Membrane potential changes in activated cells: connection with cytosolic calcium oscillator

Modeling the contributions of Ca2+ flows to spontaneous Ca2+ oscillations and cortical spreading depression-triggered Ca2+ waves in astrocyte networks

Astrocytes participate in brain functions through Ca(2+) signals, including Ca(2+) waves and Ca(2+) oscillations. Currently the mechanisms of Ca(2+) signals in astrocytes are not fully clear. Here, we present a computational model to specify the relative contributions of different Ca(2+) flows between the extracellular space, the cytoplasm and the endoplasmic reticulum of astrocytes to the generation of spontaneous Ca(2+) oscillations (CASs) and cortical spreading depression (CSD)-triggered Ca(2+) waves (CSDCWs) in a one-dimensional astrocyte network. This model shows that CASs depend primarily on Ca(2+) released from internal stores of astrocytes, and CSDCWs depend mainly on voltage-gated Ca(2+) influx. It predicts that voltage-gated Ca(2+) influx is able to generate Ca(2+) waves during the process of CSD even after depleting internal Ca(2+) stores. Furthermore, the model investigates the interactions between CASs and CSDCWs and shows that the pass of CSDCWs suppresses CASs, whereas CASs do not prevent the generation of CSDCWs. This work quantitatively analyzes the generation of astrocytic Ca(2+) signals and indicates different mechanisms underlying CSDCWs and non-CSDCWs. Research on the different types of Ca(2+) signals might help to understand the ways by which astrocytes participate in information processing in brain functions.

Effect of copper chloride exposure on the membrane potential and cytosolic free calcium in primary cultured chicken hepatocytes

This study was conducted to examine the effects of copper on membrane potential and cytosolic free calcium in isolated primary chicken hepatocytes which were exposed to different concentration of Cu(2+) (0, 10, 50, 100 μM) or a mixture of Cu(2+) and vitamin C (50 and 50 μM, respectively). Viability, membrane potential, and cytosolic free Ca(2+) of monolayer cultured hepatocytes were investigated at the indicated time point. Results showed that, among the different concentrations of Cu(2+) exposure, the viability of hepatocytes treated with 100 μM Cu(2+) was the worst at the 12th and 24th hours. The effects of Cu(2+) on viability and proliferation were time and dose dependent. Further investigation indicated that Cu(2+) exposure significantly enhanced cytosolic free Ca(2+) in hepatocytes, compared to that in control group, at the 24th hour. Meanwhile, membrane potential was noticeably reduced in hepatocytes increasing concentration of Cu(2+). Taking these results together, we have shown that Cu(2+) can cause toxicity to primary chicken hepatocytes in excessive dose and the effect of Cu(2+) exposure on membrane potential is not site specific, which is probably mediated by the changes of cytosolic free Ca(2+).

Modelling of simple and complex calcium oscillations. From single-cell responses to intercellular signalling

This review provides a comparative overview of recent developments in the modelling of cellular calcium oscillations. A large variety of mathematical models have been developed for this wide-spread phenomenon in intra- and intercellular signalling. From these, a general model is extracted that involves six types of concentration variables: inositol 1,4,5-trisphosphate (IP3), cytoplasmic, endoplasmic reticulum and mitochondrial calcium, the occupied binding sites of calcium buffers, and the fraction of active IP3 receptor calcium release channels. Using this framework, the models of calcium oscillations can be classified into 'minimal' models containing two variables and 'extended' models of three and more variables. Three types of minimal models are identified that are all based on calcium-induced calcium release (CICR), but differ with respect to the mechanisms limiting CICR. Extended models include IP3--calcium cross-coupling, calcium sequestration by mitochondria, the detailed gating kinetics of the IP3 receptor, and the dynamics of G-protein activation. In addition to generating regular oscillations, such models can describe bursting and chaotic calcium dynamics. The earlier hypothesis that information in calcium oscillations is encoded mainly by their frequency is nowadays modified in that some effect is attributed to amplitude encoding or temporal encoding. This point is discussed with reference to the analysis of the local and global bifurcations by which calcium oscillations can arise. Moreover, the question of how calcium binding proteins can sense and transform oscillatory signals is addressed. Recently, potential mechanisms leading to the coordination of oscillations in coupled cells have been investigated by mathematical modelling. For this, the general modelling framework is extended to include cytoplasmic and gap-junctional diffusion of IP3 and calcium, and specific models are compared. Various suggestions concerning the physiological significance of oscillatory behaviour in intra- and intercellular signalling are discussed. The article is concluded with a discussion of obstacles and prospects.

Diffusion model for growth factors--cell receptors interaction

A theoretical model describing the interaction between growth factor molecules and their receptors from the cell surface within an 'off-centre' diffusion approximation is developed in this paper. It is assumed that a number of non interacting particles (growth-factor molecules) more diffusively in the presence of traps (specific receptors) which are located at the surfaces of a number of cells uniformly distributed in space. The diffusion equations system is solved by a perturbative method. The model predicts a nonlinear dependence of the receptor occupation and of the time needed to reach a threshold value of receptor occupation on the total number of cell receptors. An autocrine binding, when the ligand is secreted by the responsive cells accounts for the interaction between IL-2 and helper T-cells.