Abstract
The spatial responses of many of the cells recorded in all layers of rodent medial entorhinal cortex (mEC) show mutually aligned grid patterns. Recent experimental findings have shown that grids can often be better described as elliptical rather than purely circular and that, beyond the mutual alignment of their grid axes, ellipses tend to also orient their long axis along preferred directions. Are grid alignment and ellipse orientation aspects of the same phenomenon? Does the grid alignment result from single-unit mechanisms or does it require network interactions? We address these issues by refining a single-unit adaptation model of grid formation, to describe specifically the spontaneous emergence of conjunctive grid-by-head-direction cells in layers III, V, and VI of mEC. We find that tight alignment can be produced by recurrent collateral interactions, but this requires head-direction (HD) modulation. Through a competitive learning process driven by spatial inputs, grid fields then form already aligned, and with randomly distributed spatial phases. In addition, we find that the self-organization process is influenced by any anisotropy in the behavior of the simulated rat. The common grid alignment often orients along preferred running directions (RDs), as induced in a square environment. When speed anisotropy is present in exploration behavior, the shape of individual grids is distorted toward an ellipsoid arrangement. Speed anisotropy orients the long ellipse axis along the fast direction. Speed anisotropy on its own also tends to align grids, even without collaterals, but the alignment is seen to be loose. Finally, the alignment of spatial grid fields in multiple environments shows that the network expresses the same set of grid fields across environments, modulo a coherent rotation and translation. Thus, an efficient metric encoding of space may emerge through spontaneous pattern formation at the single-unit level, but it is coherent, hence context-invariant, if aided by collateral interactions.
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References
Barry C, Ó Keefe J, Burgess N (2009) Effect of novelty on grid cell firing. Society for Neuroscience abstract 101.24
Boccara CN, Sargolini F, Thoresen VHH, Solstad T, Witter MP, Moser EI, Moser MBB (2010) Grid cells in pre- and parasubiculum. Nat Neurosci 13(8): 987–994
Brandon MP, Bogaard AR, Libby CP, Connerney MA, Gupta K, Hasselmo ME (2011) Reduction of theta rhythm dissociates grid cell spatial periodicity from directional tuning. Science 332: 595–599
Burak Y, Fiete IR (2009) Accurate path integration in continuous attractor network models of grid cells. PLoS Comput Biol 5(2): e1000291
Burgess N (2008) Grid cells and theta as oscillatory interference: theory and predictions. Hippocampus 18(12): 1157–1174
Burgess N, Barry C, O’Keefe J (2007) An oscillatory interference model of grid cell firing. Hippocampus 17(9): 901–912
Colgin LL, Moser EI, Moser MB (2008) Understanding memory through hippocampal remapping. Trends Neurosci 31(9): 469–477
Derdikman D, Whitlock JR, Tsao A, Fyhn M, Hafting T, Moser MBB, Moser EI (2009) Fragmentation of grid cell maps in a multicompartment environment. Nat Neurosci 12(10): 1325–1332
Dhillon A, Jones RSG (2000) Laminar differences in recurrent excitatory transmission in the rat entorhinal cortex in vitro. Neuroscience 99(3): 413–422
Fiete IR, Burak Y, Brookings T (2008) What grid cells convey about rat location. J Neurosci 28(27): 6858–6871
Fuhs M, Touretzky D (2006) A spin glass model of path integration in rat medial entorhinal cortex. J Neurosci 26: 4266–4276
Fyhn M, Molden S, Witter M, Moser E, Moser MB (2004) Spatial representation in the entorhinal cortex. Science 305: 1258–1264
Fyhn M, Hafting T, Treves A, Moser MB, Moser E (2007) Hippocampal remapping and grid realignment in entorhinal cortex. Nature 446: 190–194
Garden DL, Dodson PD, O’Donnell C, White MD, Nolan MF (2008) Tuning of synaptic integration in the medial entorhinal cortex to the organization of grid cell firing fields. Neuron 60(5): 875–889
Giocomo LM, Zilli EA, Fransén E, Hasselmo ME (2007) Temporal frequency of subthreshold oscillations scales with entorhinal grid cell field spacing. Science 315(5819): 1719–1722
Giocomo LM, Moser MB, Moser EI (2011) Computational models of grid cells. Neuron 71(4): 589–603
Guanella A, Kiper D, Verschure P (2007) A model of grid cells based on a twisted torus topology. Int J Neural Syst 17(4): 231–240
Hafting T, Fyhn M, Molden S, Moser MBB, Moser EI (2005) Microstructure of a spatial map in the entorhinal cortex. Nature 436(7052): 801–806
Hasselmo ME (2008) Grid cell mechanisms and function: contributions of entorhinal persistent spiking and phase resetting. Hippocampus 18(12): 1213–1229
Koenig J, Linder AN, Leutgeb JK, Leutgeb S (2011) The spatial periodicity of grid cells is not sustained during reduced theta oscillations. Science 332(6029): 592–595
Kropff E, Treves A (2008) The emergence of grid cells: intelligent design or just adaptation?. Hippocampus 18: 1256–1269
Langston RF, Ainge JA, Couey JJ, Canto CB, Bjerknes TL, Witter MP, Moser EI, Moser MBB (2010) Development of the spatial representation system in the rat. Science 328(5985): 1576–1580
McNaughton B, Battaglia F, Jensen O, Moser E, Moser MB (2006) Path integration and the neural basis of the “cognitive map”. Nat Rev Neurosci 7: 663–678
Milford MJ, Wiles J, Wyeth GF (2010) Solving navigational uncertainty using grid cells on robots. PLoS Comput Biol 6(11): e1000995
Navratilova Z, Giocomo LM, Fellous JMM, Hasselmo ME, McNaughton BL (2011) Phase precession and variable spatial scaling in a periodic attractor map model of medial entorhinal grid cells with realistic after-spike dynamics. Hippocampus 22: 772–789
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(1): 171–175
Petkovic MS (2009) Famous puzzles of great mathematicians. American Mathematical Society, College Station
Rolls E, Stringer S, Elliot T (2006) Entorhinal cortex grid cells can map to hippocampal place cells by competitive learning. Network 15: 447–465
Samsonovich A, McNaughton BL (1997) Path integration and cognitive mapping in a continuous attractor neural network model. J Neurosci 17(15): 5900–5920
Samu D, Erős P, Ujfalussy B, Kiss T (2009) Robust path integration in the entorhinal grid cell system with hippocampal feed-back. Biol Cybern 101: 19–34
Sargolini F, Fyhn M, Hafting T, Mcnaughton BL, Witter MP, Moser MB, Moser EI (2006) Conjunctive representation of position, direction, and velocity in entorhinal cortex. Science 312(5774):758–762. http://www.ntnu.no/cbm/gridcell. Accessed May 2011
Scoville WB, Milner B (1957) Loss of recent memory after bilateral hippocampal lesions. J Neurol Neurosurg Psychiatry 20: 11–21
Si B, Treves A (2009) The role of competitive learning in the generation of DG fields from EC inputs. Cogn Neurodyn 3(2): 177–187
Si B, Herrmann JM, Pawelzik K (2007) Gain-based exploration: From multi-armed bandits to partially observable environments. In: proceedings of the international conference on natural computation, Haikou, pp 177–182
Solstad T, Moser E, Einevoll G (2006) From grid cells to place cells: a mathematical model. Hippocampus 16: 1026–1031
Stensland H, Kirkesola T, Moser E, Moser MB (2010) Orientational geometry of entorhinal grid cells. Society for Neuroscience abstract 101.14
Taube JS, Muller RU, Ranck JB (1990) Head-direction cells recorded from the postsubiculum in freely moving rats. I. Description and quantitative analysis. J Neurosci 10(2): 420–435
Treves A (2003) Computational constraints that may have favoured the lamination of sensory cortex. J Comput Neurosci 14: 271–282
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(8): 943–952
Walters DM, Stringer SM (2010) Path integration of head direction: updating a packet of neural activity at the correct speed using neuronal time constants. Biol Cybern 103: 21–41
Wills TJ, Cacucci F, Burgess N, O’Keefe J (2010) Development of the hippocampal cognitive map in preweanling rats. Science 328(5985): 1573–1576
Zar JH (1998) Biostatistical analysis, 4th edn. Prentice Hall, Upper Saddle River
Zhang K (1996) Representation of spatial orientation by the intrinsic dynamics of the head-direction cell ensemble: a theory. J Neurosci 16(6): 2112–2126
Zilli EA, Hasselmo ME (2010) Coupled noisy spiking neurons as velocity-controlled oscillators in a model of grid cell spatial firing. J Neurosci 30(41): 13850–13860
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Si, B., Kropff, E. & Treves, A. Grid alignment in entorhinal cortex. Biol Cybern 106, 483–506 (2012). https://doi.org/10.1007/s00422-012-0513-7
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DOI: https://doi.org/10.1007/s00422-012-0513-7