Toroidal topology of population activity in grid cells

Abstract

The medial entorhinal cortex (MEC) is part of a neural system for mapping a subject's position within a physical environment. Grid cells, a key component of this system, fire in a characteristic hexagonal pattern of locations, and are organized in modules which collectively form a population code for the animal's allocentric position1. The invariance of the correlation structure of this population code across environments and behavioural states, independently of specific sensory inputs, has pointed to intrinsic, recurrently connected continuous attractor networks (CANs) as a possible substrate of the grid pattern. However, whether grid cell networks show continuous attractor dynamics, and how they interface with inputs from the environment, has remained elusive due to the small samples of cells obtained to date. Here we show, with simultaneous recordings from many hundreds of grid cells, and subsequent topological data analysis, that the joint activity of grid cells from an individual module resides on a toroidal manifold, as expected in a two-dimensional CAN. Positions on the torus correspond to the moving animal's position in the environment. Individual cells are preferentially active at singular positions on the torus. Their positions are maintained, with minimal distortion, between environments and from wakefulness to sleep, as predicted by CAN models for grid cells but not by alternative feed-forward models where grid patterns are created from external inputs by Hebbian plasticity. This demonstration of network dynamics on a toroidal manifold provides the first population-level visualization of CAN dynamics in grid cells.

Grid-cell modules remain coordinated when neural activity is dissociated from external sensory cues

“…Recently, techniques that enable simultaneous recording of activity in dozens to hundreds of neurons (Ghosh et al, 2011;Jun et al, 2017;Steinmetz et al, 2021;Zong et al, 2017) have enabled a shift from the measurement of single cell activity in relationship to external correlates, to investigation of the joint population activity patterns in large neural ensembles. This change of perspective has led to various attempts to characterize neural activity patterns as residing within restricted, low dimensional spaces using linear (Gallego et al, 2018;Mazor and Laurent, 2005;Stringer et al, 2019) or non-linear (Chaudhuri et al, 2019;Gardner et al, 2021;Rubin et al, 2019;Rybakken et al, 2019) dimensionality reduction techniques. One of the most striking outcomes of these attempts has emerged in neural circuits involved in the representation of an animal's position relative to the environment.…”

“…One of the most striking outcomes of these attempts has emerged in neural circuits involved in the representation of an animal's position relative to the environment. In several such circuits in flies and mammals, neural activity patterns have been shown to robustly reside in low-dimensional nonlinear manifolds, even when the neural activity is dissociated from external inputs to the network (Chaudhuri et al, 2019;Gardner et al, 2021;Kim et al, 2017;Rybakken et al, 2019;Seelig and Jayaraman, 2015). This finding opens up the possibility to decode the low-dimensional variable that is represented within these circuits, and to examine how the brain utilizes such representations across multiple sub-circuits to implement computational functions.…”

The RIFF: an automated environment for studying the neural basis of auditory-guided complex behavior

“…Importantly, the RIFF is more than its current implementation: it represents a concept that can be easily extended by adding more cameras and other sensors for documentation of behavior (for example a motion capture setup 56, 57 ), more actuators for interacting with the animals, and higher channel count electrodes for recording electrophysiological signals. The RIFF shifts the emphasis in the design of an experiment and the analysis of behavior from single, simplistic measures of behavior such as success and failure into the documentation of a high rate, on-going process that is better adapted, and therefore easier to link, to the dynamics of the mammalian brain.…”

Learning to represent continuous variables in heterogeneous neural networks

“…1Aiii) and average activity, which is independent of the location on the manifold. Such a perfection of geometry in the brain is not supported by experimental evidence: while recent studies suggest that neuronal representations of continuous features might exhibit the topology of a ring [Chaudhuri et al, 2019, Rubin et al, 2019] or a torus [Gardner et al, 2021], in agreement with the manifold attractor hypothesis, there is no evidence for a perfect geometrical symmetry in these representations. Symmetric-connectome attractor models are thus inconsistent with synaptic heterogeneity and diverse tuning profiles of neurons and cannot support imperfect geometries in neural manifolds.…”

“…A common framework to study such continuous internal representations is the theory of computations by manifold attractor networks [Amari, 1977, Ben-Yishai et al, 1995, Seung, 1996, Burak and Fiete, 2009, Wimmer et al, 2014, Hansel and Mato, 2013, Chaudhuri et al, 2019, Gardner et al, 2021]. In these networks, the variable of interest is represented as a point in the space of neural activity, with the continuum of values forming a low-dimensional manifold of attractor states in the high-dimensional space of neural firing rates.…”