Goldbeter et al. (1990), Meyer and Stryer (1991), Two Models of Calcium Spiking
The landmark observation that calcium salts are needed for heart contraction, made by Sidney Ringer while studying the contraction of isolated rat hearts in 1883  revealed the importance of calcium in signal transduction. Calcium is an important early messenger that is essential for wound repair and for the initiation of cellular events such as the fertilisation of oocytes, gene transcription, muscle contraction, cell proliferation, and hormone and peptide secretion. It accompanies cells throughout their entire lifespan, from their origin at fertilisation, to their eventual demise at the end of the life cycle.
Calcium enters into the cell through channels that are gated by voltage, G proteins, and cytosolic messengers. Calcium is actively pumped from the cytosol through calcium-ATPase (SERCA) pumps and accumulated in the endoplasmic reticulum (ER), and sometimes in the mitochondria, to maintain its cytosolic concentration. The resting concentration of calcium in the cytoplasm is normally maintained in the range of 10-100 nM (the external concentrations of calcium is typically four orders of magnitude higher than internal levels). The cytosolic calcium level is regulated by multiple channels, pumps and exchangers (see Figure 1, taken from ). The calcium-ATPase pump and the sodium-calcium exchanger in the plasma membrane extrude calcium from cells.
If the cytosolic calcium concentration is not controlled, it increases persistently in the interior of the cell above the optimal level, and as a consequence all calcium controlled activities become permanently activated, including those (e.g. proteases) that are potentially harmful to cells. This ultimately causes cell death or apoptosis. New insights into the underlying causes of congenital and acquired diseases and the potential targets for calcium associated diseases are described and discussed in the book by Carafoli and Brini (2007) . The dysfunction of membrane transporters (including channels that control the fluxes of calcium in and out of the cytoplasm), and malfunctioning of calcium sensor proteins that are modulated by calcium and process its signal can cause pathological processes ranging from common diseases (e.g. migraine, diabetes, epilepsy, manic depression, infertility, cancer, Alzheimer's disease, Brody's disease and muscular dystrophy) to rare genetic conditions (e.g. genetic heart conditions, autoimmune retinopathies, night blindness, hereditary amyloid polyneuropathy, malignant hyperthermia, cerebellar ataxia, Huntington's disease and atherothrombotic disease).
Figure 1: Control of cytosolic calcium concentration and calcium signalling mechanisms. Figure taken from .
Signalling is activated by a temporary increase in intracellular calcium concentration through the opening of calcium channels in the plasma membrane or the intracellular calcium stores (e.g. Endoplasmic/sarcoplasmic reticulum (ER/SR)). Figure 1 illustrates the calcium signalling mechanism. Cell stimulation by agonists (hormone or neurotransmitters) activate the formation of second messengers (e.g. IP3) that induce the release of calcium stored in the endoplasmic reticulum (ER) through the IP3 receptor (upon IP3 binding) and/or IP3-insensitive receptor (induced by calcium itself, e.g. ryanodine receptor (RyR) -- upon cADPr-cyclic adenosine diphosphate ribose binding) based on the cell type. Decrease in the calcium in the ER is 'sensed' by certain molecules, which in turn activates calcium channels in the plasma membrane. Mobilisation of calcium from the intracellular store (ER) (initially from IP3-sensitive channels) begins with the binding of a hormone or other agonist to a cell-surface receptor. The receptors that trigger the phosphoinositide cascade belong to the seven-trans-membrane-helix family. The excitation signal generated by the binding of a hormone or other agonist to the cell-surface receptor is carried by a G protein to the effector enzyme, phospholipase C (PLC). PLC catalyses the hydrolysis of phosphatidylinositol 4,5-biphosphate to inositol 1,4,5-triphosphate (IP3) and diacylglycerol. The binding of four IP3 molecules each on one subunit of the heterotetrameric IP3 receptor (heterotetramers of different isoforms) in the ER activates the channel and induces the release of calcium primarily into the cytosol. Diacylglycerol activates protein kinase C.
Figure 2: Calcium spiking in a single rat hepatocyte. The cell was stimulated by perfusion with vasopressin, a calcium-mobilising hormone. The cytosolic Ca2+ level was determined from the rate of emission of microinjected aequorin, a calcium-sensitive photoprotein. Figure taken from , originally from .
The IP3 receptor is responsible for generation and control of very complex calcium signals. Various studies have shown that IP3-receptors and other calcium sensor proteins should be considered as potential therapeutic targets for the treatment of Huntington's disease. The calcium released from IP3 channels, in turn, induces the release of calcium into the cytosol from the IP3-insensitive channel (i.e. Calcium-Induced-Calcium-Release channel -- CICR channel) which is opened by calcium itself. The CICR channel is characteristically found in muscle cells but with isoforms in non-muscle cells. It is also present in skeletal, neurons and chromaffin cells. Electron microscopy shows that the IP3-gated channel and the CICR channel (ryanodine receptor) both form tetrameric structures with similar cross-sectional areas in the plane of the membrane.
Repetitive spikes of calcium arise due to the periodic opening of plasma membrane channels or due to the periodic emptying of stores. This was first observed in 1987 by Peter Cobbold and coworkers  in agonist (hormone)-stimulated hepatocytes and has now been observed in practically every cell type. The increase in the frequency of spiking was observed with the raise in concentration of the hormone, with the amplitude and duration of spikes being unaltered (see Figure 2 taken from ).
At least four classes of spike generating mechanisms (see Figure 3) have been proposed so far . Meyer and Stryer, in their 1991 review , have discussed the two quantitative models (IP3-Calcium cross coupling (ICC) and Calcium-Induced-Calcium-Release (CICR) models) that were first developed based on the positive feedback mechanism of calcium. These two models are strongly supported by experimental studies on a wide range of cells. In the ICC model (BIOMD0000000224, [5,8], model 4 of Figure 3), the receptor-triggered formation of IP3 leads to calcium release from the endoplasmic reticulum. The rise in intracellular calcium stimulates phospholipase C to generate IP3, creating a positive-feedback loop. In the CICR model (BIOMD0000000098, , model 2 of Figure 3), the rise in intracellular calcium elicited by IP3 opens channels in a different calcium store, one that is insensitive to IP3. Here, positive feedback comes from calcium directly catalysing its own release. Calcium waves, the spatial counterpart of calcium spiking, arise by the propagation of triggering levels of IP3 in the ICC model and of calcium in the CICR model.
Figure 3: Four classes of calcium spike generating mechanisms. Abbreviations: HR, hormone-receptor complex or other activated receptor on the plasma membrane; G, GTP-binding coupling protein; PLC, phospholipase C; DG, diacylglycerol; IP3, inositol-1,4,5-triphosphate; CICR, Calcium-Induced-Calcium-Release; PKC, protein kinase C. Stimulatory linkages are shown as solid arrows, inhibitory linkages as dashed arrows. The dashed pathways labelled exhaustion indicate that positive feedback of Calcium on its own release is soon limited by exhaustion of those stores. The matrix at the right shows the experimental tests applied here, where + and -, respectively, indicate agreement and disagreement with each theoretical mechanism and a blank indicates that the theory makes no strong prediction. The highlighted models 2 and 4 are CICR and ICC models, respectively. Figure taken from .
Cooperative opening of calcium channels by IP3 has been observed in RBL cells, hepatocytes and oocytes, and opening by CICR has been clearly demonstrated in cardiac and skeletal muscle, and apparently occurs in neurons, chromaffin cells and pancreatic acinar cells. In the ICC model, calcium spiking requires IP3 spiking, and calcium spiking would vanish when IP3 level is clamped.
Figure 4 shows the spiking pattern of IP3 and cytosolic calcium and also the channel inhibition parameter (g, which equals 0 when the channel is fully active and 1 when the channel is totally inactive) and R, the fractional activation of cell-surface receptor generated by ICC model. In the CICR model, although the IP3 level at a given stimulus intensity is constant, the calcium spikes continue. So, the only role of IP3 in the CICR model is to induce a constant efflux of calcium from the IP3-sensitive store. Figure 5 shows the spiking pattern of cytosolic calcium and concentration of calcium in the IP3-insensitive intracellular store. Many complex models of calcium signalling pathway have been published since then, based on these two models and we have several of them in the BioModels database.
Figure 5: Calcium Spike - CICR model (BIOMD0000000098). The time course of calcium in the cytosol (red) and intracellular store (green).
Figure 4: Calcium Spike - ICC model (BIOMD0000000224). The time course of cytosolic calcium, IP3, and fraction of channels inhibited (g) are shown for 9% receptor (R) activation.
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