Modeling of glucose-induced cAMP oscillations in pancreatic β cells: cAMP rocks when metabolism rolls

Abstract

Recent advances in imaging technology have revealed oscillations of cyclic adenosine monophosphate (cAMP) in insulin-secreting cells. These oscillations may be in phase with cytosolic calcium oscillations or out of phase. cAMP oscillations have previously been modeled as driven by oscillations in calcium, based on the known dependence of the enzymes that generate cAMP (adenylyl cyclase) and degrade it (phosphodiesterase). However, cAMP oscillations have also been reported to occur in the absence of calcium oscillations. Motivated by similarities between the properties of cAMP and metabolic oscillations in pancreatic β cells, we propose here that in addition to direct control by calcium, cAMP is controlled by metabolism. Specifically, we hypothesize that AMP inhibits adenylyl cyclase. We incorporate this hypothesis into the dual oscillator model for β cells, in which metabolic (glycolytic) oscillations cooperate with modulation of ion channels and metabolism by calcium. We show that the combination of oscillations in AMP and calcium in the dual oscillator model can account for the diverse oscillatory patterns that have been observed, as well as for experimental perturbations of those patterns. Predictions to further test the model are provided.

Figure 1

cAMP oscillations can occur without calcium oscillations. Application of Dz is simulated by setting the K(ATP) channel open fraction to 1 (Eq. 9). In the left column, GK activity ($J_{\text{GK}}=0.14$μM/s) is slightly larger than in the right column ($J_{\text{GK}}=0.12$μM/s). Although Ca²⁺ oscillations cease in both (A) and (B), FBP, AMP (E and F), and cAMP (G and H) oscillations may be abolished (left column) or persist (right column). ${\overline{g}}_{\text{katp}}$ = 16,000 pS.

Figure 2

Glucose elevation, but not Ca²⁺ oscillations, are required for cAMP oscillations. Depolarization with KCl in the presence of Dz (simulated by raising the reversal potential for K⁺ from $-75$ mV to $-$ 62.5 mV) is ineffective at generating oscillations in calcium (A) or cAMP (D). However, raising glucose to a stimulatory level (simulated by increasing $J_{\text{GK}}$ from 0.03 μM/s to 0.12 μM/s) induces oscillations in FBP (B), AMP (C), and cAMP without oscillations in Ca²⁺. ${\overline{g}}_{\text{katp}}$ = 16,000 pS.

Figure 3

Model prediction that depolarization can rescue cAMP oscillations. Sustained oscillations in Ca²⁺ (A), metabolism (B and C), and cAMP (D) in stimulatory glucose ($J_{\text{GK}}=0.13$μM/s) are suppressed by application of Dz. Ca²⁺ immediately stops oscillating and cAMP transiently rings to an elevated steady state. Depolarization with extracellular potassium (simulated by increasing the K⁺ Nernst potential, $V_{\text{K}}$, to $-50$ mV) is effective at generating oscillations in metabolism and cAMP (D), but not in Ca²⁺ (A). ${\overline{g}}_{\text{katp}}$ = 16,000 pS.

Figure 4

Sensitivities of AC and PDE to changes in Ca²⁺ control the phase relationship in fast EOs. (A) Electrical oscillations, obtained by setting $J_{\text{GK}}=0.21$μM/s and ${\overline{g}}_{\text{katp}}$ = 18,000 pS, drive the use of ATP, generating small-amplitude AMP oscillations. (B) When basal Ca²⁺ saturates AC $\left(K_{\text{acca}}=0.05\mu \text{M}\right)$, cAMP is out of phase with Ca²⁺, as in Landa et al. (7). (Out-of-phase oscillations can alternatively be produced by lowering ${\beta }_{\text{ac}}$ from 3.0 to 1.0, similar to the procedure in the Landa study (7).) (C) When basal Ca²⁺ does not saturate AC $\left(K_{\text{acca}}=0.1\mu \text{M}\right)$, cAMP and Ca²⁺ are in phase, as in Dyachok et al. (15).

Figure 5

Sensitivities of AC and PDE to changes in Ca²⁺ control the phase relationship of fast oscillations during compound bursting (${\overline{g}}_{\text{katp}}$ = 17,500 pS and $J_{\text{GK}}=0.19$μM/s). (A) Slow MOs combine with [Ca²⁺]_i oscillations to produce compound AMP oscillations. (B and C) Two cases of AC and PDE sensitivity, as in the corresponding panels of Fig. 4. The slow AMP oscillations add a slow component to cAMP oscillations. The AMP teeth and fast [Ca²⁺]_i bursts within each slow episode affect cAMP production as in the pure fast EOs in Fig. 4, resulting in cAMP oscillations that are in phase or out of phase with Ca²⁺.

Figure 6

The range of cAMP oscillations depends on AMP oscillations and AC sensitivity to AMP. (A) The portion of cAMP dynamics that depends on AMP (F in Eq. 4) is plotted versus AMP for three affinity values (thick black curves). The range of AMP values produced by an MO with the DOM is shown as the longer magenta bars. The range of AMP values produced by an EO is shown as the shorter blue bars. The change in F ($\Delta F$) during an MO is shown in magenta on the left axis, whereas the change that occurs during an EO is shown in blue on the right axis. (B) $\Delta F$ as a function of the AMP affinity parameter $K_{\text{acamp}}$ for either MOs or EOs.

Figure 7

Central hypothesis. Pathways for fast oscillations (A) and slow or coumpound oscillations (B). Glucose activates glycolysis, which may either be steady or oscillate. Calcium oscillations are driven by either MOs or EOs or both. Calcium oscillations can lead to cAMP oscillations through calcium-sensitive ACs and PDEs. We propose in addition that oscillations in AMP, an inhibitor of AC, also directly and independently drive cAMP oscillations.