Calcium and Metabolic Oscillations in Pancreatic Islets: Who's Driving the Bus?*

Abstract

Pancreatic islets exhibit bursting oscillations in response to elevated blood glucose. These oscillations are accompanied by oscillations in the free cytosolic Ca²⁺ concentration (Ca_c ), which drives pulses of insulin secretion. Both islet Ca²⁺ and metabolism oscillate, but there is some debate about their interrelationship. Recent experimental data show that metabolic oscillations in some cases persist after the addition of diazoxide (Dz), which opens K(ATP) channels, hyperpolarizing β-cells and preventing Ca²⁺ entry and Ca²⁺ oscillations. Further, in some islets in which metabolic oscillations were eliminated with Dz, increasing the cytosolic Ca²⁺ concentration by the addition of KCl could restart the metabolic oscillations. Here we address why metabolic oscillations persist in some islets but not others, and why raising Ca_c restarts oscillations in some islets but not others. We answer these questions using the dual oscillator model (DOM) for pancreatic islets. The DOM can reproduce the experimental data and shows that the model supports two different mechanisms for slow metabolic oscillations, one that requires calcium oscillations and one that does not.

Keywords: calcium; dual oscillator model; metabolic; oscillations; pancreatic β-cells.

Figure 1

Successive reductions of the DOM. (A) The three interconnected components of the DOM. (B) Reduced DOM with simplified mitochondria and ADP_c set to steady state. (C) Dual planar system with a simplified calcium component for phase-plane analysis. (D) Glycolytic oscillations forced by Ca_c. See the text for details.

Figure 2

Effects of Dz on Ca²⁺ and metabolic oscillations with the reduced DOM. (A) When J_GK = 0.143 μM ms⁻¹, metabolic oscillations are sustained. (B) When J_GK = 0.153 μM ms⁻¹, metabolic oscillations are terminated.

Figure 3

Metabolic oscillations that are terminated with Dz can be restored in some cases (A) but not others (B). (A) Continuation of simulation in Figure 2B with KCl added at t = 120 min, simulated by raising the K⁺ reversal potential from −75 mV to −50 mV. Ca_c rises but remains nonoscillatory, and FBP oscillations are restored. (B) FBP oscillations cannot be restored when J_GK is increased slightly (0.19 μM ms⁻¹).

Figure 4

Two-parameter bifurcation diagram of the glycolytic subsystem illustrating the region of Ca²⁺ independent (CaI) oscillations. The open square corresponds to Figure 2A after the addition of Dz, the open circle corresponds to Figure 3A, and the open triangle corresponds to Figure 3B. The filled circle corresponds to Figure 3A after KCl is raised to restore oscillations, and the closed triangle corresponds to Figure 3B. The left set of vertical dashed lines are the leftmost (blue) and rightmost (red) J_GK values of the HB_L curve, while the right set of vertical dashed lines are the leftmost (red) and rightmost (blue) J_GK values of the SNP_R curve.

Figure 5

Forcing of the glycolytic subsystem with J_GK = 0.19 μM ms⁻¹. (A) Ca_c is a square-wave oscillation. (B) The phase plane for the GO. The GO chases two different steady states that switch as Ca_c jumps from high to low. The FBP (green) and G6P (orange) nullclines move to the left as Ca_c increases. The trajectory is solid black; the dashed black line indicates that the phase point would have gone to the low Ca_c steady state if Ca_c had not jumped.

Figure 6

Phase plane analysis of the dual planar model. The GO is coupled to a FitzHugh–Nagumo-like oscillator consisting of Ca_c and Ca_ER in place of the original EO. (A) Ca_c oscillations. (B) FBP oscillations. (C) Phase plane for the EO. The Ca_c nullcline is cubic (green) and moves to the right as FBP increases. The Ca_ER nullcline is linear (orange). (D) Phase plane for the GO. The FBP (green) and G6P (orange) nullclines move to the left as Ca_c increases. The trajectories for the EO and GO are in black (J_GK=0.19 μM ms⁻¹).

Figure 7

Bifurcation diagram for the reduced DOM (A) and the dual planar model (B).

Figure 8

Periods for the reduced DOM (filled circles) and the dual phase-plane model (open circles) as a function of J_GK.

Figure 9

Periods observed in islets [42] (A) and synthetic data for the reduced DOM (B). Synthetic data generated by taking a Gaussian distribution of J_GK values with mean 0.1575 and standard deviation 0.0475. The horizontal lines represent mean values.