Complex patterns of metabolic and Ca²⁺ entrainment in pancreatic islets by oscillatory glucose

Abstract

Glucose-stimulated insulin secretion is pulsatile and driven by intrinsic oscillations in metabolism, electrical activity, and Ca(2+) in pancreatic islets. Periodic variations in glucose can entrain islet Ca(2+) and insulin secretion, possibly promoting interislet synchronization. Here, we used fluorescence microscopy to demonstrate that glucose oscillations can induce distinct 1:1 and 1:2 entrainment of oscillations (one and two oscillations for each period of exogenous stimulus, respectively) in islet Ca(2+), NAD(P)H, and mitochondrial membrane potential. To our knowledge, this is the first demonstration of metabolic entrainment in islets, and we found that entrainment of metabolic oscillations requires voltage-gated Ca(2+) influx. We identified diverse patterns of 1:2 entrainment and showed that islet synchronization during entrainment involves adjustments of both oscillatory phase and period. All experimental findings could be recapitulated by our recently developed mathematical model, and simulations suggested that interislet variability in 1:2 entrainment patterns reflects differences in their glucose sensitivity. Finally, our simulations and recordings showed that a heterogeneous group of islets synchronized during 1:2 entrainment, resulting in a clear oscillatory response from the collective. In summary, we demonstrate that oscillatory glucose can induce complex modes of entrainment of metabolically driven oscillations in islets, and provide additional support for the notion that entrainment promotes interislet synchrony in the pancreas.

Figure 1

Characterization of 1:1 islet Ca²⁺ entrainment to glucose. (A) Representative experiment in which the cytosolic Ca²⁺ responses of seven Fura-2-loaded islets were imaged simultaneously. The islets were stimulated with an extracellular glucose profile as indicated above the recordings (mean: 10 mM; amplitude: 20%; period: 4 min). (B) Illustration of interislet phase synchronization upon exposure to glucose forcing as shown in panel A. The sinusoidal glucose stimulus was initiated at 32 min (dashed line). The arrow indicates the approximate time at which the islets synchronized their Ca²⁺ oscillations. (C) Islet Ca²⁺ oscillation periods quantified pre- and postentrainment to the glucose stimulus shown in panel A. Horizontal bars indicate mean ± SE (p = 0.005 by Wilcoxon signed-rank test, n = 13 islets from two mice).

Figure 2

Model simulations of 1:1 entrainment. Two identical model islets were started out of phase in 10 mM constant glucose. (A–D) After 20 min, glucose (A) was made to oscillate with amplitude 2 mM and period 7 min, which induced rapid entrainment involving phase shift and period modulation as illustrated by the cytosolic [Ca²⁺] (B), mitochondrial [NADH] (C), and mitochondrial membrane potential (ΔΨ_m) (D).

Figure 3

Heterogeneous patterns of 1:2 islet entrainment to slowly oscillating glucose. (A) Examples illustrating various 1:2 entrainment patterns of islet Ca²⁺ to an oscillating extracellular glucose profile with a period of 10 min, 10 mM mean, and 20% amplitude. The islet recordings in panels A_ii and A_iii are from separate experiments with identical extracellular glucose stimulation profiles. Note that this and all subsequent Fura Red recordings are shown on an inverted intensity scale to reflect the direction of changes in cytosolic Ca²⁺. (B and C) Autocorrelation and spectral analyses of the cytosolic Ca²⁺ profile in panel A_iii. Solid and dashed lines indicate the properties before and after the onset of the oscillating glucose signal, respectively. The shift in period illustrates the 1:2 entrainment to the extracellular signal (representative of 16 islets from two mice). (D) Comparison of cytosolic Ca²⁺ oscillation periods of islets exposed to constant 10 mM glucose and islets during steady-state recordings in oscillatory glucose with 10 min period and 20% amplitude (p < 0.0001; n = 35 islets from six mice and 22 islets from three mice, respectively). (E) Mean cytosolic Ca²⁺ profiles of the islets quantified in panel D (left: constant glucose; right: oscillatory glucose). Before autocorrelation analysis and averaging, the individual islet recordings were detrended as described in Materials and Methods. Shaded gray bars represent mean ± SE. (F) Example of 1:2 islet Ca²⁺ entrainment to an oscillating glucose signal with 8 min period (representative of n = 6 islets from two mice).

Figure 4

Model simulations of 1:2 entrainment. (A–D) In response to slowly oscillating glucose concentrations (A; mean 10 mM, amplitude 2 mM, period 18 min), various 1:2 entrainment patterns are seen (B–D). (E) The Ca²⁺ pattern in D resembles 1:1 entrainment despite being a result of clear 1:2 entrainment of the underlying metabolic oscillator, illustrated by mitochondrial NADH. Parameters take default values except that in C, K_GK = 8.0 mM and $\overline{g}$_K(ATP) = 14,300 pS, and in D and E, K_GK = 8.0 mM. (F) Slow glucose oscillations synchronize eight heterogeneous and out-of-phase model islets (gray curves). Islet heterogeneity was modeled by different K_GK-values (9.3–10.0 mM in steps of 0.1 mM). Synchronization by glucose gives rise to distinct pulses in the average Ca²⁺ concentration (black, thick curve).

Figure 5

Metabolic entrainment by glucose. (A) Rh123 recordings demonstrate the endogenous oscillations in the mitochondrial membrane potential (ΔΨ_m) in islets exposed to 10 mM glucose, and their 1:2 entrainment in response to subsequent glucose oscillations with 10 min period and 20% amplitude (representative of six islets from one mouse). (B) Representative steady-state ΔΨ_m recording (B_i), and associated spectral (B_ii) and autocorrelation (B_iii) profiles during 1:2 entrainment by a slowly oscillating glucose stimulus (representative of 11 islets from one mouse). (C) Steady-state NAD(P)H recording (C_i) and associated spectral analysis profile of an islet 1:2 entrained by a slowly oscillating glucose stimulus (C_ii; representative of 12 islets from two mice). (D) Comparison of NAD(P)H oscillation periods of islets exposed to constant 10 mM glucose and islets during steady-state recordings in oscillatory glucose with 10 min period and 20% amplitude (p < 0.0001; n=29 islets from five mice and 19 islets from three mice, respectively). (E) Mean NAD(P)H profiles of the islets quantified in panel D (left: constant glucose; right: steady-state oscillatory glucose). Before autocorrelation analysis and averaging, the individual islet recordings were detrended as described in Materials and Methods. Shaded gray bars represent mean ± SE.

Figure 6

Close correlation of islet metabolic and [Ca²⁺]_c entrainment and evidence for 3:7 mode locking. (A) Simultaneous recordings of pancreatic islet NAD(P)H autofluorescence and cytosolic Ca²⁺ during entrainment to a slowly oscillating glucose stimulus reveal that each peak in metabolism coincides with a peak in [Ca²⁺]_c (representative of 13 islets from two mice). This specific recording was chosen to illustrate one of a few islets in which glucose oscillations with 10 min period induced an apparent 3:7 entrainment pattern rather than the predominant 1:2 frequency-locking mode (cf. Figs. 3 and 5). (B) Simulated 3:7 entrainment of model islets to glucose oscillations with period 19.6 min (mean: 10 mM; amplitude: 20%).

Figure 7

Voltage-gated Ca²⁺ influx is required for metabolic entrainment. (A) An oscillating glucose stimulus of 10 min period and 20% amplitude around a 10 mM mean concentration was started after islet hyperpolarization by 250 μM diazoxide. NAD(P)H autofluorescence measurements demonstrate that the normal 1:2 entrainment of islet metabolic oscillations is lost and replaced by an apparent 1:1 profile (representative of n = 16 islets from two mice). A similar change is seen in the NAD(P)H response when diazoxide is added during the entrainment, and is also observed in Rh123-based ΔΨ_m recordings (data not shown). (B) Model simulation reproducing the experiment in panel A. The glucose oscillations (upper panel) were as in Fig. 4. Diazoxide application was simulated by raising the maximal K(ATP) conductance $\overline{g}$_K(ATP) to 30.000 pS during the period indicated by the gray bars.