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The Effects of Dendritic Properties on the Dynamics of Oscillatory Neurons

Mathematical Biology

Speaker: Mike Schwemmer, UC Davis Math
Location: 2112 MSB
Start time: Mon, Feb 8 2010, 3:10PM

Neurons can have extensive spatial geometries, but they are often modeled as single-compartment objects that ignore the spatial anatomy of the cell. This simplification is made for mathematical tractability and computational efficiency. However, many neurons are not electrotonically compact, and single-compartment models cannot be expected to fully capture their behavior. Dendritic properties can have substantial effects on the dynamics of single neurons, as well as the activity in neuronal networks.

We study the influences of thin and general diameter passive dendrites on the dynamics of single neuronal oscillators. For sufficiently thin dendrites and general somatic dynamics, we elucidate the mechanisms by which dendrites modulate the firing frequency of neurons. We find that the average value of the somatic oscillator's phase response curve indicates whether or not the dendrite will cause an increase or decrease in firing frequency. For general diameter dendrites and idealized somatic dynamics, we find that the neuron displays bistable behavior between periodic firing and quiescence. In this case, the dendritic properties cause the cell to behave like a neuronal switch. Furthermore, we identify the mechanism that causes this bistability to occur. This mechanism was previously only described in models that contain active dendritic conductances.