Filtering of calcium transients by the endoplasmic reticulum in pancreatic beta-cells

Abstract

Calcium handling in pancreatic beta-cells is important for intracellular signaling, the control of electrical activity, and insulin secretion. The endoplasmic reticulum (ER) is a key organelle involved in the storage and release of intracellular Ca2+. Using mathematical modeling, we analyze the filtering properties of the ER and clarify the dual role that it plays as both a Ca2+ source and a Ca2+ sink. We demonstrate that recent time-dependent data on the free Ca2+ concentration in pancreatic islets and beta-cell clusters can be explained with a model that uses a passive ER that takes up Ca2+ when the cell is depolarized and the cytosolic Ca2+ concentration is elevated, and releases Ca2+ when the cell is repolarized and the cytosolic Ca2+ is at a lower concentration. We find that Ca2+-induced Ca2+ release is not necessary to explain the data, and indeed the model is inconsistent with the data if Ca2+-induced Ca2+ release is a dominating factor. Finally, we show that a three-compartment model that includes a subspace compartment between the ER and the plasma membrane provides the best agreement with the experimental Ca2+ data.

FIGURE 1

Illustration of the Ca²⁺ fluxes incorporated in (A) the two-compartment model and (B) the three-compartment subspace model. The thin arrow in B represents a small flux from the ER to the bulk cytosol.

FIGURE 2

(A) Simulated voltage protocol mimicking the biphasic response to an increase in glucose concentration. (B) Cytosolic Ca²⁺ response with SERCA pumps enabled (solid line) and disabled (dashed line). During each imposed oscillation, the nadir is defined as the lowest value of C during the repolarized phase. The amplitude is the difference between the peak and the nadir. (C) The ER Ca²⁺ concentration. No driving force is established between the ER and the cytosol when SERCA pumps are disabled (dashed line).

FIGURE 3

(A) Doubling the rate of Ca²⁺ release from the ER, p_er, has a transient effect on the cytosolic Ca²⁺ response (dashed line) to the voltage protocol, but no long-term effect. (B) C_er adapts to the doubling in p_er (dashed line) by declining to a value one-half that of the control.

FIGURE 4

(A) Reducing the rate of pumping across the plasma membrane by half (dashed line) slightly increases the amplitude of the Ca²⁺ response to depolarization and greatly increases the Ca²⁺ nadir. (B) The increase in the Ca²⁺ nadir is due to an increase in C_er.

FIGURE 5

(A) An increase in the glucose concentration is mimicked (at arrow) by increasing the depolarized phase duration from 8 s to 12 s, while keeping the oscillation period fixed at 24 s. (B) In the control simulation (solid line), increasing the duration of depolarization results in an increase in the Ca²⁺ nadir, but not in the amplitude, whereas there is no effect when SERCA pumps are disabled (dashed line). (C) In the control simulation, an increase in the ER Ca²⁺ concentration is responsible for the increased cytosolic Ca²⁺ nadir.

FIGURE 6

(A) When the Ca²⁺ channel conductance, g_Ca, is doubled (at arrow), both the Ca²⁺ amplitude and nadir are increased. This is true with SERCA pumps enabled (solid line) or disabled (dashed line), although the nadir increase in the latter case is quite small. (B) As in Fig. 5, the nadir increase is due primarily to an increase in the ER Ca²⁺ concentration, although increased Ca²⁺ entry also plays a role.

FIGURE 7

(A) Voltage protocol for compound bursting. (B) In the control system the Ca²⁺ nadir rises during a compound burst and slowly falls between (solid line). This does not occur when the SERCA pumps are disabled (dashed line). (C) The rise and fall of the nadir reflects the dynamics of ER Ca²⁺.

FIGURE 8

Demonstration that the slow rise and fall of the cytosolic Ca²⁺ nadir depends critically on the speed at which the ER takes up and releases Ca²⁺. (A) The speed of the ER is increased by setting f_er = 0.1 (solid line), or decreased by setting f_er = 0.0002 (dashed line). (B) There are no slow C_er dynamics when f_er = 0.1, and there is only a small increase in C_er during a compound burst when f_er = 0.0002.

FIGURE 9

Ca²⁺ response to a sequence of depolarizations when CICR dominates release from the ER. (A) Sequence of brief depolarizations. (B) Cytosolic Ca²⁺ rises during depolarization and falls during repolarization. (C) The ER releases Ca²⁺ during the depolarization due to CICR, and refills during the repolarization.

FIGURE 10

(A) Biphasic voltage protocol applied to the model in which CICR dominates. (B) Even with active SERCA pumps the Ca²⁺ nadir is not elevated and the amplitude is large (solid line), so that blocking SERCA pumps has only a small effect (dashed line). (C) The cytosolic Ca²⁺ nadir is not elevated despite the fact that the ER is filled.

FIGURE 11

Ca²⁺ concentrations during a sustained depolarization from −70 mV to −30 mV with the three-compartment subspace model. (A) The weighted average of the bulk cytosolic Ca²⁺ and the subspace Ca²⁺ concentrations is lower when SERCA pumps are inhibited (dashed line) than in the control system (solid line). The ER Ca²⁺ concentration (B) and the subspace Ca²⁺ concentration (D) are lower when SERCA pumps are inhibited. (C) The bulk cytosolic concentration satisfies Eq. 16, so its steady state is independent of the C_er or ER parameters.