Once the NMDA receptor allows for there to be a large amount of Calcium influx into the cell, a protein cascade is triggered that potentiates the synapse. It is thought that there are two calcium thresholds - the upper threshold is for potentiation (the synapse gets stronger), but STDP has both potentiation and depression. There is a lower calcium threshold that triggers depression - this happens when the NMDA receptor doesn't quite flux enough calcium and other calcium channels (i.e. VGCCs) let in a small amount - if the post-synaptic AP is before the pre-synaptic AP then a slight amount of Ca gets through triggering the depression cascade.
The calcium spikes triggered ala Larkum would then be signals for potentiation. An actual Calcium spike would be much more robust as a learning signal for LTP than just a threshold. A calcium spike would be consistent and also would send a signal forward to the rest of the neuron. This would be a much more reliable situation for implementing STDP. Plus the calcium spike would more reliably trigger action-potentials.
An extra possibility of the Calcium spike is that it could be communicated to the next neuron. In cortex it is known that neurons can get in a bursting mode. It is thought that these bursts are action-potentials that are riding on-top of a calcium spike (calcium-spikes are typically longer in duration than action-potentials). What's also interesting is that bursting can influence synaptic release - a burst is typically a much more reliable signal for synaptic release than a single action-potential. It may be possible that this burst could signal to the next neuron that some learning was happening - possibly as a back-propagation signal.
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