Specific evidence of low-dimensional continuous attractor dynamics in grid cells


We examined simultaneously recorded spikes from multiple rat grid cells, to explain mechanisms underlying their activity. Among grid cells with similar spatial periods, the population activity was confined to lie close to a two-dimensional (2D) manifold: grid cells differed only along two dimensions of their responses and otherwise were nearly identical. Relationships between cell pairs were conserved despite extensive deformations of single-neuron responses. Results from novel environments suggest such structure is not inherited from hippocampal or external sensory inputs. Across conditions, cell-cell relationships are better conserved than responses of single cells. Finally, the system is continually subject to perturbations that, were the 2D manifold not attractive, would drive the system to inhabit a different region of state space than observed. These findings have strong implications for theories of grid-cell activity and substantiate the general hypothesis that the brain computes using low-dimensional continuous attractors.

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Figure 1: Spatial grid parameters other than phase are identical across cells recorded on the same or nearby tetrodes; cell-cell relationships are stable over time.
Figure 2: Across time in familiar environments, the relative phases between cells are more stable than the phases of single cells.
Figure 3: Grid parameter ratios and relative phases are stable even when grid parameters are rescaled as the environment is resized.
Figure 4: Spatial patterns of grid cells become less stable and expand in novel enclosures, but grid parameter ratios between cells remain stable.
Figure 5: Relative phase remains stable in novel enclosures.
Figure 6: Stability of cell-cell relationships is independent of distance in spatial phase.
Figure 7: Evidence of external perturbation and attractor dynamics in grid-cell activity.


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We are grateful to D. Tank for insightful comments. We thank members of the Moser laboratory for public release of some of their data sets, which we used in this study. I.R.F. is funded as a Sloan Foundation Fellow, a Searle Scholar and a McKnight Scholar. We acknowledge funding from the Wellcome Trust, UK and the Office of Naval Research through ONR MURI N00014-10-1-0936 and the ONR-Young Investigator Program to I.R.F.

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K.Y. performed the analysis. K.Y., M.A.B., C.B., N.B. and I.R.F. contributed ideas and plans for the analysis. C.B. and R.H. collected some of the data presented. K.Y. and I.R.F. wrote the paper with input from M.A.B., C.B. and N.B.

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Correspondence to Ila R Fiete.

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Yoon, K., Buice, M., Barry, C. et al. Specific evidence of low-dimensional continuous attractor dynamics in grid cells. Nat Neurosci 16, 1077–1084 (2013). https://doi.org/10.1038/nn.3450

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