Learning in the brain is thought to be accomplished by changes in the connectivity between cells. There is evidence for regulation of the strength of existing synapses, as well as growth and pruning of synaptic contacts. One common learning rule, deemed Hebbian synaptic plasticity, declares that a synaptic connection between two cells will become stronger if the two cells are repeatedly co-activated. The back-propagating action potential, bAP, is thought to convey the necessary feedback to the synapses required for this coincidence detection.

We study the behavior of bAPs by initiating them from the soma, while measuring the degree of activation from many points on the dendrites, using the fluorescent calcium indicator, OGB-1. As expected, we see a wave of calcium fluorescence that extends deep into the dendrites. The amplitudes of the bAP-associated calcium transients exhibit several behaviors which reflect its dependence on the bAP. The calcium transients decrease in amplitude with distance from the soma, and on the dendrites, they also show a decrease in amplitude with successive spikes in a train. Furthermore, it is responsive to the transient K⁺ channel blocker, Ba²⁺. We also see amplification of the bAP evoked calcium signal, which is restricted to the distal dendrites, in response to pairing with presynaptic stimulation. This is consistent with extending the distance of propagation of the bAP.

To analyze these data, I have developed two new strategies for time series analysis of the fluorescent response to a train of action potentials. Furthermore, I have implemented a method for functional data analysis that works for data defined on a branched domain. The end result of this analysis is a smooth functional representation of the degree of activation for all parts of the cell within the field of view of the microscope.

In another experiment, we examine the abstract neuron model called the clusteron, which learns to recognize specific input patterns by structural rearrangement of its synapses. We demonstrate that the model can also learn sequences of input patterns, and perform an exclusive-or operation: two tasks not typically solvable by single neuron models.