Neural Representation of Spatial Topology in the Rodent Hippocampus

Abstract

Pyramidal cells in the rodent hippocampus often exhibit clear spatial tuning in navigation. Although it has been long suggested that pyramidal cell activity may underlie a topological code rather than a topographic code, it remains unclear whether an abstract spatial topology can be encoded in the ensemble spiking activity of hippocampal place cells. Using a statistical approach developed previously, we investigate this question and related issues in greater details. We recorded ensembles of hippocampal neurons as rodents freely foraged in one and two-dimensional spatial environments, and we used a “decode-to-uncover” strategy to examine the temporally structured patterns embedded in the ensemble spiking activity in the absence of observed spatial correlates during periods of rodent navigation or awake immobility. Specifically, the spatial environment was represented by a finite discrete state space. Trajectories across spatial locations (“states”) were associated with consistent hippocampal ensemble spiking patterns, which were characterized by a state transition matrix. From this state transition matrix, we inferred a topology graph that defined the connectivity in the state space. In both one and two-dimensional environments, the extracted behavior patterns from the rodent hippocampal population codes were compared against randomly shuffled spike data. In contrast to a topographic code, our results support the efficiency of topological coding in the presence of sparse sample size and fuzzy space mapping. This computational approach allows us to quantify the variability of ensemble spiking activity, to examine hippocampal population codes during off-line states, and to quantify the topological complexity of the environment.

A Bayesian nonparametric approach for uncovering rat hippocampal population codes during spatial navigation

“…We have previously proposed a Bayesian deviance information criterion to select the model size m of HMM (Chen et al, 2012a, 2014). Here we extend the finite-state HMM to an HDP-HMM, a nonparametric Bayesian extension of the HMM that allows for a potentially infinite number of hidden states (Teh et al, 2006; Beal et al, 2002).…”

“…In our previous work (Chen et al, 2012a, 2014), we have developed a parametric Bayesian approach to uncover the neural representation of spatial topology embedded in rodent hippocampal population codes during spatial navigation. Here we extend the preceding work and consider a nonparametric Bayesian approach.…”

What can topology tell us about the neural code?

“…6 It is not true, however, that any code can arise from a good cover or a convex cover-that is, an open cover consisting of convex open sets. The algebraic framework of the neural ideal can be used to determine, in many cases, whether or not a given code has a convex realization [10].…”

“…The place cell code thus naturally reflects the topology of the represented space. These and related observations have led some researchers to speculate that the hippocampal place cell code is fundamentally topological in nature [6,14], while others (including this author) have argued that considerable geometric information is also present and can be extracted using topological methods [11,20]. In order to disambiguate topological and geometric features, Dabaghian et al performed an elegant experiment using linear tracks with flexible joints [13].…”

Neurocontrol: Methods, models and technologies for manipulating dynamics in the brain

“…A highly successful approach to these problems has been through the development of statistical models, often embedded in formal state space methods [21], [22], to describe observed patterns of neuronal activation [23]. In statistical models, such as those embedded in the point process generalized linear model paradigm [24], the probability of a neuron producing a spike at a given time t is described by a rate λ(t), akin to the rate parameter of a renewal stochastic process.…”