Spatially periodic computation in the entorhinal-hippocampal circuit during navigation
- Beijing Academy of Artificial Intelligence, China
- Tsinghua Laboratory of Brain and Intelligence & Department of Psychological and Cognitive Sciences, Tsinghua University, China
- Division of Humanities and Social Sciences, California Institute of Technology, United States
Figures
Figure 1 with 4 supplements
Experimental design.
(A) Depiction of the Greeble prototype (Gauthier and Tarr, 1997) and its two defining features, namely ‘Loogit’ and ‘Vacso’. (B) Inside the MRI scanner, participants adjusted the length of Loogit and Vacso to match the prototype by stepwise button presses, within a 10 s time limit. (C) Conceptual object space. Each orange dot within the ring-shaped area represents a Greeble variant, while the central blue dot indicates the Greeble prototype (i.e. the goal location). The red dots denote exemplar intermediate locations along the navigational path (i.e., the black line). (D) Density distribution of participants’ ending locations indicated an overall superior behavioral performance for detecting the periodic activity of the HPC.
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Figure 1—source data 1
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Figure 1—figure supplement 1
The averaged number of path directions across all paths (i.e., trials).
The original path directions towards East (e.g. key 1 on the response box), West (e.g. key 2), North (e.g. key 3), and South (e.g. key 4) were identified based on three consecutive movement steps within each path. On average, participants moved in 3.8 directions, suggesting a ‘Radial Adjustment’ strategy and excluding the possibility of the ‘horizontal-vertical movement’ strategy, which would result in two path directions (black dashed line) per path (t(32) = 15.76, p<0.001; two-tailed; Cohen’s d=2.78). The error bars indicate SEM.
Figure 1—figure supplement 2
Histograms of path directions for each participant.
Path directions were binned into 36 bins of 10° each. The uniformity of the distributions was assessed using the Rayleigh test. For all participants, no significant deviations from uniformity were observed (all p>0.05, Bonferroni-corrected across participants). Bar height indicates the number of samples per bin.
Figure 1—figure supplement 3
Learning effect of the object matching task.
The 2-day design effectively eliminated the learning effect from the MRI experiment. On day 1, participants’ behavioral performance increased as a function of experimental sessions, resulting in a significantly negative slope (gray bar, t(32) = –2.46, p=0.019, two-tailed; Cohen’s d=0.44). In contrast, no significant learning effect was found on day 2 (red bar, t(32) = –0.74, p=0.462, two-tailed; Cohen’s d=0.13). The dots indicate individual participants. The error bars indicate SEM.
Figure 1—figure supplement 4
Movement paths of human participants during Greeble morphing in the MRI experiment.
Orange and red dots represent the starting and ending locations, respectively. The black lines indicate the movement paths. Participants’ behavioral performance, calculated as the sum of path length and error size, is shown in the title, with smaller score indicating better performance.
Figure 2 with 1 supplement
Sixfold periodicity in the EC.
(A) Schematic defining path directions in the sixfold modulation. Participants’ path directions (Top) were extracted from the original paths (Left) by connecting the starting and ending locations, with 0° arbitrarily set to the East as the reference, and were then classified as ‘aligned’ or ‘misaligned’ (right and bottom). The original paths of each participant were referred to Figure 1—figure supplement 4. (B) Voxel-based sinusoidal modulation revealed significant sixfold periodicity within the right EC (voxel-based analysis: initial threshold: p=0.05, two-tailed; cluster-based small volume correction (SVC) for multiple comparisons: p<0.05; Cohen’s d=0.63; Peak MNI coordinate: 32, –6, –30). Volumetric results are displayed in radiological orientation; numbers below the brain slices indicate MNI coordinates. (C) ROI-based analysis, using a functional mask derived from the significant right EC cluster and constrained within the anatomical EC, confirmed a significant sixfold periodicity (t(32) = 3.56, p=0.006, two-tailed, corrected for multiple comparisons across rotational symmetries; Cohen’s d=0.62). The black line indicates the boundary of the EC. (D) Schematic illustrating the sixfold directional tuning curve reconstructed from sinusoidal modulation (Left) and its representation in the 2D Greeble space (Right). The error bars indicate SEM.
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Figure 2—source data 1
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Figure 2—source data 2
Related to Figure 2D.
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Figure 2—figure supplement 1
Distribution of grid orientations in the EC.
Grid orientations ranging from –30° to 30° were estimated for each voxel. The uniformity of grid orientations was assessed using both the Rayleigh test and PPC. Significantly clustering was observed in 30 out of 33 participants, indicated by * (* p<0.05, ** p<0.01, *** p<0.001, Bonferroni-corrected across participants). Bar length indicates the number of voxels. Black line denotes the mean orientation.
Figure 3 with 3 supplements
Threefold periodicity in the HPC.
(A) Schematic illustration of the spectral analysis procedure. (B–C) Voxel-based spectral analysis revealed significant threefold periodicity in the bilateral HPC and sixfold periodicity in the bilateral EC (initial threshold: p=0.05, two-tailed; Cluster-based SVC correction for multiple comparisons: p<0.05; For the HPC: Cohen’s d=1.06; Peak MNI coordinate: −24, –20, –18; For the EC: Cohen’s d=1.27; Peak MNI coordinate: −22, –14, –30). The black lines indicate the boundaries of the HPC and EC. (D–E) Threefold periodicity in the bilateral HPC identified using sinusoidal modulation (initial threshold: p=0.05, two-tailed; cluster-based SVC correction: p<0.05; Cohen’s d=0.68; peak MNI coordinate: −24, –18, −12). ROI-based analysis using a functional mask of this cluster within the anatomical HPC confirmed the effect (t(32) = 3.94, p=0.002; Cohen’s d=0.70). Volumetric results are displayed in radiological orientation; numbers below the brain slices indicate MNI coordinates. (F) Schematic illustrating the threefold directional tuning curve reconstructed from sinusoidal modulation (Left) and its representation in the 2D Greeble space (Right). The error bars indicate SEM.
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Figure 3—source data 1
Related to Figure 3E.
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Figure 3—source data 2
Related to Figure 3F.
- https://cdn.elifesciences.org/articles/107517/elife-107517-fig3-data2-v1.xlsx
Figure 3—figure supplement 1
Threefold periodicity of the HPC examined using 20° bin.
Significant clusters were revealed in the right HPC (initial threshold: p=0.05, two-tailed; clustered based SVC correction for multiple comparisons: p<0.05; Cohen’s d=1.18; Peak MNI coordinate: 22, –24, –14). The black lines indicate the outline of the HPC and EC. Volumetric results are displayed in radiological orientation; numbers above the brain slices indicate MNI coordinates.
Figure 3—figure supplement 2
Three and sixfold periodicity of participant groups revealed by spectral analysis.
All individual groups showed significant clusters of three and sixfold periodicity in the HPC and EC, respectively (initial threshold: p=0.05, two-tailed. Cluster-based SVC correction for multiple comparisons: p<0.05). The peak MNI coordinates are shown on the bottom (threefold: Group 1–3, t(9) = 8.0, t(9) = 7.6, t(12) = 10.8, Cohen’s d=0.67, 0.87, 1.21; sixfold: Group 1–3, t(9) = 13.8, t(9) = 8.7, t(12) = 6.7; Cohen’s d=0.83, 0.63, 0.96). The black lines indicate the outline of the HPC and EC. Volumetric results are displayed in radiological orientation; numbers below the brain slices indicate MNI coordinates.
Figure 3—figure supplement 3
Whole brain representations of six and threefold periodicity revealed by spectral analysis.
Significant clusters (Red) within the DMN were identified as representing threefold periodicity, whereas sixfold periodicity revealed clusters within the Salience Network, including the ACC and INS (initial threshold: p=0.05, two-tailed. Whole brain cluster-based correction for multiple comparisons: p<0.05). The gray lines represent the cortical parcellation based on the DKT Atlas.
Figure 4
Phase synchronization between the HPC and EC activity in the directional space.
(A) Cross-participant circular–circular correlation analysis revealed a significant coupling between the EC and HPC phases (r=0.42, p<0.001). The green (outer ring) and purple (inner ring) dots denote HPC and EC phases, respectively. Each line connecting the EC and HPC phases represents one participant, with its color indicating the HPC phase (0–120°). (B) Schematic illustration of a hypothetical peak-overlapping pattern (blue ellipse) between the HPC and EC activity in corresponding to spatial phase (one-cycle). (C) Amplitude-phase modulation analysis revealed significant coupling between the threefold HPC activity and sixfold EC activity in the bin centered at phase 0 (t(32) = 2.57, p=0.02, Bonferroni-corrected across tests; Cohen’s d=0.45). The coupling strength was computed as the difference between the observed modulation index () and the mean surrogate modulation index (). No significant coupling was observed in the control analyses testing phase synchronization between the threefold HPC and the ninefold or twelvefold EC periodicities (p>0.05). The error bars indicate SEM.
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Figure 4—source data 1
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Figure 4—source data 2
Related to Figure 4C.
- https://cdn.elifesciences.org/articles/107517/elife-107517-fig4-data2-v1.xlsx
Figure 5 with 1 supplement
Threefold periodicity in behavioral performance.
(A) Schematic illustration of visuospatial task performance potentially inheriting HPC’s threefold periodicity. (B) Participants’ behavioral performance, measured by a composite index of path length and deviation from the goal to ending locations, fluctuated as a function of path directions. The shaded area denotes SE. (C) Spectral analysis revealed significant power at the threefold of participants’ behavioral performance (p<0.05, corrected for multiple comparisons). The red dashed line represents the baseline derived from permutation. (D) Significantly higher phase-locking values were observed between participants’ behavioral performance and HPC activity compared to surrogate dataset (t(32) = 8.10, p<0.001; Cohen’s d=1.14). The error bars indicate SEM.
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Figure 5—source data 1
Related to Figure 5B.
- https://cdn.elifesciences.org/articles/107517/elife-107517-fig5-data1-v1.xlsx
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Figure 5—source data 2
Related to Figure 5C.
- https://cdn.elifesciences.org/articles/107517/elife-107517-fig5-data2-v1.xlsx
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Figure 5—source data 3
Related to Figure 5D.
- https://cdn.elifesciences.org/articles/107517/elife-107517-fig5-data3-v1.xlsx
Figure 5—figure supplement 1
Spectral analysis of human behavior.
(A and B) Behavioral periodicity of path length and error size (deviation from the goal to ending locations). The shaded areas denote SE. (C and D) Spectral analysis revealed significant threefold power for path length (p<0.05), corrected for multiple comparisons, whereas no significant periodicity was observed for error size (p>0.05). The red dashed line indicates the permutation-based baseline.
Figure 6
The EC-HPC PhaseSync model.
(A) Schematic illustrating the population activity of grid cells during mental planning. The simulated grid cell population was activated by visiting discrete locations (the black circles in the right panel) in the Greeble space along directions either aligned (purple) or misaligned (gray) relative to the grid axes. (B) The threefold periodicity of the path code represented in the HPC. A path code is symmetrical for path direction and +180°, representing a unique spatial orientation ranging from 0° to 180°. The value (y-axis) indicates the degree to which the spatial orientation of a path code aligns with the grid axes, with larger values (e.g. the spatial orientation [1, 3, and 5]) indicating a perfect match between and grid axes. (C) Simulated vectorial representation of the HPC for centered-goal-based navigation. The threefold periodicity is driven by vectorial gradients inherited from . (D) Random-goal-based navigational simulation. Significant spectral power of model performance was observed at threefold across 100 randomly selected goal locations (the blue dots and gray lines; p<0.05, corrected for multiple comparisons). The red dashed line indicates the significance threshold derived from permutation. The blue-shaded areas denote the standard error. Gray lines represent the spectral powers of goal-dependent simulations.
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Figure 6—source data 1
Related to Figure 6C.
- https://cdn.elifesciences.org/articles/107517/elife-107517-fig6-data1-v1.xlsx
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Figure 6—source data 2
Related to Figure 6D.
- https://cdn.elifesciences.org/articles/107517/elife-107517-fig6-data2-v1.xlsx
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Spatially periodic computation in the entorhinal-hippocampal circuit during navigation
eLife 14:RP107517.
https://doi.org/10.7554/eLife.107517.4
