Organizing conceptual knowledge in humans with a gridlike code

Abstract

It has been hypothesized that the brain organizes concepts into a mental map, allowing conceptual relationships to be navigated in a manner similar to that of space. Grid cells use a hexagonally symmetric code to organize spatial representations and are the likely source of a precise hexagonal symmetry in the functional magnetic resonance imaging signal. Humans navigating conceptual two-dimensional knowledge showed the same hexagonal signal in a set of brain regions markedly similar to those activated during spatial navigation. This gridlike signal is consistent across sessions acquired within an hour and more than a week apart. Our findings suggest that global relational codes may be used to organize nonspatial conceptual representations and that these codes may have a hexagonal gridlike pattern when conceptual knowledge is laid out in two continuous dimensions.

Fig. 1. Experimental design for navigation in abstract space.

(A) Subjects were trained to associate stimuli (birds) with outcomes (Christmas symbols). (B) Example trajectory in abstract space. A location in this abstract space was represented by a bird stimulus. A trajectory was equivalent to visually morphing one bird into another (Fig. 1C). The direction θ of the trajectory depended on the ratio of the rates of change of the legs and the neck (Movie S1). Subjects were not consciously aware that these associations could be organized in a continuous “bird space”. (C) Example trial corresponding to the trajectory with direction θ. (D) Trajectories can be categorized as aligned (red sectors) or misaligned (grey sectors) with the mean orientation φ of the hexagonal grid Note that φ is different for each participant (see(26) for details on how φ was calculated). Here, the direction θ is aligned with the grid. (E) fMRI markers of grid cells showing hexagonal symmetry: the signal is bigger for trajectories aligned versus those misaligned with the grid. (F) Color-coded trajectory maps illustrating time spent in each part of the environment during the “explore” task in the first (quantile1) and last parts of training (quantile5). Yellow is maximum and dark blue is 0. Barplots showing the amount of time spent at the locations/stimuli paired with outcomes in each epoch relative to the total time spent navigating (“time at outcomes” quantile1 vs quantile5, t₂₂=-3.17, ** p<0.01). (G) In the “collect” task, participants made significant improvements in training day 2 compared to training day 1: the percentage of trials with an angle error < 15° (t₃₃=2.37, * p<0.05) and with only one transition increased (t₃₃=2.55, * p<0.05). In the “recall” task, participants made significantly more correct responses in day 2 compared to day 1 (t₄₁=3.89, *** p<0.001). (H) Example data from the most commonly used schedule: even distribution of trajectory angles across all trials (light grey), outcome trials (medium grey) and non-outcome trials (dark grey). (I) Example data from the most commonly used schedule: we tested if the sin(6θ) and cos(6θ) regressors correlated with multiple confounding factors. These regressors did not correlate with the start neck, start legs, end neck and end legs lengths, whether the subject responded accurately or whether the morph passed through an outcome (all coefficients of determination R² averaged across all subjects < 0.02). (D and E are adapted by permission from Nature, Doeller et al, 2010).

Fig. 2. Identifying hexagonally symmetric signals across the whole brain.

(A) Hexagonal modulation in a network of brain regions including the medial prefrontal cortex, with a peak in its ventral region (vmPFC; peak Montreal Neurological Institute coordinates -8/42/0, peak Z-score = 4.09), the medial entorhinal (ERH; -18/0/-38; Z = 4.41), the orbitofrontal (OFC; 6/44/-10; Z = 4.27), the posterior cingulate (PCC; 0/-32/28; Z = 4.3), retrosplenial (RSC; 6/-52/24; Z = 4.73) and lateral parietal cortices (LPC; 30/-62/28; Z = 4.96) and the temporoparietal junction (TPJ; 52/-42/40; Z = 4.13). For visualization purposes, the maps are cluster corrected at a cluster threshold Z = 3.1 and p < 0.05 for all brain regions apart from the ERH where we used a more lenient threshold of Z = 2.3 and p < 0.05. (B) Subjects who performed better at the task had significantly more hexagonal signal modulation in the vmPFC (correlation coefficient r = 0.432, p = 0.039).

Fig. 3. Grid angle consistency between separate sessions acquired within the same day.

(A) Left: Whole brain level grid angle consistency in vmPFC (cluster corrected Z = 2.3 and p < 0.05; 16/54/-2; Z = 3.76, p < 0.0001). Right: participants with higher hexagonal consistency performed more accurately on the task (r = 0.431, p = 0.039). (B-C) Left panels: 6-fold modulation signals aligned to the same grid angle in the vmPFC (t₂₆ = 2.61, * p < 0.05) and ERH (t₂₇ = 2.36, * p < 0.05). The effect is plotted separately for all aligned (red) and misaligned (grey) trajectories. Right panels: this effect was specific for 6-fold, but not any other control periodicities between 4- and 8-fold (all p > 0.15).

Fig. 4. Grid angle consistency between separate sessions acquired more than a week apart.

(A) Cross-day consistency of the grid angle in vmPFC (left panel t₂₀ = 3.65, ** p<0.01; right panel all p > 0.18 for control periodicities). (B) Within- and cross-day consistency in vmPFC (left panel t₂₀ = 3.41, ** p < 0.01; right panel all control p > 0.15). (C) Cross-region consistency between the ERH and vmPFC (left panel t₂₁ = 2.18, * p < 0.05; right panel all control p > 0.46).