Spatial representability of neuronal activity

D Akhtiamov,Y Dabaghian,A G Cohn

doi:10.1038/s41598-021-00281-y

Abstract

A common approach to interpreting spiking activity is based on identifying the firing fields—regions in physical or configuration spaces that elicit responses of neurons. Common examples include hippocampal place cells that fire at preferred locations in the navigated environment, head direction cells that fire at preferred orientations of the animal’s head, view cells that respond to preferred spots in the visual field, etc. In all these cases, firing fields were discovered empirically, by trial and error. We argue that the existence and a number of properties of the firing fields can be established theoretically, through topological analyses of the neuronal spiking activity. In particular, we use Leray criterion powered by persistent homology theory, Eckhoff conditions and Region Connection Calculus to verify consistency of neuronal responses with a single coherent representation of space.

Highlights

A common approach to interpreting spiking activity is based on identifying the firing fields—regions in physical or configuration spaces that elicit responses of neurons
The neuronal spikings in this case are generated as responses to the rat’s appearances within preconstructed, convex firing domains, e.g., stepping into randomly scattered place fields or facing towards head direction fields centered around randomly chosen preferred angles
Topological analyses of the spiking data allow testing whether a given type neuronal activity may arise from a “spatial map,” i.e., whether each neuron’s spiking marks a domain similar to a place field, a head direction field, a view field, etc., in a certain low-dimensional space

Summary

Introduction

A common approach to interpreting spiking activity is based on identifying the firing fields—regions in physical or configuration spaces that elicit responses of neurons. Common examples include hippocampal place cells that fire at preferred locations in the navigated environment, head direction cells that fire at preferred orientations of the animal’s head, view cells that respond to preferred spots in the visual field, etc In all these cases, firing fields were discovered empirically, by trial and error. The principles of information processing in sensory and somatosensory cortices were deciphered in terms of receptive fields—domains in sensory spaces, whose stimulation elicits in spiking responses of the corresponding neurons[34,35,36,37,38,39] In all these cases, referencing an individual neuron’s activity to a particular domain in a suitable representing space X40 is key for understanding its contribution and for reasoning about functions of neuronal ensembles in terms of the corresponding “maps”[16,17,18]. This raises a natural question: when is a “spatial” interpretation of Scientific Reports | (2021) 11:20957

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Conclusion