Path integration and the neural basis of the 'cognitive map'

Key Points

  • Accumulating evidence indicates that the foundation of mammalian spatial orientation and learning is based on an internal network that can keep track of relative position and orientation (from an arbitrary starting point) on the basis of integration of self-motion cues derived from locomotion, vestibular activation and optic flow (path integration).

  • Place cells in the hippocampal formation exhibit elevated activity at discrete spots in a given environment, and this spatial representation is determined primarily on the basis of which cells were active at the starting point and how far and in what direction the animal has moved since then. Environmental features become associatively bound to this intrinsic spatial framework and can serve to correct for cumulative error in the path integration process.

  • Theoretical studies suggested that a path integration system could involve cooperative interactions (attractor dynamics) among a population of place coding neurons, the synaptic coupling of which defines a two-dimensional attractor map. These cells would communicate with an additional group of neurons, the activity of which depends on the conjunction of movement speed, location and orientation (head direction) information, allowing position on the attractor map to be updated by self-motion information.

  • The attractor map hypothesis contains an inherent boundary problem: what happens when the animal's movements carry it beyond the boundary of the map? One solution to this problem is to make the boundaries of the map periodic by coupling neurons at each edge to those on the opposite edge, resulting in a toroidal synaptic matrix. This solution predicts that, in a sufficiently large space, place cells would exhibit a regularly spaced grid of place fields, something that has never been observed in the hippocampus proper.

  • Recent discoveries in layer II of the medial entorhinal cortex (MEC), the main source of hippocampal afferents, indicate that these cells do have regularly spaced place fields (grid cells). In addition, cells in the deeper layers of this structure exhibit grid fields that are conjunctive for head orientation and movement speed. Pure head direction neurons are also found there. Therefore, all of the components of previous theoretical models for path integration appear in the MEC, suggesting that this network is the core of the path integration system.

  • The scale of MEC spatial firing grids increases systematically from the dorsal to the ventral poles of this structure, in much the same way as is observed for hippocampal place cells, and we show how non-periodic hippocampal place fields could arise from the combination of inputs from entorhinal grid cells, if the inputs cover a range of spatial scales rather than a single scale. This phenomenon, in the spatial domain, is analogous to the low frequency 'beats' heard when two pure tones of slightly different frequencies are combined.

  • The problem of how a two-dimensional synaptic matrix with periodic boundary conditions, postulated to underlie grid cell behaviour, could be self-organized in early development is addressed. Based on principles derived from Alan Turing's theory of spontaneous symmetry breaking in chemical systems, we suggest that topographically organized, grid-like patterns of neural activity might be present in the immature cortex, and that these activity patterns guide the development of the proposed periodic synaptic matrix through a mechanism involving competitive synaptic plasticity.


The hippocampal formation can encode relative spatial location, without reference to external cues, by the integration of linear and angular self-motion (path integration). Theoretical studies, in conjunction with recent empirical discoveries, suggest that the medial entorhinal cortex (MEC) might perform some of the essential underlying computations by means of a unique, periodic synaptic matrix that could be self-organized in early development through a simple, symmetry-breaking operation. The scale at which space is represented increases systematically along the dorsoventral axis in both the hippocampus and the MEC, apparently because of systematic variation in the gain of a movement-speed signal. Convergence of spatially periodic input at multiple scales, from so-called grid cells in the entorhinal cortex, might result in non-periodic spatial firing patterns (place fields) in the hippocampus.

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Figure 1: One-dimensional attractor map model for head direction encoding based on neural integration of head angular velocity signals.
Figure 2: Extension of the one-dimensional attractor map concept to two dimensions: a model for path integration.
Figure 3: Solving the boundary problem for the path integration network.
Figure 4: Grid cells in the medial entorhinal cortex.
Figure 5: Changing the gain of the self-motion signal changes the scale of the spatial representation.
Figure 6: Combining multiple periodic grids at different spatial scales can result in non-periodic place fields.
Figure 7: Symmetry breaking and the emergence of a grid-like firing pattern.
Figure 8: Developmental model for an anatomically non-topographic MEC path integrator.


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This work was supported by a US PHS grant (B.L.M.), by a grant from The Netherlands Organization for Scientific Research, and by a Centre of Excellence grant from the Norwegian Research Council.

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Correspondence to Bruce L. McNaughton.

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Attractor dynamics

Attractor dynamics refer to the properties of a broad class of neural networks that have one or more stable states. These stable states are determined by the weights of the recurrent connections between the units (neurons) in the network. Depending on the initial conditions, the network will end up in one of the stable states. Attractor dynamics have been used in associative memory models, pattern recognition and as a mechanism for working memory maintenance.

Continuous attractor

Networks with continuous attractor properties can maintain a stable activity state over time; however, the possible states are not discrete as in attractor networks but can vary continuously. Continuous attractor networks have, for example, been used to represent the dynamics of the head direction system in which an arbitrary angle has to be maintained over time.

Vestibular system

The vestibular system provides information about movement and orientation in space. Receptors in the semicircular canals and otolith organs of the inner ear are sensitive to movements consisting of rotational and translational accelerations. Vestibular information can be processed in the CNS to derive relative changes in head direction or position.

Rotational visual flow

As the head turns, visual information flows past the eye. The rotational visual flow can be used to calculate and update relative head direction.


Consider an elastic rectangular sheet. When gluing together the two longer sides of the sheet a tube is formed. After gluing together the ends of the tube, a doughnut-shaped object is formed, which is termed a torus. If the elastic sheet represents a map of a spatial area, the creation of the torus will form a map with periodic boundary conditions along two perpendicular dimensions.


Mathematically, two lists of numbers (vectors) with a correlation of exactly zero are said to be orthogonal. Hippocampal spatial codes are said to be orthogonal with respect to two arbitrary spatial environments if the locations and rates at which cells fire relative to each other are statistically independent.

Allocentric space

In contrast to egocentric spatial representations, in which locations are encoded relative to a body axis (for example, 'three feet to one's left'), allocentric representations are independent of the observer's orientation (for example, 'three feet to the north of one's current location') or possibly even position (for example, '32 °N, 111 °W'). A road map is an example of an allocentric representation of space.

Population vectors

A population vector is a list of the instantaneous firing rates of a population of neurons. For N neurons, it represents a point in an abstract, N-dimensional space. It provides a convenient representation of the state of a neural ensemble.

Theta rhythm

Spontaneous oscillatory activity (4–12 Hz) detected in the local field potential of the rat hippocampus. The theta rhythm is produced by large ensembles of hippocampal neurons oscillating in synchrony, and is coherent in phase throughout the hippocampus. Its amplitude, however, varies systematically along the septotemporal axis of the hippocampus.

'Beat' effect

When two pure tones (or periodic signals of any kind) of different frequencies are added together, a tone of lower frequency (the difference between the two fundamentals) emerges due to the gradual shift of relative phase of the two signals, which causes cancellation and summation alternately. In music terminology, this lower frequency is called a 'beat'.

Difference of Gaussians or Mexican hat

If two Gaussian curves with different variances are subtracted from one another, the outcome is a curve that has a central peak with surrounding troughs (or vice versa). Depending on the difference in variance of the initial curves, the outcome can resemble a sombrero or 'Mexican hat'. This description has been applied, for example, to simple cells of the visual system with excitatory centres and inhibitory surrounds.


Extracellular potentials generated by a spiking neuron decline with distance from the current source. A tetrode is a four channel recording probe that can be used to isolate spike trains simultaneously from multiple neurons within a small region of brain, based on the relative amplitudes of spikes appearing simultaneously on the different channels.


When stimulated by a constant synaptic current, many neurons exhibit a firing rate response that is relatively high at stimulus onset, but soon settles to a lower level. This neural accommodation is often mediated by slow-opening K+ channels, which reduce membrane resistance and thereby reduce membrane depolarization for a given current.

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McNaughton, B., Battaglia, F., Jensen, O. et al. Path integration and the neural basis of the 'cognitive map'. Nat Rev Neurosci 7, 663–678 (2006).

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