Gap junction coupling and calcium waves in the pancreatic islet

Abstract

The pancreatic islet is a highly coupled, multicellular system that exhibits complex spatiotemporal electrical activity in response to elevated glucose levels. The emergent properties of islets, which differ from those arising in isolated islet cells, are believed to arise in part by gap junctional coupling, but the mechanisms through which this coupling occurs are poorly understood. To uncover these mechanisms, we have used both high-speed imaging and theoretical modeling of the electrical activity in pancreatic islets under a reduction in the gap junction mediated electrical coupling. Utilizing islets from a gap junction protein connexin 36 knockout mouse model together with chemical inhibitors, we can modulate the electrical coupling in the islet in a precise manner and quantify this modulation by electrophysiology measurements. We find that after a reduction in electrical coupling, calcium waves are slowed as well as disrupted, and the number of cells showing synchronous calcium oscillations is reduced. This behavior can be reproduced by computational modeling of a heterogeneous population of beta-cells with heterogeneous levels of electrical coupling. The resulting quantitative agreement between the data and analytical models of islet connectivity, using only a single free parameter, reveals the mechanistic underpinnings of the multicellular behavior of the islet.

FIGURE 1

Calcium wave velocity and islet [Ca²⁺]_i oscillation synchronization. (A) Fluorescence intensity image of a Fluo-4 stained islet in a microfluidic flow device. Scale bar represents 100 μm. (B) Time course of the Fluo-4 intensity in the-two-islet cells highlighted in A. Oscillations of cell 1 (black line) precede those of cell 2 (red line) by the propagation time of the calcium wave from cell 1 to cell 2 (indicated by dumbbell line). (C) False color scale phase map representing the propagation of the calcium wave across the islet from regions colored in red (early [Ca²⁺]_i increase) to regions colored in blue/purple (later [Ca²⁺]_i increase). (D) Example cross correlation trace of cell 1 and cell 2 with the whole islet oscillations. Difference in time between the peaks of the cross correlation represents the wave propagation time between the two cells, which is mapped in C. The peak cross correlation coefficients represent the degree of correlation with the average islet oscillations, which is high for both cells.

FIGURE 2

Summary of measured wave velocities. (A) Histogram of measured calcium wave velocities. The mean velocity is 69 ± 5 μm/s, which is many times faster than would be seen by simple diffusion of calcium across the islet. (B) The mean velocity calculated for different size ranges of islets studied. There is a trend for the wave velocity to decrease with increasing islet size, as expected if v ≈ √g ≈ 1/√l.

FIGURE 3

Chemical inhibitors of gap junction activity slow the calcium wave velocity. (A) Phase map of the calcium wave propagation across the islet before (left) and after (right) the application of 50 μM αGA. Dashed white lines indicated the direction of propagation from yellow/red regions to blue/purple regions. The phase difference of the oscillations increases after partial gap junction inhibition with αGA, representing a decrease in wave velocity. Scale bar represents 100 μm. (B) Decrease in the mean calcium wave velocity with increasing concentration of αGA. Error bars represent mean ± SE.

FIGURE 4

Genetic knockout of gap junctions disrupts wave propagation and islet oscillation synchronization. (A) Phase map of [Ca²⁺]_i oscillations in an islet of the heterozygous Cx36+/− knockout mouse used in B. No wave propagation is visible from examination of the individual phases of the β-cells; however, there are still synchronous phase-locked oscillations in a proportion of the islet cells as highlighted. (B) Representative oscillations of [Ca²⁺]_i in four cells of the Cx36+/− islet shown in A. Traces correspond to areas of the islet that are synchronized (blue, red) and unsynchronized (green, yellow). (C) Phase map of [Ca²⁺]_i oscillations in an islet of the heterozygous Cx36−/− knockout mouse used in D. Cells are not synchronized with the oscillations of any other cell. (D) Representative oscillations of [Ca²⁺]_i in four cells of the Cx36−/− islet shown in C. Oscillations are on a wide range of timescales from ∼1 s to ∼2 min. (E) Decrease in the proportion of cells in the islet that undergo synchronous oscillations. The decrease in islet synchronization is greater for the Cx36 gap junction knockout islets than the αGA treated islets. (F) The decrease in the wave velocity is greater for the Cx36 gap junction knockout islets (* when propagating calcium waves are still observed) than the αGA treated islets. Scale bars in A and C represent 100 μm.

FIGURE 5

Computational modeling of coupled β-cell electrical activity. (A) A heterogeneous population of β-cells' [Ca²⁺]_i oscillations are seen when β-cells are not electrically coupled, similar to that seen in islets from Cx36−/− mice. (B) Phase map showing that in the absence of gap junction coupling, oscillations in individual cells are not synchronized. (C) Gap junction electrical coupling produces synchronized oscillations on an intermediate timescale to the oscillations produced in the uncoupled islet, as is also observed in islets from Cx36+/+ (WT) mice. (D) With gap junction coupling, calcium waves are observed associated with the oscillatory increases in [Ca²⁺]_i. The wave propagates from the top right to bottom left of the islet and crosses the 10 × 10 × 10 islet in ∼1 s. (E) A single [Ca²⁺]_i oscillation in D at the start (red), middle (green), and end (purple) of the wave showing the temporal offset of the oscillation at different points in the islet. (F) Reducing the mean coupling conductance by ∼50% disrupts wave propagation and reduces islet synchrony, as is also observed in islets from a proportion of the heterozygous Cx36+/− mice.

FIGURE 6

Dependence of [Ca²⁺]_i wave velocity and oscillation synchronization with gap junction conductance. (A) The measured decrease in coupling conductance (g_coup) for each treatment used to modify gap junction coupling. The decrease in coupling conductance in Cx36+/− (46%) is much more than that seen after αGA treatment (maximum 22%). (B) A two-dimensional schematic representation of the three-dimensional lattice resistor model used for the percolating model of islet β-cell electrical connectivity. Resistors represent electrical coupling between β-cells. Missing resistors represent missing connections due to vasculature or other endothelial cell types. Blockage or removal of gap junctions is represented by a reduction in the number of resistor connections. (C) Experimental data of calcium wave propagation, displaying the normalized change in wave velocity with the normalized mean coupling conductance in the islet. Solid line is theoretical and represents the percolating (discrete) model of islet connectivity; dashed line represents the ohmic (continuous) model of islet connectivity. The experimental data have better agreement with the percolation model than with the ohmic model. (D) Percolation model, ohmic model, and data of proportion of islet cells synchronized. The experimental data have good agreement with the percolation model and poor agreement with the ohmic model.