Milan Brumen

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.

Physical chemistry of encapsulation and release

This review describes recently introduced methods of coating colloidal particles and fabrication of hollow multilayer polyelectrolyte capsules. Diffusion through multilayer, Donnan equilibria for ions inside and outside hollow spheres and mechanical properties are given in quantitative aspects.

Polymeric membrane formation by wet-phase separation; turbidity and shrinkage phenomena as evidence for the elementary processes

Abstract The direct accumulation of polymer, the nucleation and growth of the polymer lean as well as the polymer rich phase and the spinodal phase separation are postulated as four elementary processes of the mechanisms of the polymeric membrane formation by wet-phase separation. With the study of five different polymer/solvent:water systems they are discriminated by the investigation of the turbidity and the shrinkage phenomena taking place during (proto)membrane formation, as well as by the measurement of the pure water permeability and by the inspection of the membranes’ cross-section morphology. The general scheme of membrane formation mechanisms is arranged by gathering the groups of different modes of mass transport and the group of nonsolvent/solvent/polymer forms of solidification as elementary processes; by forming combinations of the so postulated elementary processes in time and space particular mechanisms are established.

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.

Lipid layers on polyelectrolyte multilayer supports

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.

MODELLING THE INTERRELATIONS BETWEEN 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.

278 - Osmotic states of the red blood cells

Abstract 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.

Modelling oscillations of calcium and endoplasmic reticulum transmembrane potential: Role of the signalling and buffering proteins and of the size of the Ca2+ sequestering ER subcompartments

Abstract Intracellular calcium oscillations provide a natural clock that may be of crucial importance for the timing of many cellular processes. Elucidating of the mechanisms underlying these oscillations is of particular interest. The theoretical description presented here extends existing models of calcium oscillations by allowing for two types of proteins differing in their calcium-binding properties. This model reflects experimental findings by considering both a fast calcium-binding process to low-affinity protein binding sites such as found in the N-domains of calmodulin or troponin C and a class of high-affinity calcium binding proteins with slow binding kinetics (e.g., parvalbumin or the C-domains of calmodulin and troponin C). Furthermore, recalling that calcium is mainly stored in small subcompartments of the ER, it is argued that only a small fraction of its overall volume participates in the rapid release and uptake of calcium. The effect of the size of this fraction is studied. The hypothesis saying that any electric potential difference across the ER membrane would be dissipated by the highly permeant ions is critically examined by an analytical estimation based on the electroneutrality condition and by numerical integration of the complete model equations. It is predicted theoretically that the transmembrane potential of the ER calcium stores, which is up to now virtually impossible to determine in experiment, builds up in the millivolt range at physiological concentrations of monovalent ions. The phenomenology of oscillations is studied by numerical integration. The model reproduces experimentally observed values of frequency and amplitude as well as the typical spike-like shape of oscillations. The model reveals also the time course of a shift of the bound Ca2+ population from the low-affinity binding sites to the high-affinity binding sites.

Theoretical model of the interactions between Ca2+, calmodulin and myosin light chain kinase.

Active Ca2+/calmodulin (CaM)‐dependent myosin light chain kinase (MLCK) plays an important role in the process of MLC phosphorylation and consecutive smooth muscle contraction. Here, we propose a mathematical model of a detailed kinetic scheme describing interactions among Ca2+, CaM and MLCK and taking into account eight different aggregates. The main model result is the prediction of the Ca2+ dependent active form of MLCK, which is in the model taken as proportional to the concentration of Ca4CaM · MLCK complex. Wegscheiders condition is additionally applied as a constraint enabling the prediction of some parameter values that have not yet been obtained by experiments.

Contribution of Rho kinase to the early phase of the calcium-contraction coupling in airway smooth muscle

We investigated theoretically and experimentally the role of Rho kinase (RhoK) in Ca2+–contraction coupling in rat airways. Isometric contraction was measured on tracheal, extrapulmonary and intrapulmonary bronchial rings. Intracellular [Ca2+] was recorded in freshly isolated tracheal myocytes. Stimulation by carbachol (0.3 and 10 μm) and 50 mm external KCl induced a short‐time, Hill‐shaped contraction obtained within 90 s, followed by a sustained or an additional delayed contraction. Responses of [Ca2+]i to acetylcholine consisted in a fast peak followed by a plateau and, in 42% of the cells, superimposed Ca2+ oscillations. The RhoK inhibitor Y27632 (10 μm) did not alter the [Ca2+]i response. Whatever the agonist, Y27632 did not modify the basal tension but decreased the amplitude of the short‐duration response, without altering the additional delayed contraction. The Myosin Light Chain Phosphatase (MLCP) inhibitor calyculin A increased the basal tension and abolished the effect of RhoK. KN93 (Ca2+–calmodulin‐dependent protein kinase II inhibitor) and DIDS (inhibitor of Ca2+‐activated Cl− channels) had no influence on the RhoK effect. We built a theoretical model of Ca2+‐dependent active/inactive RhoK ratio and subsequent RhoK‐dependent MLCP inactivation, which was further coupled with a four‐state model of the contractile apparatus and Ca2+‐dependent MLCK activation. The model explains the time course of the short‐duration contraction and the role of RhoK by Ca2+‐dependent activation of MLCK and RhoK, which inactivates MLCP. Oscillatory and non‐oscillatory [Ca2+]i responses result in a non‐oscillatory contraction, the amplitude of which is encoded by the plateau value and oscillation frequency. In conclusion, Ca2+‐dependent but CaMK II‐independent RhoK activation contributes to the early phase of the contractile response via MLCP inhibition.