Accurate Path Integration in Continuous Attractor Network Models of Grid Cells

Abstract

Grid cells in the rat entorhinal cortex display strikingly regular firing responses to the animal's position in 2-D space and have been hypothesized to form the neural substrate for dead-reckoning. However, errors accumulate rapidly when velocity inputs are integrated in existing models of grid cell activity. To produce grid-cell-like responses, these models would require frequent resets triggered by external sensory cues. Such inadequacies, shared by various models, cast doubt on the dead-reckoning potential of the grid cell system. Here we focus on the question of accurate path integration, specifically in continuous attractor models of grid cell activity. We show, in contrast to previous models, that continuous attractor models can generate regular triangular grid responses, based on inputs that encode only the rat's velocity and heading direction. We consider the role of the network boundary in the integration performance of the network and show that both periodic and aperiodic networks are capable of accurate path integration, despite important differences in their attractor manifolds. We quantify the rate at which errors in the velocity integration accumulate as a function of network size and intrinsic noise within the network. With a plausible range of parameters and the inclusion of spike variability, our model networks can accurately integrate velocity inputs over a maximum of approximately 10-100 meters and approximately 1-10 minutes. These findings form a proof-of-concept that continuous attractor dynamics may underlie velocity integration in the dorsolateral medial entorhinal cortex. The simulations also generate pertinent upper bounds on the accuracy of integration that may be achieved by continuous attractor dynamics in the grid cell network. We suggest experiments to test the continuous attractor model and differentiate it from models in which single cells establish their responses independently of each other.

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References 50

1. 1.

   Hafting T, Fyhn M, Molden S, Moser MB, Moser E. Microstructure of a spatial map in the entorhinal cortex. Nature. 2005;436:801-806.

   Not in our library10.1038/nature03721

2. 2.

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

   Not in our library10.1523/jneurosci.4353-05.2006

3. 3.

   Burak Y, Fiete I. Do we understand the emergent dynamics of grid cell activity? J Neurosci. 2006;26:9352-9354.

   Not in our library10.1523/jneurosci.2857-06.2006

4. 4.

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

   Not in our library10.1038/nrn1932

5. 5.

   Burgess N, Barry C, O'Keefe J. An oscillatory interference model of grid cell firing. Hippocampus. 2007;17:801-812.

   Not in our library10.1002/hipo.20327

6. 6.

   Hasselmo ME, Giocomo LM, Zilli EA. Grid cell firing may arise from interference of theta frequency membrane potential oscillations in single neurons. Hippocampus. 2007;17:1252-1271.

   Not in our library10.1002/hipo.20374

7. 7.

   Guanella A, Kiper D, Verschure P. A model of grid cells based on a twisted torus topology. Int J Neural Syst. 2007;17:231-240.

   Not in our library10.1142/s0129065707001093

8. 8.

   Skaggs WE, Knierim JJ, Kudrimoti HS, McNaughton BL. A model of the neural basis of the rat's sense of direction. Adv Neural Inf Process Syst. 1995;7:173-180.

   Not in our library

9. 9.

   Seung HS. How the brain keeps the eyes still. Proc Natl Acad Sci U S A. 1996;93:13339-13344.

   Not in our library10.1073/pnas.93.23.13339

10. 10.

    Zhang K. Representation of spatial orientation by the intrinsic dynamics of the head-direction cell ensemble: a theory. J Neurosci. 1996;16:2112-2126.

    Not in our library10.1523/jneurosci.16-06-02112.1996

11. 11.

    Samsonovich A, McNaughton BL. Path integration and cognitive mapping in a continuous attractor neural network model. J Neurosci. 1997;17:5900-5920.

    Not in our library10.1523/jneurosci.17-15-05900.1997

12. 12.

    Tsodyks M. Attractor neural network models of spatial maps in hippocampus. Hippocampus. 1999;9:481-489.

    Not in our library10.1002/(sici)1098-1063(1999)9:4<481::aid-hipo14>3.0.co;2-s

13. 13.

    Goodridge JP, Touretzky DS. Modeling attractor deformation in the rodent head-direction system. J Neurophysiol. 2000;83:3402-3410.

    Not in our library10.1152/jn.2000.83.6.3402

14. 14.

    Xie X, Hahnloser RHR, Seung HS. Double-ring network model of the head-direction system. Phys Rev E Stat Nonlin Soft Matter Phys. 2002;66:041902.

    Not in our library10.1103/physreve.66.041902

15. 15.

    Stringer SM, Rolls ET, Trappenberg TP. Self-organising continuous attractor networks with multiple activity packets, and the representation of space. Neural Netw. 2004;17:5-27.

    Not in our library10.1016/s0893-6080(03)00210-7

16. 16.

    O'Keefe J, Burgess N. Dual phase and rate coding in hippocampal place cells: theoretical significance and relationship to entorhinal grid cells. Hippocampus. 2005;15:853-866.

    Not in our library10.1002/hipo.20115

17. 17.

    Giocomo LM, Zilli EA, Fransen E, Hasselmo ME. Temporal frequency of subthreshold oscillations scales with entorhinal grid cell field spacing. Science. 2007;315:1719-1722.

    Not in our library10.1126/science.1139207

18. 18.

    Mittelstaedt M, Mittelstaedt H. Homing by path integration in a mammal. Naturwissenschaften. 1980;67:566-567.

    Not in our library

19. 19.

    Maaswinkel H, Jarrard LE, Whishaw IQ. Hippocampectomized rats are impaired in homing by path integration. Hippocampus. 1999;9:553-561.

    Not in our library10.1002/(sici)1098-1063(1999)9:5<553::aid-hipo9>3.0.co;2-g

20. 20.

    Sharp PE, Tinkelman A, Cho J. Angular velocity and head direction signals recorded from the dorsal tegmental nucleus of gudden in the rat: implications for path integration in the head direction cell circuit. Behav Neurosci. 2001;115:571-588.

    Not in our library

21. 21.

    Etienne AS, Jeffery KJ. Path integration in mammals. Hippocampus. 2004;14:180-192.

    Not in our library10.1002/hipo.10173

22. 22.

    Alonso A, Llinas RR. Subthreshold Na+-dependent theta-like rhythmicity in stellate cells of entorhinal cortex layer II. Nature. 1989;342:175-177.

    Not in our library10.1038/342175a0

23. 23.

    Alonso A, Klink R. Differential electroresponsiveness of stellate and pyramidal-like cells of medial entorhinal cortex layer II. J Neurophysiol. 1993;70:128-143.

    Not in our library10.1152/jn.1993.70.1.128

24. 24.

    Mitchell SJ, Ranck JBJ. Generation of theta rhythm in medial entorhinal cortex of freely moving rats. Brain Res. 1980;189:49-66.

    Not in our library10.1016/0006-8993(80)90006-2

25. 25.

    Alonso A, Garcia-Austt E. Neuronal sources of theta rhythm in the entorhinal cortex of the rat. ii. phase relations between unit discharges and theta field potentials. Exp Brain Res. 1987;67:502-509.

    Not in our library10.1007/bf00247283

26. 26.

    Murray JD. Mathematical Biology. 2003.

    Not in our library

27. 27.

    Cohen M, Grossberg S. Absolute stability of global pattern-formation and parallel memory storage by competitive neural networks. IEEE Trans Syst Man Cybern. 1983;13:815-826.

    Not in our library

28. 28.

    Hopfield JJ. Neurons with graded response have collective computational properties like those of two-state neurons. Proc Natl Acad Sci USA. 1984;81:3088-3092.

    Not in our library10.1073/pnas.81.10.3088

29. 29.

    Softky WR, Koch C. The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs. J Neurosci. 1993;13:334-350.

    Not in our library10.1523/jneurosci.13-01-00334.1993

30. 30.

    Shadlen MN, Newsome WT. Noise, neural codes and cortical organization. Curr Opin Neurobiol. 1994;4:569-579.

    Not in our library10.1016/0959-4388(94)90059-0

31. 31.

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

    Not in our library10.1038/nn1905

32. 32.

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

    Not in our library10.1038/nature05601

33. 33.

    Sargolini F, Fyhn M, Hafting T, McNaughton BL, Witter MP, et al. Conjunctive representation of position, direction, and velocity in entorhinal cortex. Science. 2006;312:758-762.

    Not in our library10.1126/science.1125572

34. 34.

    Taube JS, Muller RU, Ranck JB. Head-direction cells recorded from the postsubiculum in freely moving rats. I. Description and quantitative analysis. J Neurosci. 1990;10:420-435.

    Not in our library10.1523/jneurosci.10-02-00420.1990

35. 35.

    Taube JS. Head direction cells recorded in the anterior thalamic nuclei of freely moving rats. J Neurosci. 1995;15:70-86.

    Not in our library10.1523/jneurosci.15-01-00070.1995

36. 36.

    Savelli D, Yoganarasimha D, Knierim J. Influence of boundary removal on the spatial representations of the medial entorhinal cortex. Hippocampus. 2008;18:1270-1282.

    Not in our library10.1002/hipo.20511

37. 37.

    Solstad T, Boccara CN, Kropff E, Moser MB, Moser EI. Representation of geometric borders in the entorhinal cortex. Science. 2008;322:1865-1868.

    Not in our library10.1126/science.1166466

38. 38.

    Ernst UA, Pawelzik KR, Sahar-Pikielny C, Tsodyks MV. Intracortical origin of visual maps. Nat Neurosci. 2001;4:431-436.

    Not in our library10.1038/86089

39. 39.

    Amaral DG, Ishizuka N, Claiborne B. Neurons, numbers and the hippocampal network. Prog Brain Res. 1990;83:1-11.

    Not in our library10.1016/s0079-6123(08)61237-6

40. 40.

    Mulders WH, West MJ, Slomianka L. Neuron numbers in the presubiculum, parasubiculum, and entorhinal area of the rat. J Comp Neurol. 1997;385:83-94.

    Not in our library

41. 41.

    Augustinack JC, van der Kouwe AJW, Blackwell ML, Salat DH, Wiggins CJ, et al. Detection of entorhinal layer II using 7 tesla magnetic resonance imaging. Ann Neurol. 2005;57:489-494.

    Not in our library10.1002/ana.20426

42. 42.

    Fiete IR, Burak Y, Brookings T. What grid cells convey about rat location. J Neurosci. 2008;28:6856-6871.

    Not in our library10.1523/jneurosci.5684-07.2008

43. 43.

    Hevner RF, Wong-Riley MT. Entorhinal cortex of the human, monkey, and rat: metabolic map as revealed by cytochrome oxidase. J Comp Neurol. 1992;326:451-469.

    Not in our library10.1002/cne.903260310

44. 44.

    Goldenberg TM, Bakay RA, Ribak CE. Electron microscopy of cell islands in layer ii of the primate entorhinal cortex. J Comp Neurol. 1995;355:51-66.

    Not in our library10.1002/cne.903550108

45. 45.

    Solodkin A, Van Hoesen GW. Entorhinal cortex modules of the human brain. J Comp Neurol. 1996;365:610-617.

    Not in our library10.1002/(sici)1096-9861(19960219)365:4<610::aid-cne8>3.0.co;2-7

46. 46.

    Witter MP, Moser EI. Spatial representation and the architecture of the entorhinal cortex. Trends Neurosci. 2006;29:671-678.

    Not in our library10.1016/j.tins.2006.10.003

47. 47.

    Dickson CT, Biella G, de Curtis M. Evidence for spatial modules mediated by temporal synchronization of carbachol-induced gamma rhythm in medial entorhinal cortex. J Neurosci. 2000;20:7846-7854.

    Not in our library10.1523/jneurosci.20-20-07846.2000

48. 48.

    Seung HS, Lee DD, Reis BY, Tank DW. Stability of the memory of eye position in a recurrent network of conductance-based model neurons. Neuron. 2000;26:259-271.

    Not in our library10.1016/s0896-6273(00)81155-1

49. 49.

    Stringer SM, Rolls ET, Trappenberg TP, de Araujo IET. Self-organizing continuous attractor networks and motor function. Neural Netw. 2003;16:161-182.

    Not in our library10.1016/s0893-6080(02)00237-x

50. 50.

    Hafting T, Fyhn M, Molden S, Moser MB, Moser E.

    Not in our library

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