  Experiments have shown that the same stimulation pattern that causes
Long-Term Potentiation in proximal synapses, will induce Long-Term Depression
in distal ones. In order to understand these, and other, surprising
observations we use a phenomenological model of Hebbian plasticity at the
location of the synapse. Our computational model describes the Hebbian
condition of joint activity of pre- and post-synaptic neuron in a compact form
as the interaction of the glutamate trace left by a presynaptic spike with the
time course of the postsynaptic voltage. We test the model using experimentally
recorded dendritic voltage traces in hippocampus and neocortex. We find that
the time course of the voltage in the neighborhood of a stimulated synapse is a
reliable predictor of whether a stimulated synapse undergoes potentiation,
depression, or no change. Our model can explain the existence of different --
at first glance seemingly paradoxical -- outcomes of synaptic potentiation and
depression experiments depending on the dendritic location of the synapse and
the frequency or timing of the stimulation.
