Resetting Behavior in a Model of Bursting in Secretory Pituitary Cells: Distinguishing Plateaus from Pseudo-Plateaus
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We study a recently discovered class of models for plateau bursting, inspired by models for endocrine pituitary cells. In contrast to classical models for fold-homoclinic (square-wave) bursting, the spikes of the active phase are not supported by limit cycles of the frozen fast subsystem, but are transient oscillations generated by unstable limit cycles emanating from a subcritical Hopf bifurcation around a stable steady state. Experimental time courses are suggestive of such fold-subHopf models because the spikes tend to be small and variable in amplitude; we call this pseudo-plateau bursting. We show here that distinct properties of the response to attempted resets from the silent phase to the active phase provide a clearer, qualitative criterion for choosing between the two classes of models. The fold-homoclinic class is characterized by induced active phases that increase towards the duration of the unperturbed active phase as resets are delivered later in the silent phase. For the fold-subHopf class of pseudo-plateau bursting, resetting is difficult and succeeds only in limited windows of the silent phase but, paradoxically, can dramatically exceed the native active phase duration.
KeywordsBursting Calcium oscillations Pituitary Stable and unstable manifolds Fast-slow systems
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- Baer, S.M., Rinzel, J., 1988. Threshold for repetitive activity for a slow stimulus ramp: a memory effect and its dependence on fluctuations. Biophys. J. 54(3), 551–555. Google Scholar
- Butera, R. Jr., Rinzel, J., Smith, J.C., 1999. Models of respiratory rhythm generation in the pre-Bötzinger complex. I. Bursting pacemaker neurons. J. Neurophysiol. 82(1), 382–397. Google Scholar
- Chay, T.R., Keizer, J., 1983. Minimal model for membrane oscillations in the pancreatic β-cell. Biophys. J. 42, 181–190. Google Scholar
- Golubitsky, M., Josic, K., Kaper, T.J., 2001. An unfolding theory approach to bursting in fast-slow systems. In: H. Broer, B. Krauskopf, G. Vegter (Eds.), Analysis of Dynamical Systems: Festschrift Dedicated to Floris Takens on the Occasion of his 60th Birthday, pp. 277–308. Institute of Physics, Bristol. Google Scholar
- Rinzel, J., 1987. A formal classification of bursting mechanisms in excitable systems. In: E. Teramoto, M. Yamaguti (Eds.), Mathematical Topics in Population Biology, Morphogenesis, and Neurosciences. Lecture Notes in Biomathematics, vol. 71, pp. 267–281. Springer, New York. Google Scholar
- Sherman, A., Rinzel, J., Keizer, J., 1988. Emergence of organized bursting in clusters of pancreatic β-cells by channel sharing. Biophys. J. 54, 411–425. Google Scholar
- Tabak, J., Senn, W., O’Donovan, M.J., Rinzel, J., 2000. Modeling of spontaneous activity in developing spinal cord using activity-dependent depression in an excitatory network. J. Neurosci. 20(8), 3041–3056. Google Scholar
- Tabak, J., Toporikova, N., Freeman, M.E., Bertram, R., 2007. Low dose of dopamine may stimulate prolactin secretion by increasing fast potassium currents. J. Comput. Neurosci. Epub. Ahead of print DOI 10.1007/s10,827-006-0008-4.
- van Goor, F., Li, Y.X., Stojilkovic, S., 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, 5902–5915. Google Scholar