Bursting and calcium oscillations in pancreatic beta-cells: specific pacemakers for specific mechanisms

Abstract

Oscillatory phenomenon in electrical activity and cytoplasmic calcium concentration in response to glucose are intimately connected to multiple key aspects of pancreatic β-cell physiology. However, there is no single model for oscillatory mechanisms in these cells. We set out to identify possible pacemaker candidates for burst activity and cytoplasmic Ca(2+) oscillations in these cells by analyzing published hypotheses, their corresponding mathematical models, and relevant experimental data. We found that although no single pacemaker can account for the variety of oscillatory phenomena in β-cells, at least several separate mechanisms can underlie specific kinds of oscillations. According to our analysis, slowly activating Ca(2+)-sensitive K(+) channels can be responsible for very fast Ca(2+) oscillations; changes in the ATP/ADP ratio and in the endoplasmic reticulum calcium concentration can be pacemakers for both fast bursts and cytoplasmic calcium oscillations, and cyclical cytoplasmic Na(+) changes may underlie patterning of slow calcium oscillations. However, these mechanisms still lack direct confirmation, and their potential interactions raises new issues. Further studies supported by improved mathematical models are necessary to understand oscillatory phenomena in β-cell physiology.

Fig. 1.

General scheme of the main processes involved in bursting and intracellular Ca²⁺ oscillations in pancreatic β-cells. Plasma membrane currents: voltage-dependent Ca²⁺ current (I_VCa), calcium pump current (I_Cap), Na⁺/Ca²⁺ exchange current (I_NaCa), Ca²⁺ release-activated nonselective cation current (I_SOC), inward Na⁺ currents (I_Na), sodium-potassium pump current (I_NaK), slow Ca²⁺-sensitive K⁺ current (I_KCas), delayed rectifying K⁺ current (I_KDr), small conductance Ca²⁺-activated K⁺ current (I_KCa), ATP-sensitive K⁺ current (I_KATp). k_sg is a coefficient of the sequestration rate of Ca²⁺ by the secretory granules. SERCA is a calcium pump in endoplasmic reticulum (ER), and Ca²⁺ leaks from ER throw into inositol 1,4,5-triphosphate (IP₃) receptor (IP₃R) and ryanodine receptor (RyaR). ATP is the free cytosolic form of ATP, and ADP_f is free cytosolic ADP. Signals originating from fuel metabolism increase cytosolic calcium. F6P, fructose 6-phosphate. Synthesis and degradation of cAMP are catalyzed by adenylyl cyclase (AC) and phosphodiesterase (PDE), respectively. AC was activated by stimulatory G protein and Ca²⁺ and deactivated by inhibited G protein, whereas PDE activity was enhanced by Ca²⁺. Synthesis of IP₃ is catalyzed by phospholipase C (PLC). PLC was activated by stimulatory G protein. Solid lines indicate fluxes, and dashed lines indicate inhibitory or stimulatory influences on currents or fluxes.

Fig. 2.

Temporal correlation between membrane potential (MP) and cytosolic free calcium concentration ([Ca²⁺]_c) oscillations (adapted from Ref. 11). Islets from wild mice were perifused with a solution containing 8 (C and D) or 10 mM glucose(A and B) as indicated. The MP was measured in a β-cell within an islet, and [Ca²⁺]_c was measured simultaneously in the same islet.

Fig. 3.

Slow-activated Ca²⁺-sensitive K⁺ channels as pacemaker for ultrafast burst and [Ca²⁺]_c oscillations. Burst behavior of the membrane potential (V_P; A), the oscillation pattern of [Ca²⁺]_c (B), and slow Ca²⁺-sensitive K⁺ current (I_KCas; C). Simulations were made according the model from the appendix.

Fig. 4.

Slow ATP/ADP ratio changes as a pacemaker. Burst behavior of the MP and the oscillation patterns of [Ca²⁺]_c, free ADP ([ADP]), and I_KATP are illustrated. It was simulated using a model (51) by a step increase of glucose level. Several variables, [Na⁺]_c, [IP₃], and [Ca²⁺]_ER, were frozen at constant levels to eliminate other mechanisms of fast and slow [Ca²⁺]_c oscillations ([Na⁺]_c = 7 mM, [IP₃] = 3 μM, and [Ca²⁺]_ER = 20 μM). Several coefficients were set as g_mSOC = 2 pS⁻¹ mV, g_mKATP = 200,000 pS, g_mKCa = 80 pS, g_mVCa = 710 pS, g_NaCa = 500 pS, k_ADP = 0.001 ms, k_ATP = 0.000001 ms, k_ATP,Ca = 0.0000218 μM/ms, and P_NaK = 400 fA. All other parameter settings are as in Ref. . A: action potential (V_P). B: [Ca²⁺]_c. C: [ADP]. D: I_KATP.

Fig. 5.

Effect of tolbutamide and thapsigargin on slow Ca²⁺ oscillations in mouse islets. Mouse islets were loaded with fura-2, and relative [Ca²⁺]_c changes were recorded as the 340/380 nm fluorescence excitation ratio changes obtained with the indicator fura-2 during incubation in 2 mM glucose with 50 μM tolbutamide, with subsequent addition of 1 μM thapsigargin.

Fig. 6.

Slow [Na⁺]_c changes as a pacemaker. Typical computer simulations using the model by Fridlyand et al. (51). Slow bursting and the oscillation patterns of Ca²⁺ and Na⁺ are illustrated. The other slow variables were frozen ([ATP] = 3,300 μM, [IP₃] = 3 μM, and [Ca²⁺]_ER = 50 μM) at constant levels to eliminate other mechanism of [Ca²⁺]_c oscillations. All other parameter settings are as in Ref. . A: V_P. B: [Ca²⁺]_c. C: [Na⁺]_c. D: I_NaK.

Fig. 7.

Simulation of glucose-induced slow oscillations and SERCA blocking. Glucose-induced slow electrical bursting and [Ca²⁺]_c oscillations were simulated at a step increase of the rate constant of ATP production from a low to an intermediate value at t = 0. A: [Ca²⁺]_c. B: MP. C: Ca²⁺ in ER. D: cytosolic ATP. E: cytosolic IP₃. F: intracellular Na⁺ concentration. For simulation of thapsigargin action, the maximal rate of ER (SERCA; P_CaER) was decreased from 0.105 to 0.013 μM/ms at arrow in B (adapted from Ref. 51).

Fig. 8.

Effect of veratridine on slow Ca²⁺ oscillations in mouse islets. The experiments were performed in medium containing 2.5 mM Ca²⁺ and 14 mM glucose. Veratridine (μM) was added as indicated. The concentration of cytoplasmic Ca²⁺ is presented as the 340/380 nm fluorescence excitation ratio obtained with the indicator fura-2.

Fig. 9.

Simulated influence of veratridine on slow [Ca²⁺]_c oscillations in β-cells. Addition of veratridine was simulated by decrease of half-activated potential for Na⁺ channels in the model by Fridlyand et al. (51). (Half-activated potential for Na⁺ channels was decreased from −104 to −94 mV at arrow 1 and from −94 to −84 mV at arrow 2 in B). A: V_P. B: [Ca²⁺]_c. C: [Na⁺]_c. D: I_Na.

Fig. 10.

Slow [Ca²⁺]_ER changes as a pacemaker. Simulations were made as in Fig. 4. [Ca²⁺]_ER is the only slow parameter at frozen ADP, ATP, Na⁺, and IP₃ concentrations that eliminated other possible mechanisms of bursting and Ca²⁺ oscillations in the model by Fridlyand et al. (51). ([Na⁺]_c = 6 mM, [IP₃] = 1 μM, [ATP] = 3,400 μM, and k_ADP = 0.00045 ms⁻¹). All other parameter settings are as in Fridlyand et al. (51). A: V_P. B: [Ca²⁺]_c. C: [Ca²⁺]_ER. D: I_SOC.