Two important aspects were missing in the model from the last post:
- Self-inhibition should always be present.
- The magnitude/release probability of self-inhibition should increase when the parent granule cell is excited.
In this post we’ll update the model to incorporate these effects.
The approach will be to assume that the baseline self-inhibition that an MC receives upon spiking, $\delta$, can increase to $\Delta > \delta$ if its granule cell was recently activated.
The phase plane for such a model is simple. The resets are purely horizontal and vertical. Synchronization will occur if the periods of the two oscillators are the same. The total voltage unit 1 has to increase by to reach threshold is $1 + \delta_1 + \Delta_1$, and similarly for unit 2.
Therefore, equating periods, our synchrony condition is $$\underbrace{{1 + \delta_1 + \Delta_1 \over I_1}}_{T_1} = \underbrace{{1 + \delta_2 + \Delta_2 \over I_2}}_{T_2}.$$
It’s interesting to note that if the magnitude of the inhibition was proportional to the current drive into each cell, then the two periods would be approximately the same.
It’s clear that synchrony requires inhibition to be set appropriately. Can that be learned, perhaps during an initial burst of activity in response to the odour?
$$\blacksquare$$
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