Replays of spatial memories suppress topological fluctuations in cognitive map

Abstract

The spiking activity of the hippocampal place cells plays a key role in producing and sustaining an internalized representation of the ambient space—a cognitive map. These cells do not only exhibit location-specific spiking during navigation, but also may rapidly replay the navigated routs through endogenous dynamics of the hippocampal network. Physiologically, such reactivations are viewed as manifestations of “memory replays” that help to learn new information and to consolidate previously acquired memories by reinforcing synapses in the parahippocampal networks. Below we propose a computational model of these processes that allows assessing the effect of replays on acquiring a robust topological map of the environment and demonstrate that replays may play a key role in stabilizing the hippocampal representation of space.

Evaluating state space discovery by persistent cohomology in the spatial representation system

“…The application of persistent (co)homology to neuroscience data is still in its developing stages. Notable lines of work include: dimensionality reduction for manifold decoding in head direction cells [29,30]; simulations of hippocampal place cells in spatial environments with nontrivial topology [31,32,33,34,35];…”

From Topological Analyses to Functional Modeling: The Case of Hippocampus

“…For a given map , a trajectory γ( t ) and fixed physiological parameters (firing rates, place field sizes, etc. ), the Betti numbers depend primarily on the links' decay time τ (Babichev and Dabaghian, 2017a , b ; Babichev et al, 2018 , 2019 ). One would expect that if τ is too small (e.g., if the coactivity simplexes tend to disappear between two consecutive co-activations of the corresponding cells), then the flickering complex should rapidly deteriorate without attaining an adequate topological shape.…”

“…The characteristic size of grows to about a half of the size of , with about 15% fluctuations ( Figure 6B ). Thus, the population of simplexes in is indeed transient: although the size of fluctuates slowly from one moment of time to the next, the set of simplexes that are present at a given moment of time t but missing at a later moment t ′, grows as a function of temporal separation | t − t ′|, becoming close to the sizes of either or in approximately one learning period (Babichev et al, 2018 , 2019 ).…”

“…In fact, even if the functional connections between place cells are established and pruned randomly, at a rate that matches the statistics (2), the resulting random connectivity graph produces a random clique complex whose Betti numbers converge to the Betti numbers of the environment at the same timescale as the Betti numbers of or , exhibiting similar pattern of the topological fluctuations. Importantly, in the latter case, the details of these processes are controlled by the physiological parameters, e.g., by the number of active cells and their firing rates (see Figure 6C and Babichev et al, 2018 , 2019 ).…”

Editorial: Topological Neuroscience

“…In the context of event-related fMRI, Ellis, Lesnick, Henselman-Petrusek, Keller, and Cohen (2019) investigate the feasibility of topological techniques for recovering signal representations under different conditions. At the mesoscopic scale, Babichev, Morozov, and Dabaghian (2019) propose a computational model to assess the effect of memory replays in parahippocampal networks on the development and stabilization of hippocampal topological maps of space. At an even smaller scale, Bardin, Spreemann, and Hess (2019) show that topological features of spike-train data can be used to understand how individual neurons give rise to network dynamics, and hence to classify topologically such emergent behaviors.…”