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Modeling of the gap junction of pancreatic β -cells and the robustness of insulin secretion

View Article: PubMed Central - PubMed

ABSTRACT

Pancreatic β-cells are interconnected by gap junctions, which allow small molecules to pass from cell to cell. In spite of the importance of the gap junctions in cellular communication, modeling studies have been limited by the complexity of the system. Here, we propose a mathematical gap junction model that properly takes into account biological functions, and apply this model to the study of the β-cell cluster. We consider both electrical and metabolic features of the system. Then, we find that when a fraction of the ATP-sensitive K+ channels are damaged, robust insulin secretion can only be achieved by gap junctions. Our finding is consistent with recent experiments conducted by Rocheleau et al. Our study also suggests that the free passage of potassium ions through gap junctions plays an important role in achieving metabolic synchronization between β-cells.

No MeSH data available.


Synchronization is achieved immediately when both potassium ions and calcium ions are allowed to pass through gap junctions between two β-cells (a), but is not achieved when only calcium ions are allowed to pass through gap junctions (b). Here, ḡCa =1000 pS, and ḡK(ATP) =40000 pS, and the extracellular glucose concentration is 7 mM. The solid line and dotted line indicate different β-cells.
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f4-6_37: Synchronization is achieved immediately when both potassium ions and calcium ions are allowed to pass through gap junctions between two β-cells (a), but is not achieved when only calcium ions are allowed to pass through gap junctions (b). Here, ḡCa =1000 pS, and ḡK(ATP) =40000 pS, and the extracellular glucose concentration is 7 mM. The solid line and dotted line indicate different β-cells.

Mentions: To clarify the role of gap junctions in the cellular processes, we have conducted extensive numerical investigations. From many numerical experiments, first, we show the result for the two β-cell system in Fig. 4, where we adopt ionic mobilities in water at 298 K24, namely, uK = 7.62×10−8 m2s−1V−1, uCa = 6.17 × 10−8 m2s−1V−1 as an approximation since specific values for the ionic mobilities in the β-cells are not currently available to our knowledge. In Fig. 4(a), both K+ ions and Ca2+ ions are allowed to pass through gap junctions. In this case, synchronization is achieved immediately although very different initial parameter values are adopted for the different cells. On the other hand, in Fig. 4(b), only Ca2+ ions are allowed to pass through gap junctions. It is clear that without free flow of K+ ions through the gap junction, synchronization cannot be achieved. The result is reasonable since the K+ ion concentration is much higher than the Ca2+ ion concentration within cells. Although we have also tested the case when only K+ ions are allowed to pass through gap junctions, we do not show it here because the obtained figure is nearly identical to Fig. 4(a). For our next example, we show the result for the 100 β-cell system in Fig. 5, where the 10×10 square lattice with the periodic boundary condition is used. Once again, we observed synchronous bursting. We do not provide any figure of channel number dependence because no qualitative change was observed when Nc is changed from 1 to 100.


Modeling of the gap junction of pancreatic β -cells and the robustness of insulin secretion
Synchronization is achieved immediately when both potassium ions and calcium ions are allowed to pass through gap junctions between two β-cells (a), but is not achieved when only calcium ions are allowed to pass through gap junctions (b). Here, ḡCa =1000 pS, and ḡK(ATP) =40000 pS, and the extracellular glucose concentration is 7 mM. The solid line and dotted line indicate different β-cells.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC5036665&req=5

f4-6_37: Synchronization is achieved immediately when both potassium ions and calcium ions are allowed to pass through gap junctions between two β-cells (a), but is not achieved when only calcium ions are allowed to pass through gap junctions (b). Here, ḡCa =1000 pS, and ḡK(ATP) =40000 pS, and the extracellular glucose concentration is 7 mM. The solid line and dotted line indicate different β-cells.
Mentions: To clarify the role of gap junctions in the cellular processes, we have conducted extensive numerical investigations. From many numerical experiments, first, we show the result for the two β-cell system in Fig. 4, where we adopt ionic mobilities in water at 298 K24, namely, uK = 7.62×10−8 m2s−1V−1, uCa = 6.17 × 10−8 m2s−1V−1 as an approximation since specific values for the ionic mobilities in the β-cells are not currently available to our knowledge. In Fig. 4(a), both K+ ions and Ca2+ ions are allowed to pass through gap junctions. In this case, synchronization is achieved immediately although very different initial parameter values are adopted for the different cells. On the other hand, in Fig. 4(b), only Ca2+ ions are allowed to pass through gap junctions. It is clear that without free flow of K+ ions through the gap junction, synchronization cannot be achieved. The result is reasonable since the K+ ion concentration is much higher than the Ca2+ ion concentration within cells. Although we have also tested the case when only K+ ions are allowed to pass through gap junctions, we do not show it here because the obtained figure is nearly identical to Fig. 4(a). For our next example, we show the result for the 100 β-cell system in Fig. 5, where the 10×10 square lattice with the periodic boundary condition is used. Once again, we observed synchronous bursting. We do not provide any figure of channel number dependence because no qualitative change was observed when Nc is changed from 1 to 100.

View Article: PubMed Central - PubMed

ABSTRACT

Pancreatic β-cells are interconnected by gap junctions, which allow small molecules to pass from cell to cell. In spite of the importance of the gap junctions in cellular communication, modeling studies have been limited by the complexity of the system. Here, we propose a mathematical gap junction model that properly takes into account biological functions, and apply this model to the study of the β-cell cluster. We consider both electrical and metabolic features of the system. Then, we find that when a fraction of the ATP-sensitive K+ channels are damaged, robust insulin secretion can only be achieved by gap junctions. Our finding is consistent with recent experiments conducted by Rocheleau et al. Our study also suggests that the free passage of potassium ions through gap junctions plays an important role in achieving metabolic synchronization between β-cells.

No MeSH data available.