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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.

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The general structure of gap junctions23. Within a gap junction, there are a few to many thousands channels of diameter 1.5 nm. The length of the cell gap is about 2∼4 nm. The thickness of the cell membrane is about 5 nm. Thus, the length of the gap junctions d is nearly 13 nm. The channels allow inorganic ions and molecules with a mass of less than 1 kDa to pass into the other cell.
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f3-6_37: The general structure of gap junctions23. Within a gap junction, there are a few to many thousands channels of diameter 1.5 nm. The length of the cell gap is about 2∼4 nm. The thickness of the cell membrane is about 5 nm. Thus, the length of the gap junctions d is nearly 13 nm. The channels allow inorganic ions and molecules with a mass of less than 1 kDa to pass into the other cell.

Mentions: We generalize the single β-cell model proposed by Pedersen et al to a multicellular system as follows. Our equation for the membrane potential (v) of the i-th β-cell is given by(1)Cmdvidt+IK(v)(i)+ICa(v)(i)+IK(Ca)(i)+IK(ATP)(i)=IG(i),where Cm is the membrane capacitance, is the v-dependent K+ current, is the v-dependent Ca2+ current, is the calcium-activated K+ current, is the ATP-sensitive K+ current, and is the gap current. Figure 3 shows the general structure of gap junctions. We also assume that the flow of ions through gap junctions is driven not only by the electric field but also by the concentration gradient. Thus, we obtain the Nernst-Planck equation for the flow of ions21(2)JG(A)=−SGDA(dcAdx+ZAFcARTdϕdx),where ϕ is the electrical potential, cA is the concentration of type A ions, F is Faraday’s constant, z is the valence of ions, DA is the diffusion constant of type A ions, SG is the cross-sectional area of the gap junction, and RT is the gas constant multiplied by the absolute temperature. Then, the gap current IG isIG=∑AzAFJG(A).We also use , where rC ≅ 0.75 nm is the radius of a single channel and NC is number of channels in a gap junction. It is known that NC is a few to many thousands23. When the length of the gap junctions is d (see Fig. 3b), the potential difference in the gap junction can be approximated (Goldman, Hogkin, and Katz21) asdϕdx≅(ϕ(i)−ϕ(j))d=vi−vjd.Next, we obtain the following current equation of type A ions for the gap junctions(3)IG(A)i←j=     −DAdzA2F2RTSG(vi−vj)cA(i)−cA(j)exp [−zAF(vi−vj)[RT]1−exp [−zAF(vi−vj)[RT](4)=−uAdzAFSG(vi−vj)cA(i)−cA(j) exp [−zAF(vi−vj)[RT]1−exp [−zAF(vi−vj)[RT],where the Einstein relation between the diffusion coeffcient DA and the ionic mobility uA, namely DA = uART/zAF is used. Thus, the gap current becomes(5)IG(i)=∑j,AIG(A)i←j,where j is the nearest-neighbor cell of cell i.


Modeling of the gap junction of pancreatic β -cells and the robustness of insulin secretion
The general structure of gap junctions23. Within a gap junction, there are a few to many thousands channels of diameter 1.5 nm. The length of the cell gap is about 2∼4 nm. The thickness of the cell membrane is about 5 nm. Thus, the length of the gap junctions d is nearly 13 nm. The channels allow inorganic ions and molecules with a mass of less than 1 kDa to pass into the other cell.
© Copyright Policy
Related In: Results  -  Collection

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

f3-6_37: The general structure of gap junctions23. Within a gap junction, there are a few to many thousands channels of diameter 1.5 nm. The length of the cell gap is about 2∼4 nm. The thickness of the cell membrane is about 5 nm. Thus, the length of the gap junctions d is nearly 13 nm. The channels allow inorganic ions and molecules with a mass of less than 1 kDa to pass into the other cell.
Mentions: We generalize the single β-cell model proposed by Pedersen et al to a multicellular system as follows. Our equation for the membrane potential (v) of the i-th β-cell is given by(1)Cmdvidt+IK(v)(i)+ICa(v)(i)+IK(Ca)(i)+IK(ATP)(i)=IG(i),where Cm is the membrane capacitance, is the v-dependent K+ current, is the v-dependent Ca2+ current, is the calcium-activated K+ current, is the ATP-sensitive K+ current, and is the gap current. Figure 3 shows the general structure of gap junctions. We also assume that the flow of ions through gap junctions is driven not only by the electric field but also by the concentration gradient. Thus, we obtain the Nernst-Planck equation for the flow of ions21(2)JG(A)=−SGDA(dcAdx+ZAFcARTdϕdx),where ϕ is the electrical potential, cA is the concentration of type A ions, F is Faraday’s constant, z is the valence of ions, DA is the diffusion constant of type A ions, SG is the cross-sectional area of the gap junction, and RT is the gas constant multiplied by the absolute temperature. Then, the gap current IG isIG=∑AzAFJG(A).We also use , where rC ≅ 0.75 nm is the radius of a single channel and NC is number of channels in a gap junction. It is known that NC is a few to many thousands23. When the length of the gap junctions is d (see Fig. 3b), the potential difference in the gap junction can be approximated (Goldman, Hogkin, and Katz21) asdϕdx≅(ϕ(i)−ϕ(j))d=vi−vjd.Next, we obtain the following current equation of type A ions for the gap junctions(3)IG(A)i←j=     −DAdzA2F2RTSG(vi−vj)cA(i)−cA(j)exp [−zAF(vi−vj)[RT]1−exp [−zAF(vi−vj)[RT](4)=−uAdzAFSG(vi−vj)cA(i)−cA(j) exp [−zAF(vi−vj)[RT]1−exp [−zAF(vi−vj)[RT],where the Einstein relation between the diffusion coeffcient DA and the ionic mobility uA, namely DA = uART/zAF is used. Thus, the gap current becomes(5)IG(i)=∑j,AIG(A)i←j,where j is the nearest-neighbor cell of cell i.

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.