A Plane-Dependent Model of 3D Grid Cells for Representing Both 2D and 3D Spaces Under Various Navigation Modes.

Ziyi Gong,Fangwen Yu

doi:10.3389/fncom.2021.739515

Abstract

Grid cells are crucial in path integration and representation of the external world. The spikes of grid cells spatially form clusters called grid fields, which encode important information about allocentric positions. To decode the information, studying the spatial structures of grid fields is a key task for both experimenters and theorists. Experiments reveal that grid fields form hexagonal lattice during planar navigation, and are anisotropic beyond planar navigation. During volumetric navigation, they lose global order but possess local order. How grid cells form different field structures behind these different navigation modes remains an open theoretical question. However, to date, few models connect to the latest discoveries and explain the formation of various grid field structures. To fill in this gap, we propose an interpretive plane-dependent model of three-dimensional (3D) grid cells for representing both two-dimensional (2D) and 3D space. The model first evaluates motion with respect to planes, such as the planes animals stand on and the tangent planes of the motion manifold. Projection of the motion onto the planes leads to anisotropy, and error in the perception of planes degrades grid field regularity. A training-free recurrent neural network (RNN) then maps the processed motion information to grid fields. We verify that our model can generate regular and anisotropic grid fields, as well as grid fields with merely local order; our model is also compatible with mode switching. Furthermore, simulations predict that the degradation of grid field regularity is inversely proportional to the interval between two consecutive perceptions of planes. In conclusion, our model is one of the few pioneers that address grid field structures in a general case. Compared to the other pioneer models, our theory argues that the anisotropy and loss of global order result from the uncertain perception of planes rather than insufficient training.

Highlights

Navigation is crucial for animals to survive in nature
To explain the observed grid field structures, we propose an overarching theory on the grid cell computation in 3D, and implement the theory with a training-free recurrent neural network (RNN) extended from (Gao et al, 2021)
We compare our model with two interpretive models considering special 3D cases (Horiuchi and Moss, 2015; Wang et al, 2021) and two training models in 3D space (Stella and Treves, 2015; Soman et al, 2018), FIGURE 1 | (A) A Schematic of the screw axis system. (B–D) Plane-dependent computation. (B) The motion is projected onto a single plane, such as the horizontal plane defined by gravity and is a special case of (C). (C) The motion is projected onto instantaneous planes, such as the tangent planes to the motion manifold. (D) Path integration depends on the local cylindrical systems with respect to the planes. (E) Plane-independent computation; the path is interpreted as a curve in the static Euclidean space R3

Summary

Introduction

Navigation is crucial for animals to survive in nature. Grid cells in mammalian medial entorhinal cortex (mEC) are crucial for this process, representing space like a coordinate system (McNaughton et al, 2006; Fiete et al, 2008; Horner et al, 2016; Gil et al, 2018; Ridler et al, 2020). The spatial firing fields of grid cells, called grid fields, form hexagonal lattice during horizontal planar navigation (Hafting et al, 2005; Fyhn et al, 2008; Doeller et al, 2010; Yartsev et al, 2011; Killian et al, 2012; Jacobs et al, 2013). It is natural to inquire about the grid fields beyond planar navigation, as animals live in a three-dimensional (3D) world and carry multiple modes of navigation–planar, multilayered, and volumetric (Finkelstein et al, 2016). Because hexagonal lattice is the most efficient packing in two-dimensional (2D) space, a reasonable prediction is one of the maximally efficient 3D structures: face-centered cubic (FCC) or hexagonal-close-packed (HCP) (Gauss, 1840; Mathis et al, 2015)

Methods

Results

Conclusion