.Low Amplitude Oscillations in the Inferior Olive: A model based on electrical coupling of neurons with heterogeneous channel densities} Yair Manor and John Rinzel and Idan Segev and Yosef Yarom. Hebrew University, Neurobiology Dept., Jerusalem 91904, ISRAEL; Mathematical Research Branch, NIDDK, National Institutes of Health, 9190 Wisconsin Ave., Suite 350, Bethesda, MD 20814, Volen Center for Complex Systems, Brandeis Univ., 415 South St., Waltham 02254, MA.
APStracts 4:0016N, 1997.
ABSTRACT
The mechanism underlying subthreshold oscillations in inferior olivary cells is not known. To study this question, we developed a single-compartment, two- variable, Hodgkin-Huxley-like model for inferior olive neurons. The model consists of a leakage current and a low-threshold calcium current, whose kinetics were experimentally measured in slices. Depending on the maximal calcium and leak conductances we found that a neuron model's response to current injection could be of four qualitatively different types: always stable, spontaneously oscillating, oscillating with injection of current, and bistable with injection of current. By using phase plane techniques, numerical integration and bifurcation analysis, we subdivided the two-parameter space of channel densities into four regions corresponding to these behavioral types. We further developed, using such techniques, an empirical rule-of-thumb that characterizes whether two cells when coupled electrically can generate sustained, synchronized oscillations like those observed in inferior olivary cells in slices, of low amplitude (0.1-10 mV) in the frequency range 4-10 Hz. We found that it is not necessary that either cell is a spontaneous oscillator in order to obtain a sustained oscillation. On the other hand, two spontaneous oscillators always form an oscillating network, when electrically coupled with any arbitrary coupling conductance. In the case of an oscillating pair of electrically coupled non-identical cells, the coupling current varies periodically and is non-zero even for very large coupling values. The coupling current acts as an equalizing current to reconcile the differences between the two cells' ionic currents. It transiently depolarizes one cell and/or hyperpolarizes the other cell to obtain the regenerative response(s) required for the synchronized oscillation. We suggest that the subthreshold oscillations observed in the inferior olive can emerge from the electrical coupling between neurons with different channel densities, even if the inferior olive nucleus contains no or just a small proportion of spontaneously oscillating neurons. 

Received 19 April 1996; accepted in final form 2 January 1996.
APS Manuscript Number J330-6.
Article publication pending J. Neurophysiol.
ISSN 1080-4757 Copyright 1997 The American Physiological Society.
Published in APStracts on 24 January 1997