Slow Variable Dominance and Phase Resetting in Phantom Bursting

Margaret Watts, Joel Tabak, Charles Zimliki, Arthur Sherman, Richard Bertram

Bursting oscillations are common in neurons and endocrine cells. One type of bursting model with two slow variables has been called `phantom bursting' since the burst period is a blend of the time constants of the slow variables. A phant om bursting model can produce bursting with a wide range of periods: fast (short period), medium, and slow (long period). We describe a measure, which we call th e `dominance factor', of the relative contributions of the two slow variables to t he bursting produced by a simple phantom bursting model. Using this tool, we demonstrate how the control of different phases of the burst can be shifted from one slow variable to another by changing a model parameter. We then show that the dominance curves obtained as a parameter is varied can be useful in making predictions about the resetting properties of the model cells. Finally, we demonstrate two mechanisms by which phase-independent resetting of a burst can be achieved, as has been shown to occur in the electrical activity of pancreatic islets.