Ca2+ Effects on ATP Production and Consumption Have Regulatory Roles on Oscillatory Islet Activity

Abstract

Pancreatic islets respond to elevated blood glucose by secreting pulses of insulin that parallel oscillations in β-cell metabolism, intracellular Ca(2+) concentration, and bursting electrical activity. The mechanisms that maintain an oscillatory response are not fully understood, yet several models have been proposed. Only some can account for experiments supporting that metabolism is intrinsically oscillatory in β-cells. The dual oscillator model (DOM) implicates glycolysis as the source of oscillatory metabolism. In the companion article, we use recently developed biosensors to confirm that glycolysis is oscillatory and further elucidate the coordination of metabolic and electrical signals in the insulin secretory pathway. In this report, we modify the DOM by incorporating an established link between metabolism and intracellular Ca(2+) to reconcile model predictions with experimental observations from the companion article. With modification, we maintain the distinguishing feature of the DOM, oscillatory glycolysis, but introduce the ability of Ca(2+) influx to reshape glycolytic oscillations by promoting glycolytic efflux. We use the modified model to explain measurements from the companion article and from previously published experiments with islets.

Figure 1

Schematic of the DOM. I, current; J, flux; GK, glucokinase; PFK, phosphofructokinase; PDH, pyruvate dehydrogenase; ANT, adenine nucleotide translocator; ER, endoplasmic reticulum; hyd, hydrolysis; PMCA, plasma membrane Ca²⁺ ATPase. The modification to the model considered in this report is symbolized by the activating arrow from Ca²⁺ to $J_{\text{PDH}}.$ To see this figure in color, go online.

Figure 2

Simulation of a glucose-stimulated β-cell using the DOM in its original form (i.e., with $k_{\text{PDH}}^{Ca}=0$ in Eq. 2). All parameter values are as previously published corresponding to Fig. 1A in Watts et al. (25) with the exception of $g_{K\left(Ca\right)}$ = 200 pS. (A) In contrast with experimental observation, PKAR and Perceval exhibit a sustained rise throughout the active phase. (B) Metabolic fluxes and time derivatives; $d\left[\text{FBP}\right]/dt$ has the same sign as $J_{\text{PFK}}-J_{\text{PDH}}/2$ and $d\left[\text{ATP}\right]/dt$ has the same sign as $J_{\text{ANT}}-J_{\text{hyd}}.$ (C) Model schematic of metabolic fluxes.

Figure 3

Simulation of a glucose-stimulated β-cell using the modified DOM. Modifying the effects of Ca²⁺ provides agreement with experimental data. Parameter values for this and the following figures, unless otherwise specified, are listed in Table S1 in the Supporting Material. (A) PKAR and Perceval have a peak at the beginning of the active phase and a nadir near the end of the active phase. (B) Metabolic fluxes and time derivatives; $d\left[\text{FBP}\right]/dt$ has the same sign as $J_{\text{PFK}}-J_{\text{PDH}}/2$ and $d\left[\text{ATP}\right]/dt$ has the same sign as $J_{\text{ANT}}-J_{\text{hyd}}.$ (C) Model schematic of metabolic fluxes. In contrast to Fig. 2, Ca²⁺-activation of PDH is incorporated and Ca²⁺ inhibition of mitochondrial ATP production is neglected.

Figure 4

Phase plane and time series analysis of the glycolytic component in isolation (A) and in the full modified model (B). (A) Autocatalytic feedback onto PFK by its product FBP produces relaxation oscillations with F6P and PKAR as the slow and fast variables, respectively. (B) Ca²⁺ oscillations reshape endogenous glycolytic oscillations to produce a sawtooth like PKAR time course.

Figure 5

Analysis of PKAR and Perceval peak and nadir phases. (A) Examples of bursts with late phase ≈1 (left) and early phase <1 (right) PKAR and Perceval nadirs. In both examples, the peak occurs at phase ≈0. (B) Distribution of PKAR and Perceval peak and nadir phases from 1000 trials with the modified DOM while varying parameter $q_3$ between 3.4 and 6 μM/s.

Figure 6

Ca²⁺ clamp simulations, as performed in the companion article (37). Glycolytic oscillations abolished by preventing Ca²⁺ oscillations in stimulatory glucose can be restarted by raising intracellular Ca²⁺. To simulate addition of Dz, K(ATP) channel conductance $\left(g_{K\left(\text{ATP}\right)}\right)$ is set to its maximal value and to simulate addition of low and high KCl, K⁺ reversal potential (V_K) is set to −60 and −45 mV, respectively.

Figure 7

Slow oscillations without glycolytic oscillations. (A) Slow Ca²⁺ oscillations are triggered by glucose in mice deficient in the muscle type isoform of PFK subunit. Replacement of 98% of PFK-M isoform by PFK-C was simulated by replacing $J_{\text{PFK}}$ with $0.02J_{\text{PFK}}+0.98J_{\text{PFK}-C}$, where $J_{\text{PFK}-C}$ has the same form as $J_{\text{PFK}}$ but with a parameter adjusted to account for saturation by basal levels of FBP. Parameters are listed in the Supporting Material. (B) Slow Ca²⁺ oscillations are triggered by mitochondrial fuel α-ketoisocaproate (KIC). Addition of KIC was simulated by increasing $J_{\text{ANT}}$.