Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

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.

Abstract

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.

This is a preview of subscription content

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

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.

References

  1. O'Keefe, J. Place units in the hippocampus of the freely moving rat. Exp. Neurol. 51, 78–109 (1976). The first theoretical suggestion of a landmark-independent navigational system upstream of the hippocampus.

    CAS  Article  PubMed  Google Scholar 

  2. O'Keefe, J. & J. Dostrovsky The hippocampus as a spatial map: preliminary evidence from unit activity in the freely moving rat. Brain Res. 34, 171–175. (1971).

    CAS  PubMed  Article  Google Scholar 

  3. O'Keefe, J. & Nadel, L. The Hippocampus as a Cognitive Map (Clarendon, Oxford, 1978).

    Google Scholar 

  4. Mittelstaedt, M. L. & Mittelstaedt, H. Homing by path integration in a mammal. Naturwissenschaften 67, 566–567 (1980) (in German). The first report of path integration in a mammal.

    Article  Google Scholar 

  5. Taube, J. S., Muller, R. U. & Ranck, J. B. Jr. Head-direction cells recorded from the postsubiculum in freely moving rats. I. Description and quantitative analysis. J. Neurosci. 10, 420–435 (1990). The first quantitative description of head direction-sensitive cells in the brain.

    CAS  PubMed  Article  PubMed Central  Google Scholar 

  6. Ranck, J. B. in Electrical Activity of the Archicortex (eds. Buzsaki, G. & Vanderwolf, C. H.) 217–220 (Akademiai Kiado, Budapest, 1985). The first report of head direction-sensitive cells in the brain.

    Google Scholar 

  7. O'Keefe, J. Do hippocampal pyramidal cells signal non-spatial as well as spatial information? Hippocampus 9, 352–364 (1999).

    CAS  PubMed  Article  Google Scholar 

  8. Eichenbaum, H., Dudchenko, P., Wood, E., Shapiro, M & Tanila, H. The hippocampus, memory, and place cells: is it spatial memory or a memory space? Neuron 23, 209–226 (1999).

    CAS  PubMed  Article  Google Scholar 

  9. McNaughton, B. L. et al. Deciphering the hippocampal polyglot: the hippocampus as a path integration system. J. Exp. Biol. 199, 173–185 (1996).

    CAS  PubMed  Article  Google Scholar 

  10. Leutgeb, S., Leutgeb, J. K., Moser, M.-B. & Moser, E. I. Place cells, spatial maps and the population code for memory. Curr. Opin. Neurobiol. 15, 738–746 (2005).

    CAS  PubMed  Article  Google Scholar 

  11. Leutgeb, S. et al. Independent codes for spatial and episodic memory in the hippocampal neuronal ensembles. Science 309, 619–623 (2005). Evidence that hippocampal place cells can simultaneously transmit information about the location and content of an experience.

    CAS  PubMed  Article  Google Scholar 

  12. Etienne, A. S. & Jeffery, K. J. Path integration in mammals. Hippocampus 14, 180–192 (2004).

    PubMed  Article  Google Scholar 

  13. Hebb, D. O. The Organization of Behavior (Wiley, New York, 1949). A seminal work on which much of modern neural network theory is founded, including the concepts of associative synaptic plasticity, cell assemblies and phase sequences.

    Google Scholar 

  14. McNaughton, B. L., Chen, L. L. & Markus, E. J. 'Dead reckoning', landmark learning, and the sense of direction: a neurophysiological and computational hypothesis. J. Cog. Neurosci. 3, 190–202 (1991). An early version of the head direction path integrator model which formed the conceptual basis of subsequent continuous attractor models for path integration.

    CAS  Article  Google Scholar 

  15. Wilson, H. R. & Cowan, J. D. A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Kybernetik 13, 55–80 (1973).

    CAS  PubMed  Article  Google Scholar 

  16. Amari, S. Dynamics of pattern formation in lateral-inhibition type neural fields. Biol. Cybern. 27, 77–87 (1977).

    CAS  PubMed  Article  Google Scholar 

  17. Ermentrout, G. B. & Cowan, J. D. A mathematical theory of visual hallucination patterns. Biol. Cybern. 34, 137–150 (1979).

    CAS  PubMed  Article  Google Scholar 

  18. Droulez, J. & Berthoz, A. A neural network model of sensoritopic maps with predictive short-term memory properties. Proc. Natl. Acad. Sci. U.S.A. 88, 9653–9657 (1991).

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  19. Tsodyks, M. & Sejnowski, T. Associative memory and hippocampal place cells. Int. J. Neural Syst. 6, S81–S86 (1995). One of the first papers to advance the concept of a system of continuous attractors.

    Google Scholar 

  20. Tsodyks M. Attractor neural network models of spatial maps in hippocampus. Hippocampus 9, 481–489 (1999).

    CAS  PubMed  Article  Google Scholar 

  21. Battaglia, F. P. & Treves, A. Attractor neural networks storing multiple space representations: a model for hippocampal place fields. Phys. Rev. E 58, 7738–7753 (1998).

    CAS  Article  Google Scholar 

  22. Skaggs, W. E., Knierim, J. J., Kudrimoti, H. & McNaughton, B. L. in Advances in Neural Information Processing Systems Vol. 7 (eds Tesauro, G., Touretzky, D. S. & Leen, T. K.) 173–180 (MIT Press, Cambridge, Massachusetts, 1995).

    Google Scholar 

  23. Zhang, K. Representation of spatial orientation by the intrinsic dynamics of the head-direction cell ensemble: a theory. J. Neurosci. 16, 2112–2126 (1996). A periodic continuous attractor model of head direction cell by angular velocity integration.

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  24. Redish, A. D., Elga, A. N. & Touretzky, D. S. A coupled attractor model of the rodent head direction system. Netw. Comput. Neural Syst. 7, 671–685 (1996).

    Article  Google Scholar 

  25. Touretzky, D. S. & Redish, A. D. Theory of rodent navigation based on interacting representations of space. Hippocampus 6, 247–270 (1996).

    CAS  PubMed  Article  Google Scholar 

  26. Samsonovich, A. & McNaughton, B. L. Path integration and cognitive mapping in a continuous attractor neural network model. J. Neurosci. 17, 5900–5920 (1997). The origin of the concept of periodic boundaries in the two-dimensional continuous attractor network that might underlie path integration and the medial entorhinal grid cells.

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  27. Conklin, J. & Eliasmith, C. A controlled attractor network model of path integration in the rat. J. Comput. Neurosci. 18, 183–203 (2005).

    PubMed  Article  Google Scholar 

  28. McNaughton, B. L., Leonard, B. & Chen, L. Cortical-hippocampal interactions and cognitive mapping: a hypothesis based on reintegration of the parietal and inferotemporal pathways for visual processing. Psychobiol. 17, 236–246 (1989).

    Article  Google Scholar 

  29. Shen, J., Barnes, C. A., McNaughton, B. L., Skaggs, W. E. and Weaver, K. L. The effect of aging on experience-dependent plasticity of hippocampal place cells. J. Neurosci. 17, 6769–6782 (1997).

    CAS  PubMed  Article  PubMed Central  Google Scholar 

  30. Maurer, A. D. et al. Organization of hippocampal cell assemblies based on theta phase precession. Hippocampus (in the press).

  31. Wilson, M. A. & McNaughton, B. L. Dynamics of the hippocampal ensemble code for space. Science 261, 1055–1058 (1993). Modern empirical understanding of hippocampal neurodynamics is strongly aided by the ability to record simultaneously from many neurons in the freely behaving animal, for which this paper was a landmark.

    CAS  PubMed  Article  Google Scholar 

  32. Quirk G. J., Muller R. U. & Kubie, J. L. The firing of hippocampal place cells in the dark depends on the rat's recent experience. J. Neurosci. 10, 2008–2017 (1990).

    CAS  PubMed  Article  PubMed Central  Google Scholar 

  33. Gothard, K. M., Skaggs, W. E. & McNaughton, B. L. Dynamics of mismatch correction in the hippocampal ensemble code for space: interaction between path integration and environmental cues. J. Neurosci. 16, 8027–8040 (1996).

    CAS  PubMed  Article  PubMed Central  Google Scholar 

  34. Gothard, K. M., Hoffman, K. L., Battaglia, F. P. & McNaughton, B. L. Dentate gyrus and CA1 ensemble activity during spatial reference frame shifts in the presence and absence of visual input. J. Neurosci. 21, 7284–7292 (2001).

    CAS  PubMed  Article  PubMed Central  Google Scholar 

  35. Knierim, J. J., Kudrimoti, H. S. & McNaughton, B. L. Place cells, head direction cells, and the learning of landmark stability. J. Neurosci. 15, 1648–1659 (1995).

    CAS  PubMed  Article  PubMed Central  Google Scholar 

  36. Redish, A. D. & Touretzky, D. S. The role of the hippocampus in solving the Morris water maze. Neural Comput. 10, 73–111 (1998).

    CAS  PubMed  Article  Google Scholar 

  37. Sharp, P. E. Complimentary roles for hippocampal versus subicular/entorhinal place cells in coding place, context, and events. Hippocampus 9, 432–443 (1999).

    CAS  PubMed  Article  Google Scholar 

  38. Fyhn, M., Molden, S., Witter, M. P., Moser, E. I. & Moser, M.-B. Spatial representation in the entorhinal cortex. Science 305, 1258–1264 (2004). Preceding the discovery of grid cells, this study reports that spatial position is represented accurately among ensembles of principal neurons in superficial layers of the MEC. The scale of representation increases along the dorsoventral axis of the MEC.

    CAS  PubMed  Article  Google Scholar 

  39. Hafting, T., Fyhn, M., Molden, S., Moser, M.-B. & Moser, E. I. Microstructure of a spatial map in the entorhinal cortex. Nature 436, 801–806 (2005). Reports the discovery of grid cells. Based on the regular and invariant firing structure of these cells and their insensitivity to external environmental perturbation, grid cells are suggested as a foundation for a universal path integration-based neuronal map of the spatial environment.

    CAS  PubMed  Article  Google Scholar 

  40. Fyhn, M., Hafting, T., Treves, A., Moser, M.-B. & Moser, E. I. Preserved spatial and temporal firing structure in entorhinal grid cells during remapping in the hippocampus. Soc. Neurosci. Abstr. 198. 6 (2005).

    Google Scholar 

  41. Goodridge, J. P. & Taube, J. S. Preferential use of the landmark navigational system by head direction cells in rats. Behav. Neurosci. 109, 49–61 (1995).

    CAS  PubMed  Article  Google Scholar 

  42. Sharp, P. E. Subicular cells generate similar spatial firing patterns in two geometrically and visually distinctive environments: comparison with hippocampal place cells. Behav. Brain Res. 85, 71–92 (1997).

    CAS  PubMed  Article  Google Scholar 

  43. Sargolini, F. et al. Conjunctive representation of position, direction and velocity in the medial entorhinal cortex. Science 312, 758–762 (2006). Reports the discovery of head direction cells and cells with conjunctive grid and head direction properties in separate layers of the MEC.

    CAS  Article  PubMed  Google Scholar 

  44. van Haeften, T., Wouterlood, F. G., Jorritsma-Byham, B. & Witter, M. P. GABAergic presubicular projections to the medial entorhinal cortex of the rat J. Neurosci. 17, 862–874 (1997).

    CAS  PubMed  Article  PubMed Central  Google Scholar 

  45. Burwell, R. D. The parahippocampal region: corticocortical connectivity. Ann. NY Acad. Sci. 911, 25–42 (2000).

    CAS  PubMed  Article  Google Scholar 

  46. Witter, M. P. & Amaral, D. G. in The Rat Nervous System 3rd edn (ed. Paxinos, G.) 637–703 (Academic, San Diego, 2004). A systematic and comprehensive overview of the anatomy of hippocampal and parahippocampal areas.

    Google Scholar 

  47. van Haeften, T., Baks- te-Bulte, L., Goede, P. H., Wouterlood, F. G. & Witter, M. P. Morphological and numerical analysis of synaptic interactions between neurons in deep and superficial layers of the entorhinal cortex of the rat. Hippocampus 13, 943–952 (2003). Provides direct electron microscopic evidence for synaptic interactions between cells in deep and superficial layers of the MEC.

    PubMed  Article  Google Scholar 

  48. Kloosterman, F., van Haeften, T., Witter, M. P. & Lopes Da Silva, F. H. Electrophysiological characterization of interlaminar entorhinal connections: an essential link for re-entrance in the hippocampal-entorhinal system. Eur. J. Neurosci. 18, 3037–3052 (2003).

    PubMed  Article  Google Scholar 

  49. Lingenhohl, K. & Finch, D. M. Morphological characterization of rat entorhinal neurons in vivo: soma-dendritic structure and axonal domains. Exp. Brain Res. 84, 57–74 (1991).

    CAS  PubMed  Article  Google Scholar 

  50. Dhillon, A. & Jones, R. S. Laminar differences in recurrent excitatory transmission in the rat entorhinal cortex in vitro. Neuroscience 99, 413–422 (2000).

    CAS  PubMed  Article  Google Scholar 

  51. Fuhs, M. C. & Touretzky, D. S. A spin glass model of path integration in rat medial entorhinal cortex. J. Neurosci. 26, 4266–4276 (2006).

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  52. Parron, C. & Save, E. Evidence for entorhinal and parietal cortices involvement in path integration in the rat. Exp. Brain Res. 159, 349–359 (2004).

    PubMed  Article  Google Scholar 

  53. O'Keefe, J. & Conway, D. H. Hippocampal place units in the freely moving rat: why they fire where they fire. Exp. Brain Res. 31, 573–590 (1978).

    CAS  PubMed  Article  Google Scholar 

  54. Markus, E. J., et al. Interactions between location and task affect the spatial and directional firing of hippocampal neurons. J. Neurosci. 15, 7079–7094 (1995).

    CAS  PubMed  Article  PubMed Central  Google Scholar 

  55. Bostock, E., Muller, R. U. & Kubie, J. L. Experience-dependent modifications of hippocampal place cell firing. Hippocampus 1, 193–205 (1991). The first systematic report of remapping in hippocampal place cells.

    CAS  PubMed  Article  Google Scholar 

  56. Wood, E. R., Dudchenko, P. A., Robitsek, R. J. & Eichenbaum, H. Hippocampal neurons encode information about different types of memory episodes occurring in the same location. Neuron 27, 623–633 (2000).

    CAS  PubMed  Article  Google Scholar 

  57. Bower, M. R., Euston, D. R. & McNaughton, B. L. Sequential-context-dependent hippocampal activity is not necessary to learn sequences with repeated elements. J. Neurosci. 25, 1313–1323 (2005).

    CAS  PubMed  Article  PubMed Central  Google Scholar 

  58. Gloveli, T., Dugladz, T., Schmitz, D. & Heineman, U. Properties of entorhinal cortex deep layer neurons projecting to the rat dentate gyrus. Eur. J. Neurosci. 13, 413–420 (2001).

    CAS  PubMed  Article  Google Scholar 

  59. Muller, R. U., Stead, M. & Pach, J. The hippocampus as a cognitive graph. J. Gen. Physiol. 107, 663–694 (1996).

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  60. Terrazas, A., et al. Self-motion and the hippocampal spatial metric. J. Neurosci. 25, 8085–8096 (2005). By attenuating self-motion signals, the authors show that a speed signal is essential for determining the scale of the hippocampal place representation.

    CAS  PubMed  Article  PubMed Central  Google Scholar 

  61. McNaughton, B. L., Barnes, C. A. & O'Keefe, J. The contributions of position, direction, and velocity to single unit activity in the hippocampus of freely-moving rats. Exp. Brain Res. 52, 41–49 (1983).

    CAS  PubMed  Article  Google Scholar 

  62. Jung, M. W., Wiener, S. I. & McNaughton, B. L. Comparison of spatial firing characteristics of units in dorsal and ventral hippocampus of the rat. J. Neurosci. 14, 7347–7356 (1994).

    CAS  PubMed  Article  PubMed Central  Google Scholar 

  63. Maurer, A. P., VanRhoads, S. R., Sutherland, G. R., Lipa, P. & McNaughton, B. L. Self-motion and the origin of differential spatial scaling along the septo-temporal axis of the hippocampus. Hippocampus 15, 841–852 (2005). Suggests that the increase in spatial scale along the dorsoventral axis of the hippocampus is accompanied by a systematic reduction in the gain of self-motion signals to the hippocampus.

    PubMed  Article  Google Scholar 

  64. Kjelstrup, K. B. et al. Spatial scale expansion along the dorsal-to-ventral axis of hippocampal area CA3 in the rat. FENS Abstr. R11945 (2006).

  65. Vanderwolf, C. H. Hippocampal electrical activity and voluntary movement in the rat. Electroencephalogr. Clin. Neurophysiol. 26, 407–418 (1969). The original description of the relationship between hippocampal electroencephalograms and awake behaviour.

    CAS  PubMed  Article  Google Scholar 

  66. Whishaw, I. Q. & Vanderwolf, C. H. Hippocampal EEG and behavior: changes in amplitude and frequency of RSA (theta rhythm) associated with spontaneous and learned movement patterns in rats and cats. Behav. Biol. 8, 461–484 (1973).

    CAS  PubMed  Article  Google Scholar 

  67. Morris, R. G. M. & Hagan, J. J. in Neurobiology of the Hippocampus (ed. Seifert, W.) 321–331 (Academic, New York, 1983).

    Google Scholar 

  68. Shen, J., Barnes, C. A., McNaughton, B. L., Skaggs, W. E. & Weaver, K. L. The effect of aging on experience-dependent plasticity of hippocampal place cells. J. Neurosci. 17, 6769–6782 (1997).

    CAS  PubMed  Article  PubMed Central  Google Scholar 

  69. Ekstrom, A. D., Meltzer, J., McNaughton, B. L. & Barnes, C. A. NMDA receptor antagonism blocks experience-dependent expansion of hippocampal 'place fields'. Neuron 31, 631–638 (2001).

    CAS  PubMed  Article  Google Scholar 

  70. Czurko, A., Hirase, H., Csicsvari, J. & Buzsáki, G. Sustained activation of hippocampal pyramidal cells by 'space clamping' in a running wheel. Eur. J. Neurosci. 11, 344–352 (1999).

    CAS  PubMed  Article  Google Scholar 

  71. Foster, T. C., Castro, C. A. & McNaughton, B. L. Spatial selectivity of hippocampal neurons: dependence on preparedness for movement. Science 244, 1580–1582 (1989).

    CAS  PubMed  Article  Google Scholar 

  72. McNaughton, B. L. & Nadel, L. in Neuroscience and Connectionist Theory (eds. Gluck, M. A. & Rumelhart, D. E.) 1–63 (Lawrence Erlbaum Associates, Hillsdale, 1989).

    Google Scholar 

  73. Treves, A. & Rolls, E. T. Computational constraints suggest the need for two distinct input systems to the hippocampal CA3 network. Hippocampus 2, 189–199 (1992).

    CAS  PubMed  Article  Google Scholar 

  74. Muller, R. U., Kubie, J. L., Bostock, E. M., Taube, J. S. & Quirk, G. J. in Brain and Space (ed. Paillard, J.) 296–333 (Oxford University Press, London, 1991).

    Google Scholar 

  75. Muller, R. U. & Kubie, J. L. The effects of changes in the environment on the spatial firing of hippocampal complex-spike cells. J. Neurosci. 7, 1951–1968, (1987).

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  76. Bostock, E., Muller, R. U. & Kubie, J. L. Experience-dependent modifications of hippocampal place cell firing. Hippocampus 1, 193–205 (1991).

    CAS  PubMed  Article  Google Scholar 

  77. Kentros, C. et al. Abolition of long-term stability of new hippocampal place cell maps by NMDA receptor blockade. Science 280, 2121–2126 (1998).

    CAS  PubMed  Article  Google Scholar 

  78. Markus, E. J. et al. Interactions between location and task affect the spatial and directional firing of hippocampal neurons. J. Neurosci. 15, 7079–7094 (1995).

    CAS  PubMed  Article  PubMed Central  Google Scholar 

  79. Barnes, C. A., Suster, M. S., Shen, J. & McNaughton, B. L. Multistability of cognitive maps in the hippocampus of old rats. Nature 388, 272–275 (1997).

    CAS  PubMed  Article  Google Scholar 

  80. Marr, D. A theory of cerebellar cortex. J. Physiol. (Lond.) 202, 437–470 (1969).

    CAS  Article  Google Scholar 

  81. Albus, J. A theory of cerebellar function. Math. Biosci. 10, 25–61 (1971).

    Article  Google Scholar 

  82. Leutgeb, S., Leutgeb, J. K., Treves, A., Moser, M.-B. & Moser, E. I. Distinct ensemble codes in hippocampal areas CA3 and CA1. Science 305, 1295–1298 (2004).

    CAS  PubMed  Article  Google Scholar 

  83. Vazdarjanova, A. & Guzowski, J. F. Differences in hippocampal neuronal population responses to modifications of an environmental context: evidence for distinct, yet complementary, functions of CA3 and CA1 ensembles. J. Neurosci. 24, 6489–6496 (2004).

    CAS  PubMed  Article  PubMed Central  Google Scholar 

  84. Fuhs, M. C., VanRhoads, S. R., Casale, A. E. McNaughton, B. L. & Touretzky D. S. Influence of path integration versus environmental orientation on place cell remapping between visually identical environments. J. Neurophysiol. 94, 2603–2616 (2005).

    PubMed  Article  Google Scholar 

  85. Wills, T. J., Lever, C., Cacucci, F., Burgess, N. & O'Keefe, J. Attractor dynamics in the hippocampal representation of the local environment. Science 308, 873–876 (2005).

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  86. Hafting, T., Fyhn, M., Treves, A., Moser, E. I. & Moser, M. B. Coherent realignment of entorhinal grid cells coincides global remapping in the hippocampus. FENS Abstr. R11641 (2006).

  87. Hargreaves, E. L., Rao, G., Lee, I. & Knierim, J. J. Major dissociation between medial and lateral entorhinal input to dorsal hippocampus. Science 308, 1792–1794 (2005).

    CAS  PubMed  Article  Google Scholar 

  88. Witter, M. P., Holtrop, R. & van de Loosdrecht, A. A. Direct projections from the periallocortical subicular complex to the fascia dentata in the rat: an anatomical tracing study using phaseolus vulgaris leucoagglutinin. Neurosci. Res. Commun. 2, 61–68 (1988).

    Google Scholar 

  89. Naber, P. A., Witter, M. P. & Lopez da Silva, F. H. Perirhinal cortex input to the hippocampus in the rat: evidence for parallel pathways, both direct and indirect. A combined physiological and anatomical study. Eur. J. Neurosci. 11, 4119–4133 (1999).

    CAS  PubMed  Article  Google Scholar 

  90. Naber, P. A., Witter, M. P., Lopes da Silva, F. H. Evidence for a direct projection from the postrhinal cortex to the subiculum in the rat. Hippocampus 11, 105–117 (2001).

    CAS  PubMed  Article  Google Scholar 

  91. Turing A. M. The chemical basis of morphogenesis. Phil. Trans. R. Soc. B 237, 37–72 (1953); reprinted in Bull. Math. Biol. 52, 153–197 (1990). A landmark paper demonstrating that symmetry breaking can occur in the simple reaction-diffusion system. It is proposed that the symmetry breaking that results in spatially periodic structures can account for pattern formation in nature.

    Google Scholar 

  92. Swindale N. V. A model for the formation of ocular dominance stripes. Proc. R. Soc. Lond. B Biol. Sci. 208, 243–264 (1980). A neuronal model for the development of ocular dominance columns based on short-range excitation and long-range inhibition is proposed. The conceptual resemblance to Turing's theory is pointed out.

    CAS  PubMed  Article  Google Scholar 

  93. Murray, J. D. Mathematical Biology (Springer, Heidelberg, 1989).

    Book  Google Scholar 

  94. Jensen, O., Mosekilde, E., Borckmans, P. & Dewel, G. Computer simulation of Turing tructures in the chloride-iodide-malonic acid system. Physica Scripta 53, 243–251 (1996).

    CAS  Article  Google Scholar 

  95. Treves, A., Kropff, E. & Biswas, A. On the triangular grid of entorhinal place fields. Soc. Neurosci. Abstr. 198. 11 (2005).

    Google Scholar 

  96. Martinetz, T. & Schulten, K. A. in Artificial Neural Networks (eds. Kohonen, T., Makisara, K., Simula, O. & Kangas, J.) 397–402 (Elsevier, Amsterdam, 1991). Describes a neural network algorithm for extracting topology from an input set, which could be used to wire up a recurrent synaptic matrix with the appropriate periodicity to reproduce grid cell behaviour.

    Google Scholar 

  97. Bienenstock, E. L., Cooper, L. N. & Munro, P. W. Theory for the development of neuron selectivity: orientation specificity and binocular interaction in visual cortex. J. Neurosci. 2, 32–48 (1982). One of the first papers to show how a bi-directional, activity-dependent synaptic plasticity mechanism might account for the experience-dependent tuning of feature selectivity in the visual cortex. The postulated mechanism, now known as the BCM rule (after the first letters of the authors' last names), has been experimentally observed as an activity-dependent balance between long-term depression and long-term potentiation of synaptic transmission (see reference 99).

    CAS  PubMed  Article  PubMed Central  Google Scholar 

  98. Bear, M. F., Cooper, L. N. & Ebner, F. F. A physiological-basis for a theory of synapse modification. Science 237, 42–48 (1987).

    CAS  PubMed  Article  Google Scholar 

  99. Bear, M. F. & Malenka, R. C. Synaptic plasticity: LTP and LTD. Curr. Opin. Neurobiol., 4, 389–399 (1994).

    CAS  Article  Google Scholar 

  100. Law, C. & Cooper, L. Formation of receptive fields according to the BCM theory in realistic visual environments. Proc. Natl Acad. Sci. USA 91, 7797–7801 (1994).

    CAS  PubMed  Article  PubMed Central  Google Scholar 

  101. Intrator, N. & Cooper, L. N. Objective function formulation of the BCM theory of visual cortical plasticity: Statistical connections, stability conditions. Neural Networks 5, 3–17 (1992).

    Article  Google Scholar 

  102. Ichinohe, N. & Rockland, K. S. Region specific micromodularity in the uppermost layers in primate. Cereb. Cortex 14, 1173–1184 (2004).

    PubMed  Article  Google Scholar 

  103. Ikeda, J. et al. A columnar arrangement of dendritic processes of entorhinal cortex neurons revealed by a monoclonal antibody. Brain Res. 505, 176–179 (1989).

    CAS  PubMed  Article  Google Scholar 

  104. Solodkin, A. & Vanhoesen, G. W. Entorhinal cortex modules of the human brain. J. Comp. Neurol. 365, 610–627 (1996).

    CAS  PubMed  Article  Google Scholar 

  105. Feller, M. B. Spontaneous correlated activity in developing neural circuits. Neuron 22, 653–656 (1999).

    CAS  PubMed  Article  Google Scholar 

  106. Katz, L. C. & Shatz, C. J. Synaptic activity and the construction of cortical circuits. Science 274, 1133–1138 (1996).

    CAS  PubMed  Article  Google Scholar 

  107. McLaughlin, T., Torborg, C. L., Feller, M. B. & O'Leary, D. D. M. Retinotopic map refinement requires spontaneous retinal waves during a brief critical period of development. Neuron 40, 1147–1160 (2003).

    CAS  PubMed  Article  Google Scholar 

  108. Garaschuk, O., Linn, J., Eilers, J. & Konnerth, A. Large scale oscillatory calcium waves in the immature cortex. Nature Neurosci. 3, 452–459 (2000).

    CAS  PubMed  Article  Google Scholar 

  109. Aguilo, A., et al. Involvement of Cajal-Retzius neurons in spontaneous correlated activity of embryonic and postnatal layer 1 from wild-type and Reeler mice. J. Neurosci. 19, 10856–10868 (1999).

    CAS  PubMed  Article  PubMed Central  Google Scholar 

  110. Yuste, R., Nelson, D. A., Rubin, W. W. & Katz, L. C. Neuronal domains in developing neocortex: mechanisms of coactivation. Neuron 14, 7–17 (1995).

    CAS  PubMed  Article  Google Scholar 

  111. Peinado, A. Traveling slow waves of neural activity: a novel form of network activity in developing neocortex. J. Neurosci. 20, RC54(1–6) (2000). Along with reference 108, this paper is an important illustration of the rich neurodynamics that occur during the early postnatal development of the cortex, which might have an important role in the self-organization of the path integrator system.

    Article  Google Scholar 

  112. Buzsaki, G. Theta oscillations in the hippocampus. Neuron 33, 325–340 (2002).

    CAS  PubMed  Article  Google Scholar 

  113. Skaggs, W. E., McNaughton, B. L., Wilson, M. A. & Barnes, C. A. Theta phase precession in hippocampal neuronal populations and the compression of temporal sequences. Hippocampus 6, 149–172 (1996).

    CAS  PubMed  Article  Google Scholar 

  114. O'Keefe, J. & Recce M. L. Phase relationship between hippocampal place units and the EEG theta rhythm. Hippocampus 3, 317–330 (1993).

    CAS  PubMed  Article  Google Scholar 

  115. Yamaguchi, Y., Aota, Y., McNaughton, B. L. & Lipa, P. Bimodality of theta phase precession in hippocampal place cells in freely running rats. J. Neurophysiol. 87, 2629–2642 (2002).

    PubMed  Article  Google Scholar 

  116. Mehta, M. R., Barnes, C. A. & McNaughton, B. L. Experience-dependent, asymmetric expansion of hippocampal place fields. Proc. Natl Acad. Sci. USA 94, 8918–8921 (1997).

    CAS  PubMed  Article  PubMed Central  Google Scholar 

  117. Rosenzweig, E. S., Ekstrom, A. D., Redish, A. D., McNaughton, B. L. & Barnes, C. A. Phase precession as an experience-independent process: hippocampal pyramidal cell phase precession in a novel environment and under NMDA-receptor blockage. Soc. Neurosci. Abstr. 367. 10 (2000).

    Google Scholar 

  118. Kjelstrup, K. B. et al. Spatial scale expansion along the dorsal-to-ventral axis of hippocampal area CA3 in the rat. FENS Abstr. R11945 (2006).

  119. Teyler T. J. & Discenna, P. The hippocampal memory indexing system. Behav. Neurosci. 100, 147–154 (1986).

    CAS  PubMed  Article  Google Scholar 

  120. Squire L. R., Cohen, N. J. & Nadel, L. in Memory Consolidation (eds Weingartner, G. & Parker, E.) 185–210 (Earlbaum, Hillsdale, 1984).

    Google Scholar 

  121. O'Kane, D. & Treves, A. Why the simplest notion of neocortex as an autoassociative memory would not work. Network 3, 379–384 (1992).

    Article  Google Scholar 

  122. Paller, K. A. Consolidating dispersed neocortical memories: the missing link in amnesia. Memory 5, 73–88 (1997).

    CAS  PubMed  Article  Google Scholar 

  123. McClelland, J. L., McNaughton, B. L. & O'Reilly, R. C. Why there are complementary learning systems in the hippocampus and neocortex: insights from the successes and failures of connectionist models of learning and memory. Psychol. Rev. 102, 419–457 (1995).

    PubMed  Article  Google Scholar 

  124. McNaughton, B. L., et al. in Sleep and Brain Plasticity (eds Maguet, P., Smith, C. & Stickgold, B.) 225–246 (Oxford University Press, London, 2003).

    Book  Google Scholar 

  125. Nadel, L., Willner, J. & Kurz, E. M. in Context and Learning (eds Balsam, P. & Tomie, A.) 385–406 (Lawrence Erlbaum & Associates, Hillsdale, New Jersey, 1985).

    Google Scholar 

  126. Burke, S. N. et al. Differential encoding of behavior and spatial context in deep and superficial layers of the neocortex. Neuron 45, 667–674 (2005).

    CAS  PubMed  Article  Google Scholar 

  127. Skaggs, W. E. & McNaughton, B. L. Replay of neuronal firing sequences in rat hippocampus during sleep following spatial experience. Science 271, 1870–1873 (1996).

    CAS  PubMed  Article  Google Scholar 

  128. Barlow, J. S. Inertial navigation as a basis for animal navigation. J. Theor. Biol. 6, 76–117 (1964).

    CAS  PubMed  Article  Google Scholar 

  129. Witter, M. P., Groenewegen, H. J., Lopes da Silva, F. H. & Lohman, A. H. Functional organization of the extrinsic and intrinsic circuitry of the parahippocampal region. Prog. Neurobiol. 33, 161–253 (1989).

    CAS  PubMed  Article  Google Scholar 

  130. Lavenex, P. & Amaral, D. G. Hippocampal-neocortical interaction: a hierarchy of associativity. Hippocampus 10, 420–430 (2000).

    CAS  PubMed  Article  Google Scholar 

  131. Dolorfo, C. L. & Amaral, D. G. Entorhinal cortex of the rat: topographic organization of the cells of origin of the perforant path projection to the dentate gyrus. J. Comp. Neurol. 398, 25–48 (1998).

    CAS  PubMed  Article  Google Scholar 

  132. Dolorfo, C. L. & Amaral, D. G. Entorhinal cortex of the rat: organization of intrinsic connections. J. Comp. Neurol. 398, 49–82 (1998).

    CAS  PubMed  Article  Google Scholar 

  133. Germroth, P., Schwerdtfeger, W. K. & Buhl, E. H. Ultrastructure and aspects of functional organization of pyramidal and nonpyramidal entorhinal projection neurons contributing to the perforant path. J. Comp. Neurol. 305, 215–231 (1991).

    CAS  PubMed  Article  Google Scholar 

  134. Klink, R. & Alonso, A. Morphological characteristics of layer II projection neurons in the rat medial entorhinal cortex. Hippocampus 7, 571–583 (1997).

    CAS  PubMed  Article  Google Scholar 

  135. Hamam, B. N., Kennedy, T. E., Alonso, A. & Amaral, D. G. Morphological and electrophysiological characteristics of layer V neurons of the rat medial entorhinal cortex. J. Comp. Neurol. 418, 457–472 (2000).

    CAS  PubMed  Article  Google Scholar 

  136. Wouterlood, F. G. in The Parahippocampal Region: Organization and Role in Cognitive Functions (eds Witter & Wouterlood) 61–88 (Oxford University Press, London, 2002).

    Google Scholar 

  137. Castets V., Dulos E., Boissonade J. & De Kepper P. Experimental evidence of sustained standing Turing-type nonequilibrium chemical patterns. Phys. Rev. Lett. 64, 2953–2956 (1990).

    CAS  PubMed  Article  Google Scholar 

  138. Borkmans, P. et al. Diffusive instabilities and chemical reactions. Int. J. of Bifurcat. Chaos 12, 2307–2332 (2002)

    Article  Google Scholar 

  139. Tenenbaum, J. B., de Silva, V. & Langford, J. C. A global geometric framework for nonlinear dimensionality reduction. Science 290, 2319–2323 (2000). A method for the visualization of metric and topological structure in high-dimensional data sets starting from distance information.

    CAS  PubMed  Article  Google Scholar 

  140. Mittelstaedt, H. & Mittelstaedt, M. -L. in Avian Navigation (eds Papi, F. & Wallraff, H. G.) 290–297 (Springer, Berlin, 1982).

    Book  Google Scholar 

Download references

Acknowledgements

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.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Bruce L. McNaughton.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Related links

Related links

FURTHER INFORMATION

Battaglia homepage

Centre for the Biology of Memory

Jensen's homepage

University of Arizona Neuroscience website

Glossary

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.

Torus

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.

Orthogonal

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.

Tetrode

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.

Accommodation

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.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

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). https://doi.org/10.1038/nrn1932

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1038/nrn1932

Further reading

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing