How does the brain solve the computational problems of spatial navigation

Flexible navigation in the real world involves the ability to maintain an ongoing estimate of one’s location in the environment, to use landmarks to help navigate, and to construct shortcuts and paths between locations. In mammals, these functions are believed to be performed by a circuit that includes the hippocampus and associated cortical areas. The physiological characterization of the neural substrates for navigation has progressed rapidly in the last four decades, together with plausible mechanistic models for the generation of such activity. However, questions about how the various components of the circuit interact to perform the overall computations that account for the navigational ability of mammals remain largely unsolved. We review physiological and anatomical data as well as models of hippocampal map building and self-localization to establish what is understood about the brain’s navigational circuits from a computational perspective. We discuss major areas where our understanding is incomplete.

[1]  Angelo Arleo,et al.  Spatial cognition and neuro-mimetic navigation: a model of hippocampal place cell activity , 2000, Biological Cybernetics.

[2]  B L McNaughton,et al.  Path Integration and Cognitive Mapping in a Continuous Attractor Neural Network Model , 1997, The Journal of Neuroscience.

[3]  Malcolm W. Brown,et al.  Different Contributions of the Hippocampus and Perirhinal Cortex to Recognition Memory , 1999, The Journal of Neuroscience.

[4]  R U Muller,et al.  Head-direction cells recorded from the postsubiculum in freely moving rats. I. Description and quantitative analysis , 1990, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[5]  T. Hafting,et al.  Microstructure of a spatial map in the entorhinal cortex , 2005, Nature.

[6]  Bruce L. McNaughton,et al.  Path integration and the neural basis of the 'cognitive map' , 2006, Nature Reviews Neuroscience.

[7]  H. Eichenbaum,et al.  Towards a functional organization of the medial temporal lobe memory system: Role of the parahippocampal and medial entorhinal cortical areas , 2008, Hippocampus.

[8]  L. Frank,et al.  Awake Hippocampal Sharp-Wave Ripples Support Spatial Memory , 2012, Science.

[9]  J. Knierim,et al.  Influence of boundary removal on the spatial representations of the medial entorhinal cortex , 2008, Hippocampus.

[10]  G. Buzsáki,et al.  Theta oscillations in somata and dendrites of hippocampal pyramidal cells in vivo: Activity‐dependent phase‐precession of action potentials , 1998, Hippocampus.

[11]  M. VanElzakker,et al.  Environmental novelty is associated with a selective increase in Fos expression in the output elements of the hippocampal formation and the perirhinal cortex. , 2008, Learning & memory.

[12]  Alessandro Treves,et al.  The emergence of grid cells: Intelligent design or just adaptation? , 2008, Hippocampus.

[13]  Frances S. Chance,et al.  Erratum: Orthogonal micro-organization of orientation and spatial frequency in primate primary visual cortex , 2013, Nature Neuroscience.

[14]  S. Tonegawa,et al.  Young Dentate Granule Cells Mediate Pattern Separation, whereas Old Granule Cells Facilitate Pattern Completion , 2012, Cell.

[15]  David S. Touretzky,et al.  Proceedings of the 1993 Connectionist Models Summer School , 2014 .

[16]  Benjamin J. Clark,et al.  The exploratory behavior of rats in an open environment optimizes security , 2006, Behavioural Brain Research.

[17]  K. Zhang,et al.  Representation of spatial orientation by the intrinsic dynamics of the head-direction cell ensemble: a theory , 1996, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[18]  M. Moser,et al.  Pattern Separation in the Dentate Gyrus and CA3 of the Hippocampus , 2007, Science.

[19]  J. Taube,et al.  Processing the head direction cell signal: A review and commentary , 1996, Brain Research Bulletin.

[20]  Ila R Fiete Losing Phase , 2010, Neuron.

[21]  E Save,et al.  Comparison of the effects of entorhinal and retrosplenial cortical lesions on habituation, reaction to spatial and non-spatial changes during object exploration in the rat , 2004, Neurobiology of Learning and Memory.

[22]  J. W. Rudy,et al.  The hippocampal indexing theory and episodic memory: Updating the index , 2007, Hippocampus.

[23]  E T Rolls,et al.  Computational constraints suggest the need for two distinct input systems to the hippocampal CA3 network , 1992, Hippocampus.

[24]  M. Quirk,et al.  Hippocampal CA3 NMDA Receptors Are Crucial for Memory Acquisition of One-Time Experience , 2003, Neuron.

[25]  Stephen Grossberg,et al.  Grid cell hexagonal patterns formed by fast self‐organized learning within entorhinal cortex , 2012, Hippocampus.

[26]  J. O’Keefe,et al.  Phase relationship between hippocampal place units and the EEG theta rhythm , 1993, Hippocampus.

[27]  M. Moser,et al.  Spatial Memory in the Rat Requires the Dorsolateral Band of the Entorhinal Cortex , 2005, Neuron.

[28]  M. Hasselmo Grid cell mechanisms and function: Contributions of entorhinal persistent spiking and phase resetting , 2008, Hippocampus.

[29]  Ashley N. Linder,et al.  The Spatial Periodicity of Grid Cells Is Not Sustained During Reduced Theta Oscillations , 2011, Science.

[30]  M. Häusser,et al.  Cellular mechanisms of spatial navigation in the medial entorhinal cortex , 2013, Nature Neuroscience.

[31]  J S Taube,et al.  Correlation between head direction cell activity and spatial behavior on a radial arm maze. , 1997, Behavioral neuroscience.

[32]  Torkel Hafting,et al.  Conjunctive Representation of Position, Direction, and Velocity in Entorhinal Cortex , 2006, Science.

[33]  Terrence J. Sejnowski,et al.  ASSOCIATIVE MEMORY AND HIPPOCAMPAL PLACE CELLS , 1995 .

[34]  Joshua P. Neunuebel,et al.  Spatial Firing Correlates of Physiologically Distinct Cell Types of the Rat Dentate Gyrus , 2012, The Journal of Neuroscience.

[35]  Inah Lee,et al.  Differential contribution of NMDA receptors in hippocampal subregions to spatial working memory , 2002, Nature Neuroscience.

[36]  Eric A. Zilli,et al.  Models of Grid Cell Spatial Firing Published 2005–2011 , 2012, Front. Neural Circuits.

[37]  T. Teyler,et al.  The hippocampal memory indexing theory. , 1986, Behavioral neuroscience.

[38]  Lisa M. Saksida,et al.  Running enhances spatial pattern separation in mice , 2010, Proceedings of the National Academy of Sciences.

[39]  J. Knierim,et al.  Comparison of population coherence of place cells in hippocampal subfields CA1 and CA3 , 2004, Nature.

[40]  Michael Recce,et al.  A model of hippocampal function , 1994, Neural Networks.

[41]  H. T. Blair,et al.  Cosine Directional Tuning of Theta Cell Burst Frequencies: Evidence for Spatial Coding by Oscillatory Interference , 2011, The Journal of Neuroscience.

[42]  M. Wilson,et al.  Dentate Gyrus NMDA Receptors Mediate Rapid Pattern Separation in the Hippocampal Network , 2007, Science.

[43]  James L. McClelland,et al.  Hippocampal conjunctive encoding, storage, and recall: Avoiding a trade‐off , 1994, Hippocampus.

[44]  M. Moser,et al.  Fast rate coding in hippocampal CA3 cell ensembles , 2006, Hippocampus.

[45]  A David Redishyx,et al.  A coupled attractor model of the rodent head direction system , 1996 .

[46]  Neil Burgess,et al.  Attractor Dynamics in the Hippocampal Representation of the Local Environment , 2005, Science.

[47]  M. Hasselmo,et al.  Coupled Noisy Spiking Neurons as Velocity-Controlled Oscillators in a Model of Grid Cell Spatial Firing , 2010, The Journal of Neuroscience.

[48]  H. Eichenbaum,et al.  Memory Representation within the Parahippocampal Region , 1997, The Journal of Neuroscience.

[49]  Tony J. Prescott,et al.  Spatial Representation for Navigation in Animats , 1996, Adapt. Behav..

[50]  A. Treves,et al.  What is the mammalian dentate gyrus good for? , 2008, Neuroscience.

[51]  Michael R. Hunsaker,et al.  The interactions and dissociations of the dorsal hippocampus subregions: how the dentate gyrus, CA3, and CA1 process spatial information. , 2008, Behavioral neuroscience.

[52]  Sachin S. Deshmukh,et al.  Representation of Non-Spatial and Spatial Information in the Lateral Entorhinal Cortex , 2011, Front. Behav. Neurosci..

[53]  Gordon Wyeth,et al.  Persistent Navigation and Mapping using a Biologically Inspired SLAM System , 2010, Int. J. Robotics Res..

[54]  R. Muller,et al.  The firing of hippocampal place cells in the dark depends on the rat's recent experience , 1990, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[55]  R. Muller,et al.  The positional firing properties of medial entorhinal neurons: description and comparison with hippocampal place cells , 1992, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[56]  J. O’Keefe,et al.  An oscillatory interference model of grid cell firing , 2007, Hippocampus.

[57]  G. Buzsáki,et al.  Theta Oscillations Provide Temporal Windows for Local Circuit Computation in the Entorhinal-Hippocampal Loop , 2009, Neuron.

[58]  Mark C. Fuhs,et al.  Influence of path integration versus environmental orientation on place cell remapping between visually identical environments. , 2005, Journal of neurophysiology.

[59]  G. Buzsáki,et al.  Single granule cells reliably discharge targets in the hippocampal CA3 network in vivo , 2002, Nature Neuroscience.

[60]  Benjamin A. Dunn,et al.  Recurrent inhibitory circuitry as a mechanism for grid formation , 2013, Nature Neuroscience.

[61]  B. McNaughton,et al.  Hippocampal synaptic enhancement and information storage within a distributed memory system , 1987, Trends in Neurosciences.

[62]  J. O’Keefe,et al.  Dual phase and rate coding in hippocampal place cells: Theoretical significance and relationship to entorhinal grid cells , 2005, Hippocampus.

[63]  Brandy Schmidt,et al.  Changes in Task Demands Alter the Pattern of zif268 Expression in the Dentate Gyrus , 2011, The Journal of Neuroscience.

[64]  J. Taube The head direction signal: origins and sensory-motor integration. , 2007, Annual review of neuroscience.

[65]  Thomas J. Wills,et al.  Long-term plasticity in hippocampal place-cell representation of environmental geometry , 2002, Nature.

[66]  Nicolas Brunel,et al.  A Continuous Attractor Network Model Without Recurrent Excitation: Maintenance and Integration in the Head Direction Cell System , 2005, Journal of Computational Neuroscience.

[67]  J. Knierim,et al.  Coupling between place cells and head direction cells during relative translations and rotations of distal landmarks , 2004, Experimental Brain Research.

[68]  S Grossberg,et al.  Pavlovian pattern learning by nonlinear neural networks. , 1971, Proceedings of the National Academy of Sciences of the United States of America.

[69]  A. Treves,et al.  Distinct Ensemble Codes in Hippocampal Areas CA3 and CA1 , 2004, Science.

[70]  H. T. Blair,et al.  Conversion of a phase‐ to a rate‐coded position signal by a three‐stage model of theta cells, grid cells, and place cells , 2008, Hippocampus.

[71]  Roland Vollgraf,et al.  From grids to places , 2007, Journal of Computational Neuroscience.

[72]  Yoram Burak,et al.  Do We Understand the Emergent Dynamics of Grid Cell Activity? , 2006, The Journal of Neuroscience.

[73]  Stefan Leutgeb,et al.  Pattern separation, pattern completion, and new neuronal codes within a continuous CA3 map. , 2007, Learning & memory.

[74]  M. Fyhn,et al.  Progressive increase in grid scale from dorsal to ventral medial entorhinal cortex , 2008, Hippocampus.

[75]  E. Capaldi,et al.  The organization of behavior. , 1992, Journal of applied behavior analysis.

[76]  A. Lansner Associative memory models: from the cell-assembly theory to biophysically detailed cortex simulations , 2009, Trends in Neurosciences.

[77]  H. Eichenbaum,et al.  The global record of memory in hippocampal neuronal activity , 1999, Nature.

[78]  R. J. McDonald,et al.  Lesions of the medial or lateral perforant path have different effects on hippocampal contributions to place learning and on fear conditioning to context , 1999, Behavioural Brain Research.

[79]  K. Jeffery,et al.  Experience-dependent rescaling of entorhinal grids , 2007, Nature Neuroscience.

[80]  Stephen Grossberg,et al.  A Global Prediction ( or Learning ) Theory for Some Nonlinear Functional-Differential Equations , 2004 .

[81]  Hugh Durrant-Whyte,et al.  Simultaneous localization and mapping (SLAM): part II , 2006 .

[82]  M. Witter,et al.  Anatomical Organization of the Parahippocampal‐Hippocampal Network , 2000, Annals of the New York Academy of Sciences.

[83]  J. O’Keefe,et al.  Geometric determinants of the place fields of hippocampal neurons , 1996, Nature.

[84]  K. Jeffery,et al.  Context‐specific acquisition of location discrimination by hippocampal place cells , 2003, The European journal of neuroscience.

[85]  James J Knierim,et al.  Lateral entorhinal neurons are not spatially selective in cue‐rich environments , 2011, Hippocampus.

[86]  Lisa M. Giocomo,et al.  Computational Models of Grid Cells , 2011, Neuron.

[87]  M. Moser,et al.  Understanding memory through hippocampal remapping , 2008, Trends in Neurosciences.

[88]  D. Zipser A computational model of hippocampal place fields. , 1985, Behavioral neuroscience.

[89]  Boris S. Gutkin,et al.  Democracy-Independence Trade-Off in Oscillating Dendrites and Its Implications for Grid Cells , 2010, Neuron.

[90]  M. Hasselmo How We Remember: Brain Mechanisms of Episodic Memory , 2011 .

[91]  Ila R Fiete,et al.  Grid cells: The position code, neural network models of activity, and the problem of learning , 2008, Hippocampus.

[92]  R. Muller,et al.  The effects of changes in the environment on the spatial firing of hippocampal complex-spike cells , 1987, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[93]  Mark P. Brandon,et al.  Reduction of Theta Rhythm Dissociates Grid Cell Spatial Periodicity from Directional Tuning , 2011, Science.

[94]  A. Fenton,et al.  Increasing adult hippocampal neurogenesis is sufficient to improve pattern separation , 2011, Nature.

[95]  Raymond P. Kesner,et al.  An analysis of the dentate gyrus function , 2013, Behavioural Brain Research.

[96]  G. Buzsáki,et al.  Memory, navigation and theta rhythm in the hippocampal-entorhinal system , 2013, Nature Neuroscience.

[97]  A. Pérez-Villalba Rhythms of the Brain, G. Buzsáki. Oxford University Press, Madison Avenue, New York (2006), Price: GB £42.00, p. 448, ISBN: 0-19-530106-4 , 2008 .

[98]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[99]  Ila Fiete,et al.  Grid cells generate an analog error-correcting code for singularly precise neural computation , 2011, Nature Neuroscience.

[100]  Bruce L. McNaughton,et al.  Corrigendum: neuronal Mechanisms Underlying the Interaction between Visual Landmarks and Path Integration in the rat , 1996, Int. J. Neural Syst..

[101]  David J. Foster,et al.  Reverse replay of behavioural sequences in hippocampal place cells during the awake state , 2006, Nature.

[102]  N. Logothetis,et al.  Cholinergic Control of Visual Categorization in Macaques , 2011, Front. Behav. Neurosci..

[103]  E. Tolman,et al.  Studies in spatial learning: Orientation and the short-cut. , 1946, Journal of experimental psychology.

[104]  David S. Touretzky,et al.  The Role of the Hippocampus in Solving the Morris Water Maze , 1998, Neural Computation.

[105]  E. Rolls,et al.  Self-organizing continuous attractor networks and path integration: one-dimensional models of head direction cells , 2002, Network.

[106]  W E Skaggs,et al.  Deciphering the hippocampal polyglot: the hippocampus as a path integration system. , 1996, The Journal of experimental biology.

[107]  B. McNaughton,et al.  Physiological identification and analysis of dentate granule cell responses to stimulation of the medial and lateral perforant pathways in the rat , 1977, The Journal of comparative neurology.

[108]  G. Paxinos The Rat nervous system , 1985 .

[109]  Yuri Dabaghian,et al.  A Topological Paradigm for Hippocampal Spatial Map Formation Using Persistent Homology , 2012, PLoS Comput. Biol..

[110]  J. Magee Dendritic mechanisms of phase precession in hippocampal CA1 pyramidal neurons. , 2001, Journal of neurophysiology.

[111]  Derek A. Hamilton,et al.  Movement characteristics support a role for dead reckoning in organizing exploratory behavior , 2006, Animal Cognition.

[112]  Adam Johnson,et al.  Neural Ensembles in CA3 Transiently Encode Paths Forward of the Animal at a Decision Point , 2007, The Journal of Neuroscience.

[113]  H. Sompolinsky,et al.  Theory of orientation tuning in visual cortex. , 1995, Proceedings of the National Academy of Sciences of the United States of America.

[114]  M. W. Brown,et al.  Neuronal Sianallina of Information Imoortant to Visual Recognition‐Memory in Rat Rhinal aid Neighbouring Cortices , 1995, The European journal of neuroscience.

[115]  R. Muller,et al.  Head-direction cells recorded from the postsubiculum in freely moving rats. II. Effects of environmental manipulations , 1990, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[116]  P. E. Sharp Subicular place cells generate the same “map” for different environments: Comparison with hippocampal cells , 2006, Behavioural Brain Research.

[117]  J. O’Keefe,et al.  Modeling place fields in terms of the cortical inputs to the hippocampus , 2000, Hippocampus.

[118]  Andrea Klug,et al.  The Hippocampus Book , 2016 .

[119]  M. Yartsev,et al.  Grid cells without theta oscillations in the entorhinal cortex of bats , 2011, Nature.

[120]  René Hen,et al.  NR2B-Dependent Plasticity of Adult-Born Granule Cells is Necessary for Context Discrimination , 2012, The Journal of Neuroscience.

[121]  Mark C. Fuhs,et al.  A Spin Glass Model of Path Integration in Rat Medial Entorhinal Cortex , 2006, The Journal of Neuroscience.

[122]  T. Bliss,et al.  The Hippocampus Book , 2006 .

[123]  C. Stark,et al.  Pattern separation in the hippocampus , 2011, Trends in Neurosciences.

[124]  K. Jeffery,et al.  Directional control of hippocampal place fields , 1997, Experimental Brain Research.

[125]  David S. Touretzky,et al.  Neural Representation of Space Using Sinusoidal Arrays , 1993, Neural Computation.

[126]  Dori Derdikman,et al.  Are the Boundary-Related Cells in the Subiculum Boundary-Vector Cells? , 2009, The Journal of Neuroscience.

[127]  S. Tronel,et al.  Adult‐born neurons are necessary for extended contextual discrimination , 2012, Hippocampus.

[128]  Raymond P. Kesner,et al.  Selective lesions of the dentate gyrus produce disruptions in place learning for adjacent spatial locations , 2012, Neurobiology of Learning and Memory.

[129]  L F Abbott,et al.  Modular Realignment of Entorhinal Grid Cell Activity as a Basis for Hippocampal Remapping , 2011, The Journal of Neuroscience.

[130]  Patricia E. Sharp,et al.  Computer simulation of hippocampal place cells , 1991, Psychobiology.

[131]  R. Kesner A behavioral analysis of dentate gyrus function. , 2007, Progress in brain research.

[132]  F. Gage,et al.  Resolving New Memories: A Critical Look at the Dentate Gyrus, Adult Neurogenesis, and Pattern Separation , 2011, Neuron.

[133]  E N Brown,et al.  A Statistical Paradigm for Neural Spike Train Decoding Applied to Position Prediction from Ensemble Firing Patterns of Rat Hippocampal Place Cells , 1998, The Journal of Neuroscience.

[134]  J. Taube,et al.  Firing Properties of Head Direction Cells in the Rat Anterior Thalamic Nucleus: Dependence on Vestibular Input , 1997, The Journal of Neuroscience.

[135]  P. Dayan,et al.  Decision theory, reinforcement learning, and the brain , 2008, Cognitive, affective & behavioral neuroscience.

[136]  Ila R Fiete,et al.  What Grid Cells Convey about Rat Location , 2008, The Journal of Neuroscience.

[137]  Paul E. Gilbert,et al.  Dissociating hippocampal subregions: A double dissociation between dentate gyrus and CA1 , 2001, Hippocampus.

[138]  B. McNaughton,et al.  Sparse, environmentally selective expression of Arc RNA in the upper blade of the rodent fascia dentata by brief spatial experience , 2005, Hippocampus.

[139]  Hugh F. Durrant-Whyte,et al.  Simultaneous localization and mapping: part I , 2006, IEEE Robotics & Automation Magazine.

[140]  D. Tank,et al.  Membrane potential dynamics of grid cells , 2013, Nature.

[141]  H. Eichenbaum,et al.  Hippocampal Neurons Encode Information about Different Types of Memory Episodes Occurring in the Same Location , 2000, Neuron.

[142]  Yoram Burakyy,et al.  Accurate Path Integration in Continuous Attractor Network Models of Grid Cells , 2009 .

[143]  E. Bostock,et al.  Experience‐dependent modifications of hippocampal place cell firing , 1991, Hippocampus.

[144]  R. Passingham The hippocampus as a cognitive map J. O'Keefe & L. Nadel, Oxford University Press, Oxford (1978). 570 pp., £25.00 , 1979, Neuroscience.

[145]  C. Barry,et al.  Specific evidence of low-dimensional continuous attractor dynamics in grid cells , 2013, Nature Neuroscience.

[146]  M. Fyhn,et al.  Spatial Representation in the Entorhinal Cortex , 2004, Science.

[147]  J. Knierim,et al.  Head Direction Cell Representations Maintain Internal Coherence during Conflicting Proximal and Distal Cue Rotations: Comparison with Hippocampal Place Cells , 2006, The Journal of Neuroscience.

[148]  A. Treves,et al.  Hippocampal remapping and grid realignment in entorhinal cortex , 2007, Nature.

[149]  J. O'Keefe,et al.  The hippocampus as a spatial map. Preliminary evidence from unit activity in the freely-moving rat. , 1971, Brain research.

[150]  S. Mizumori,et al.  Directionally selective mnemonic properties of neurons in the lateral dorsal nucleus of the thalamus of rats , 1993, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[151]  Simon M Stringer,et al.  Entorhinal cortex grid cells can map to hippocampal place cells by competitive learning , 2006, Network.

[152]  Matthew A. Wilson,et al.  Hippocampal Replay of Extended Experience , 2009, Neuron.

[153]  M. Witter,et al.  Projections from the presubiculum and the parasubiculum to morphologically characterized entorhinal-hippocampal projection neurons in the rat , 2004, Experimental Brain Research.

[154]  RU Muller,et al.  The hippocampus as a cognitive graph , 1996, The Journal of general physiology.

[155]  J. Guzowski,et al.  Differences in Hippocampal Neuronal Population Responses to Modifications of an Environmental Context: Evidence for Distinct, Yet Complementary, Functions of CA3 and CA1 Ensembles , 2004, The Journal of Neuroscience.

[156]  J. Knierim,et al.  Hippocampal place cells: Parallel input streams, subregional processing, and implications for episodic memory , 2006, Hippocampus.

[157]  M. Witter CHAPTER 21 – Hippocampal Formation , 2004 .

[158]  J. Magee,et al.  Pathway Interactions and Synaptic Plasticity in the Dendritic Tuft Regions of CA1 Pyramidal Neurons , 2009, Neuron.

[159]  Michael E. Hasselmo,et al.  Evaluation of the Oscillatory Interference Model of Grid Cell Firing through Analysis and Measured Period Variance of Some Biological Oscillators , 2009, PLoS Comput. Biol..

[160]  N. Schmajuk Role of the hippocampus in temporal and spatial navigation An adaptive neural network , 1990, Behavioural Brain Research.

[161]  Lisa M. Giocomo,et al.  Temporal Frequency of Subthreshold Oscillations Scales with Entorhinal Grid Cell Field Spacing , 2007, Science.

[162]  Mattias P. Karlsson,et al.  Awake replay of remote experiences in the hippocampus , 2009, Nature Neuroscience.

[163]  Diano F. Marrone,et al.  Increased pattern separation in the aged fascia dentata , 2011, Neurobiology of Aging.

[164]  Benjamin A. Dunn,et al.  Grid cells require excitatory drive from the hippocampus , 2013, Nature Neuroscience.

[165]  G. Buzsáki,et al.  Forward and reverse hippocampal place-cell sequences during ripples , 2007, Nature Neuroscience.

[166]  L. Nadel,et al.  The Hippocampus as a Cognitive Map , 1978 .

[167]  T. van Groen,et al.  The postsubicular cortex in the rat: characterization of the fourth region of the subicular cortex and its connections , 1990, Brain Research.

[168]  M. Wilson,et al.  Trajectory Encoding in the Hippocampus and Entorhinal Cortex , 2000, Neuron.

[169]  Sachin S. Deshmukh,et al.  Influence of local objects on hippocampal representations: Landmark vectors and memory , 2013, Hippocampus.

[170]  David S. Touretzky,et al.  Towards a Computational Theory of Rat Navigation , 1999 .

[171]  B. McNaughton,et al.  Independent Codes for Spatial and Episodic Memory in Hippocampal Neuronal Ensembles , 2005, Science.

[172]  Diano F. Marrone,et al.  Disambiguating the similar: The dentate gyrus and pattern separation , 2012, Behavioural Brain Research.

[173]  D Marr,et al.  Simple memory: a theory for archicortex. , 1971, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[174]  M. Lengyel,et al.  Dynamically detuned oscillations account for the coupled rate and temporal code of place cell firing , 2003, Hippocampus.

[175]  G. Dragoi,et al.  Preplay of future place cell sequences by hippocampal cellular assemblies , 2011, Nature.

[176]  E. Tolman Cognitive maps in rats and men. , 1948, Psychological review.

[177]  Neil Burgess,et al.  Predictions derived from modelling the hippocampal role in navigation , 2000, Biological Cybernetics.

[178]  J. Lisman,et al.  Role of the dual entorhinal inputs to hippocampus: a hypothesis based on cue/action (non-self/self) couplets. , 2007, Progress in brain research.

[179]  S. Grossberg A prediction theory for some nonlinear functional-differential equations. II. Learning of patterns☆ , 1968 .

[180]  M. Moser,et al.  Optogenetic Dissection of Entorhinal-Hippocampal Functional Connectivity , 2013, Science.

[181]  Ofer Tchernichovski,et al.  The dynamics of long-term exploration in the rat , 1998, Biological Cybernetics.

[182]  K. Jeffery,et al.  The Boundary Vector Cell Model of Place Cell Firing and Spatial Memory , 2006, Reviews in the neurosciences.

[183]  Jonathan R. Whitlock,et al.  Fragmentation of grid cell maps in a multicompartment environment , 2009, Nature Neuroscience.

[184]  Laura A. Ewell,et al.  Neurogenesis in the dentate gyrus: carrying the message or dictating the tone , 2013, Front. Neurosci..

[185]  J. O’Keefe Place units in the hippocampus of the freely moving rat , 1976, Experimental Neurology.

[186]  J. Taube Head direction cells recorded in the anterior thalamic nuclei of freely moving rats , 1995, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[187]  Lisa M. Giocomo,et al.  Grid cell firing may arise from interference of theta frequency membrane potential oscillations in single neurons , 2007, Hippocampus.

[188]  E. Save,et al.  Distinct roles of medial and lateral entorhinal cortex in spatial cognition. , 2013, Cerebral cortex.

[189]  David Eilam,et al.  Stopping behavior: constraints on exploration in rats (Rattus norvegicus) , 1993, Behavioural Brain Research.

[190]  James L. McClelland,et al.  Distributed memory and the representation of general and specific information. , 1985, Journal of experimental psychology. General.

[191]  E. Save,et al.  Flexible use of proximal objects and distal cues by hippocampal place cells , 2007, Hippocampus.

[192]  B. McNaughton,et al.  Spatial selectivity of unit activity in the hippocampal granular layer , 1993, Hippocampus.

[193]  E. Save,et al.  Evidence for entorhinal and parietal cortices involvement in path integration in the rat , 2004, Experimental Brain Research.

[194]  H S Seung,et al.  How the brain keeps the eyes still. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[195]  K M Gothard,et al.  Dynamics of Mismatch Correction in the Hippocampal Ensemble Code for Space: Interaction between Path Integration and Environmental Cues , 1996, The Journal of Neuroscience.

[196]  Robert E. Hampson,et al.  Distribution of spatial and nonspatial information in dorsal hippocampus , 1999, Nature.

[197]  Bruce L. McNaughton,et al.  A Model of the Neural Basis of the Rat's Sense of Direction , 1994, NIPS.

[198]  J. O’Keefe,et al.  Boundary Vector Cells in the Subiculum of the Hippocampal Formation , 2009, The Journal of Neuroscience.

[199]  P. E. Sharp,et al.  Spatial correlates of firing patterns of single cells in the subiculum of the freely moving rat , 1994, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[200]  James J Knierim,et al.  Dominance of the proximal coordinate frame in determining the locations of hippocampal place cell activity during navigation. , 2008, Journal of neurophysiology.

[201]  D. Amit The Hebbian paradigm reintegrated: Local reverberations as internal representations , 1995, Behavioral and Brain Sciences.

[202]  D. Eilam,et al.  Home base behavior of rats (Rattus norvegicus) exploring a novel environment , 1989, Behavioural Brain Research.

[203]  M. V. Rossum,et al.  Feedback Inhibition Enables Theta-Nested Gamma Oscillations and Grid Firing Fields , 2013, Neuron.

[204]  M. Hasselmo,et al.  Free recall and recognition in a network model of the hippocampus: simulating effects of scopolamine on human memory function , 1997, Behavioural Brain Research.

[205]  D. Amaral,et al.  The dentate gyrus: fundamental neuroanatomical organization (dentate gyrus for dummies). , 2007, Progress in brain research.

[206]  Simon Benhamou,et al.  A model for place navigation in mammals , 1995 .

[207]  Charlotte N. Boccara,et al.  Grid cells in pre- and parasubiculum , 2010, Nature Neuroscience.

[208]  David Filliat,et al.  Map-based navigation in mobile robots: II. A review of map-learning and path-planning strategies , 2003, Cognitive Systems Research.

[209]  K. Jeffery,et al.  How heterogeneous place cell responding arises from homogeneous grids—A contextual gating hypothesis , 2008, Hippocampus.

[210]  Andrew M. Wikenheiser,et al.  Changes in reward contingency modulate the trial-to-trial variability of hippocampal place cells. , 2011, Journal of neurophysiology.

[211]  Nestor A. Schmajuk,et al.  Place Learning and the Dynamics of Spatial Navigation: A Neural Network Approach , 1993, Adapt. Behav..

[212]  M. Moser,et al.  Representation of Geometric Borders in the Entorhinal Cortex , 2008, Science.

[213]  Carol A Barnes,et al.  Impaired hippocampal rate coding after lesions of the lateral entorhinal cortex , 2013, Nature Neuroscience.

[214]  H. Eichenbaum,et al.  Robust Conjunctive Item–Place Coding by Hippocampal Neurons Parallels Learning What Happens Where , 2009, The Journal of Neuroscience.

[215]  B. McNaughton,et al.  Place cells, head direction cells, and the learning of landmark stability , 1995, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[216]  Vasant Honavar,et al.  Spatial Learning and Localization in Rodents: A Computational Model of the Hippocampus and its Implications for Mobile Robots , 1999, Adapt. Behav..

[217]  May-Britt Moser,et al.  The entorhinal grid map is discretized , 2012, Nature.

[218]  D. Touretzky,et al.  Cognitive maps beyond the hippocampus , 1997, Hippocampus.

[219]  G. Buzsáki,et al.  Inhibitory CA1-CA3-hilar region feedback in the hippocampus. , 1994, Science.

[220]  Inah Lee,et al.  A Double Dissociation between Hippocampal Subfields Differential Time Course of CA3 and CA1 Place Cells for Processing Changed Environments , 2004, Neuron.

[221]  G. Einevoll,et al.  From grid cells to place cells: A mathematical model , 2006, Hippocampus.

[222]  L. Saksida,et al.  A Functional Role for Adult Hippocampal Neurogenesis in Spatial Pattern Separation , 2009, Science.

[223]  Howard Eichenbaum,et al.  A cognitive map for object memory in the hippocampus. , 2009, Learning & memory.

[224]  B. McNaughton,et al.  Comparison of spatial and temporal characteristics of neuronal activity in sequential stages of hippocampal processing. , 1990, Progress in brain research.

[225]  R. Kempter,et al.  Grid cells in rat entorhinal cortex encode physical space with independent firing fields and phase precession at the single-trial level , 2012, Proceedings of the National Academy of Sciences.

[226]  Bruce L McNaughton,et al.  Attractor-map versus autoassociation based attractor dynamics in the hippocampal network. , 2010, Journal of neurophysiology.

[227]  Paul F. M. J. Verschure,et al.  A Model of Grid Cells Based on a Twisted Torus Topology , 2007, Int. J. Neural Syst..

[228]  D S Touretzky,et al.  Theory of rodent navigation based on interacting representations of space , 1996, Hippocampus.

[229]  Francesco Savelli,et al.  Hebbian analysis of the transformation of medial entorhinal grid-cell inputs to hippocampal place fields. , 2010, Journal of neurophysiology.

[230]  Surya Ganguli,et al.  Behavioral/systems/cognitive Spatial Information Outflow from the Hippocampal Circuit: Distributed Spatial Coding and Phase Precession in the Subiculum , 2022 .