Universality of Logarithmic Coding for Neurons

In this paper we document lognormal distributions for spike rates, synaptic weights and intrinsic excitability (gain) for neurons in various brain areas, such as auditory or visual cortex, cerebellum, striatum, midbrain nuclei. We find a remarkable consistency of power-law, specifically lognormal, distributions for rates, weights and gains in all brain areas, such as cortex, cerebellum, striatum, midbrain. The difference between strongly recurrent and transfer connectivity (cortex vs. striatum and cerebellum), neurotransmitter (GABA or glutamate) 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 appears as a functional phenomenon that is always present. Secondly, we created a generic neural model to show that Hebbian learning will create and maintain lognormal distributions. We could prove with the model 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 settles a long-standing question about the type of plasticity exhibited by intrinsic excitability.