Skip to main content
Log in

Robust path integration in the entorhinal grid cell system with hippocampal feed-back

  • Original Paper
  • Published:
Biological Cybernetics Aims and scope Submit manuscript

Abstract

Animals are able to update their knowledge about their current position solely by integrating the speed and the direction of their movement, which is known as path integration. Recent discoveries suggest that grid cells in the medial entorhinal cortex might perform some of the essential underlying computations of path integration. However, a major concern over path integration is that as the measurement of speed and direction is inaccurate, the representation of the position will become increasingly unreliable. In this paper, we study how allothetic inputs can be used to continually correct the accumulating error in the path integrator system. We set up the model of a mobile agent equipped with the entorhinal representation of idiothetic (grid cell) and allothetic (visual cells) information and simulated its place learning in a virtual environment. Due to competitive learning, a robust hippocampal place code emerges rapidly in the model. At the same time, the hippocampo-entorhinal feed-back connections are modified via Hebbian learning in order to allow hippocampal place cells to influence the attractor dynamics in the entorhinal cortex. We show that the continuous feed-back from the integrated hippocampal place representation is able to stabilize the grid cell code.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Amaral DG, Lavenex P (2006) Hippocampal neuroanatomy, chap 3. In: The hippocampus book. Oxford University Press, NY

  • Amaral DG, Witter MP (1989) The three dimensional organization of the hippocampal formation: a review of anatomical data. Neuroscience 31: 571–591

    Article  PubMed  CAS  Google Scholar 

  • Arleo A, Gerstner W (2000) Spatial cognition and neuro-mimetic navigation: a model of hippocampal place cell activity. Biol Cybern 83: 287–299

    Article  PubMed  CAS  Google Scholar 

  • Barry C, Burgess N (2007) Learning in a geometric model of place cell firing. Hippocampus 17: 786–800

    Article  PubMed  Google Scholar 

  • Barry C, Lever C, Hayman R, Hartley T, Burton S, O’Keefe J, Jeffery K, Burgess N (2006) The boundary vector cell model of place cell firing and spatial memory. Rev Neurosci 17: 71–97

    PubMed  Google Scholar 

  • Barry C, Hayman R, Burgess N, Jeffery KJ (2007) Experience-dependent rescaling of entorhinal grids. Nat Neurosci 10: 682–684

    Article  PubMed  CAS  Google Scholar 

  • Bi Gq, Poo Mm (2001) Synapticmodification by correlated activity: Hebb’s postulate revisited. Annu Rev Neurosci 24: 139–166

    Article  PubMed  CAS  Google Scholar 

  • Blair HT, Welday AC, Zhang K (2007) Scale-invariant memory representations emerge from moiré interference between grid fields that produce theta oscillations: a computational model. J Neurosci 27: 3211–3229

    Article  PubMed  CAS  Google Scholar 

  • Blais BS, Shouval HZ, Cooper LN (1999) The role of presynaptic activity in monocular deprivation: comparison of homosynaptic and heterosynaptic mechanisms. Proc Natl Acad Sci USA 96(3): 1083–1084

    Article  PubMed  CAS  Google Scholar 

  • Burgess N, O’Keefe J (1996) Neuronal computations underlying the firing of place cells and their role in navigation. Hippocampus 6: 749–762

    Article  PubMed  CAS  Google Scholar 

  • Burgess N, Recce M, O’Keefe J (1994) A model of hippocampal function. Neural Netw 7: 1065–1081

    Article  Google Scholar 

  • Burgess N, Jackson A, Hartley T, O‘Keefe J (2000) Predictions derived from modelling the hippocampal role in navigation. Biol Cybern 83(3): 301–312

    Article  PubMed  CAS  Google Scholar 

  • Burgess N, Barry C, O’Keefe J (2007) An oscillatory interference model of grid cell firing. Hippocampus 17(9): 801–812

    Article  PubMed  Google Scholar 

  • Collett T, Zeil J (1998) Places and landmarks: an arthropod perspective. In: Healy S (eds) Spatial representation in animals. Oxford University Press, NY, pp 18–53

    Google Scholar 

  • Érdi P, Somogyvári Z (2002) Post-Hebbian learning algorithms. In: Arbib MA (eds) The handbook of brain theory and neural networks, 2nd edn. The MIT Press, Cambridge, pp 533–539

    Google Scholar 

  • Etienne AS, Jeffery KJ (2004) Path integration in mammals. Hippocampus 14: 180–192

    Article  PubMed  Google Scholar 

  • Etienne AS, Maurer R, Séguinot V (1996) Path integration in mammals and its interaction with visual landmarks. J Exp Biol 199: 201–209

    PubMed  CAS  Google Scholar 

  • Etienne AS, Berlie J, Georgakopoulos J, Maurer R (1998) Role of dead reckoning in navigation. In: Healy S (ed) Spatial representation in animals, Oxford University Press, NY, pp 54–68

  • Fuhs MC, Touretzky DS (2006) A spin glass model of path integration in rat medial entorhinal cortex. J Neurosci 26: 4266–4276

    Article  PubMed  CAS  Google Scholar 

  • Fyhn M, Hafting T, Treves A, Moser MB, Moser EI (2007) Hippocampal remapping and grid realignment in entorhinal cortex. Nature 446: 190–194

    Article  PubMed  CAS  Google Scholar 

  • Gaussier P, Banquet JP, Sargolini F, Giovannangeli C, Save E, Poucet B (2007) A model of grid cells involving extra hippocampal path integration, and the hippocampal loop. J Integr Neurosci 6: 447–476

    Article  PubMed  CAS  Google Scholar 

  • Gerstner W, Kistler W (2002) Spiking Neuron Models. Cambridge University Press, London. http://icwww.epfl.ch/~gerstner/SPNM

  • Giocomo L, Zilli E, Fransen E, Hasselmo M (2007) Temporal frequency of subthreshold oscillations scales with entorhinal grid cell field spacing. Science 315(5819): 1719–1722

    Article  PubMed  CAS  Google Scholar 

  • Gothard KM, Skaggs WE, McNaughton BL (1996) Dynamics of mismatch correction in the hippocampal ensemble code for space: Interaction between path integration and environmental cues. J Neurosci 16: 8027–8040

    PubMed  CAS  Google Scholar 

  • Grossberg S (1974) Classical and instrumental conditioning by neural networks. Prog Theor Biol 3: 51–141

    CAS  Google Scholar 

  • Grossberg S (1976a) Adaptive pattern classification and universal recoding I: parallel development and coding of neural feature detectors. Biol Cybern 23: 121–134

    Article  PubMed  CAS  Google Scholar 

  • Grossberg S (1976b) Adaptive pattern classification and universal recoding II: feedback, expectation, olfaction, and illusions. Biol Cybern 23: 187–202

    Article  PubMed  CAS  Google Scholar 

  • Guanella A, Verschure PFMJ (2006) A model of grid cells based on a path integration mechanism. In: Kollias S, Stafylopatis A, Duch W, Oja E (eds) Artificial Neural Networks—ICANN 2006, Lecture Notes in Computer Science, vol 4131. Springer, Berlin, pp 740–749

  • Hafting T, Fyhn M, Molden S, Moser MB, Moser EI (2005) Microstructure of a spatial map in the entorhinal cortex. Nature 436: 801– 806

    Article  PubMed  CAS  Google Scholar 

  • Hafting T, Fyhn M, Bonnevie T, Moser MB, Moser EI (2008) Hippocampus-independent phase precession in entorhinal grid cells. Nature 453(7199): 1248–1252

    Article  PubMed  CAS  Google Scholar 

  • Hasselmo M, Giocomo L, Zilli E (2007) Grid cell firing may arise from interference of theta frequency membrane potential oscillations in single neurons. Hippocampus 17(12): 1252–1271

    Article  PubMed  Google Scholar 

  • Hebb DO (1949) The organization of behavior. Wiley, New York

    Google Scholar 

  • Jeffery KJ (1998) Learning of landmark stability and instability by hippocampal place cells. Neuropharmacology 37: 677–687

    Article  PubMed  CAS  Google Scholar 

  • Jeffery KJ (2007) Integration of the sensory inputs to place cells: what, where, why, and how. Hippocampus 17: 775–785

    Article  PubMed  Google Scholar 

  • Jeffery KJ, O’Keefe J (1999) Learned interaction of visual and idiothetic cues in the control of place field orientation. Exp Brain Res 127: 151–161

    Article  PubMed  CAS  Google Scholar 

  • Kloosterman F, Van Haeften T, Witter MP, Lopes Da Silva FH (2003) Electrophysiological characterization of interlaminar entorhinal connections: an essential link for re-entrance in the hippocampal-entorhinal system. Eur J Neurosci 18: 3037–3052

    Article  PubMed  Google Scholar 

  • Knierim JJ, Kudrimoti HS, McNaughton BL (1995) Place cells, head direction cells, and the learning of landmark stability. J Neurosci 15: 1648–1659

    PubMed  CAS  Google Scholar 

  • Lengyel M, Kwag J, Paulsen O, Dayan P (2005) Matching storage and recall: hippocampal spike timing-dependent plasticity and phase response curves. Nat Neurosci 8(12): 1677–1683

    Article  PubMed  CAS  Google Scholar 

  • Leutgeb JK, Leutgeb S, Moser MB, Moser EI (2007) Pattern separation in the dentate gyrus and CA3 of the hippocampus. Science 315: 961–966

    Article  PubMed  CAS  Google Scholar 

  • Lőrincz A, Buzsáki G (2000) Two-phase computational model training long-term memories in the entorhinal-hippocampal region. Ann NY Acad Sci 911: 83–111

    Article  PubMed  Google Scholar 

  • Maaswinkel H, Whishaw IQ (1999) Homing with locale, taxon, and dead reckoning strategies by foraging rats: sensory hierarchy in spatial navigation. Behav Brain Res 99: 143–152

    Article  PubMed  CAS  Google Scholar 

  • McNaughton BL, Barnes C, Gerrard J, Gothard K, Jung M, Knierim J, Kudrimoti H, Qin Y, Skaggs W, Suster M, Weaver K (1996) Deciphering the hippocampal polyglot: the hippocampus as a path integration system. J Exp Biol 199: 173–185

    PubMed  CAS  Google Scholar 

  • McNaughton BL, Battaglia FP, Jensen O, Moser EI, Moser MB (2006) Path integration and the neural basis of the ‘cognitive map’. Nat Rev Neurosci 7: 663–678

    Article  PubMed  CAS  Google Scholar 

  • Michel O (2004) Webots: professional mobile robot simulation. J Adv Robot Syst 1(1):39–42. http://www.ars-journal.com/ars/SubscriberArea/Volume1/39-42.pdf

    Google Scholar 

  • Muller RU, Kubie JL (1987) The effects of changes in the environment on the spatial firing of hippocampal complex-spike cells. J Neurosci 7: 1951–1968

    PubMed  CAS  Google Scholar 

  • Nardini M, Jones P, Bedford R, Braddick O (2008) Development of cue integration in human navigation. Curr Biol 18: 689–693

    Article  PubMed  CAS  Google Scholar 

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

    Article  PubMed  Google Scholar 

  • O’Keefe J, Nadel L (1978) The Hippocampus as a Cognitive Map. Oxford University Press, NY. http://www.cognitivemap.net/

  • O’Keefe J, Burgess N (2005) Dual phase and rate coding in hippocampal place cells: theoretical significance and relationship to entorhinal grid cells. Hippocampus 15: 853–866

    Article  PubMed  Google Scholar 

  • Oser HJ, Murchland JD, Daley DJ, Vaughan RJ (1990) An average distance. In: Klamkin MS (ed) Problems in Applied Mathematics: Selections from SIAM Review, Society for Industrial Mathematics, Philadelphia, pp 76–79

  • R Development Core Team (2007) R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. http://www.R-project.org, ISBN 3-900051-07-0

  • Rolls ET (1995) A model of the operation of the hippocampus and entorhinal cortex in memory. Int J Neural Syst 6: 51–71

    Google Scholar 

  • Rolls ET, Kesner RP (2006) A computational theory of hippocampal function, and empirical tests of the theory. Prog Neurobiol 79: 1–48

    Article  PubMed  CAS  Google Scholar 

  • Rolls ET, Stringer SM, Elliot T (2006) Entorhinal cortex grid cells can map to hippocampal place cells by competitive learning. Network 17: 447–465

    Article  PubMed  Google Scholar 

  • Sargolini F, Fyhn M, Hafting T, McNaughton BL, Witter MP, Moser MB, Moser EI (2007) Conjunctive representation of position, direction, and velocity in entorhinal cortex. Science 312: 758–762

    Article  CAS  Google Scholar 

  • Séguinot V, Maurer R, Etienne AS (1993) Dead reckoning in a small mammal: the evaluation of distance. J Comp Physiol A 173: 103–113

    Article  PubMed  Google Scholar 

  • Sharp PE (1991) Computer simulation of hippocampal place cells. Psychobiology 19(2): 103–115

    Google Scholar 

  • Shibata H (1988) A direct projection from the entorhinal cortex to the mammillary nuclei in the rat. Neurosci Lett 90: 6–10

    Article  PubMed  CAS  Google Scholar 

  • Solstad T, Moser EI, Einevoll GT (2006) From grid cells to place cells: a mathematical model. Hippocampus 16: 1026–1031

    Article  PubMed  Google Scholar 

  • Solstad T, Boccara CN, Kropff E, Moser MB, Moser EI (2008) Representation of geometric borders in the entorhinal cortex. Science 19(5909): 1865–1868

    Article  CAS  Google Scholar 

  • Taube JS (2007) The head direction signal: Origins and sensory-motor integration. Annu Rev Neurosci 30: 181–207

    Article  PubMed  CAS  Google Scholar 

  • Touretzky DS, Redish AD (1996) Theory of rodent navigation based on interacting representations of space. Hippocampus 6(3): 247–270

    Article  PubMed  CAS  Google Scholar 

  • Treves A, Rolls ET (1994) Computational analysis of the role of the hippocampus in memory. Hippocampus 4: 374–391

    Article  PubMed  CAS  Google Scholar 

  • Ujfalussy B, Erős P, Somogyvári Z, Kiss T (2008) Episodes in space: a modelling study of hippocampal place representation. In: Asada M, Hallam JCT, Meyer JA, Tani J (eds) From animals to animats, ISAB, Springer, Lecture Notes in Artificial Intelligence, vol 5040, pp 123–136

  • van Haeften T, Baks-te-Bulte L, Goede PH, Wouterlood FG, Witter MP (2003) 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

    Article  PubMed  Google Scholar 

  • Wiener SI, Korshunov VA, Garcia R, A B (1995) Inertial, substratal and landmark cue control of hippocampal CA1 place cell activity. Eur J Neurosci 7: 2206–2219

    Article  PubMed  CAS  Google Scholar 

  • Wilson MA, McNaughton BL (1993) Dynamics of the hippocampal ensemble code for space. Science 261: 1055–1058

    Article  PubMed  CAS  Google Scholar 

  • Witter MP, Naber PA, van Haeften T, Machielsen WCM, Rombouts SARB, Barkhof F, Scheltens P, Lopesda Silva FH (2000) Cortico-hippocampal communication by way of parallel parahippocampal-subicular pathways. Hippocampus 10: 398–410

    Article  PubMed  CAS  Google Scholar 

  • Zipser D (1985) A computational model of hippocampal place fields. Behav Neurosci 99(5): 1006–1018

    Article  PubMed  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Tamás Kiss.

Additional information

This research was supported by the EU Framework 6 ICEA project (IST-4-027819-IP).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Samu, D., Erős, P., Ujfalussy, B. et al. Robust path integration in the entorhinal grid cell system with hippocampal feed-back. Biol Cybern 101, 19–34 (2009). https://doi.org/10.1007/s00422-009-0311-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00422-009-0311-z

Keywords

Navigation