Intrinsic islet heterogeneity and gap junction coupling determine spatiotemporal Ca²⁺ wave dynamics

Abstract

Insulin is released from the islets of Langerhans in discrete pulses that are linked to synchronized oscillations of intracellular free calcium ([Ca(2+)]i). Associated with each synchronized oscillation is a propagating calcium wave mediated by Connexin36 (Cx36) gap junctions. A computational islet model predicted that waves emerge due to heterogeneity in β-cell function throughout the islet. To test this, we applied defined patterns of glucose stimulation across the islet using a microfluidic device and measured how these perturbations affect calcium wave propagation. We further investigated how gap junction coupling regulates spatiotemporal [Ca(2+)]i dynamics in the face of heterogeneous glucose stimulation. Calcium waves were found to originate in regions of the islet having elevated excitability, and this heterogeneity is an intrinsic property of islet β-cells. The extent of [Ca(2+)]i elevation across the islet in the presence of heterogeneity is gap-junction dependent, which reveals a glucose dependence of gap junction coupling. To better describe these observations, we had to modify the computational islet model to consider the electrochemical gradient between neighboring β-cells. These results reveal how the spatiotemporal [Ca(2+)]i dynamics of the islet depend on β-cell heterogeneity and cell-cell coupling, and are important for understanding the regulation of coordinated insulin release across the islet.

Figure 1

The computational islet model predicts that heterogeneity correlates with calcium wave propagation. (A) Representative phase map of the surface of a modeled islet, showing the temporal progression of wave propagation. (B) Map of the metabolic flux (r) at the surface in panel A. ^∗ and † indicate the start and end of a wave, respectively. (C) Representative time courses of [Ca²⁺]_i in cells corresponding to the start (^∗red) and end († blue) of the wave, indicated in A and B, when electrically isolated from the modeled islet. (D) Mean (± SEM) metabolic flux (r) in cells averaged over the start and end of the wave (n = 3–8 cells per region) and over the whole islet. (E) Correlation between the calcium wave velocity and the difference in glucose metabolic flux (Δr) between the start and end of the wave. The solid line indicates a linear fit. Equation 2 describes gap junction coupling. Data in D and E were averaged over 10 modeled islets. ^∗∗∗ indicates significant difference comparing each group indicated (p < 0.001, Student’s t-test). To see this figure in color, go online.

Figure 2

Testing the dependence of calcium wave propagation on islet heterogeneity via a glucose gradient. (A) Schematic of the islet and microfluidic device used. Inset shows Rhodamine B applied to a single channel, indicating no cross-talk. (B) Normalized (norm.) NAD(P)H response, indicating glucose metabolic flux across the islet under each glucose stimulation pattern used. The x axis indicates the estimated glucose. (C) Calcium wave direction with respect to the long axis of the islet, plotted as a function of islet elongation (short axis length/long axis length, where short/long = 1 represents a spherical islet). The solid line delineates islets with a long axis 25% greater than the short axis. (D) Representative time courses of [Ca²⁺]_i at positions indicated in the islet under a glucose gradient (11mM-2mM) and uniform elevated glucose (11mM-11mM). Inset: close-up of a single pulse, indicating the propagation of a calcium wave under each condition. Time courses are offset for clarity; vertical bar indicates a 50% increase in fluorescence. To see this figure in color, go online.

Figure 3

Experimental dependence of calcium wave propagation direction on intrinsic islet heterogeneity and applied heterogeneity. (A) Proportion of calcium waves that propagate with respect to an applied glucose gradient originating from the side at elevated glucose (high to low) or the side at low glucose (low to high), or in an unrelated direction (indeterminate). (B) Proportion of calcium waves under a glucose gradient that propagate with respect to the preferred wave direction at uniform glucose levels, where the gradient is applied toward or against the preferred direction. (C) Proportion of calcium waves under uniform elevated glucose that propagate with respect to a previously applied glucose gradient, as in A. (D) Proportion of calcium waves under uniform elevated glucose that propagate with respect to the preferred wave direction, where a gradient is previously applied toward or against the preferred direction. The dashed line indicates that the direction is solely determined by intrinsic cellular heterogeneity. Data in A and B were averaged over 22 islets. Data in C and D were averaged over 16 islets. ^∗∗∗ indicates significant difference comparing the indicated groups (p < 0.001 Student’s t-test). ns, no significant difference (p > 0.05). To see this figure in color, go online.

Figure 4

Computational model dependence of calcium wave propagation direction on islet heterogeneity. (A) Representative time courses of [Ca²⁺]_i at positions across the modeled islet under a gradient of glucose metabolism (11mM-2mM) and uniform elevated glucose metabolism (11mM-11mM). Inset: close-up of a single pulse, indicating the propagation of a calcium wave under each condition. Time courses are offset for clarity; vertical bar indicates a change of 0.1 μM. (B) Proportion of calcium waves that propagate with respect to an applied glucose metabolism gradient originating from the side at elevated glucose metabolism (high to low) or the side at low glucose metabolism (low to high), or in an unrelated direction (indeterminate). (C) Proportion of calcium waves under a gradient that propagate with respect to the preferred wave direction at uniform glucose metabolism, where the gradient is applied toward or against the preferred direction. (D) Proportion of calcium waves under uniform glucose metabolism that propagate in directions with respect to a previous gradient, as in B. (E) Proportion of calcium waves under uniform glucose metabolism that propagate with respect to the preferred wave direction, where a gradient is previously applied toward or against the preferred direction. The dashed line indicates that the direction is solely determined by intrinsic cellular heterogeneity. Equation 2 describes gap junction coupling. Data in B–E were averaged over 10 modeled islets. ^∗∗∗ indicates significant difference comparing the indicated experimental groups (p < 0.001, Student’s t-test). ns, no significant difference (p > 0.05). To see this figure in color, go online.

Figure 5

Gap junction dependence of [Ca²⁺]_i under a glucose gradient. (A) Representative time courses of [Ca²⁺]_i across a Cx36^−/− islet under a glucose gradient (11mM-2mM) and uniform elevated glucose (11mM-11mM). Time courses are offset for clarity; vertical bar indicates a 50% increase in fluorescence. (B) Mean (± SEM) distance across the islet, with equivalent glucose levels, at which [Ca²⁺]_i oscillations propagate in WT islets and Cx36^−/− islets. (C) Representative islet indicating the extent to which the initial [Ca²⁺]_i elevation (first phase) and the subsequent calcium waves (second phase) propagate. (D) Mean (± SEM) distance across the islet, with equivalent glucose levels, at which each phase of [Ca²⁺]_i elevation propagates. ^∗∗ indicates significant difference comparing each group in B and D as indicated (p < 0.01, Student’s t-test). (E) Coupling conductance as a function of glucose, normalized to the conductance at 2 mM glucose. ^∗ indicates significant elevation (p < 0.05). To see this figure in color, go online.

Figure 6

Modeling the dependence of the [Ca²⁺]_i response on gap junction coupling under a glucose gradient. (A) Map of [Ca²⁺]_i elevation upon a gradient of glucose metabolism, with [Ca²⁺]_i time courses from cells indicated by ^∗. Time courses are offset for clarity; vertical bar indicates a change of 0.1 μM. Excitation bleed-through is circled. (B) Mean [Ca²⁺]_i response across the islet for different levels of gap junction conductance (mean values indicated). (C) Mean [Ca²⁺]_i response as a function of gap junction conductance, at positions across the islet equivalent to the glucose concentrations indicated. (D) Mean [Ca²⁺]_i response as a function of gap junction conductance as in D, for the model accounting for the gap junction electrochemical gradient. (E) Equivalent glucose concentration at which the [Ca²⁺]_i response is 50% of the maximum, as a function of gap junction conductance for the original model (original) and improved model (refined). In C–E, areas in gray correspond to Cx36^−/− and WT gap junction conductance values. A–C and E utilize Eq. 2, and D and E utilize Eq. 5 to describe gap junction coupling. To see this figure in color, go online.