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.
Subscribe to Journal
Get full journal access for 1 year
only $22.08 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
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.
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).
O'Keefe, J. & Nadel, L. The Hippocampus as a Cognitive Map (Clarendon, Oxford, 1978).
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.
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.
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.
O'Keefe, J. Do hippocampal pyramidal cells signal non-spatial as well as spatial information? Hippocampus 9, 352–364 (1999).
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).
McNaughton, B. L. et al. Deciphering the hippocampal polyglot: the hippocampus as a path integration system. J. Exp. Biol. 199, 173–185 (1996).
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).
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.
Etienne, A. S. & Jeffery, K. J. Path integration in mammals. Hippocampus 14, 180–192 (2004).
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.
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.
Wilson, H. R. & Cowan, J. D. A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Kybernetik 13, 55–80 (1973).
Amari, S. Dynamics of pattern formation in lateral-inhibition type neural fields. Biol. Cybern. 27, 77–87 (1977).
Ermentrout, G. B. & Cowan, J. D. A mathematical theory of visual hallucination patterns. Biol. Cybern. 34, 137–150 (1979).
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).
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.
Tsodyks M. Attractor neural network models of spatial maps in hippocampus. Hippocampus 9, 481–489 (1999).
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).
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).
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.
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).
Touretzky, D. S. & Redish, A. D. Theory of rodent navigation based on interacting representations of space. Hippocampus 6, 247–270 (1996).
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.
Conklin, J. & Eliasmith, C. A controlled attractor network model of path integration in the rat. J. Comput. Neurosci. 18, 183–203 (2005).
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).
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).
Maurer, A. D. et al. Organization of hippocampal cell assemblies based on theta phase precession. Hippocampus (in the press).
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.
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).
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).
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).
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).
Redish, A. D. & Touretzky, D. S. The role of the hippocampus in solving the Morris water maze. Neural Comput. 10, 73–111 (1998).
Sharp, P. E. Complimentary roles for hippocampal versus subicular/entorhinal place cells in coding place, context, and events. Hippocampus 9, 432–443 (1999).
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.
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.
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).
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).
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).
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.
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).
Burwell, R. D. The parahippocampal region: corticocortical connectivity. Ann. NY Acad. Sci. 911, 25–42 (2000).
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.
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.
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).
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).
Dhillon, A. & Jones, R. S. Laminar differences in recurrent excitatory transmission in the rat entorhinal cortex in vitro. Neuroscience 99, 413–422 (2000).
Fuhs, M. C. & Touretzky, D. S. A spin glass model of path integration in rat medial entorhinal cortex. J. Neurosci. 26, 4266–4276 (2006).
Parron, C. & Save, E. Evidence for entorhinal and parietal cortices involvement in path integration in the rat. Exp. Brain Res. 159, 349–359 (2004).
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).
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).
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.
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).
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).
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).
Muller, R. U., Stead, M. & Pach, J. The hippocampus as a cognitive graph. J. Gen. Physiol. 107, 663–694 (1996).
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.
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).
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).
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.
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).
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.
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).
Morris, R. G. M. & Hagan, J. J. in Neurobiology of the Hippocampus (ed. Seifert, W.) 321–331 (Academic, New York, 1983).
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).
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).
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).
Foster, T. C., Castro, C. A. & McNaughton, B. L. Spatial selectivity of hippocampal neurons: dependence on preparedness for movement. Science 244, 1580–1582 (1989).
McNaughton, B. L. & Nadel, L. in Neuroscience and Connectionist Theory (eds. Gluck, M. A. & Rumelhart, D. E.) 1–63 (Lawrence Erlbaum Associates, Hillsdale, 1989).
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).
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).
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).
Bostock, E., Muller, R. U. & Kubie, J. L. Experience-dependent modifications of hippocampal place cell firing. Hippocampus 1, 193–205 (1991).
Kentros, C. et al. Abolition of long-term stability of new hippocampal place cell maps by NMDA receptor blockade. Science 280, 2121–2126 (1998).
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).
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).
Marr, D. A theory of cerebellar cortex. J. Physiol. (Lond.) 202, 437–470 (1969).
Albus, J. A theory of cerebellar function. Math. Biosci. 10, 25–61 (1971).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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.
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.
Murray, J. D. Mathematical Biology (Springer, Heidelberg, 1989).
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).
Treves, A., Kropff, E. & Biswas, A. On the triangular grid of entorhinal place fields. Soc. Neurosci. Abstr. 198. 11 (2005).
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.
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).
Bear, M. F., Cooper, L. N. & Ebner, F. F. A physiological-basis for a theory of synapse modification. Science 237, 42–48 (1987).
Bear, M. F. & Malenka, R. C. Synaptic plasticity: LTP and LTD. Curr. Opin. Neurobiol., 4, 389–399 (1994).
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).
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).
Ichinohe, N. & Rockland, K. S. Region specific micromodularity in the uppermost layers in primate. Cereb. Cortex 14, 1173–1184 (2004).
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).
Solodkin, A. & Vanhoesen, G. W. Entorhinal cortex modules of the human brain. J. Comp. Neurol. 365, 610–627 (1996).
Feller, M. B. Spontaneous correlated activity in developing neural circuits. Neuron 22, 653–656 (1999).
Katz, L. C. & Shatz, C. J. Synaptic activity and the construction of cortical circuits. Science 274, 1133–1138 (1996).
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).
Garaschuk, O., Linn, J., Eilers, J. & Konnerth, A. Large scale oscillatory calcium waves in the immature cortex. Nature Neurosci. 3, 452–459 (2000).
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).
Yuste, R., Nelson, D. A., Rubin, W. W. & Katz, L. C. Neuronal domains in developing neocortex: mechanisms of coactivation. Neuron 14, 7–17 (1995).
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.
Buzsaki, G. Theta oscillations in the hippocampus. Neuron 33, 325–340 (2002).
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).
O'Keefe, J. & Recce M. L. Phase relationship between hippocampal place units and the EEG theta rhythm. Hippocampus 3, 317–330 (1993).
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).
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).
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).
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).
Teyler T. J. & Discenna, P. The hippocampal memory indexing system. Behav. Neurosci. 100, 147–154 (1986).
Squire L. R., Cohen, N. J. & Nadel, L. in Memory Consolidation (eds Weingartner, G. & Parker, E.) 185–210 (Earlbaum, Hillsdale, 1984).
O'Kane, D. & Treves, A. Why the simplest notion of neocortex as an autoassociative memory would not work. Network 3, 379–384 (1992).
Paller, K. A. Consolidating dispersed neocortical memories: the missing link in amnesia. Memory 5, 73–88 (1997).
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).
McNaughton, B. L., et al. in Sleep and Brain Plasticity (eds Maguet, P., Smith, C. & Stickgold, B.) 225–246 (Oxford University Press, London, 2003).
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).
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).
Skaggs, W. E. & McNaughton, B. L. Replay of neuronal firing sequences in rat hippocampus during sleep following spatial experience. Science 271, 1870–1873 (1996).
Barlow, J. S. Inertial navigation as a basis for animal navigation. J. Theor. Biol. 6, 76–117 (1964).
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).
Lavenex, P. & Amaral, D. G. Hippocampal-neocortical interaction: a hierarchy of associativity. Hippocampus 10, 420–430 (2000).
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).
Dolorfo, C. L. & Amaral, D. G. Entorhinal cortex of the rat: organization of intrinsic connections. J. Comp. Neurol. 398, 49–82 (1998).
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).
Klink, R. & Alonso, A. Morphological characteristics of layer II projection neurons in the rat medial entorhinal cortex. Hippocampus 7, 571–583 (1997).
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).
Wouterlood, F. G. in The Parahippocampal Region: Organization and Role in Cognitive Functions (eds Witter & Wouterlood) 61–88 (Oxford University Press, London, 2002).
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).
Borkmans, P. et al. Diffusive instabilities and chemical reactions. Int. J. of Bifurcat. Chaos 12, 2307–2332 (2002)
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.
Mittelstaedt, H. & Mittelstaedt, M. -L. in Avian Navigation (eds Papi, F. & Wallraff, H. G.) 290–297 (Springer, Berlin, 1982).
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.
The authors declare no competing financial interests.
- 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.
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
Visual cue-related activity of cells in the medial entorhinal cortex during navigation in virtual reality
Nature Neuroscience (2020)
IEEE Robotics and Automation Letters (2020)
Developmental Designs and Adult Functions of Cortical Maps in Multiple Modalities: Perception, Attention, Navigation, Numbers, Streaming, Speech, and Cognition
Frontiers in Neuroinformatics (2020)
Cell type, sub-region, and layer-specific speed representation in the hippocampal–entorhinal circuit
Scientific Reports (2020)