  In this paper, we present data for the lognormal distributions of spike
rates, synaptic weights and intrinsic excitability (gain) for neurons in
various brain areas, such as auditory or visual cortex, hippocampus,
cerebellum, striatum, midbrain nuclei. We find a remarkable consistency of
heavy-tailed, specifically lognormal, distributions for rates, weights and
gains in all brain areas examined. The difference between strongly recurrent
and feed-forward connectivity (cortex vs. striatum and cerebellum),
neurotransmitter (GABA (striatum) or glutamate (cortex)) or the level of
activation (low in cortex, high in Purkinje cells and midbrain nuclei) turns
out to be irrelevant for this feature. Logarithmic scale distribution of
weights and gains appears to be a general, functional property in all cases
analyzed. We then created a generic neural model to investigate adaptive
learning rules that create and maintain lognormal distributions. We
conclusively demonstrate that not only weights, but also intrinsic gains, need
to have strong Hebbian learning in order to produce and maintain the
experimentally attested distributions. This provides a solution to the
long-standing question about the type of plasticity exhibited by intrinsic
excitability.
