Abstract
Grid cells (GCs) in the medial entorhinal cortex (mEC) have the property of having their firing activity spatially tuned to a regular triangular lattice. Several theoretical models for grid field formation have been proposed, but most assume that place cells (PCs) are a product of the grid cell system. There is, however, an alternative possibility that is supported by various strands of experimental data. Here we present a novel model for the emergence of gridlike firing patterns that stands on two key hypotheses: (1) spatial information in GCs is provided from PC activity and (2) grid fields result from a combined synaptic plasticity mechanism involving inhibitory and excitatory neurons mediating the connections between PCs and GCs. Depending on the spatial location, each PC can contribute with excitatory or inhibitory inputs to GC activity. The nature and magnitude of the PC input is a function of the distance to the place field center, which is inferred from rate decoding. A biologically plausible learning rule drives the evolution of the connection strengths from PCs to a GC. In this model, PCs compete for GC activation, and the plasticity rule favors efficient packing of the space representation. This leads to gridlike firing patterns. In a new environment, GCs continuously recruit new PCs to cover the entire space. The model described here makes important predictions and can represent the feedforward connections from hippocampus CA1 to deeper mEC layers.
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References
Abarbanel HD, Huerta R, Rabinovich MI (2002) Dynamical model of long-term synaptic plasticity. Proc Natl Acad Sci USA 99(15):10132–10137. doi:10.1073/pnas.132651299
Acquas E, Wilson C, Fibiger HC (1996) Conditioned and unconditioned stimuli increase frontal cortical and hippocampal acetylcholine release: effects of novelty, habituation, and fear. J Neurosci Off J Soc Neurosci 16(9):3089–3096
Barry C, Ginzberg LL, O’Keefe J, Burgess N (2012) Grid cell firing patterns signal environmental novelty by expansion. Proc Natl Acad Sci USA 109(43):17687–17692. doi:10.1073/pnas.1209918109
Barry C, Hayman R, Burgess N, Jeffery KJ (2007) Experience-dependent rescaling of entorhinal grids. Nat Neurosci 10(6):682–684. doi:10.1038/nn1905
Blair HT, Gupta K, Zhang K (2008) Conversion of a phase- to a rate-coded position signal by a three-stage model of theta cells, grid cells, and place cells. Hippocampus 18(12):1239–1255. doi:10.1002/hipo.20509
Boccara CN, Sargolini F, Thoresen VH, Solstad T, Witter MP, Moser EI, Moser MB (2010) Grid cells in pre- and parasubiculum. Nat Neurosci 13(8):987–994. doi:10.1038/nn.2602
Bonnevie T, Dunn B, Fyhn M, Hafting T, Derdikman D, Kubie JL, Roudi Y, Moser EI, Moser MB (2013) Grid cells require excitatory drive from the hippocampus. Nat Neurosci 16(3):309–317. doi:10.1038/nn.3311
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(6029):595–599. doi:10.1126/science.1201652
Burak Y, Fiete IR (2009) Accurate path integration in continuous attractor network models of grid cells. PLoS Comput Biol 5(2):e1000291. doi:10.1371/journal.pcbi.1000291
Burgess N, Barry C, O’Keefe J (2007) An oscillatory interference model of grid cell firing. Hippocampus 17(9):801–812. doi:10.1002/hipo.20327
Castro L, Aguiar P (2012) Phase precession through acceleration of local theta rhythm: a biophysical model for the interaction between place cells and local inhibitory neurons. J Comput Neurosci 33(1):141–150. doi:10.1007/s10827-011-0378-0
Couey JJ, Witoelar A, Zhang SJ, Zheng K, Ye J, Dunn B, Czajkowski R, Moser MB, Moser EI, Roudi Y, Witter MP (2013) Recurrent inhibitory circuitry as a mechanism for grid formation. Nat Neurosci 16(3):318–324. doi:10.1038/nn.3310
Hines ML, Morse T, Migliore M, Carnevale NT, Shepherd GM (2004) ModelDB: a database to support computational neuroscience. J Comput Neurosci 17(1):7–11. doi:10.1023/B:JCNS.0000023869.22017.2e
Dhillon A, Jones RS (2000) Laminar differences in recurrent excitatory transmission in the rat entorhinal cortex in vitro. Neuroscience 99(3):413–422
Freund TF, Gulyas AI (1997) Inhibitory control of GABAergic interneurons in the hippocampus. Can J Physiol Pharmacol 75(5):479– 487
Fuhs MC, Touretzky DS (2006) A spin glass model of path integration in rat medial entorhinal cortex. J Neurosci Off J Soc Neurosci 26(16):4266–4276. doi:10.1523/JNEUROSCI.4353-05.2006
Fyhn M, Hafting T, Treves A, Moser MB, Moser EI (2007) Hippocampal remapping and grid realignment in entorhinal cortex. Nature 446(7132):190–194. doi:10.1038/nature05601
Fyhn M, Molden S, Witter MP, Moser EI, Moser MB (2004) Spatial representation in the entorhinal cortex. Science 305(5688):1258–1264. doi:10.1126/science.1099901
Giocomo LM, Zilli EA, Fransen E, Hasselmo ME (2007) Temporal frequency of subthreshold oscillations scales with entorhinal grid cell field spacing. Science 315(5819):1719–1722. doi:10.1126/science.1139207
Grossberg S, Pilly PK (2012) How entorhinal grid cells may learn multiple spatial scales from a dorsoventral gradient of cell response rates in a self-organizing map. PLoS Comput Biol 8(10):e1002648. doi:10.1371/journal.pcbi.1002648
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, Bonnevie T, Moser MB, Moser EI (2008) Hippocampus-independent phase precession in entorhinal grid cells. Nature 453(7199):1248–1252. doi:10.1038/nature06957
Hafting T, Fyhn M, Molden S, Moser MB, Moser EI (2005) Microstructure of a spatial map in the entorhinal cortex. Nature 436(7052):801–806. doi:10.1038/nature03721
Hasselmo ME (2006) The role of acetylcholine in learning and memory. Curr Opin Neurobiol 16(6):710–715. doi:10.1016/j.conb.2006.09.002
Hasselmo ME, Giocomo LM, Zilli EA (2007) Grid cell firing may arise from interference of theta frequency membrane potential oscillations in single neurons. Hippocampus 17(12):1252–1271. doi:10.1002/hipo.20374
Heys JG, Schultheiss NW, Shay CF, Tsuno Y, Hasselmo ME (2012) Effects of acetylcholine on neuronal properties in entorhinal cortex. Front Behav Neurosci 6:32. doi:10.3389/fnbeh.2012.00032
Jung MW, Wiener SI, McNaughton BL (1994) Comparison of spatial firing characteristics of units in dorsal and ventral hippocampus of the rat. J Neurosci Off J Soc Neurosci 14(12):7347–7356
Karlsson MP, Frank LM (2008) Network dynamics underlying the formation of sparse, informative representations in the hippocampus. J Neurosci Off J Soc Neurosci 28(52):14271–14281. doi:10.1523/JNEUROSCI.4261-08.2008
Kjelstrup KB, Solstad T, Brun VH, Hafting T, Leutgeb S, Witter MP, Moser EI, Moser M-B (2008) Finite Scale of Spatial Representation in the Hippocampus. Science 321(5885):140–143. doi:10.1126/science.1157086
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. doi:10.1126/science.1201685
Kropff E, Treves A (2008) The emergence of grid cells: Intelligent design or just adaptation? Hippocampus 18(12):1256–1269. doi:10.1002/hipo.20520
Langston RF, Ainge JA, Couey JJ, Canto CB, Bjerknes TL, Witter MP, Moser EI, Moser MB (2010) Development of the spatial representation system in the rat. Science 328(5985):1576–1580. doi:10.1126/science.1188210
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(8):663–678. doi:10.1038/nrn1932
Mhatre H, Gorchetchnikov A, Grossberg S (2012) Grid cell hexagonal patterns formed by fast self-organized learning within entorhinal cortex. Hippocampus 22(2):320–334. doi:10.1002/hipo.20901
Moser EI, Moser MB (2008) A metric for space. Hippocampus 18(12):1142–1156. doi:10.1002/hipo.20483
Muller RU, Kubie JL, Ranck JB Jr (1987) Spatial firing patterns of hippocampal complex-spike cells in a fixed environment. J Neurosci Off J Soc Neurosci 7(7):1935–1950
Navratilova Z, Giocomo LM, Fellous JM, Hasselmo ME, McNaughton BL (2012) Phase precession and variable spatial scaling in a periodic attractor map model of medial entorhinal grid cells with realistic after-spike dynamics. Hippocampus 22(4):772–789. doi:10.1002/hipo.20939
Quirk G, Muller R, Kubie J, Ranck J (1992) The positional firing properties of medial entorhinal neurons: description and comparison with hippocampal place cells. J Neurosci 12(5):1945–1963
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. doi:10.1126/science.1125572
Si B, Kropff E, Treves A (2012) Grid alignment in entorhinal cortex. Biol Cybern 106(8–9):483–506. doi:10.1007/s00422-012-0513-7
Solstad T, Moser EI, Einevoll GT (2006) From grid cells to place cells: a mathematical model. Hippocampus 16(12):1026–1031. doi:10.1002/hipo.20244
Stensola H, Stensola T, Solstad T, Froland K, Moser MB, Moser EI (2012) The entorhinal grid map is discretized. Nature 492(7427):72–78. doi:10.1038/nature11649
Wills TJ, Cacucci F, Burgess N, O’Keefe J (2010) Development of the hippocampal cognitive map in preweanling rats. Science 328(5985):1573–1576. doi:10.1126/science.1188224
Zilli EA, Hasselmo ME (2010) Coupled noisy spiking neurons as velocity-controlled oscillators in a model of grid cell spatial firing. J Neurosci Off J Soc Neurosci 30(41):13850–13860. doi:10.1523/JNEUROSCI.0547-10.2010
Acknowledgments
Supported by Fundação para a Ciência e a Tecnologia (FCT) through the Centro de Matemática da Universidade do Porto. Luísa Castro was supported by the Grant SFRH/BD/46329/2008 from FCT. The authors would like to thank the reviewers for important and insightful suggestions.
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Castro, L., Aguiar, P. A feedforward model for the formation of a grid field where spatial information is provided solely from place cells. Biol Cybern 108, 133–143 (2014). https://doi.org/10.1007/s00422-013-0581-3
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DOI: https://doi.org/10.1007/s00422-013-0581-3