding to intracellular haemoglobin is associated with optical changes. Information on the relative abundance of different haemoglobin components inside single erythrocytes of trout blood was obtained from spectra of air equilibrated samples, taking advantage of the extreme pH sensitivity of one of the four haemoglobin components. The kinetics of oxygen and carbon monoxide binding to haemoglobin has been followed and demonstrated to correspond to a zero order process, with a rate much slower than that characteristic for haemoglobin in solution. These results demonstrate that the process is diffusion limited; computer simulations suggest that ligand uptake is limited by the time required for the diffusion from the extracellular space of enough ligand molecules for total saturation of intraerythrocytic haemoglobin. Finally, oxygen dissociation curves in single red blood cells can be obtained by means of particular flow cell, with promising results for the study of physiological and pathological processes (namely red cell sickling in drepanocytosis).

A microspectroscopic analysis of ligand binding in single erythrocyte.

The kinetics of ligand uptake by erythrocytes has been analyzed by single cell microspectroscopy measurements carried out in parallel with mathematical simulations. The main experimental feature is the linear shape of the ligand binding progress curves, whose slope is dependent on the free ligand concentration in the speciman. From the computer simulation a predominant role has been shown to be played by the ligand diffusion from the extracellular space.

A metabolic osmotic model of human erythrocytes.

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.

A mechanism for indirect allosteric action of charged effectors.

A mechanism for indirect allosteric action of charged effectors on substrate binding to a macromolecule is proposed. It is accounted for by electrostatic interaction among effectors in the solution, away from their receptors. The possibility of the mechanism proposed is tested in the allosteric action of univalent salt and 2,3-diphosphoglycerate on oxygen binding to hemoglobin. A model for electrostatic interaction between these two effectors in the solution and for their overall effect on oxygen binding is introduced. The 2,3-diphosphoglycerate binding constant to deoxygenated hemoglobin as a function of univalent salt concentration and the median ligand activity as a function of the concentration of univalent salt and 2,3-diphoshoglycerate are calculated and compared with experimental data. The obtained results indicate that electrostatic interaction in the solution may significantly contribute to indirect allosteric action of charged effectors.

A model of the pH-dependence of the number of oxygen-linked chloride binding sites in hemoglobin.

A model is presented of the pH-dependence of the number of oxygen-linked chloride binding sites established by nuclear magnetic resonance quadrupole-relaxation studies on various mutant and chemically modified hemoglobins. The predictions of the model are in good qualitative agreement with the measured pH-dependences of the linewidth of the 35Cl- NMR signal. The obtained agreement implies that more chloride is bound to oxygenated than to deoxygenated hemoglobin.