Russian version English version
About the Journal
Editorial Board
Instructions for Authors
Information for Readers and Authors
Current Issue
Archive
Contact Us
Search

Send manuscript
 


Volume 9   Issue 1   Year 2014
Tsukerman V.D., Kharybina Z.S., Kulakov S.V.

A Mathematical Model of Hippocampal Spatial Encoding. II. Neurodynamic Correlates of Mental Trajectories and Decision-Making Problem

Mathematical Biology & Bioinformatics. 2014;9(1):216-256.

doi: 10.17537/2014.9.216.

References

  1. Hafting T, Fyhn M, Molden S, Moser MB, Moser EI. Microstructure of a spatial map in the entorhinal cortex. Nature. 2005;436:801–806.
    2. doi: 10.1038/nature03721
  2. 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.
    3. doi: 10.1038/nrn1932
  3. Barry C, Hayman R, Burgess N, Jeffery KJ. Experience-dependent rescaling of entorhinal grids. Nat. Neurosci. 2007;10:682–684.
    4. doi: 10.1038/nn1905
  4. Derdikman D, Moser EI. A manifold of spatial maps in the brain. Trends Cogn. Sci. 2010;14:561–569.
    5. doi: 10.1016/j.tics.2010.09.004
  5. Doeller CF, Barry C, Burgess N. Evidence for grid cells in a human memory network. Nature. 2010;463:657–661.
    6. doi: 10.1038/nature08704
  6. Navratilova J, Giocomo LM, Fellous J-M, Hasselmo ME, McNaughton BL. Phase precession and variable spatial scaling in a periodic attractor map model of medial entorhinal grid cells with realistic after-spike dynamics. Hippocampus. 2012;22:772–789.
    7. doi: 10.1002/hipo.20939
  7. Giocomo LM, Roudi Y. The neural encoding of space in parahippocampal cortices. Front. Neural Circuits. 2012;6:53.
    8. doi: 10.3389/fncir.2012.00053
  8. O’Keefe J, Dostrovsky J. The hippocampus as a spatial map: preliminary evidence from unit activity in the freely moving rat. Brain Res. 1971;34:171–175.
    9. doi: 10.1016/0006-8993(71)90358-1
  9. 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.
    10. doi: 10.1002/hipo.20115
  10. O’Keefe J, Burgess N. Geometric determinants of the place fields of hippocampal neurons. Nature. 1996;381:425–428.
    11. doi: 10.1038/381425a0
  11. Ekstrom AD, Kahana MJ, Caplan JB, Fields TA, Isham EA, Newman EL, Fried I. Cellular networks underlying human spatial navigation. Nature. 2003;425:184–187.
    12. doi: 10.1038/nature01964
  12. Geisler C, Robbe D, Zugaro M, Sirota A, Buzsaki G. Hippocampal place cell assemblies are speed controlled oscillators. PNAS USA. 2007;104:8149–8154.
    13. doi: 10.1073/pnas.0610121104
  13. Diba K, Buzsaki G. Forward and reverse hippocampal place-cell sequences during ripples. Nat. Neurosci. 2007;10:1241–1242.
    14. doi: 10.1038/nn1961
  14. Moser EI, Kropff E, Moser MB. Place cells, grid cells, and the brain’s spatial representation system. Ann. Rev. Neurosci. 2008;31:69–89.
    15. doi: 10.1146/annurev.neuro.31.061307.090723
  15. Taube JS, Muller RU, Ranck JBJr. Head-direction cells recorded from the postsubiculum in freely moving rats. I. Description and quantitative analysis. J. Neurosci. 1990;10:420–435.
  16. Taube JS, Muller RU, Ranck JrJB. Head-direction cells recorded from the postsubiculum in freely moving rats. II. Effects of environmental manipulations. J. Neurosci. 1990;10:436–447.
  17. Blair HT, Sharp PE. Anticipatory head direction signals in anterior thalamus: evidence for a thalamocortical circuit that integrates angular head motion to compute head direction. J. Neurosci. 1995;15:6260–6270.
  18. Zhang K. Representation of spatial orientation by the intrinsic dynamics of the head direction cell ensemble: a theory. J. Neurosci. 1996;16:2112–2126.
  19. Taube JS. Head direction cells and the neurophysiological basis for a sence of direction. Progr. Neurobiol. 1998;55:225–256.
    20. doi: 10.1016/S0301-0082(98)00004-5
  20. Sharp PE, Blair HT, Cho J. The anatomical and computational basis of the rat head-direction cell signal. Trends Neurosci. 2001;24:289–294.
    21. doi: 10.1016/S0166-2236(00)01797-5
  21. Zugaro MB, Arleo A, Berthoz A, Wiener SI. Rapid spatial reorientation and head direction cells. J. Neurosci. 2003;23:3478–3482.
  22. Taube JS, Bassett JP. Persistent neural activity in head direction cells. Cereb. Cortex. 2003;13:1162–1172.
    23. doi: 10.1093/cercor/bhg102
  23. Taube JS. The head direction signal: origins and sensory-motor integration. Annu. Rev. Neurosci. 2007;30:181–207.
    24. doi: 10.1146/annurev.neuro.29.051605.112854
  24. Sargolini F, Fyhn M, Hafting T, McNaughton BL, Witter MP, Moser MB, Moser EI. Conjunctive representation of position, direction, and velocity in entorhinal cortex. Science. 2006;312:758–762.
    25. doi: 10.1126/science.1125572
  25. Doeller CF, King JA, Burgess N. Parallel striatal and hippocampal systems for landmarks and boundaries in spatial memory. PNAS USA. 2008;105:5915–5920.
    26. doi: 10.1073/pnas.0801489105
  26. Solstad T, Boccara CN, Kropff E, Moser MB, Moser EI. Representation of geometric borders in the entorhinal cortex. Science. 2008;322:1865–1868.
    27. doi: 10.1126/science.1166466
  27. Savelli F, Yoganarasimha D, Knierim JJ. Influence of boundary removal on the spatial representations of the medial entorhinal cortex. Hippocampus. 2008;18:1270–1282.
    28. doi: 10.1002/hipo.20511
  28. Lever C, Burton S, Jeewajee A, O’Keefe J, Burgess N. Boundary vector cells in the subiculum of the hippocampal formation. J. Neurosci. 2009;29:9771–9777.
    29. doi: 10.1523/JNEUROSCI.1319-09.2009
  29. Bird CM, Capponi C, King JA, Doeller CF, Burgess N. Establishing the boundaries: the hippocampal contribution to imagining scenes. J. Neurosci. 2010;30:11688–11695.
    30. doi: 10.1523/JNEUROSCI.0723-10.2010
  30. Itskov V, Curto C, Pastalkova E, Buzsaki G. Cell assembly sequences arising from spike threshold adaptation keep track of time in the hippocampus. J. Neurosci. 2011;31:2828–2834.
    31. doi: 10.1523/JNEUROSCI.3773-10.2011
  31. MacDonald CJ, Lepage KQ, Eden UT, Eichenbaum H. Hippocampal «time cells» bridge the gap in memory for discontiguous events. Neuron. 2011;71:737–749.
    32. doi: 10.1016/j.neuron.2011.07.012
  32. Kraus BJ, Robinson RJ, White JA, Eichenbaum H, Hasselmo ME. Hippocampal «time cells»: time versus path integration. Neuron. 2013;78:1–12.
    33. doi: 10.1016/j.neuron.2013.04.015
  33. Eichenbaum H. Memory on time. Trends Cogn. Sciences. 2013;17:81–88.
    34. doi: 10.1016/j.tics.2012.12.007
  34. Tsukerman VD, Kharybina ZS, Kulakov SV. In: trudy III Vserossiiskoi konf. «Nelineinaia dinamika v kognitivnykh issledovaniiakh-2013» (III All-Russian conference proceedings. "Nonlinear dynamics in cognitive studies 2013"). Nizhny Novgorod: IAP RAS; 2013. P. 183–186 (in Russ.).
  35. Burgess N, Barry C, O'Keefe J. An oscillatory interference model of grid cell firing. Hippocampus. 2007;17:801–812.
    36. doi: 10.1002/hipo.20327
  36. Burgess N. Grid cells and theta as oscillatory interference: theory and predictions. Hippocampus. 2008;18:1157–1174.
    37. doi: 10.1002/hipo.20518
  37. Jeewajee A, Barry C, O’Keefe J, Burgess N. Grid cells and theta as oscillatory interference: electrophysiological data from freely moving rats. Hippocampus. 2008;18:1175–1185.
    38. doi: 10.1002/hipo.20510
  38. Samsonovich A, McNaughton BL. Path integration and cognitive mapping in a continuous attractor neural network model. J. Neurosci. 1997;17:5900–5920.
  39. Battaglia FP, Treves A. Attractor neural networks storing multiple space representations: a model for hippocampal place fields. Physical Rev. E. 1998;58:7738–7753.
    40. doi: 10.1103/PhysRevE.58.7738
  40. Fuhs MC, Touretzky DS. A spin glass model of path integration in rat medial entorhinal cortex. J. Neurosci. 2006;26:4266–4276.
    41. doi: 10.1523/JNEUROSCI.4353-05.2006
  41. McNaughton BL, Battaglia FP, Jensen O, Moser EI, Moser M-B. Path integration and the neural basis of the «cognitive map». Nat. Rev. Neurosci. 2006;7:663–678.
    42. doi: 10.1038/nrn1932
  42. 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.
    43. doi: 10.1142/S0129065707001093
  43. Burak Y, Fiete IR. Accurate path integration in continuous attractor network models of grid cells. PLoS Comput. Biol. 2009;5(2):e1000291.
    44. doi: 10.1371/journal.pcbi.1000291
  44. Hasselmo ME, Brandon MP. A model combining oscillations and attractor dynamics for generation of grid cell firing. Front. Neur. Circuits. 2012;6:30.
    45. doi: 10.3389/fncir.2012.00030
  45. Pastoll H, Solanka L, van Rossum MCW, Nolan MF. Feedback inhibition enables theta-nested gamma oscillations and grid firing fields. Neuron. 2013;77:141–154.
    46. doi: 10.1016/j.neuron.2012.11.032
  46. Tsukerman VD, Cheshkov GN. In: Neirokomp'iutery: razrabotka,  primenenie (Neurocomputers: Development and Application). 2002;7-8:65-72 (in Russ.).
  47. Tsukerman VD, Kulakov SV.  In: Neirokomp'iutery: razrabotka,  primenenie (Neurocomputers: Development and Application). 2004;11:15-25 (in Russ.).
  48. Tsukerman VD. Mathematical Model of Phase Coding of Events in the Brain. Matematicheskaya biologiya i bioinformatika (Mathematical Biology and Bioinformatics). 2006;1(1):97–107 (in Russ.).
    49. doi: 10.17537/2006.1.97
  49. Tsukerman VD, Kulakov SV, Karimova OV. Rippling Codes of Event Sequences. Matematicheskaya biologiya i bioinformatika (Mathematical Biology and Bioinformatics). 2006;1(1):108–122 (in Russ.).
    50. doi: 10.17537/2006.1.108
  50. Tsukerman VD, Karimova OV, Kulakov SV, Sazykin AA. In: Neirokomp'iutery: razrabotka,  primenenie (Neurocomputers: Development and Application). 2010;2:17-27 (in Russ.).
  51. Tsukerman VD. In: Nelineinye volny-2010 (Nonlinear Waves-2010). Eds. Gaponova-Grekhova AV, Nekorkina VI. Nizhny Novgorod; 2011. P. 396-411 (in Russ.).
  52. Tsukerman VD, Eremenko ZS, Karimova OV, Sazykin AA, Kulakov SV. Mathematical Model of Spatial Encoding in Hippocampal Formation. I. Grid Cells Neurodynamics. Matematicheskaya biologiya i bioinformatika (Mathematical Biology and Bioinformatics). 2012;7(1):87–124 (in Russ.).
  53. Stensola H, Stensola T, Solstad T, Froland K, Moser M-B, Moser EI. The entorhinal grid map is discretized. Nature. 2012;492:72–78.
    54. doi: 10.1038/nature11649
  54. Kim S, Lee J, Lee I. The hippocampus is required for visually cued contextual response selection, but not for visual discrimination of contexts. Front. Behav. Neurosci. 2012;6:66.
    55. doi: 10.3389/fnbeh.2012.00066
  55. Brun VH, Solstad T, Kjelstrup KB, Fyhn M, Witter MP, Moser EI, Moser M-B. Progressive increase in grid scale from dorsal to ventral medial entorhinal cortex. Hippocampus. 2008;18:1200–1212.
    56. doi: 10.1002/hipo.20504
  56. Maurer AP, McNaughton BL. Network and intrinsic cellular mechanisms underlying theta phase precession of hippocampal neurons. Trends Neurosci. 2007;30:325–333.
    57. doi: 10.1016/j.tins.2007.05.002
  57. van der Meer MAA, Redish AD. Theta phase precession in rat ventral striatum links place and reward information. J. Neurosci. 2011;31:2843–2854.
    58. doi: 10.1523/JNEUROSCI.4869-10.2011
  58. Cheng S, Frank LM. New experiences enhance coordinated neural activity in the hippocampus. Neuron. 2008;57:303–313.
    59. doi: 10.1016/j.neuron.2007.11.035
  59. Kubie JL, Fenton AA. Linear look-ahead in conjunctive cells an entorhinal mechanism for vector-based navigation. Front. Neur. Circuits. 2012;6:20.
    60. doi: 10.3389/fncir.2012.00020
  60. Burgess N, Becker S, King JA, O’Keefe J. Memory for events and their spatial context: models and experiments. Philos. Trans. R. Soc. Lond. B Biol. Sci. 2001;356:1493–1503.
    61. doi: 10.1098/rstb.2001.0948
  61. Burgess N. Spatial memory: how egocentric and allocentric combine. Tren. Cog. Sci. 2006;10:551–557.
    62. doi: 10.1016/j.tics.2006.10.005
  62. Waller D, Hodgson E. Transient and enduring spatial representations under disorientation and self-rotation. J. Exp. Psychol. Learn. Mem. Cogn. 2006;32:867–882.
    63. doi: 10.1037/0278-7393.32.4.867
  63. Burgess N, Jackson A, Hartley T, O’Keefe J. Predictions derived from modelling the hippocampal role in navigation. Biol. Cybern. 2000;83:301–312.
    64. doi: 10.1007/s004220000172
  64. Hartley T, Burgess N, Lever C, Cacucci F, O’Keefe J. Modeling place fields in terms of the cortical inputs to the hippocampus. Hippocampus. 2000;10:369–379.
    65. doi: 10.1002/1098-1063(2000)10:4<369::AID-HIPO3>3.0.CO;2-0
  65. Save E, Poucet B. Involvement of the hippocampus and associative parietal cortex in the use of proximal and distal landmarks for navigation. Behav. Brain Res. 2000;109:195–206.
    66. doi: 10.1016/S0166-4328(99)00173-4
  66. Zugaro MB, Berthoz A, Wiener SI. Background, but not foreground, spatial cues are taken as references for head direction responses by rat anterodorsal thalamus neurons. J. Neurosci. 2001;21(14):RC154.
  67. Knierim JJ, Rao G. Distal landmarks and hippocampal place cells: effects of relative translation versus rotation. Hippocampus. 2003;13:604–617.
    68. doi: 10.1002/hipo.10092
  68. Yoganarasimha D, Knierim JJ. Coupling between place cells and head direction cells during relative translations and rotations of distal landmarks. Exp. Brain Res. 2005;160:344–359.
    69. doi: 10.1007/s00221-004-2016-9
  69. Knierim JJ, Hamilton DA. Framing spatial cognition: neural representations of proximal and distal frames of reference and their roles in navigation. Physiol. Rev. 2011;91:1245–1279.
    70. doi: 10.1152/physrev.00021.2010
  70. Fuhs MC, Touretzky DS. A spin glass model of path integration in rat medial entorhinal cortex. J. Neurosci. 2006;26:4266–4276.
    71. doi: 10.1523/JNEUROSCI.4353-05.2006
  71. Barry C, Hayman R, Burgess N, Jeffery KJ. Experience-dependent rescaling of entorhinal grids. Nat. Neurosci. 2007;10:682–684.
    72. doi: 10.1038/nn1905
  72. Yoganarasimha D, Yu X, Knierim JJ. Head direction cell representations maintain internal coherence during conflicting proximal and distal cue rotations: comparison with hippocampal place cells. J. Neurosci. 2006;26:622–631.
    73. doi: 10.1523/JNEUROSCI.3885-05.2006
  73. Fyhn M, Hafting T, Treves A, Moser MB, Moser EI. Hippocampal remapping and grid realignment in entorhinal cortex. Nature. 2007;446:190–194.
    74. doi: 10.1038/nature05601
  74. Markus EJ, Qin YL, Leonard B, Skaggs WE, McNaughton BL, Barnes CA. Interactions between location and task affect the spatial and directional firing of hippocampal neurons. J. Neurosci. 1995;15:7079–7094.
  75. Wood ER, Dudchenko PA, Robitsek RJ, Eichenbaum H. Hippocampal neurons encode information about different types of memory episodes occurring in the same location. Neuron. 2000;27:623–633.
    76. doi: 10.1016/S0896-6273(00)00071-4
  76. Griffin AL, Eichenbaum H, Hasselmo ME. Spatial representations of hippocampal CA1 neurons are modulated by behavioral context in a hippocampus-dependent memory task. J. Neurosci. 2007;27:2416–2423.
    77. doi: 10.1523/JNEUROSCI.4083-06.2007
  77. Foster DJ, Knierim JJ. Sequence learning and the role of the hippocampus in rodent navigation. Curr. Opin. Neurobiol. 2012;22:294–300.
    78. doi: 10.1016/j.conb.2011.12.005
  78. Pfeiffer BE, Foster DJ. Hippocampal place-cell sequences depict future paths to remembered goals. Nature. 2013;497:74–80.
    79. doi: 10.1038/nature12112
  79. Morris RG, Garrud P, Rawlins JN, O’Keefe J. Place navigation impaired in rats with hippocampal lesions. Nature. 1982;297:681–683.
    80. doi: 10.1038/297681a0
  80. Redish AD, Touretzky DS. The role of the hippocampus in solving the Morris water maze. Neural Comput. 1998;10:73–111.
    81. doi: 10.1162/089976698300017908
  81. Koene RA, Gorchetchnikov A, Cannon RC, Hasselmo ME. Modeling goal directed spatial navigation in the rat based on physiological data from the hippocampal formation. Neural Netw. 2003;16:577–584.
    82. doi: 10.1016/S0893-6080(03)00106-0
  82. Hok V, Lenck-Santini P-P, Roux S, Save E, Muller RU, Poucet B. Goal-related activity in hippocampal place cells. J. Neurosci. 2007;27:472–482.
    83. doi: 10.1523/JNEUROSCI.2864-06.2007
  83. Ferbinteanu J, Shapiro ML. Prospective and retrospective memory coding in the hippocampus. Neuron. 2003;40:1227–1239.
    84. doi: 10.1016/S0896-6273(03)00752-9
  84. O’Keefe J, Recce ML. Phase relationship between hippocampal place units and the EEG theta rhythm. Hippocampus. 1993;3:317–330.
    85. doi: 10.1002/hipo.450030307
  85. Skaggs WE, McNaughton BL, Wilson MA, Barnes CA. Theta phase precession in hippocampal neuronal populations and the compression of temporal sequences. Hippocampus. 1996;6:49–172.
    86. doi: 10.1002/(SICI)1098-1063(1996)6:2<149::AID-HIPO6>3.0.CO;2-K
  86. Foster DJ, Wilson MA. Hippocampal theta sequences. Hippocampus. 2007;17:1093–1099.
    87. doi: 10.1002/hipo.20345
  87. Johnson A, Redish AD. Neural ensembles in CA3 transiently encode paths forward of the animal at a decision point. J. Neurosci. 2007;27:12176–12189.
    88. doi: 10.1523/JNEUROSCI.3761-07.2007
  88. Dragoi G, Buzsaki G. Temporal encoding of place sequences by hippocampal cell assemblies. Neuron. 2006;50:145–157.
    89. doi: 10.1016/j.neuron.2006.02.023
  89. Lisman J, Redish AD. Prediction, sequences and the hippocampus. Phil. Trans. R. Soc. B. 2009;364:1193–1201.
    90. doi: 10.1098/rstb.2008.0316
  90. Lee AK, Wilson MA. Memory of sequential experience in the hippocampus during slow wave sleep. Neuron. 2002;36:1183–1194.
    91. doi: 10.1016/S0896-6273(02)01096-6
  91. Foster DJ, Wilson MA. Reverse replay of behavioural sequences in hippocampal place cells during the awake state. Nature. 2006;440:680–683.
    92. doi: 10.1038/nature04587
  92. Csicsvari J, O'Neill J, Allen K, Senior T. Place-selective firing contributes to the reverse-order reactivation of CA1 pyramidal cells during sharp waves in open-field exploration. Eur. J. Neurosci. 2007;26:704–716.
    93. doi: 10.1111/j.1460-9568.2007.05684.x
  93. Diba K, Buzsaki G. Forward and reverse hippocampal place-cell sequences during ripples. Nat. Neurosci. 2007;10:1241–1242.
    94. doi: 10.1038/nn1961
  94. Davidson TJ, Kloosterman F, Wilson MA. Hippocampal replay of extended experience. Neuron. 2009;63:497–507.
    95. doi: 10.1016/j.neuron.2009.07.027
  95. Karlsson MP, Frank LM. Awake replay of remote experiences in the hippocampus. Nat. Neurosci. 2009;12:913–918.
    96. doi: 10.1038/nn.2344
  96. Gupta AS, van der Meer MA, Touretzky DS, Redish AD. Hippocampal replay is not a simple function of experience. Neuron. 2010;65:695–705.
    97. doi: 10.1016/j.neuron.2010.01.034
  97. Packard MG, Knowlton BJ. Learning and memory functions of the basal ganglia. Annu. Rev. Neurosci. 2002;25:563–593.
    98. doi: 10.1146/annurev.neuro.25.112701.142937
  98. Igloi K, Doeller CF, Berthoz A, Rondi-Reig L, Burgess N. Lateralized human hippocampal activity predicts navigation based on sequence or place memory. PNAS USA. 2010;107:14466–14471.
    99. doi: 10.1073/pnas.1004243107
Table of Contents
Original Article
Math. Biol. Bioinf.
2014;9(1):216-256
doi: 10.17537/2014.9.216
published in Russian

Abstract (rus.)
Abstract (eng.)
Full text (rus., pdf)
References

 
  Copyright IMPB RAS © 2005-2024