Theoretical studies on the electrical activity of pancreatic beta-cells as a function of glucose.

The electrical activity of pancreatic beta-cells, which has been closely correlated both with intracellular Ca2+ concentration and insulin release, is characterized by a biphasic response to glucose and bursts of spiking action potentials. Recent voltage clamp and single channel patch clamp experiments have identified several transmembrane ionic channels that may play key roles in the electrophysiological behavior of beta-cells. There is a hypothesis that Ca2+-activated K+ channels are responsible for both the resting potential during low glucose concentration and the silent phase during bursting. The discovery of the ATP-inactivated K+ channel raises the possibility that the current for this latter K+ channel may dominate the resting potential, while the Ca2+-activated K+ current dominates the silent phase potential between bursts. The recent discovery that Ca2+-activated K+ channels are pH sensitive raises an interesting possibility for the biphasic electrical response. In this paper, numerical methods are presented for evaluating these hypotheses against experimental evidence.     

The ATP-sensitive potassium channel in pancreatic B-cells is inhibited in physiological bicarbonate buffer

The effects of bicarbonate buffer (HCO3-/CO2) on the activity of the two K+ channels proposed by some to control the pancreatic B-cell membrane response to glucose were studied. Single K+-channel records from membrane patches of cultured B-cells dissociated from adult rat islets exposed to a glucose- and bicarbonate-free medium (Na-Hepes in place of bicarbonate) exhibit the activity of both the ATP-sensitive as well as the [Ca2+]i-activated K+ channels. However, in the presence of bicarbonate-buffered Krebs solution, the activity of the ATP-sensitive K+ channel is inhibited leaving the activity of the K+ channel activated by intracellular [Ca2+]i unaffected. In the absence of bicarbonate (Hepes/NaOH in place of bicarbonate), lowering the external pH from 7.4 to 7.0 also has differential effects on the two K+ channels. While the K+ channel sensitive to ATP is inhibited, the K+ channel activated by a rise in [Ca2+]i is not affected. To determine whether the response of the B-cell in culture to bicarbonate is also present when the B-cell is functioning within the islet syncytium, the effects of bicarbonate removal on membrane potential of B-cells from intact mouse islets were compared. These studies showed that glucose-evoked electrical activity is also blocked in bicarbonate-free Krebs solution. Furthermore, in the absence of bicarbonate and presence of glucose (11 mM), electrical activity was recovered by lowering the pHo from 7.4 to 7.0. The ATP-sensitive K+-channel activity is greatly reduced by physiologically buffered solutions in pancreatic B-cells in culture. The most likely explanation for the bicarbonate effects is that they are mediated by cytosolic pH changes. Removal of bicarbonate (keeping the external pH at 7.4 with Hepes/NaOH as buffer) would increase the pHi. Since the activity of the [Ca2+]i-dependent K+ channels is not affected by the removal of the bicarbonate buffer, our patch-clamp data in cultured B-cells indicate an involvement of [Ca2+]i-activated K+ channels in the control of the membrane potential. For the B-cell in the islet, we propose that the burst pattern of electrical activity (Ca2+ entry) is controlled, at least in part, by the [Ca2+]i-activated K+ channel.     

Effects of extracellular calcium on electrical bursting and intracellular and luminal calcium oscillations in insulin secreting pancreatic beta-cells.

The extracellular calcium concentration has interesting effects on bursting of pancreatic beta-cells. The mechanism underlying the extracellular Ca2+ effect is not well understood. By incorporating a low-threshold transient inward current to the store-operated bursting model of Chay, this paper elucidates the role of the extracellular Ca2+ concentration in influencing electrical activity, intracellular Ca2+ concentration, and the luminal Ca2+ concentration in the intracellular Ca2+ store. The possibility that this inward current is a carbachol-sensitive and TTX-insensitive Na+ current discovered by others is discussed. In addition, this paper explains how these three variables respond when various pharmacological agents are applied to the store-operated model.     

Role of single-channel stochastic noise on bursting clusters of pancreatic beta-cells.

To study why pancreatic beta-cells prefer to burst as a multi-cellular complex, we have formulated a stochastic model for bursting clusters of excitable cells. Our model incorporated a delayed rectifier K+ channel, a fast voltage-gated Ca2+ channel, and a slow Cai-blockable Ca2+ channel. The fraction of ATP-sensitive K+ channels that may still be active in the bursting regime was included in the model as a leak current. We then developed an efficient method for simulating an ionic current component of an excitable cell that contains several thousands of channels opening simultaneously under unclamped voltage. Single channel open-close stochastic events were incorporated into the model by use of binomially distributed random numbers. Our simulations revealed that in an isolated beta-cell [Ca2+]i oscillates with a small amplitude about a low [Ca2+]i. However, in a large cluster of tightly coupled cells, stable bursts develop, and [Ca2+]i oscillates with a larger amplitude about a higher [Ca2+]i. This may explain why single beta-cells do not burst and also do not release insulin.     

Coupling between voltage sensors and activation gate in voltage-gated K+ channels

Current through voltage-gated K+ channels underlies the action potential encoding the electrical signal in excitable cells. The four subunits of a voltage-gated K+ channel each have six transmembrane segments (S1-S6), whereas some other K+ channels, such as eukaryotic inward rectifier K+ channels and the prokaryotic KcsA channel, have only two transmembrane segments (M1 and M2). A voltage-gated K+ channel is formed by an ion-pore module (S5-S6, equivalent to M1-M2) and the surrounding voltage-sensing modules. The S4 segments are the primary voltage sensors while the intracellular activation gate is located near the COOH-terminal end of S6, although the coupling mechanism between them remains unknown. In the present study, we found that two short, complementary sequences in voltage-gated K+ channels are essential for coupling the voltage sensors to the intracellular activation gate. One sequence is the so called S4-S5 linker distal to the voltage-sensing S4, while the other is around the COOH-terminal end of S6, a region containing the actual gate-forming residues.     

Differential effects of the K+ channel blockers apamin and quinine on glucose-induced electrical activity in pancreatic beta-cells from a strain of ob/ob (obese) mice

The effects of apamin and quinine on glucose-induced electrical activity in pancreatic islets from ob/ob mice (Norwich colony) were compared. Apamin (40-400 nM) increased the duration of the bursts of electrical activity, whereas quinine (50-100 microM) affected only slightly the steady-state electrical response to glucose. This sensitivity to apamin and poor response to quinine contrast with the resistance to apamin and sensitivity to quinine previously reported for pancreatic islets from albino mice. The results give further support to the idea that pancreatic beta-cells from ob/ob mice have a modified Ca2+-activated K+ permeability.     

Theory of the effect of extracellular potassium on oscillations in the pancreatic beta-cell.

Based on the observation that potassium ions are compartmentalized near the surface of pancreatic beta-cells in mouse islets (Perez-Armendariz, E.M., I. Atwater, and E. Rojas 1985, Biophys. J. 48:741-749), we present a theoretical treatment of the effect of external potassium on oscillations in the pancreatic beta-cell. Our model includes the effects of ionic diffusion, the Ca2+-activated K+ channel, voltage-gated K+ and Ca2+ channels, and some of the effects of glucose. It is described by four ordinary differential equations. Numerical integration of these equations allows us to examine the effect of glucose, external K+, quinine, and tetraethylammonium ion (TEA) on the oscillations in membrane potential, intracellular Ca2+, and compartmentalized K+. The results are in good agreement with experiment.     

Heterogeneous changes in [Ca2+]i induced by glucose, tolbutamide and K+ in single rat pancreatic B cells

The effects of glucose, tolbutamide and K+ on cytosolic free Ca2+ ([Ca2+]i) in single rat pancreatic B cells were examined using Fura-2 and dual wavelength microfluorimetry. At basal glucose concentration (2.8 mM), about half of the cells were found to display spontaneous Ca2+ oscillations. Glucose (greater than or equal to 11.1 mM), tolbutamide (greater than or equal to 50 microM) and K+ (50 mM) induced rises in [Ca2+]i that could be inhibited by the Ca2+ channel blocker D600. The pattern of response and the sensitivity to the secretagogues were characterized by a marked heterogeneity. The majority of the cells responded to glucose and tolbutamide by a progressive increase in [Ca2+]i onto which sinusoidal oscillations were superimposed. The periodicity of these oscillations was about 2.5/min. Occasionally, some cells displayed slow and major waves in Ca2+ levels (about 0.2/min). None of the cells responded to glucose by displaying an initial decrease in [Ca2+]i. Likewise, the sugar failed to decrease [Ca2+]i in the absence of extracellular Ca2+. The present study shows that, despite a large heterogeneity of the response, the majority of the pancreatic B cells respond to different secretagogues by displaying fast [Ca2+]i oscillations that are reminiscent of the bursts of electrical activity recorded in B cells.     

Functional voltage-gated Ca2+ channels in muscle fibers of the platyhelminth Dugesia tigrina

The presence and function of voltage-gated Ca(2+) channels were examined in individual muscle fibers freshly dispersed from the triclad turbellarian Dugesia tigrina. Individual muscle fibers contracted in response to elevated extracellular K(+) in a concentration-dependent fashion. These depolarization-induced contractions were blocked by extracellular Co(2+) (2.5 mM), suggesting that they were dependent on depolarization-induced Ca(2+) influx across the sarcolemma. A voltage-gated inward current was apparent in whole cell recordings when the outward K(+) current was abolished by replacement of intracellular K(+) by Cs(+). This inward current was amplified with increasing concentration (相似文献   

The effect of inactivation of calcium channels by intracellular Ca2+ ions in the bursting pancreatic β-cells

Based on recently determined ionic channel properties, a simple theoretical model for the burst activity of the pancreatic β-cell is formulated in this paper. The model contains an inward voltage-activated Ca²⁺ current which is inactivated by intracellular calcium ions and an outward K⁺ current that is activated by the membrane potential. The probability of opening of the channel gates is represented by Boltzmann equations. Our model is applicable in a regime where an ATP-blockable K⁺ channel is inhibited. In this regime, glucose is treated as an activator for the rate of efflux of intracellular Ca²⁺ ions, and hence its effect is equated tok _Ca, the efflux rate constant. In addition, intracellular H⁺ ion, which is a byproduct of the glycolytic metabolic process, is treated as a competitive inhibitor for Ca²⁺ ion. Since H⁺ is a competitive inhibitor (according to our assumption), its effect is equated to the strength of the Ca_i dissociation constantK _h. In the model, a Ca²⁺ binding site is assumed to exist in the inner membrane of the voltage-gated Ca²⁺ channel. The model predicts that a spike and burst electrical pattern can be generated by varyingk _ca and that a given pattern may produce different levels of intracellular Ca²⁺ depending onK _h. In other words, it predicts that levels of [Ca²⁺]_i can be separated from the electrical activity by controlling the concentration of glucose and pH appropriately. This may account for the experimental observation of Lebrun et al. (1985) that insulin secretion is not correlated to the burst of electrical activity.     

Evidences for Regulation of the Inward K+ channels by CDPK in Vicia faba Guard Cells

Regulation of the inward K+ -channels in the guard cell plasma membranes plays impotant roles in regulation of stomatal movement in responses to exogenous and endogenous signals. It is well-known that elevation of cytosolic Ca2+ in guard cells inactivates these inward K + channels, and consequently inhibits stomatal opening or induces stomatal closing, yet the downstream molecular mechanism for the Ca2 + -mediated inhibition of the inward K+ channels remains unknown. The calmodulin-like domain protein kinases (CDPKs) have been identified as an unique group of protein kinases in higher plant cells. As a downstream regulator, CDPK may play roles in mediating Ca2+ regulation on the inward K+ -channels in stomatal guard cells. The authors have applied the patchclamp technique to investigate if CDPK be involved in the regulation of the inward K+ -channels in Vicia faba guard cells by cytosolic Ca2+ . The presence of the 1.5 μmol/L intracellular Ca2 + result-ed in inhibition of the inward K+ channel activity by 60%, while the addition of purified CDPK from the cytoplasmic side resulted in greater inhibition than Ca2+ alone. Histone Ⅲ-S and protamine, which is the substrate and substrate competitive inhibitor of CDPKs respectively, completely reversed the Ca2+ -induced inhibition of the inward K+ channel activities. These results are the first reported evidences for that CDPKs are involved in the Ca2+ -mediated inward K+ -channel regulation in guard cells.     

High external Ca2+ levels trigger membrane potential oscillations in mouse pancreatic beta-cells during blockade of K(ATP) channels.

Glucose depolarizes the pancreatic beta-cell and induces membrane potential oscillations, but the nature of the underlying oscillatory conductance remains unknown. We have now investigated the effects of the Ca2+ ionophore ionomycin and high external Ca2+ concentration ([Ca2+]o) on glucose-induced electrical activity and whole islet intracellular free Ca2+ concentration ([Ca2+]i), under conditions where the K(ATP) channel was blocked (100 microM tolbutamide or 4 microM glibenclamide). Raising [Ca2+]o to 10.2 or 12.8 mM, but not to 5.1 or 7.7 mM, turned continuous electrical activity into bursting activity. High [Ca2+]o (12.8 mM) regenerated a pattern of fast [Ca2+]i oscillations overshooting the levels recorded in tolbutamide. Ionomycin (10 microM) raised the [Ca2+]i and synergized with 5.1 mM Ca2+ to hyperpolarize the beta-cell membrane. The data indicate that a [Ca2+]i-sensitive and sulphonylurea-insensitive oscillatory conductance underlies the beta-cell bursting activity.     

Autocrine regulation of calcium influx and gonadotropin-releasing hormone secretion in hypothalamic neurons.

Gonadotropin-releasing hormone (GnRH) receptors are expressed in hypothalamic tissues from adult rats, cultured fetal hypothalamic cells, and immortalized GnRH-secreting neurons (GT1 cells). Their activation by GnRH agonists leads to an overall increase in the extracellular Ca2+-dependent pulsatile release of GnRH. Electrophysiological studies showed that GT1 cells exhibit spontaneous, extracellular Ca2+-dependent action potentials, and that their inward currents include Na+, T-type and L-type Ca2+ components. Several types of potassium channels, including apamin-sensitive Ca2+-controlled potassium (SK) channels, are also expressed in GT1 cells. Activation of GnRH receptors leads to biphasic changes in intracellular Ca2+ concentration ([Ca2+]i), with an early and extracellular Ca2+-independent peak and a sustained and extracellular Ca2+-dependent plateau phase. During the peak [Ca2+]i response, electrical activity is abolished due to transient hyperpolarization that is mediated by SK channels. This is followed by sustained depolarization and resumption of firing with increased spike frequency and duration. The agonist-induced depolarization and increased firing are independent of [Ca2+]i and are not mediated by inhibition of K+ currents, but by facilitation of a voltage-insensitive and store depletion-activated Ca2+-conducting inward current. The dual control of pacemaker activity by SK and store depletion-activated Ca2+ channels facilitates voltage-gated Ca2+ influx at elevated [Ca2+]i levels, but also protects cells from Ca2+ overload. This process accounts for the autoregulatory action of GnRH on its release from hypothalamic neurons.     

Ion channels in smooth muscle: regulators of intracellular calcium and contractility

Smooth muscle (SM) is essential to all aspects of human physiology and, therefore, key to the maintenance of life. Ion channels expressed within SM cells regulate the membrane potential, intracellular Ca2+ concentration, and contractility of SM. Excitatory ion channels function to depolarize the membrane potential. These include nonselective cation channels that allow Na+ and Ca2+ to permeate into SM cells. The nonselective cation channel family includes tonically active channels (Icat), as well as channels activated by agonists, pressure-stretch, and intracellular Ca2+ store depletion. Cl--selective channels, activated by intracellular Ca2+ or stretch, also mediate SM depolarization. Plasma membrane depolarization in SM activates voltage-dependent Ca2+ channels that demonstrate a high Ca2+ selectivity and provide influx of contractile Ca2+. Ca2+ is also released from SM intracellular Ca2+ stores of the sarcoplasmic reticulum (SR) through ryanodine and inositol trisphosphate receptor Ca2+ channels. This is part of a negative feedback mechanism limiting contraction that occurs by the Ca2+-dependent activation of large-conductance K+ channels, which hyper polarize the plasma membrane. Unlike the well-defined contractile role of SR-released Ca2+ in skeletal and cardiac muscle, the literature suggests that in SM Ca2+ released from the SR functions to limit contractility. Depolarization-activated K+ chan nels, ATP-sensitive K+ channels, and inward rectifier K+ channels also hyperpolarize SM, favouring relaxation. The expression pattern, density, and biophysical properties of ion channels vary among SM types and are key determinants of electrical activity, contractility, and SM function.     

Modeling of Ca2+ flux in pancreatic beta-cells: role of the plasma membrane and intracellular stores

We have developed a detailed mathematical model of ionic flux in beta-cells that includes the most essential channels and pumps in the plasma membrane. This model is coupled to equations describing Ca2+, inositol 1,4,5-trisphosphate (IP3), ATP, and Na+ homeostasis, including the uptake and release of Ca2+ by the endoplasmic reticulum (ER). In our model, metabolically derived ATP activates inward Ca2+ flux by regulation of ATP-sensitive K+ channels and depolarization of the plasma membrane. Results from the simulations support the hypothesis that intracellular Na+ and Ca2+ in the ER can be the main variables driving both fast (2-7 osc/min) and slow intracellular Ca2+ concentration oscillations (0.3-0.9 osc/min) and that the effect of IP3 on Ca2+ leak from the ER contributes to the pattern of slow calcium oscillations. Simulations also show that filling the ER Ca2+ stores leads to faster electrical bursting and Ca2+ oscillations. Specific Ca2+ oscillations in isolated beta-cell lines can also be simulated.     

Calcium entry through receptor-operated channels in bovine pulmonary artery endothelial cells

The activation of endothelial cells by endothelium-dependent vasodilators has been investigated using bioassay, patch clamp and 45Ca flux methods. Cultured pulmonary artery endothelial cells have been demonstrated to release EDRF in response to thrombin, bradykinin, ATP and the calcium ionophore A23187. The resting membrane potential of the endothelial cells was -56 mV and the cells were depolarized by increasing extracellular K+ or by the addition of (0.1-1.0 mM)Ba2+ to the bathing solution. The electrophysiological properties of the cultured endothelial cells suggest that the membrane potential is maintained by an inward rectifying K+ channel with a mean single channel conductance of 35.6 pS. The absence of a depolarization-activated inward current and the reduction of 45Ca influx with high K+ solution suggests that there are no functional voltage-dependent calcium or sodium channels. Thrombin and bradykinin were shown to evoke not only an inward current (carried by Na+ and Ca2+) but also an increase in 45Ca influx suggesting that the increase in intracellular calcium necessary for EDRF release is mediated by an opening of a receptor operated channel. High doses of thrombin and bradykinin induced intracellular calcium release, however, at low doses of thrombin no intracellular calcium release was observed. We propose that the increased cytosolic calcium concentration in endothelial cells induced by endothelium dependent vasodilators is due to the influx of Ca2+ through a receptor operated ion channel and to a lesser degree to intracellular release of calcium from a yet undefined intracellular store.     

Calcium-dependent inactivation of L-type calcium channels in planar lipid bilayers.

Intracellular Ca2+ can inhibit the activity of voltage-gated Ca channels by modulating the rate of channel inactivation. Ca(2+)-dependent inactivation of these channels may be a common negative feedback process important for regulating Ca2+ entry under physiological and pathological conditions. This article demonstrates that the inactivation of cardiac L-type Ca channels, reconstituted into planar lipid bilayers and studied in the presence of a dihydropyridine agonist, is sensitive to Ca2+. The rates and extents of inactivation, determined from ensemble averages of unitary Ba2+ currents, decreased when the calcium concentration facing the intracellular surface of the channel ([Ca2+]i) was lowered from approximately 10 microM to 20 nM by the addition of Ca2+ chelators. The rates and extents of Ba2+ current inactivation could also be increased by subsequent addition of Ca2+ raising the [Ca2+]i to 15 microM, thus demonstrating that the Ca2+ dependence of inactivation could be reversibly regulated by changes in [Ca2+]i. In addition, reconstituted Ca channels inactivated more quickly when the inward current was carried by Ca2+ than when it was carried by Ba2+, suggesting that local increases in [Ca2+]i could activate Ca(2+)-dependent inactivation. These data support models in which Ca2+ binds to the channel itself or to closely associated regulatory proteins to control the rate of channel inactivation, and are inconsistent with purely enzymatic models for channel inactivation.     

Receptor-mediated calcium influx in PC12 cells. ATP and bradykinin activate two independent pathways

In the neurosecretory cell line PC12 the cytosolic free Ca2+ concentration, [Ca2+]i, and membrane potential were affected by both external ATP and the nonapeptide bradykinin, BK. The latter caused a rapid and large release of Ca2+ from intracellular stores (Ca2+ redistribution) and, in the presence of external Ca2+, a long lasting, but moderate Ca2+ influx, which was insensitive to dihydropyridine blockers. On the contrary, ATP evoked a [Ca2+]i rise which rapidly inactivated. At least three different mechanisms accounted for the ATP-induced increase in [Ca2+]i: less than 20% of the total response was due to intracellular Ca2+ redistribution, consistent with a small increase in inositol 1,4,5-trisphosphate level; the rest (over 80%) was equally accounted for by ATP-activated cation channels and voltage-gated Ca2+ channels. ATP and BK (the latter after K+ channel blockade) caused plasma membrane depolarization. With both agonists the inward current was carried by both Na+ and Ca2+, although the BK-activated current appeared to be more selective for Ca2+. Channels triggered by ATP and BK differed not only in their cation selectivity, but also in modulation by both [Ca2+]i and drugs such as the phorbol ester phorbol 12-myristate 13-acetate and the new antagonist of ligand-activated Ca2+ influx, SK&F 96365.