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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.

We investigated theoretically and experimentally the Ca2+-contraction coupling in rat tracheal smooth muscle. [Ca2+]i, isometric contraction and myosin light chain (MLC) phosphorylation were measured in response to 1 mM carbachol. Theoretical modeling consisted in coupling a model of Ca2+-dependent MLC kinase (MLCK) activation with a four-state model of smooth muscle contractile apparatus. Stimulation resulted in a short-time contraction obtained within 1 min, followed by a long-time contraction up to the maximal force obtained in 30 min. ML-7 and Wortmannin (MLCK inhibitors) abolished the contraction. Chelerythrine (PKC inhibitor) did not change the short-time, but reduced the long-time contraction. [Ca2+]i responses of isolated myocytes recorded during the first 90 s consisted in a fast peak, followed by a plateau phase and, in 28% of the cells, superimposed Ca2+ oscillations. MLC phosphorylation was maximal at 5 s and then decreased, whereas isometric contraction followed a Hill-shaped curve. The model properly predicts the time course of MLC phosphorylation and force of the short-time response. With oscillating Ca2+ signal, the predicted force does not oscillate. According to the model, the amplitude of the plateau and the frequency of oscillations encode for the amplitude of force, whereas the peak encodes for force velocity. The long-time phase of the contraction, associated with a second increase in MLC phosphorylation, may be explained, at least partially, by MLC phosphatase (MLCP) inhibition, possibly via PKC inhibition.

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.

Entropy production is calculated for bacterial chemotaxis in the case of a migrating band of bacteria in a capillary tube. It is found that the speed of the migrating band is a decreasing function of the starting concentration of the metabolizable attractant. The experimentally found dependence of speed on the starting concentration of galactose, glucose and oxygen is fitted with power-law functions. It is found that the corresponding exponents lie within the theoretically predicted interval. The effect of the reproduction of bacteria on band speed is considered, too. The acceleration of the band is predicted due to the reproduction rate of bacteria. The relationship between chemotaxis, the maximum entropy production principle and the formation of self-organizing structure is discussed.

In airway smooth muscles, kinase/phosphatase-dependent phosphorylation and dephosphorylation of the myosin light chain (MLC) have been revealed by many authors as important steps in calcium (Ca(2+)) signalling pathway from the variation of Ca(2+) concentration in cytosol to the force development. Here, a theoretical analysis of the control action of MLC-kinase (MLCK) and MLC-phosphatase (MLCP) in Ca(2+) signalling is presented and related to the general control principles of these enzymes, which were previously studied by Reinhart Heinrich and his co-workers. The kinetic scheme of the mathematical model considers interactions among Ca(2+), calmodulin (CaM) and MLCK and the well-known 4-state actomyosin latch bridge model, whereby a link between them is accomplished by the conservation relation of all species of MLCK. The mathematical model predicts the magnitude and velocity of isometric force in smooth muscles upon transient biphasic Ca(2+) signal. The properties of signal transduction in the system such as the signalling time, signal duration and signal amplitude, which are reflected in the properties of force developed, are studied by the principles of the metabolic control theory. The analysis of our model predictions confirms as shown by Reinhart Heinrich and his co-workers that MLCK controls the amplitude of signal more than its duration, whereas MLCP controls both. Finally, the simulations of elevated total content of MLCK, a typical feature of bronchial muscles of asthmatic subjects and spontaneously hypertensive rats as well as potentiation of MLCP catalytic activity, are carried out and are discussed in view of an increase in the force magnitude.

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.

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 theses 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.

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.

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.