Spatially periodic computation in the entorhinal-hippocampal circuit during navigation

The cognitive map, initially introduced by Tolman, 1948 and later supported by the discovery of place cells in the hippocampus (HPC; O’Keefe and Dostrovsky, 1971), has served as a framework for spatial navigation. Grid cells in the upstream entorhinal cortex (EC), known for their hexagonal firing pattern to provide the metric for space (Hafting et al., 2005), have also been found to represent conceptual space beyond the physical reference frame (Constantinescu et al., 2016; Bao et al., 2019; Raithel et al., 2023). These findings suggest that the EC-HPC circuit fundamentally organizes spatial and non-spatial knowledge (Epstein et al., 2017; Behrens et al., 2018; Bottini and Doeller, 2020; Park et al., 2020), and to guide flexible behaviors such as retrieving knowledge from the past and making decisions for the future (Addis et al., 2007; Hassabis and Maguire, 2007; Schacter et al., 2012).

Flexible navigation requires the mental simulation of prospective pathways on a cognitive map, which is defined by essential cues such as self-location, goal location, direction, and distance (Nyberg et al., 2022). This process necessarily involves dynamic representations of the external world relative to self-location. Converging evidence indicates that the HPC binds spatial cues into vectorial representations, providing activity gradients that reflect potential pathways toward goals. In bats, a subpopulation of CA1 neurons exhibited conjunctive tuning to both direction and distance, with activity gradually decaying within 10–15 min after the goal is displaced (Sarel et al., 2017). In rats, similar findings were observed for neurons tuned to featureless goal locations distributed across space (Ormond and O’Keefe, 2022). These neurons fire maximally when the animal is oriented toward the goal and rapidly reorganize following goal shifts. Consistently, the neural representation of prospective pathways in the human brain is affected by goal locations (Muhle-Karbe et al., 2023). The neural geometry derived from the BOLD signals in the HPC is distorted by goals, reflecting the successful learning of goal-directed navigation. Collectively, these findings suggest that the formation of prospective pathways relies on memory-based vectorial representations in the HPC. However, these studies raise the question of how grid cells in the EC contribute to this process.

We hypothesize that projections from EC grid cell populations provide a coherent cognitive-map framework in the HPC that embeds a threefold periodic structure across spatial directions to support vectorial representations and simulating the prospective pathways. Grid cells exhibit hexagonal firing patterns with nearly invariant orientations (Hafting et al., 2005; Sargolini et al., 2006; Krupic et al., 2012; Gardner et al., 2022). These properties may support the formation of vector-like representations of pathways by coactivation of grid cell populations. In the simplest case, when one mentally simulates a straight pathway aligned with the grid orientation, a subpopulation of grid cells would be sequentially activated, and the resulting population activity would manifest a near-perfect vectorial representation with constant activity strength along the pathway. In contrast, when the pathway is misaligned with the grid orientation, the corresponding grid cell population yields a distorted vectorial code. Consequently, simulating straight pathways spanning 0°–360° yields only half the number of unique activity patterns. This arises because the hexagonal grid’s 180° rotational symmetry makes orientations separated by 180° indistinguishable. We therefore speculate that the vectorial representations embedded in grid cell activity are periodic across spatial orientations and are transmitted through the EC–HPC circuit to bind prospective path directions. Consistent with this idea, reorientation paradigms in both rodents and young children demonstrate that subjects search equally at two opposite directions, reflecting successful orientation encoding but a failure to integrate spatial direction (Hermer and Spelke, 1994; Julian et al., 2015; Gallistel, 2017; Julian et al., 2018).

This hypothesis is supported by evidence from anatomical, functional, computational, and physiological findings on the EC–HPC circuit. Anatomically, the EC serves as one of the major sources of input to the downstream HPC (Witter and Amaral, 1991; van Groen et al., 2003; Garcia and Buffalo, 2020). Functionally, grid cells in the medial EC exhibited multiplexed and heterogeneous responses corresponding to position, direction, and speed before they are integrated in the HPC (Sargolini et al., 2006; Hardcastle et al., 2017). Computationally, grid cells have been proposed as the foundation of hippocampal place field formation by integrating multiple grid modules (Solstad et al., 2006; de Almeida et al., 2009; Bush et al., 2014; Bush et al., 2015; Bicanski and Burgess, 2019). Physiologically, EC lesions disrupt the precision and stability of place fields (Hales et al., 2014), leading to reduced discharge rates and field sizes (Van Cauter et al., 2008). If our hypothesis is correct, a threefold periodicity aligned with the three principal grid axes should emerge in the HPC, phase-locked with EC activity along path directions. Because simultaneous population-level recordings from the EC and HPC remain technically challenging, we employed fMRI, which has previously revealed sixfold periodicity in the EC (Doeller et al., 2010; Constantinescu et al., 2016; Bao et al., 2019; Wagner et al., 2023; Raithel et al., 2023), to test for periodicity in the HPC.

A novel 3D object, named Greeble (Figure 1A; Gauthier and Tarr, 1997), was used to create a conceptual Greeble space. Within this space, locations were represented by Greeble variants characterized by two features (‘Loogit’ and ‘Vacso’). The feature length defined the two dimensions of the space. The central Greeble served as the prototype. Participants were instructed to morph Greeble variants to match this target prototype (Figure 1B). This process generated a sequence of Greebles that resembled movements along navigational path in a two-dimensional conceptual space (Figure 1C), although participants were unaware of the underlying Greeble space. To ensure a comprehensive exploration of the Greeble space for detecting hippocampal periodicity, Greeble variants were pseudo-randomly sampled at the periphery of space. This ensured a high-resolution sampling of conceptual directions ranging from 0° to 360° (i.e. the orange locations in Figure 1C), while controlling for distance. As a result, we observed a threefold periodicity in hippocampal activity, cross-validated using sinusoidal modulation and spectral analyses. The spatial phase of the HPC was coupled with the sixfold periodicity in the EC; no spatial offset was identified. In addition, we identified a threefold periodicity in participants’ behavioral performance that was phase-locked with hippocampal activity. Finally, the EC–HPC PhaseSync model, developed to simulate EC projections into the HPC, reproduced the emergence of threefold activity periodicity across directions under randomized goal locations. Together, these empirical findings highlight a periodic representation of conceptual directions within the HPC, suggesting that vectorial representations in the hippocampus may arise through projections from periodic grid codes in the EC.

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.