The distal tuft dendrites of pyramidal neurons has been a mystery. Part of the problem is that the apical tuft is so far away and electrically uncoupled to the axon, that it is unclear how synapses here influence the axon. The key is that the dendrites are performing computation and signal the axon via their own regenerative mechanism - dendritic spiking.
The primary mediator of dendritic spiking are Calcium spikes - which are generated by NMDA receptors and Voltage-Gated Calcium Channels (VGCCs).
This paper sets up the primary idea that the different parts of the dendritic tree are acting differently and interacting. The basal tree, which branches in layer 4, is going to be primarily connected with the feed-forward inputs - thalamus, for instance, has axons that branch mainly in L4. The apical tree which branches in L1 and L2/3 is getting inputs from feed-back sources - higher cortical areas.
There is extensive evidence on the role of calcium in long-term synaptic changes. There is a ton of potential in how these calcium spikes in the apical tuft interact with the sodium spikes of action-potentials as well as the calcium spikes generated in the basal tuft. The general idea is that the apical tuft is receiving feed-back signals that are trying to predict the feed-forward signals coming in through the basal tree. If certain synapses do well at predicting the inputs then these synapses will get stronger - this could be signaled by a calcium spike in the apical tuft simultaneous or preceding an action potential.
G and H summarize it best. The apical tuft acts as its own neural network that integrates the feed-back inputs and causes a calcium spike. The basal tuft is a seperate neural network that integrates the feed-forward inputs and causes a sodium spike. These can interact and be used to implement learning rules.
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