The Ca2+ dynamics of isolated mouse beta-cells and islets: implications for mathematical models

Abstract

[Ca(2+)](i) and electrical activity were compared in isolated beta-cells and islets using standard techniques. In islets, raising glucose caused a decrease in [Ca(2+)](i) followed by a plateau and then fast (2-3 min(-1)), slow (0.2-0.8 min(-1)), or a mixture of fast and slow [Ca(2+)](i) oscillations. In beta-cells, glucose transiently decreased and then increased [Ca(2+)](i), but no islet-like oscillations occurred. Simultaneous recordings of [Ca(2+)](i) and electrical activity suggested that differences in [Ca(2+)](i) signaling are due to differences in islet versus beta-cell electrical activity. Whereas islets exhibited bursts of spikes on medium/slow plateaus, isolated beta-cells were depolarized and exhibited spiking, fast-bursting, or spikeless plateaus. These electrical patterns in turn produced distinct [Ca(2+)](i) patterns. Thus, although isolated beta-cells display several key features of islets, their oscillations were faster and more irregular. beta-cells could display islet-like [Ca(2+)](i) oscillations if their electrical activity was converted to a slower islet-like pattern using dynamic clamp. Islet and beta-cell [Ca(2+)](i) changes followed membrane potential, suggesting that electrical activity is mainly responsible for the [Ca(2+)] dynamics of beta-cells and islets. A recent model consisting of two slow feedback processes and passive endoplasmic reticulum Ca(2+) release was able to account for islet [Ca(2+)](i) responses to glucose, islet oscillations, and conversion of single cell to islet-like [Ca(2+)](i) oscillations. With minimal parameter variation, the model could also account for the diverse behaviors of isolated beta-cells, suggesting that these behaviors reflect natural cell heterogeneity. These results support our recent model and point to the important role of beta-cell electrical events in controlling [Ca(2+)](i) over diverse time scales in islets.

FIGURE 1

[Ca²⁺]_i responses of individual mouse islets to changing glucose from 0 to 10 mM. (A) Representative islet exhibiting mainly fast phase 2 oscillations. (B) Islet showing a mixture of fast and slow [Ca²⁺]_i oscillations. (C) Islet showing primarily slow [Ca²⁺]_i oscillations. Initial islet [Ca²⁺]_i changes often included initial decreases, a plateau phase, and then oscillations (see text). All time bars represent 2 min.

FIGURE 2

Deterministic simulation of first phase transient and oscillations after addition of glucose (Eqs. 1–6, Methods). (A–C) A medium cell, representing a medium islet. Parameters are as in Modeling section, except g_KATP, which is initially 1 nS and stepped down to 55 pS at T = 50 s to simulate the addition of glucose. For simplicity, no attempt is made to model the latency period or the phase 0 decrease of calcium. (D–F) A slow cell, representing a slow islet. Parameters as in A–C, except g_KATP is stepped to 62 pS.

FIGURE 3

Slow [Ca²⁺]_i oscillations with prominent interburst decaying phases. (Top) Islet where calcium slowly rose for the entire duration of the active phase, and slowly decayed during the interburst phase. (Bottom) Another islet where faster oscillations occurred on the slower oscillations as “bursts of bursts” (see text). All time bars represent 2 min.

FIGURE 4

Simultaneous recordings of [Ca²⁺]_i oscillations (top) and electrical activity (bottom) in two slow islets. (A) Islet where faster electrical bursts occurred on slower bursts and triggered concomitant fast [Ca²⁺]_i oscillations. (B) An islet having very slow electrical activity and the [Ca²⁺]_i oscillations, indicating that electrical activity can account for the slow as well as medium [Ca²⁺]_i oscillations.

FIGURE 5

Deterministic simulation of steady-state bursting in the presence of glucose showing the three Ca²⁺ compartments (Eqs. 1–6, Methods). Parameters are as in Fig. 2 except g_KATP, which is 60 pS throughout, and k_PMCA, which is 0.18 ms⁻¹. (A) Membrane potential. (B) Weighted average of [Ca²⁺]_i and [Ca²⁺]_SS, corresponding to measured cytosolic [Ca²⁺], which declines throughout the active phase. (C) Subspace [Ca²⁺], which rises throughout active phase and activates K_slow to terminate the burst. (D) Store [Ca²⁺], which rises slowly in active phase and falls slowly in silent phase.

FIGURE 6

[Ca²⁺]_i responses of individual mouse β-cells to changing glucose from 0 to 10 mM. (A) Representative β-cell exhibiting mainly fast and stochastic [Ca²⁺]_i changes, including some near oscillations. (B) β-cell showing a mixture of fast and vestigial slow [Ca²⁺]_i changes. (C) β-cell showing very irregular [Ca²⁺]_i transients after glucose addition. Initial β-cell [Ca²⁺]_i changes often included initial decreases, a plateau phase (see text). All time bars represent 2 min.

FIGURE 7

The electrical activity and [Ca²⁺]_i changes of single β-cells exposed to 11.1 mM glucose. (A) Class I continuously spiking β-cell having sustained [Ca²⁺]_i and small oscillations. (B) Class II β-cell having fast bursts of electrical activity and corresponding oscillations in [Ca²⁺]_i. (C) Class III plateau cell with close synchrony between calcium and electrical activity and negligible electrical voltage spikes.

FIGURE 8

Stochastic simulation of single-cell behavior (Eqs. 1–9). Parameters as in Fig. 2 and Modeling except g_KATP, which is 42 pS, and g_Ca, which is 1500 pS for Class I firing (A), 1400 pS for Class II (B), and 1050 pS for Class III (C).

FIGURE 9

Converting fast single-cell electrical activity to an isletlike pattern with dynamic clamp resulted in corresponding [Ca²⁺]_i oscillations that resembled those of islets. Starting at the arrow, 0.008 nS of maintained exogenous conductance were added in accordance with Eqs. 11–13. Calcium changes are shown at the top; membrane potential changes at the bottom.

FIGURE 10

Stochastic simulation of dynamic-clamp conversion (Eqs. 1–9). Deterministic parameters as in Fig. 5, except k_PMCA = 0.2 ms⁻¹. Stochastic parameters and dynamic-clamp parameters are as in Methods. Dynamic-clamp conductance is turned on at T = 20 s and maintained thereafter.