A Topological Model of the Hippocampal Cell Assembly Network

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.

A model of topological mapping of space in bat hippocampus

“…The place field map's connectivity matrix P ij is based on the place fields' spatial overlap: P ij = 1 if the distance between the place field centers is smaller than the sum of their half‐sizes, d ( c i , c j ) ≤ ( L i + L j )/2, and P ij = 0 otherwise. In principle, the matrix P ij can be deduced directly from the temporal pattern of place cell coactivity (Babichev et al, ). However, we used the place field information to simplify our analyses.…”

“…Subsequent topological (Persistent Homology) analyses were conducted using the JPlex freeware (JPlex freeware). For more computational details see Methods in (Dabaghian et al, 2012;Arai et al, 2014;Babichev et al, 2016b).…”

Maintaining Consistency of Spatial Information in the Hippocampal Network: A Combinatorial Geometry Model

“…, v i d ], where each vertex, v i , corresponds to a place cell c i (in the following, the same symbol, σ , will be used to denote a cell assembly and the simplex that represents it) (Dabaghian, Mémoli, Frank, & Carlsson, 2012; Arai, Brandt, & Dabaghian, 2014). The entire network can then be represented by a purely combinatorial simplicial complex 𝒯 (Aleksandrov, 1965; Prasolov, 2006) whose maximal simplexes correspond to place cell assemblies (Babichev, Mémoli, & Dabaghian, 2015). Simplexes in 𝒯 may overlap: physiological studies demonstrate that a given place cell may be part of many cell assemblies (Georgopoulos, Schwartz, & Kettner, 1986; Tudusciuc & Nieder, 2007).…”

“…. are contained in the c i ’s place field; thus, the higher the orders of the cell assemblies, the (statistically) smaller the l σ s (Babichev et al, 2015). Since the individual place cell spiking rates are well approximated by smooth gaussian functions of the rat’s coordinates (Eden, Frank, Barbieri, Solo, & Brown, 2004), the quantities f σ,v i remain approximately constant over l σ .…”

Through synapses to spatial memory maps via a topological model

“…From the computational perspective, the topological nature of the cognitive map suggests that the information transmitted via place cell spiking should be amenable to topological analyses. In our previous work [14][15][16][17][18], we developed a topological model that allows tracing how the information provided by the individual place cells may combine into a large-scale topological map of the navigated space and quantifying the contributions of different neurophysiological parameters. However, previous studies did not include a key physiological aspect-the contribution of the synaptic connections into the processes of assembling the map.…”