Full system bifurcation analysis of endocrine bursting models

Al-Baldawi, 1995, Cytoplasmic calcium buffer capacity determined with Nitr-5 and DM-nitrophen, Cell Calcium, 17, 409, 10.1016/0143-4160(95)90087-X Alexander, 1991, On the dynamics of bursting systems, J. Math. Biol., 29, 405, 10.1007/BF00160469 Baer, 1989, The slow passage through a Hopf bifurcation: delay, memory effects, and resonance, SIAM J. Appl. Math., 49, 55, 10.1137/0149003 Barg, 2004, Insulin secretion: a high-affinity Ca2+ sensor after all?, J. Gen. Physiol., 124, 623, 10.1085/jgp.200409206 Beauvois, 2006, Glucose-induced mixed [Ca2+]c oscillations in mouse beta-cells are controlled by the membrane potential and the SERCA3 Ca2+-ATPase of the endoplasmic reticulum, Am. J. Physiol. Cell Physiol., 290, C1503, 10.1152/ajpcell.00400.2005 Belan, 1993, Calcium clamp in isolated neurones of the snail Helix pomatia, J. Physiol., 462, 47, 10.1113/jphysiol.1993.sp019542 Belykh, 2000, Homoclinic bifurcations leading to the emergence of bursting oscillations in cell models, Eur. Phys. J. E, 3, 205, 10.1007/s101890070012 Bergsten, 2002, Role of oscillations in membrane potential, cytoplasmic Ca2+, and metabolism for plasma insulin oscillations, Diabetes, 51, S171, 10.2337/diabetes.51.2007.S171 Berlin, 1994, Intrinsic cytosolic calcium buffering properties of single rat cardiac myocytes, Biophys. J., 67, 1775, 10.1016/S0006-3495(94)80652-6 Bertram, 1995, Topological and phenomenological classification of bursting oscillations, Bull. Math. Biol., 57, 413, 10.1016/S0092-8240(05)81776-8 Bertram, 2000, The phantom burster model for pancreatic beta-cells, Biophys. J., 79, 2880, 10.1016/S0006-3495(00)76525-8 Bertram, 2004, A calcium-based phantom bursting model for pancreatic islets, Bull. Math. Biol., 66, 1313, 10.1016/j.bulm.2003.12.005 Braaksma, 1998, Singular Hopf bifurcation in systems with fast and slow variables, J. Nonlinear Sci., 8, 457, 10.1007/s003329900058 Channell, 2007, Origin of bursting through homoclinic spike adding in a neuron model, Phys. Rev. Lett., 98, 134101, 10.1103/PhysRevLett.98.134101 Chay, 1986, On the effect of the intracellular calcium-sensitive K+ channel in the bursting pancreatic β-cell, Biophys. J., 50, 765, 10.1016/S0006-3495(86)83517-2 Chay, 1983, Minimal model for membrane oscillations in the pancreatic beta-cell, Biophys. J., 42, 181, 10.1016/S0006-3495(83)84384-7 Doedel, E., Champneys, A., Fairgrieve, T., Kuznetsov, Y., Sandstede, B., Wang, X., 1997. AUTO97: continuation and bifurcation software for ordinary differential equations (with HomCont). User's guide, Concordia Univ. Duan, 2008, Two-parameter bifurcation analysis of firing activities in the Chay neuronal model, Neurocomputing, 72, 341, 10.1016/j.neucom.2008.01.019 Ermentrout, B., 2002. Simulating, Analyzing and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students. SIAM. Fierro, 1996, High endogenous calcium buffering in Purkinje cells from rat cerebellar slices, J. Physiol., 496, 617, 10.1113/jphysiol.1996.sp021713 Fleet, 1998, Calcium buffering capacity of neuronal cell cytosol measured by flash photolysis of calcium buffer NP-EGTA, Biochem. Biophys. Res. Commun., 250, 786, 10.1006/bbrc.1998.9377 Goel, 2009, The geometry of bursting in the dual oscillator model of pancreatic β-cells, SIAM J. Appl. Dyn. Syst., 8, 1664, 10.1137/08074427X Goforth, 2002, Calcium-activated K+ channels of mouse beta-cells are controlled by both store and cytoplasmic Ca2+: experimental and theoretical studies, J. Gen. Physiol., 120, 307, 10.1085/jgp.20028581 Golubitsky, 2001, An unfolding theory approach to bursting in fast-slow systems, 277 Guckenheimer, 2008, Singular Hopf bifurcation in systems with two slow variables, SIAM J. Appl. Dyn. Syst., 7, 1355, 10.1137/080718528 Hindmarsh, 1984, A model of neuronal bursting using 3 coupled 1st order differential-equations, Proc. R. Soc. London Ser. B Biol. Sci., 221, 87 Hodgkin, 1952, A quantitative description of membrane current and its application to conduction and excitation in nerve, J. Physiol. London, 117, 500, 10.1113/jphysiol.1952.sp004764 Izhikevich, 2000, Neural excitability, spiking and bursting, Int. J. Bifurcation Chaos, 10, 1171, 10.1142/S0218127400000840 Izhikevich, E.M., 2007. Dynamical systems in neuroscience: the geometry of excitability and bursting. In: Computational Neuroscience, MIT Press, Cambridge, MA. Jonas, 1998, Temporal and quantitative correlations between insulin secretion and stably elevated or oscillatory cytoplasmic Ca2+ in mouse pancreatic β-cells, Diabetes, 47, 1266 LeBeau, 1998, Analysis of a reduced model of corticotroph action potentials, J. Theor. Biol., 192, 319, 10.1006/jtbi.1998.0656 Medvedev, 2005, Reduction of a model of an excitable cell to a one-dimensional map, Phys. D Nonlinear Phenom., 202, 37, 10.1016/j.physd.2005.01.021 Medvedev, 2006, Transition to bursting via deterministic chaos, Phys. Rev. Lett., 97, 10.1103/PhysRevLett.97.048102 Müller, 1993, Calcium buffering in bursting Helix pacemaker neurons, Pflügers Archiv. Eur. J. Physiol., 425, 499, 10.1007/BF00374877 Mosekilde, 2001, Bifurcation structure of a model of bursting pancreatic cells, Biosystems, 63, 3, 10.1016/S0303-2647(01)00142-3 Neher, 1992, Calcium gradients and buffers in bovine chromaffin cells, J. Physiol., 450, 273, 10.1113/jphysiol.1992.sp019127 Pedersen, 2007, Phantom bursting is highly sensitive to noise and unlikely to account for slow bursting in β-cells: considerations in favor of metabolically driven oscillations, J. Theor. Biol., 248, 391, 10.1016/j.jtbi.2007.05.034 Rinzel, J., 1985. Bursting oscillations in an excitable membrane model. In: Lecture Notes in Mathematics, vol. 1151, pp. 304–316. Roussel, 2006, Modulation of neuronal excitability by intracellular calcium buffering: from spiking to bursting, Cell Calcium, 39, 455, 10.1016/j.ceca.2006.01.004 Schwiening, 1996, Relationship between intracellular calcium and its muffling measured by calcium iontophoresis in snail neurones, J. Physiol., 491, 621, 10.1113/jphysiol.1996.sp021244 Shilnikov, 2008, Methods of the qualitative theory for the Hindmarsh–Rose model: a case study. A tutorial, Int. J. Bifurcation Chaos, 18, 2141, 10.1142/S0218127408021634 Stern, 2008, Resetting behavior in a model of bursting in secretory pituitary cells: distinguishing plateaus from pseudo-plateaus, Bull. Math. Biol., 70, 68, 10.1007/s11538-007-9241-x Stocca, 2008, Differential dendritic Ca2+ signalling in young and mature hippocampal granule cells, J. Physiol., 586, 3795, 10.1113/jphysiol.2008.155739 Tabak, 2007, Low dose of dopamine may stimulate prolactin secretion by increasing fast potassium currents, J. Comput. Neurosci., 22, 211, 10.1007/s10827-006-0008-4 Terman, 1991, Chaotic spikes arising from a model of bursting in excitable-membranes, SIAM J. Appl. Math., 51, 1418, 10.1137/0151071 Terman, 1992, The transition from bursting to continuous spiking in excitable membrane models, J. Nonlinear Sci., 2, 135, 10.1007/BF02429854 Tsaneva-Atanasova, 2007, Mechanism of spontaneous and receptor-controlled electrical activity in pituitary somatotrophs: experiments and theory, J. Neurophysiol., 98, 131, 10.1152/jn.00872.2006 Tsaneva-Atanasova, 2006, Diffusion of calcium and metabolites in pancreatic islets: killing oscillations with a pitchfork, Biophys. J., 90, 3434, 10.1529/biophysj.105.078360 Van Goor, 2001, Paradoxical role of large-conductance calcium-activated K+ BK channels in controlling action potential-driven Ca2+ entry in anterior pituitary cells, J. Neurosci., 21, 5902, 10.1523/JNEUROSCI.21-16-05902.2001 Van Goor, 2001, Dependence of pituitary hormone secretion on the pattern of spontaneous voltage-gated calcium influx. Cell type-specific action potential secretion coupling, J. Biol. Chem., 276, 33840, 10.1074/jbc.M105386200 Vincent, 1992, Endocrine cell excitability opens the way to novel pharmacological intervention: example of the anterior pituitary cell, Cell. Biol. Toxicol., 8, 85, 10.1007/BF00130514 Wang, 1993, Genesis of bursting oscillations in the Hindmarsh–Rose model and homoclinicity to a chaotic saddle, Phys. D, 62, 263, 10.1016/0167-2789(93)90286-A Zhang, 2003, The Ca2+ dynamics of isolated mouse beta-cells and islets: implications for mathematical models, Biophys. J., 84, 2852, 10.1016/S0006-3495(03)70014-9 Zhou, 1993, Mobile and immobile calcium buffers in bovine adrenal chromaffin cells, J. Physiol., 469, 245, 10.1113/jphysiol.1993.sp019813