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

Abstract

Place cells in the rat hippocampus play a key role in creating the animal’s internal representation of the world. During active navigation, these cells spike only in discrete locations, together encoding a map of the environment. Electrophysiological recordings have shown that the animal can revisit this map mentally during both sleep and awake states, reactivating the place cells that fired during its exploration in the same sequence in which they were originally activated. Although consistency of place cell activity during active navigation is arguably enforced by sensory and proprioceptive inputs, it remains unclear how a consistent representation of space can be maintained during spontaneous replay. We propose a model that can account for this phenomenon and suggest that a spatially consistent replay requires a number of constraints on the hippocampal network that affect its synaptic architecture and the statistics of synaptic connection strengths.

Topological Schemas of Memory Spaces

“…If the cell assembly network is represented by a complex , this packet is represented by a group of “active” simplexes that moves across , tracing a simplicial path Γ (Figure 2B ). As discussed in Dabaghian et al ( 2012 ), Arai et al ( 2014 ), Basso et al ( 2016 ), Dabaghian ( 2016 ), and Hoffman et al ( 2016 ), the structure of the simplicial paths captures the shape of the corresponding physical paths and hence represents the connectivity of the environment. For example, a contractible simplicial path corresponds to a contractible physical rout, whereas a non-contractible simplicial path marks a non-traversable domain occupied by an obstacle, e.g., by a physical obstruction or by a predator (Figures 2B,C ).…”

From Topological Analyses to Functional Modeling: The Case of Hippocampus

“…For example, a sequence of place fields traversed during the rat's moves over a particular trajectory γ and the place cell combinations ignited along this trajectory can be represented, respectively, by a “nerve path” —a chain of nerve-simplexes in , or by a “coactivity path” —a chain of the coactivity-simplexes in (see also Babichev and Dabaghian, 2018 ). These simplicial paths qualitatively represent the shape of the physical trajectories: a closed simplicial path represents a closed physical route; a non-contractible simplicial path corresponds to a class of the physical paths that enclose unreachable or yet unexplored parts of the environment; two topologically equivalent simplicial paths Γ 1 ~ Γ 2 represent physical paths γ 1 and γ 2 that can be deformed into one another and so forth (Brown et al, 1998 ; Jensen and Lisman, 2000 ; Guger et al, 2011 ; Dabaghian, 2016 ). By the Alexandrov-Čech's theorem, the net pool of the simplicial paths can thus be used to describe the topological connectivity of the environment via homological characteristics of and .…”

“…A computational framework developed in Dabaghian et al ( 2012 ), Arai et al ( 2014 ), Hoffman et al ( 2016 ), Basso et al ( 2016 ), Babichev et al ( 2016a , b ), Babichev and Dabaghian ( 2018 ), Dabaghian ( 2019 ), and Dabaghian ( 2016 ) helps to understand these phenomena by integrating the activity of the individual neurons into a large-scale map of the environment and to study the dynamics of its appearance, using algebraic topology techniques. Below we review some basic ideas and key concepts used in this framework, and discuss how they may apply to hippocampal physiology and cognitive realm.…”

Replays of spatial memories suppress topological fluctuations in cognitive map

“…Neurophysiologically, place cell replays are viewed as manifestations of the animal’s “mental explorations” (Babichev & Dabaghian, 2018; Dabaghian, 2016; Hopfield, 2010; Zeithamova, Schlichting, & Preston, 2012), which help constructing the cognitive maps and consolidating memories (Ego-Stengel & Wilson, 2010; Gerrard, Kudrimoti, McNaughton, & Barnes, 2001; Girardeau, Benchenane, Wiener, Buzsáki, & Zugaro, 2009; Girardeau & Zugaro, 2011; Roux, Hu, Eichler, Stark, & Buzsáki, 2017). Although the detailed mechanisms of these phenomena remain unknown, it is believed that replays may reinforce synaptic connections that deteriorate over extended periods of inactivity (Sadowski, Jones, & Mellor, 2011, 2016; Singer, Carr, Karlsson, & Frank, 2013).…”