September  2011, 16(2): 569-588. doi: 10.3934/dcdsb.2011.16.569

A reliability study of square wave bursting $\beta$-cells with noise

1. 

Department of Dynamics and Control, Beihang University, Beijing, 100191, China

2. 

Department of Mathematics, The University of Texas at Arlington, Arlington, TX 76019, United States, United States

3. 

Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, United States

Received  May 2010 Revised  December 2010 Published  June 2011

Reliability of spike timing has been a hot topic recently. However reliability has not been considered for bursting behavior, as commonly observed in a variety of nerve and endocrine cells, including $\beta$-cells in intact pancreatic islets. In this paper, reliability of $\beta$-cells with noise is considered. A method to numerically study reliability of bursting cells is presented. Reliability of a single cell will decrease as noise level becomes larger. The reliability of networks of $\beta$-cells coupled by gap junctions or synaptic excitation is investigated. Simulations of the network of $\beta$-cells reveal that increasing noise level decreases the reliability. But the reliability of the network is higher than that of single cell. The effect of coupling strength on reliability is also investigated. Reliability will decrease when coupling strength is small and increase when coupling strength is large.
Citation: Jiaoyan Wang, Jianzhong Su, Humberto Perez Gonzalez, Jonathan Rubin. A reliability study of square wave bursting $\beta$-cells with noise. Discrete & Continuous Dynamical Systems - B, 2011, 16 (2) : 569-588. doi: 10.3934/dcdsb.2011.16.569
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show all references

References:
[1]

Diabetes, 47 (1998), 1266-1273. doi: 10.2337/diabetes.47.8.1266.  Google Scholar

[2]

J. Physiol., 374 (1986), 531-550. Google Scholar

[3]

J. Physiol., 210 (1970), 255-264. Google Scholar

[4]

Diabetologia., 21 (1981), 470-475. doi: 10.1007/BF00257788.  Google Scholar

[5]

Prog. Biophys. Mol. Biol., 54 (1989), 87-143. doi: 10.1016/0079-6107(89)90013-8.  Google Scholar

[6]

Discrete and Continuous Dynamical Systems-Series B, 14 (2010), 495-513. doi: 10.3934/dcdsb.2010.14.495.  Google Scholar

[7]

J. Theor. Biol., 207 (2000), 513-530. doi: 10.1006/jtbi.2000.2193.  Google Scholar

[8]

Phys. D, 137 (2000), 333-352. doi: 10.1016/S0167-2789(99)00191-8.  Google Scholar

[9]

Rev. Mod. Phys., 70 (1998), 223-287. doi: 10.1103/RevModPhys.70.223.  Google Scholar

[10]

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[11]

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[12]

Nature, 441 (2006), 840-846. doi: 10.1038/nature04785.  Google Scholar

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Nat Genet, 31 (2002), 69-73. doi: 10.1038/ng869.  Google Scholar

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Science, 315 (2007), 1716-1719. doi: 10.1126/science.1137455.  Google Scholar

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Cell Calcium, 4 (1983), 451-461. doi: 10.1016/0143-4160(83)90021-0.  Google Scholar

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Biophys. J., 54 (1988), 427-435. doi: 10.1016/S0006-3495(88)82976-X.  Google Scholar

[18]

Biophys. J., 54 (1988), 411-425. doi: 10.1016/S0006-3495(88)82975-8.  Google Scholar

[19]

SIAM J. Appl. Math., 67 (2007), 530-542. doi: 10.1137/060655663.  Google Scholar

[20]

Nonlinearity, 17 (2004), 133-157. doi: 10.1088/0951-7715/17/1/009.  Google Scholar

[21]

Science, 268 (1995), 1503-1506. doi: 10.1126/science.7770778.  Google Scholar

[22]

J. Neurophysiol, 98 (2007), 2647-2663. doi: 10.1152/jn.00900.2006.  Google Scholar

[23]

Neurocomputing, 52-54 (2003), 925-931. doi: 10.1016/S0925-2312(02)00838-X.  Google Scholar

[24]

PNAS, 104 (2007), 8137-8142. doi: 10.1073/pnas.0702799104.  Google Scholar

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[34]

Phys. Rev. E, 54 (1996), 5585-5590. doi: 10.1103/PhysRevE.54.5585.  Google Scholar

[35]

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Phys. D, 63 (1993), 321-340. doi: 10.1016/0167-2789(93)90114-G.  Google Scholar

[38]

Carlo Laing and Gabriel Lord (eds.), Oxford University Press, 2009.  Google Scholar

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