Logarithmically scaled, gamma distributed neuronal spiking

Naturally log-scaled quantities abound in the nervous system. Distributions of these quantities have non-intuitive properties, which have implications for data analysis and the understanding of neural circuits. Here, we review the log-scaled statistics of neuronal spiking and the relevant analytical probability distributions. Recent work using log-scaling revealed that interspike intervals of forebrain neurons segregate into discrete modes reflecting spiking at different timescales and are each well-approximated by a gamma distribution. Each neuron spends most of the time in an irregular spiking 'ground state' with the longest intervals, which determines the mean firing rate of the neuron. Across the entire neuronal population, firing rates are log-scaled and well approximated by the gamma distribution, with a small number of highly active neurons and an overabundance of low rate neurons (the 'dark matter'). These results are intricately linked to a heterogeneous balanced operating regime, which confers upon neuronal circuits multiple computational advantages and has evolutionarily ancient origins.