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NJIT Mathematical Biology Seminar

Tuesday, October 10, 2006, 4:00pm
Cullimore Hall 611
New Jersey Institute of Technology

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Canard induced mixed-mode oscillations in a medial entorhinal cortex layer II stellate cell model: Work in progress

Horacio Rotstein

Department of Mathematical Sciences
NJIT

This talk concerns the mechanism of creation of rhythmic (8 - 12 Hz) mixed-mode oscillations (MMOs) in a biophysical medial entorhinal cortex (MEC) layer II stellate cell (SCs) model. MMO patterns consist of alternating subthreshold oscillations (STOs) and spikes, in different ratios. SC models are tipically highly nonlinear (seven-dimensional) and involve multiple scales. The model we use can be reduced to a three-dimensional model describing the dynamics of the voltage (V) and the two (fast and slow) h-current gating variables (rf and rs). This reduced model has a clear time scale separation (between V and the other variables, and in some cases also between rf and rs) and it is a valid approximation of the original model in the subthreshold regime (SthR) where STOs and the onset of spikes occur. MMOs are the result of the interaction between some of the nonlinearities and the time scale separation of the model. We refer to the geometric/dynamic structure (nonlinear slow manifold and time scale separation) underlying the generation of MMOs as the canard structure. Canard structures have the potential of producing the canard phenomenon (a sudden transition between small and large amplitude oscillations). We show that the the three main components in the mechanism of generation of MMOs we are studying are (1) the creation of STOs, (2) the return mechanism to the SthR after the spike, and (3) the reset properties of the h-current (and consequently of rf and rs). To understand the role of the canard structure in (1), (2) and (3) we propose a three-dimensional toy model. This toy model is easier to analyze and it encodes the basic aspects of the reduced SC model. These are the essential (not all) nonlinearities and time scales. We show, via mathematical manipulation, that the toy model is a close description of the reduced SC model. We also show how (1), (2) and (3) interact to produced different types of complex oscillatory patterns.