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On the structure of double layers in Poisson-Boltzmann equation
Gap junctions and excitation patterns in continuum models of islets
1. | Indian Institute of Science Education and Research, Pune, Maharashtra 411021, India |
2. | Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand |
References:
[1] |
Gerda de Vries and Arthur Sherman, Beyond synchronization: Modulatory and emergent effects of coupling in square-wave bursting, in "Bursting: The Genesis of Rhythm in the Nervous System" (eds. Stephen Coombes and Paul C. Bressloff), World Scientific, London, (2005), 243-272. |
[2] |
J.-L. Auriault and H. I. Ene, Macroscopic modelling of heat transfer in composites with interfacial thermal barrier, Int. J. Heat Mass Transfer, 37 (1994), 2885-2892.
doi: 10.1016/0017-9310(94)90342-5. |
[3] |
R. K. Benninger, M. Zhang, W. S. Head, L. S. Satin and D. W. Piston, Gap junction coupling and calcium waves in the pancreatic islet, Biophys. J., 95 (2008), 5048-5061.
doi: 10.1529/biophysj.108.140863. |
[4] |
R. Bertram, L. Satin, M. Zhang, P. Smolen and A. Sherman, Calcium and glycolysis mediate multiple bursting modes in pancreatic islets, Biophys. J., 87 (2004), 3074-3087.
doi: 10.1529/biophysj.104.049262. |
[5] |
F. C. Brunicardi, J. Stagner, S. Bonner-Weir, H. Wayland, R. Kleinman, E. Livingston, P. Guth, M. Menger, R. McCuskey, M. Intaglietta, A. Charles, S. Ashley, A. Cheung, E. Ipp, S. Gilman, T. Howard and E. Passaro, Microcirculation of the islets of Langerhans, Long Beach Veterans Administration Regional Medical Education Center Symposium, Diabetes, 45 (1996), 385-392. |
[6] |
O. Cabrera, D. M. Berman, N. S. Kenyon, C. Ricordi, P. O. Berggren and A. Caicedo, The unique cytoarchitecture of human pancreatic islets has implications for islet cell function, Proc. Natl. Acad. Sci. U.S.A., 103 (2006), 2334-2339.
doi: 10.1073/pnas.0510790103. |
[7] |
B. Ermentrout and K. Bar-Eli, Oscillation death, Scholarpedia, 3 (2008), 5371. |
[8] |
G. B. Ermentrout and D. H. Terman, "Mathematical Foundations of Neuroscience," Interdisciplinary Applied Mathematics, 35, Springer, New York, 2010. |
[9] |
P. Goel and A. Sherman, The geometry of bursting in the dual oscillator model of pancreatic beta-cells, SIAM Journal on Applied Dynamical Systems, 8 (2009), 1664-1693. |
[10] |
P. Goel, A. Sherman and A. Friedman, Multiscale modeling of electrical and intracellular activity in the pancreas: The islet tridomain equations, Multiscale Modeling & Simulation, 7 (2009), 1609-1642. |
[11] |
P. Goel, J. Sneyd and A. Friedman, Homogenization of the cell cytoplasm: The calcium bidomain equations, Multiscale Modeling & Simulation, 5 (2006), 1045-1062. |
[12] |
P. E. Hand, B. E. Griffith and C. S. Peskin, Deriving macroscopic myocardial conductivities by homogenization of microscopic models, Bull. Math. Biol., 71 (2009), 1707-1726.
doi: 10.1007/s11538-009-9421-y. |
[13] |
E. Hertzberg, ed., "Gap Junctions," Advances in Molecular and Cell Biology, Elsevier Science, 2000. |
[14] |
A. Hoffman and J. Mallet-Paret, Universality of crystallographic pinning, Journal of Dynamics and Differential Equations, 22 (2010), 79-119.
doi: 10.1007/s10884-010-9157-2. |
[15] |
H. J. Hupkes, D. Pelinovsky and B. Sandstede, Propagation failure in the discrete nagumo equation, Proceedings of the American Mathematical Society, 139 (2011), 3537-3551.
doi: 10.1090/S0002-9939-2011-10757-3. |
[16] |
T. Kanno, S. O. Gopel, P. Rorsman and M. Wakui, Cellular function in multicellular system for hormone-secretion: Electrophysiological aspect of studies on alpha-, beta- and delta-cells of the pancreatic islet, Neurosci. Res., 42 (2002), 79-90.
doi: 10.1016/S0168-0102(01)00318-2. |
[17] |
J. P. Keener, Propagation and its failure in coupled systems of discrete excitable cells, SIAM Journal on Applied Mathematics, 47 (1987), 556-572.
doi: 10.1137/0147038. |
[18] |
J. P. Keener, Diffusion induced oscillatory insulin secretion, Bull. Math. Biol., 63 (2001), 625-641.
doi: 10.1006/bulm.2001.0235. |
[19] |
W. Krassowska and J. C. Neu, Effective boundary conditions for syncytial tissues, IEEE Trans Biomed Eng, 41 (1994), 143-150.
doi: 10.1109/10.284925. |
[20] |
A. Lazrak and C. Peracchia, Gap junction gating sensitivity to physiological internal calcium regardless of pH in Novikoff hepatoma cells, Biophys. J., 65 (1993), 2002-2012.
doi: 10.1016/S0006-3495(93)81242-6. |
[21] |
L. W. Maki and J. Keizer, Mathematical analysis of a proposed mechanism for oscillatory insulin secretion in perifused HIT-15 cells, Bull. Math. Biol., 57 (1995), 569-591.
doi: 10.1007/BF02460784. |
[22] |
J. C. Neu and W. Krassowska, Homogenization of syncytial tissues, Crit. Rev. Biomed. Eng., 21 (1993), 137-199. |
[23] |
G. P. and S. J., A comparison of effective conductivity in two models of gap junction coupling in tissues,, submitted. |
[24] |
C. Peracchia, Chemical gating of gap junction channels; roles of calcium, pH and calmodulin, Biochim. Biophys. Acta, 1662 (2004), 61-80. |
[25] |
M. Perez-Armendariz, C. Roy, D. C. Spray and M. V. Bennett, Biophysical properties of gap junctions between freshly dispersed pairs of mouse pancreatic beta cells, Biophys. J., 59 (1991), 76-92.
doi: 10.1016/S0006-3495(91)82200-7. |
[26] |
A. Pikovsky, M. Rosenblum and J. Kurths, "Synchronization: A Universal Concept in Nonlinear Sciences," Cambridge Nonlinear Science Series, 12, Cambridge University Press, Cambridge, 2001. |
[27] |
J. Rinzel and G. B. Ermentrout, Analysis of neural excitability and oscillations, "Methods in Neuronal Modeling," MIT Press, Cambridge, MA, USA, (1989), 135-169. |
[28] |
J. V. Rocheleau, G. M. Walker, W. S. Head, O. P. McGuinness and D. W. Piston, Microfluidic glucose stimulation reveals limited coordination of intracellular Ca2+ activity oscillations in pancreatic islets, Proc. Natl. Acad. Sci. U.S.A., 101 (2004), 12899-12903.
doi: 10.1073/pnas.0405149101. |
[29] |
A. Sherman and J. Rinzel, Model for synchronization of pancreatic beta-cells by gap junction coupling, Biophys. J., 59 (1991), 547-559.
doi: 10.1016/S0006-3495(91)82271-8. |
[30] |
C. L. Stokes and J. Rinzel, Diffusion of extracellular K+ can synchronize bursting oscillations in a model islet of Langerhans, Biophys. J., 65 (1993), 597-607.
doi: 10.1016/S0006-3495(93)81092-0. |
[31] |
K. Tsaneva-Atanasova, C. L. Zimliki, R. Bertram and A. Sherman, Diffusion of calcium and metabolites in pancreatic islets: Killing oscillations with a pitchfork, Biophys. J., 90 (2006), 3434-3446.
doi: 10.1529/biophysj.105.078360. |
show all references
References:
[1] |
Gerda de Vries and Arthur Sherman, Beyond synchronization: Modulatory and emergent effects of coupling in square-wave bursting, in "Bursting: The Genesis of Rhythm in the Nervous System" (eds. Stephen Coombes and Paul C. Bressloff), World Scientific, London, (2005), 243-272. |
[2] |
J.-L. Auriault and H. I. Ene, Macroscopic modelling of heat transfer in composites with interfacial thermal barrier, Int. J. Heat Mass Transfer, 37 (1994), 2885-2892.
doi: 10.1016/0017-9310(94)90342-5. |
[3] |
R. K. Benninger, M. Zhang, W. S. Head, L. S. Satin and D. W. Piston, Gap junction coupling and calcium waves in the pancreatic islet, Biophys. J., 95 (2008), 5048-5061.
doi: 10.1529/biophysj.108.140863. |
[4] |
R. Bertram, L. Satin, M. Zhang, P. Smolen and A. Sherman, Calcium and glycolysis mediate multiple bursting modes in pancreatic islets, Biophys. J., 87 (2004), 3074-3087.
doi: 10.1529/biophysj.104.049262. |
[5] |
F. C. Brunicardi, J. Stagner, S. Bonner-Weir, H. Wayland, R. Kleinman, E. Livingston, P. Guth, M. Menger, R. McCuskey, M. Intaglietta, A. Charles, S. Ashley, A. Cheung, E. Ipp, S. Gilman, T. Howard and E. Passaro, Microcirculation of the islets of Langerhans, Long Beach Veterans Administration Regional Medical Education Center Symposium, Diabetes, 45 (1996), 385-392. |
[6] |
O. Cabrera, D. M. Berman, N. S. Kenyon, C. Ricordi, P. O. Berggren and A. Caicedo, The unique cytoarchitecture of human pancreatic islets has implications for islet cell function, Proc. Natl. Acad. Sci. U.S.A., 103 (2006), 2334-2339.
doi: 10.1073/pnas.0510790103. |
[7] |
B. Ermentrout and K. Bar-Eli, Oscillation death, Scholarpedia, 3 (2008), 5371. |
[8] |
G. B. Ermentrout and D. H. Terman, "Mathematical Foundations of Neuroscience," Interdisciplinary Applied Mathematics, 35, Springer, New York, 2010. |
[9] |
P. Goel and A. Sherman, The geometry of bursting in the dual oscillator model of pancreatic beta-cells, SIAM Journal on Applied Dynamical Systems, 8 (2009), 1664-1693. |
[10] |
P. Goel, A. Sherman and A. Friedman, Multiscale modeling of electrical and intracellular activity in the pancreas: The islet tridomain equations, Multiscale Modeling & Simulation, 7 (2009), 1609-1642. |
[11] |
P. Goel, J. Sneyd and A. Friedman, Homogenization of the cell cytoplasm: The calcium bidomain equations, Multiscale Modeling & Simulation, 5 (2006), 1045-1062. |
[12] |
P. E. Hand, B. E. Griffith and C. S. Peskin, Deriving macroscopic myocardial conductivities by homogenization of microscopic models, Bull. Math. Biol., 71 (2009), 1707-1726.
doi: 10.1007/s11538-009-9421-y. |
[13] |
E. Hertzberg, ed., "Gap Junctions," Advances in Molecular and Cell Biology, Elsevier Science, 2000. |
[14] |
A. Hoffman and J. Mallet-Paret, Universality of crystallographic pinning, Journal of Dynamics and Differential Equations, 22 (2010), 79-119.
doi: 10.1007/s10884-010-9157-2. |
[15] |
H. J. Hupkes, D. Pelinovsky and B. Sandstede, Propagation failure in the discrete nagumo equation, Proceedings of the American Mathematical Society, 139 (2011), 3537-3551.
doi: 10.1090/S0002-9939-2011-10757-3. |
[16] |
T. Kanno, S. O. Gopel, P. Rorsman and M. Wakui, Cellular function in multicellular system for hormone-secretion: Electrophysiological aspect of studies on alpha-, beta- and delta-cells of the pancreatic islet, Neurosci. Res., 42 (2002), 79-90.
doi: 10.1016/S0168-0102(01)00318-2. |
[17] |
J. P. Keener, Propagation and its failure in coupled systems of discrete excitable cells, SIAM Journal on Applied Mathematics, 47 (1987), 556-572.
doi: 10.1137/0147038. |
[18] |
J. P. Keener, Diffusion induced oscillatory insulin secretion, Bull. Math. Biol., 63 (2001), 625-641.
doi: 10.1006/bulm.2001.0235. |
[19] |
W. Krassowska and J. C. Neu, Effective boundary conditions for syncytial tissues, IEEE Trans Biomed Eng, 41 (1994), 143-150.
doi: 10.1109/10.284925. |
[20] |
A. Lazrak and C. Peracchia, Gap junction gating sensitivity to physiological internal calcium regardless of pH in Novikoff hepatoma cells, Biophys. J., 65 (1993), 2002-2012.
doi: 10.1016/S0006-3495(93)81242-6. |
[21] |
L. W. Maki and J. Keizer, Mathematical analysis of a proposed mechanism for oscillatory insulin secretion in perifused HIT-15 cells, Bull. Math. Biol., 57 (1995), 569-591.
doi: 10.1007/BF02460784. |
[22] |
J. C. Neu and W. Krassowska, Homogenization of syncytial tissues, Crit. Rev. Biomed. Eng., 21 (1993), 137-199. |
[23] |
G. P. and S. J., A comparison of effective conductivity in two models of gap junction coupling in tissues,, submitted. |
[24] |
C. Peracchia, Chemical gating of gap junction channels; roles of calcium, pH and calmodulin, Biochim. Biophys. Acta, 1662 (2004), 61-80. |
[25] |
M. Perez-Armendariz, C. Roy, D. C. Spray and M. V. Bennett, Biophysical properties of gap junctions between freshly dispersed pairs of mouse pancreatic beta cells, Biophys. J., 59 (1991), 76-92.
doi: 10.1016/S0006-3495(91)82200-7. |
[26] |
A. Pikovsky, M. Rosenblum and J. Kurths, "Synchronization: A Universal Concept in Nonlinear Sciences," Cambridge Nonlinear Science Series, 12, Cambridge University Press, Cambridge, 2001. |
[27] |
J. Rinzel and G. B. Ermentrout, Analysis of neural excitability and oscillations, "Methods in Neuronal Modeling," MIT Press, Cambridge, MA, USA, (1989), 135-169. |
[28] |
J. V. Rocheleau, G. M. Walker, W. S. Head, O. P. McGuinness and D. W. Piston, Microfluidic glucose stimulation reveals limited coordination of intracellular Ca2+ activity oscillations in pancreatic islets, Proc. Natl. Acad. Sci. U.S.A., 101 (2004), 12899-12903.
doi: 10.1073/pnas.0405149101. |
[29] |
A. Sherman and J. Rinzel, Model for synchronization of pancreatic beta-cells by gap junction coupling, Biophys. J., 59 (1991), 547-559.
doi: 10.1016/S0006-3495(91)82271-8. |
[30] |
C. L. Stokes and J. Rinzel, Diffusion of extracellular K+ can synchronize bursting oscillations in a model islet of Langerhans, Biophys. J., 65 (1993), 597-607.
doi: 10.1016/S0006-3495(93)81092-0. |
[31] |
K. Tsaneva-Atanasova, C. L. Zimliki, R. Bertram and A. Sherman, Diffusion of calcium and metabolites in pancreatic islets: Killing oscillations with a pitchfork, Biophys. J., 90 (2006), 3434-3446.
doi: 10.1529/biophysj.105.078360. |
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