A Topological Model of the Hippocampal Cell Assembly Network.

Andrey Babichev,Facundo Mémoli,Yuri A Dabaghian,Daoyun Ji

doi:10.3389/fncom.2016.00050

Abstract

It is widely accepted that the hippocampal place cells' spiking activity produces a cognitive map of space. However, many details of this representation's physiological mechanism remain unknown. For example, it is believed that the place cells exhibiting frequent coactivity form functionally interconnected groups—place cell assemblies—that drive readout neurons in the downstream networks. However, the sheer number of coactive combinations is extremely large, which implies that only a small fraction of them actually gives rise to cell assemblies. The physiological processes responsible for selecting the winning combinations are highly complex and are usually modeled via detailed synaptic and structural plasticity mechanisms. Here we propose an alternative approach that allows modeling the cell assembly network directly, based on a small number of phenomenological selection rules. We then demonstrate that the selected population of place cell assemblies correctly encodes the topology of the environment in biologically plausible time, and may serve as a schematic model of the hippocampal network.

Highlights

The mammalian hippocampus plays a major role in spatial learning by encoding a cognitive map of space—a key component of animals’ spatial memory and spatial awareness (OKeefe and Nadel, 1978; Best et al, 2001)
The place cells’ spiking activity induces a covering of the environment by the place fields, called a place field map [see Figure 1B and (Babichev et al, 2016)], the Alexandrov-Cech’s theorem suggests that the place cells’ coactivity (Figure 1C), which marks the overlaps of the place fields, may be used by the brain to represent the topology of the environment
It is believed that groups of place cells exhibiting frequent coactivity form assemblies that jointly trigger spiking activity of their respective readout neurons, but the specific architecture of the cell assembly network has not been fully identified

Summary

Introduction

The mammalian hippocampus plays a major role in spatial learning by encoding a cognitive map of space—a key component of animals’ spatial memory and spatial awareness (OKeefe and Nadel, 1978; Best et al, 2001). The individual groups of coactive place cells, just like simplices, provide local information about the space, but together, as a neuronal ensemble, they represent space as whole—as the simplicial complex. This analogy establishes a possible approach to the long-sought connection between the cellular and systemscales, which was developed in (Dabaghian et al, 2012; Arai et al, 2014) into a working model of spatial memory. The persistent homology theory was used to estimate the rate of accumulation of global topological information, i.e., spatial learning

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