Biology subjects

Hermansen, E.

Publications and source records attributed to Hermansen, E..

6 recordsLinked to original sources

bioRxiv2026

Neural spiketrains and population vectors entangle neural representations

Neural recordings are usually analyzed by comparing neural spiketrains or comparing time bins (population vectors). If multiple variables drive the neural activity these comparisons will be affected by all of them. Our aim is to disentangle these different latent variables or covariates that drive neural activity and reveal their structure and geometry. The central idea of the paper is that a matrix is disentangled when its rows and columns are local on each other, a condition we call bidirectional locality. In such a matrix, rows and columns encode the same geometry and they respond to only one localized part of it. This suggests finding bidirectional local matrices in a given data matrix, from which we can recover the geometry of the covariates driving it in a straightforward way. We present two ways of doing just this. The first method, coherent projections, works by finding non-negative projections of the neural data matrix (neurons by time bins) that are bidirectionally local. The second method, clumps, works by finding dense submatrices of the neural data matrix, that each identify a local region of one covariate. We apply these methods to two neural datasets, showing that they can separate grid cell modules and reveal a movement-driven low-dimensional structure in the motor cortex.

neuroscience↗

bioRxiv2026

Toroidal topology of grid-cell activity precedes spatial navigation during development

The medial entorhinal cortex (MEC) is a central component of the mammalian navigation system1-5, in which spatially and directionally tuned neurons, including grid cells and head-direction cells, encode an animals position and orientation6-8. These cells form internal maps with periodic topologies: head-direction cells traverse ring-like manifolds9,10, while grid cells are organized on toroidal manifolds11. The persistence of these topologies across behavioral states and environments11,12 raises the possibility that they arise intrinsically from network architecture rather than through sensory experience4,5,13-17. Consistent with this view, observations in juvenile rats have shown that rudimentary spatial tuning appears in place cells, head direction cells and grid cells almost as soon as pups begin to explore their surroundings at 2-3 weeks of age18-20. However, it remains unclear whether spatial experience is required for the initial emergence of positional tuning and for the organization of tuned cells into periodic maps. Here we show, using large-scale ensemble recordings in rat pups, that toroidal manifolds emerge in MEC subnetworks as early as postnatal day 10 (P10), preceding eye and ear opening, upright posture, quadrupedal gait, and active exploration21,22. These toroidal networks were modular from the beginning, with increasing differentiation of their dynamics appearing on P11-12. The onset of toroidal topology coincided with a transition in MEC network activity characterized by desynchronization and increased inhibitory connectivity, a developmental shift observed broadly across cortical regions at this age23,24. In contrast, ring-like manifolds were already detectable by P9, with traces of directional tuning appearing in individual cells at P8 -- consistent with an earlier maturation of subcortical circuitry25. As pups subsequently began to explore the environment around P15-16, these internally generated maps progressively aligned with external landmarks, culminating in stable, periodic firing fields by three weeks of age. Taken together, these findings identify ring-like and toroidal manifolds as instinctive computational motifs of the developing brain. Their early emergence, preceding major sensory input and navigation, supports the view that spatial representations are preconfigured and later anchored to the external world through experience-dependent plasticity.

neuroscience↗

bioRxiv2024

Hexagons all the way down: Grid cells as a conformal isometric map of space

The brains ability to navigate is often attributed to spatial cells in the hippocampus and entorhinal cortex. Grid cells, found in the entorhinal cortex, are known for their hexagonal spatial activity patterns and are traditionally believed to be the neural basis for path integration. However, recent studies have cast grid cells as a distance-preserving representation. We further investigate this role in a model of grid cells based on a superposition of plane waves. In a module of such grid cells, we optimise their phases to form a conformal isometry (CI) of two-dimensional flat space. With this setup, we demonstrate that a module of at least seven grid cells can achieve a CI, with phases forming a regular hexagonal arrangement. This pattern persists when increasing the number of cells, significantly diverging from a random uniform distribution. In particular, when optimised for CI, the phase distribution becomes distinctly regular and hexagonal, offering a clear experimentally testable prediction. Moreover, grid modules encoding a CI maintain constant energy expenditure across space, providing a new perspective on the role of energy constraints in normative models of grid cells. Finally, we investigate the minimum number of grid cells required for various spatial encoding tasks, including a unique representation of space, the population activity forming a torus, and achieving a CI, where we find that all three are achieved when the module encodes a CI. Our study not only underscores the versatility of grid cells beyond path integration but also highlights the importance of geometric principles in neural representations of space.

neuroscience↗

bioRxiv2023

A topological perspective on the dual nature of the neural state space and the correlation structure

When analysing neural activity, one often studies either the neural correlations or the state space of population vectors. However, the reason for choosing one over the other is seldom discussed. Here, with methods from the mathematical field of topology, we compare these approaches and propose using both for unsupervised inference of neural representations. If the recorded neurons have convex receptive fields on a single covariate space, there is a duality between the topological signatures derived from correlations on the one hand and population vectors on the other hand. However, in the presence of multiple neural modules with non convex receptive fields, this duality breaks down. We explain how to leverage complementary information derived from both approaches to sucessfully characterize the represented covariate spaces directly from the data also under these challenging circumstances. Furthermore, we prove appropriate reconstruction results and showcase applications to multiple neural datasets from various brain regions and diverse neural modules.

neuroscience↗

bioRxiv2022

Uncovering 2-D toroidal representations in grid cell ensemble activity during 1-D behavior

Neuroscience is pushing toward studying the brain during naturalistic behaviors with open-ended tasks. Grid cells are a classic example, where free behavior was key to observing their characteristic spatial representations in two-dimensional environments [1]. In contrast, it has been difficult to identify grid cells and study their computations in more restrictive experiments, such as head-fixed wheel running [2-6]. Here, we challenge this view by showing that shifting the focus from single neurons to the population level changes the minimal experimental complexity required to study grid cell representations. Specifically, we combine the manifold approximation in UMAP [7] with persistent homology [8] to study the topology of the population activity. With these methods, we show that the population activity of grid cells covers a similar two-dimensional toroidal state space during wheel running as in open field foraging [9, 10], with and without a virtual reality setup. Trajectories on the torus correspond to single trial runs in virtual reality and changes in experimental conditions are reflected in the internal representation, while the toroidal representation undergoes occasional shifts in its alignment to the environment. These findings show that our method can uncover latent topologies that go beyond the complexity of the task, allowing us to investigate internal dynamics in simple experimental settings in which the analysis of grid cells has so far remained elusive.

neuroscience↗

bioRxiv2021

Toroidal topology of population activity in grid cells

The medial entorhinal cortex (MEC) is part of a neural system for mapping a subjects position within a physical environment1,2. Grid cells, a key component of this system, fire in a characteristic hexagonal pattern of locations3, and are organized in modules4,5 which collectively form a population code for the animals allocentric position1,6-8. The invariance of the correlation structure of this population code across environments9,10 and behavioural states11,12, independently of specific sensory inputs, has pointed to intrinsic, recurrently connected continuous attractor networks (CANs) as a possible substrate of the grid pattern1,2,13-16. 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 animals 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 plasticity17-22. This demonstration of network dynamics on a toroidal manifold provides the first population-level visualization of CAN dynamics in grid cells.

neuroscience↗