Logarithmically scaled, gamma distributed neuronal spiking

Abstract

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.

Extreme distributions in the preconfigured developing brain

“…In these models, we investigated how the simulated firing statistics were impacted by three structural parameters: (i) whether the size of synapses followed a normal or a log-normal distribution, (ii) whether the number of synapses of individual neurons followed a normal or a log-normal distribution, and (iii) whether the number of dendritic and axonic (incoming and outgoing) synapses were correlated or uncorrelated with each other (Figure 5B). This resulted in a total of 2 3 =8 possible synaptic parameters combinations. To avoid choosing an arbitrary network architecture to test the effect of these three variables, a set of other parameters (average size of AMPA and GABA synapses, average connectivity, and the strength of the noisy input driving PYRs and INs) were randomly drawn from a range of biologically constrained values (see Materials and Methods for details) (Figure 5C).…”

“…A fascinating property of the adult brain is that a large number of parameters, ranging from the size of synapses to the power of extracellular currents 1,3,4 , follow extreme distributions. This organization has been suggested to have many desirable properties 10,27 , but how and when it arises is still a matter of debate.…”

“…In these networks, we studied the influence on the simulated SUA statistics exerted by three synaptic parameters: whether the size of synapses followed a normal or a log-normal distribution, whether the number of synapses of individual neurons followed a normal or a log-normal distribution, and whether the number of dendritic and axonic (incoming and outgoing) synapses were correlated or uncorrelated with each other. The 2 possible configurations for the 3 synaptic parameters resulted in 2 3 =8 different network types, of which we simulated 1000 each. These 3 synaptic parameters were simultaneously varied for the entire network and not in a neuronal population-specific manner.…”

“…In the adult brain, many structural and functional parameters follow right-skewed distributions with heavy right tails such as the log-normal 1,2 , gamma 3 , or power law 4,5 distribution. A non-exhaustive list of parameters that is characterized by such distributions includes: size and number of synapses [6][7][8][9] , size of post-synaptic currents [10][11][12] , diameter of axons 13 , density of neurons 14 , in vivo single-unit firing rate [15][16][17] , spike transmission probability 10,17 , pairwise correlations among spike trains 18 , and power of the LFP 19,20 , EEG [21][22][23] , MEG [22][23][24] and BOLD 25 signals.…”

Seventy years later: the legacy of the Hodgkin and Huxley model in computational neuroscience

“…The review explores the question whether degeneracy, sloppiness and representational drift challenge the idea of a tight structure-function relationship, or alternatively they offer insights into the organising principles of neuronal network dynamics. Finally, the review of Levenstein & Okun (2023) summarises present knowledge of the basic statistical properties of neuronal spiking activity in vivo and the analytical probability distributions that best capture them. The last review in this special issue explores the relevance of computational models in a clinical setting.…”