Hysteresis and bi-stability by an interplay of calcium oscillations and action potential firing

Many cell types exhibit oscillatory activity, such as repetitive action potential firing due to the Hodgkin-Huxley dynamics of ion channels in the cell membrane or reveal intracellular inositol triphosphate (IP$_3$) mediated calcium oscillations (CaOs) by calcium-induced calcium release channels (IP$_3$-receptor) in the membrane of the endoplasmic reticulum (ER). The dynamics of the excitable membrane and that of the IP$_3$-mediated CaOs have been the subject of many studies. However, the interaction between the excitable cell membrane and IP$_3$-mediated CaOs, which are coupled by cytosolic calcium which affects the dynamics of both, has not been studied. This study for the first time applied stability analysis to investigate the dynamic behavior of a model, which includes both an excitable membrane and an intracellular IP$_3$-mediated calcium oscillator. Taking the IP$_3$ concentration as a control parameter, the model exhibits a novel rich spectrum of stable and unstable states with hysteresis. The four stable states of the model correspond in detail to previously reported growth-state dependent states of the membrane potential of normal rat kidney fibroblasts in cell culture. The hysteresis is most pronounced for experimentally observed parameter values of the model, suggesting a functional importance of hysteresis. This study shows that the four growth-dependent cell states may not reflect the behavior of cells that have differentiated into different cell types with different properties, but simply reflect four different states of a single cell type, that is characterized by a single model.Comment: 29 pages, 6 figure

Stabilizing Role of Calcium Store-Dependent Plasma Membrane Calcium Channels in Action-Potential Firing and Intracellular Calcium Oscillations

In many biological systems, cells display spontaneous calcium oscillations (CaOs) and repetitive action-potential firing. These phenomena have been described separately by models for intracellular inositol trisphosphate (IP(3))-mediated CaOs and for plasma membrane excitability. In this study, we present an integrated model that combines an excitable membrane with an IP(3)-mediated intracellular calcium oscillator. The IP(3) receptor is described as an endoplasmic reticulum (ER) calcium channel with open and close probabilities that depend on the cytoplasmic concentration of IP(3) and Ca(2+). We show that simply combining this ER model for intracellular CaOs with a model for membrane excitability of normal rat kidney (NRK) fibroblasts leads to instability of intracellular calcium dynamics. To ensure stable long-term periodic firing of action potentials and CaOs, it is essential to incorporate calcium transporters controlled by feedback of the ER store filling, for example, store-operated calcium channels in the plasma membrane. For low IP(3) concentrations, our integrated NRK cell model is at rest at −70 mV. For higher IP(3) concentrations, the CaOs become activated and trigger repetitive firing of action potentials. At high IP(3) concentrations, the basal intracellular calcium concentration becomes elevated and the cell is depolarized near −20 mV. These predictions are in agreement with the different proliferative states of cultures of NRK fibroblasts. We postulate that the stabilizing role of calcium channels and/or other calcium transporters controlled by feedback from the ER store is essential for any cell in which calcium signaling by intracellular CaOs involves both ER and plasma membrane calcium fluxes