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

V. D. Tsukerman ; Z. S. Kharybina ; S. V. Kulakov

Matematičeskaâ biologiâ i bioinformatika, Tome 9 (2014) no. 1, pp. 216-256.

Résumé

The work is a continuation of studies related to the construction of conceptual neurodynamic model of formation of environment spatial representations and purposeful behavior in the mammals brain, the first part of which has been published earlier. The effective vector–phase way of neuron network representations of spatial trajectories episodes is proposed in development of this model. The results of the modeling of medial entorinal cortex "grid cells" and hippocampal "place cells" functional interaction in the generation of straight lines and the reverse temporary sequences of events (replays) are described. The phenomenon of disparity of "mental" representations of episodes in ipsi- and contralateral reference systems is obtained for the first time due to the bilateral organization of networks with even cyclic inhibition (ECI-networks). Neurodynamical correlates of numerous predictive (look-ahead) generation of trajectories with various starting and final positions in contralateral system and unique trajectories — in ipsilateral system on the basis of which a choice (decision-making) of movement route can be made are presented. The universal nature hypothesis of egocentric representations formation in ipsilateral reference system and allocentric in contralateral system of each hemisphere of a brain is offered in the paper. On the basis of the obtained results the problem of future research for decision-making mechanisms depending on a goal and an existential context in a behavior episode is formulated.

Bibliographie

[1] Hafting T., Fyhn M., Molden S., Moser M. B., Moser E. I., “Microstructure of a spatial map in the entorhinal cortex”, Nature, 436 (2005), 801–806 | DOI

[2] McNaughton B. L., Battaglia F. P., Jensen O., Moser E. I., Moser M. B., “Path integration and the neural basis of the «cognitive map»”, Nat. Rev. Neurosci., 7 (2006), 663–678 | DOI

[3] Barry C., Hayman R., Burgess N., Jeffery K. J., “Experience-dependent rescaling of entorhinal grids”, Nat. Neurosci., 10 (2007), 682–684 | DOI

[4] Derdikman D., Moser E. I., “A manifold of spatial maps in the brain”, Trends Cogn. Sci., 14 (2010), 561–569 | DOI

[5] Doeller C. F., Barry C., Burgess N., “Evidence for grid cells in a human memory network”, Nature, 463 (2010), 657–661 | DOI

[6] Navratilova J., Giocomo L. M., Fellous J.-M., Hasselmo M. E., McNaughton B. L., “Phase precession and variable spatial scaling in a periodic attractor map model of medial entorhinal grid cells with realistic after-spike dynamics”, Hippocampus, 22 (2012), 772–789 | DOI

[7] Giocomo L. M., Roudi Y., “The neural encoding of space in parahippocampal cortices”, Front. Neural Circuits, 6 (2012), 53 | DOI

[8] O'Keefe J., Dostrovsky J., “The hippocampus as a spatial map: preliminary evidence from unit activity in the freely moving rat”, Brain Res., 34 (1971), 171–175 | DOI

[9] O'Keefe J., Burgess N., “Dual phase and rate coding in hippocampal place cells: theoretical significance and relationship to entorhinal grid cells”, Hippocampus, 15 (2005), 853–866 | DOI

[10] O'Keefe J., Burgess N., “Geometric determinants of the place fields of hippocampal neurons”, Nature, 381 (1996), 425–428 | DOI

[11] Ekstrom A. D., Kahana M. J., Caplan J. B., Fields T. A., Isham E. A., Newman E. L., Fried I., “Cellular networks underlying human spatial navigation”, Nature, 425 (2003), 184–187 | DOI

[12] Geisler C., Robbe D., Zugaro M., Sirota A., Buzsaki G., “Hippocampal place cell assemblies are speed controlled oscillators”, PNAS USA, 104 (2007), 8149–8154 | DOI

[13] Diba K., Buzsaki G., “Forward and reverse hippocampal place-cell sequences during ripples”, Nat. Neurosci., 10 (2007), 1241–1242 | DOI

[14] Moser E. I., Kropff E., Moser M. B., “Place cells, grid cells, and the brain's spatial representation system”, Ann. Rev. Neurosci., 31 (2008), 69–89 | DOI

[15] Taube J. S., Muller R. U., Ranck J. B. (Jr.), “Head-direction cells recorded from the postsubiculum in freely moving rats. I: Description and quantitative analysis”, J. Neurosci., 10 (1990), 420–435

[16] Taube J. S., Muller R. U., Ranck J. B. (Jr.), “Head-direction cells recorded from the postsubiculum in freely moving rats. II: Effects of environmental manipulations”, J. Neurosci., 10 (1990), 436–447

[17] Blair H. T., Sharp P. E., “Anticipatory head direction signals in anterior thalamus: evidence for a thalamocortical circuit that integrates angular head motion to compute head direction”, J. Neurosci., 15 (1995), 6260–6270

[18] Zhang K., “Representation of spatial orientation by the intrinsic dynamics of the head direction cell ensemble: a theory”, J. Neurosci., 16 (1996), 2112–2126

[19] Taube J. S., “Head direction cells and the neurophysiological basis for a sence of direction”, Progr. Neurobiol., 55 (1998), 225–256 | DOI

[20] Sharp P. E., Blair H. T., Cho J., “The anatomical and computational basis of the rat head-direction cell signal”, Trends Neurosci., 24 (2001), 289–294 | DOI

[21] Zugaro M. B., Arleo A., Berthoz A., Wiener S. I., “Rapid spatial reorientation and head direction cells”, J. Neurosci., 23 (2003), 3478–3482

[22] Taube J. S., Bassett J. P., “Persistent neural activity in head direction cells”, Cereb. Cortex, 13 (2003), 1162–1172 | DOI

[23] Taube J. S., “The head direction signal: origins and sensory-motor integration”, Annu. Rev. Neurosci., 30 (2007), 181–207 | DOI

[24] Sargolini F., Fyhn M., Hafting T., McNaughton B. L., Witter M. P., Moser M. B., Moser E.I., “Conjunctive representation of position, direction, and velocity in entorhinal cortex”, Science, 312 (2006), 758–762 | DOI

[25] Doeller C. F., King J. A., Burgess N., “Parallel striatal and hippocampal systems for landmarks and boundaries in spatial memory”, PNAS USA, 105 (2008), 5915–5920 | DOI

[26] Solstad T., Boccara C. N., Kropff E., Moser M. B., Moser E. I., “Representation of geometric borders in the entorhinal cortex”, Science, 322 (2008), 1865–1868 | DOI

[27] Savelli F., Yoganarasimha D., Knierim J. J., “Influence of boundary removal on the spatial representations of the medial entorhinal cortex”, Hippocampus, 18 (2008), 1270–1282 | DOI

[28] Lever C., Burton S., Jeewajee A., O'Keefe J., Burgess N., “Boundary vector cells in the subiculum of the hippocampal formation”, J. Neurosci., 29 (2009), 9771–9777 | DOI

[29] Bird C. M., Capponi C., King J. A., Doeller C. F., Burgess N., “Establishing the boundaries: the hippocampal contribution to imagining scenes”, J. Neurosci., 30 (2010), 11688–11695 | DOI

[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., 31 (2011), 2828–2834 | DOI

[31] MacDonald C. J., Lepage K. Q., Eden U. T., Eichenbaum H., “Hippocampal «time cells» bridge the gap in memory for discontiguous events”, Neuron, 71 (2011), 737–749 | DOI

[32] Kraus B. J., Robinson R. J., White J. A., Eichenbaum H., Hasselmo M. E., “Hippocampal «time cells»: time versus path integration”, Neuron, 78 (2013), 1–12 | DOI

[33] Eichenbaum H., “Memory on time”, Trends Cogn. Sciences, 17 (2013), 81–88 | DOI

[34] Tsukerman V. D., Kharybina Z. S., Kulakov S. V., “Kognitivnaya fragmentatsiya prostranstvennogo povedeniya neironnymi mikroskhemami mozga”, Tr. III Vserossiiskoi konf. «Nelineinaya dinamika v kognitivnykh issledovaniyakh-2013», IPF RAN, N. Novgorod, 2013, 183–186 (data obrascheniya: 24.11.2013) http://www.nd-ogsci.iapras.ru/2013/img/ND-2013.pdf

[35] Burgess N., Barry C., O'Keefe J., “An oscillatory interference model of grid cell firing”, Hippocampus, 17 (2007), 801–812 | DOI

[36] Burgess N., “Grid cells and theta as oscillatory interference: theory and predictions”, Hippocampus, 18 (2008), 1157–1174 | DOI

[37] Jeewajee A., Barry C., O'Keefe J., Burgess N., “Grid cells and theta as oscillatory interference: electrophysiological data from freely moving rats”, Hippocampus, 18 (2008), 1175–1185 | DOI

[38] Samsonovich A., McNaughton B. L., “Path integration and cognitive mapping in a continuous attractor neural network model”, J. Neurosci., 17 (1997), 5900–5920

[39] Battaglia F. P., Treves A., “Attractor neural networks storing multiple space representations: a model for hippocampal place fields”, Physical Rev. E, 58 (1998), 7738–7753 | DOI

[40] Fuhs M. C., Touretzky D. S., “A spin glass model of path integration in rat medial entorhinal cortex”, J. Neurosci., 26 (2006), 4266–4276 | DOI

[41] McNaughton B. L., Battaglia F. P., Jensen O., Moser E. I., Moser M.-B., “Path integration and the neural basis of the «cognitive map»”, Nat. Rev. Neurosci., 7 (2006), 663–678 | DOI

[42] Guanella A., Kiper D., Verschure P., “A model of grid cells based on a twisted torus topology”, Int. J. Neural Syst., 17 (2007), 231–240 | DOI

[43] Burak Y., Fiete I. R., “Accurate path integration in continuous attractor network models of grid cells”, PLoS Comput. Biol., 5:2 (2009), e1000291 | DOI

[44] Hasselmo M. E., Brandon M. P., “A model combining oscillations and attractor dynamics for generation of grid cell firing”, Front. Neur. Circuits, 6 (2012), 30

[45] Pastoll H., Solanka L., van Rossum M. C.W., Nolan M. F., “Feedback inhibition enables theta-nested gamma oscillations and grid firing fields”, Neuron, 77 (2013), 141–154 | DOI

[46] Tsukerman V. D., Cheshkov G. N., “Osnovy nelineinoi dinamiki sensornogo vospriyatiya. I. Fazovoe kodirovanie v ostsillyatornykh setyakh s chetnym tsiklicheskim tormozheniem”, Neirokompyutery: razrabotka, primenenie, 2002, no. 7–8, 65–72

[47] Tsukerman V. D., Kulakov S. V., “Biologicheskie algoritmy kodirovaniya sensornykh sobytii”, Neirokompyutery: razrabotka, primenenie, 2004, no. 11, 15–25

[48] Tsukerman V. D., “Matematicheskaya model fazovogo kodirovaniya sobytii v mozge”, Matematicheskaya biologiya i bioinformatika, 1:1 (2006), 97–107 (data obrascheniya: 02.12.2013) http://www.matbio.org/downloads/Tsukerman2006

[49] Tsukerman V. D., Kulakov S. V., Karimova O. V., “Pulsiruyuschie kody sobytiinykh posledovatelnostei”, Matematicheskaya biologiya i bioinformatika, 1:1 (2006), 108–122 (data obrascheniya: 02.12.2013) http://www.matbio.org/downloads/Tsukerman2006

[50] Tsukerman V. D., Karimova O. V., Kulakov S. V., Sazykin A. A., “Sovremennye neirobiologicheskie dannye i novoe v neirodinamike navigatsionnogo povedeniya”, Neirokompyutery: razrabotka, primenenie, 2010, no. 2, 17–27 (data obrascheniya: 28.11.2013) http://www.radiotec.ru/catalog.php?cat=jr7&art=7306

[51] Tsukerman V. D., “Neirodinamicheskie osnovy navigatsionnogo povedeniya”, Nelineinye volny-2010, eds. Gaponov-Grekhov A. V., Nekorkin V. I., IPF RAN, Nizhnii Novgorod, 2011, 396–411

[52] Tsukerman V. D., Eremenko Z. S., Karimova O. V., Sazykin A. A., Kulakov S. V., “Matematicheskaya model prostranstvennogo kodirovaniya v gippokampalnoi formatsii. I: Neirodinamika reshetchatykh kletok”, Matematicheskaya biologiya i bioinformatika, 7:1 (2012), 87–124 (data obrascheniya: 02.12.2013) http://www.matbio.org/2012/Tsukerman2012

[53] Stensola H., Stensola T., Solstad T., Froland K., Moser M.-B., Moser E. I., “The entorhinal grid map is discretized”, Nature, 492 (2012), 72–78 | DOI

[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., 6 (2012), 66

[55] Brun V. H., Solstad T., Kjelstrup K. B., Fyhn M., Witter M. P., Moser E. I., Moser M.-B., “Progressive increase in grid scale from dorsal to ventral medial entorhinal cortex”, Hippocampus, 18 (2008), 1200–1212 | DOI

[56] Maurer A. P., McNaughton B. L., “Network and intrinsic cellular mechanisms underlying theta phase precession of hippocampal neurons”, Trends Neurosci., 30 (2007), 325–333 | DOI

[57] van der Meer M. A. A., Redish A. D., “Theta phase precession in rat ventral striatum links place and reward information”, J. Neurosci., 31 (2011), 2843–2854 | DOI

[58] Cheng S., Frank L. M., “New experiences enhance coordinated neural activity in the hippocampus”, Neuron, 57 (2008), 303–313 | DOI

[59] Kubie J. L., Fenton A. A., “Linear look-ahead in conjunctive cells an entorhinal mechanism for vector-based navigation”, Front. Neur. Circuits, 6 (2012), 20

[60] Burgess N., Becker S., King J. A., O'Keefe J., “Memory for events and their spatial context: models and experiments”, Philos. Trans. R. Soc. Lond. B Biol. Sci., 356 (2001), 1493–1503 | DOI

[61] Burgess N., “Spatial memory: how egocentric and allocentric combine”, Tren. Cog. Sci., 10 (2006), 551–557 | DOI

[62] Waller D., Hodgson E., “Transient and enduring spatial representations under disorientation and self-rotation”, J. Exp. Psychol. Learn. Mem. Cogn., 32 (2006), 867–882 | DOI

[63] Burgess N., Jackson A., Hartley T., O'Keefe J., “Predictions derived from modelling the hippocampal role in navigation”, Biol. Cybern., 83 (2000), 301–312 | DOI

[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, 10 (2000), 369–379 | 3.0.CO;2-0 class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI

[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., 109 (2000), 195–206 | DOI

[66] Zugaro M. B., Berthoz A., Wiener S. I., “Background, but not foreground, spatial cues are taken as references for head direction responses by rat anterodorsal thalamus neurons”, J. Neurosci., 21:14 (2001), RC154

[67] Knierim J. J., Rao G., “Distal landmarks and hippocampal place cells: effects of relative translation versus rotation”, Hippocampus, 13 (2003), 604–617 | DOI

[68] Yoganarasimha D., Knierim J. J., “Coupling between place cells and head direction cells during relative translations and rotations of distal landmarks”, Exp. Brain Res., 160 (2005), 344–359 | DOI

[69] Knierim J. J., Hamilton D. A., “Framing spatial cognition: neural representations of proximal and distal frames of reference and their roles in navigation”, Physiol. Rev., 91 (2011), 1245–1279 | DOI

[70] Fuhs M. C., Touretzky D. S., “A spin glass model of path integration in rat medial entorhinal cortex”, J. Neurosci., 26 (2006), 4266–4276 | DOI

[71] Barry C., Hayman R., Burgess N., Jeffery K. J., “Experience-dependent rescaling of entorhinal grids”, Nat. Neurosci., 10 (2007), 682–684 | DOI

[72] Yoganarasimha D., Yu X., Knierim J. J., “Head direction cell representations maintain internal coherence during conflicting proximal and distal cue rotations: comparison with hippocampal place cells”, J. Neurosci., 26 (2006), 622–631 | DOI

[73] Fyhn M., Hafting T., Treves A., Moser M. B., Moser E. I., “Hippocampal remapping and grid realignment in entorhinal cortex”, Nature, 446 (2007), 190–194 | DOI

[74] Markus E. J., Qin Y. L., Leonard B., Skaggs W. E., McNaughton B. L., Barnes C. A., “Interactions between location and task affect the spatial and directional firing of hippocampal neurons”, J. Neurosci., 15 (1995), 7079–7094

[75] Wood E. R., Dudchenko P. A., Robitsek R. J., Eichenbaum H., “Hippocampal neurons encode information about different types of memory episodes occurring in the same location”, Neuron, 27 (2000), 623–633 | DOI

[76] Griffin A. L., Eichenbaum H., Hasselmo M. E., “Spatial representations of hippocampal CA1 neurons are modulated by behavioral context in a hippocampus-dependent memory task”, J. Neurosci., 27 (2007), 2416–2423 | DOI

[77] Foster D. J., Knierim J. J., “Sequence learning and the role of the hippocampus in rodent navigation”, Curr. Opin. Neurobiol., 22 (2012), 294–300 | DOI

[78] Pfeiffer B. E., Foster D. J., “Hippocampal place-cell sequences depict future paths to remembered goals”, Nature, 497 (2013), 74–80 | DOI

[79] Morris R. G., Garrud P., Rawlins J. N., O'Keefe J., “Place navigation impaired in rats with hippocampal lesions”, Nature, 297 (1982), 681–683 | DOI

[80] Redish A. D., Touretzky D. S., “The role of the hippocampus in solving the Morris water maze”, Neural Comput., 10 (1998), 73–111 | DOI

[81] Koene R. A., Gorchetchnikov A., Cannon R. C., Hasselmo M. E., “Modeling goal directed spatial navigation in the rat based on physiological data from the hippocampal formation”, Neural Netw., 16 (2003), 577–584 | DOI

[82] Hok V., Lenck-Santini P.-P., Roux S., Save E., Muller R. U., Poucet B., “Goal-related activity in hippocampal place cells”, J. Neurosci., 27 (2007), 472–482 | DOI

[83] Ferbinteanu J., Shapiro M. L., “Prospective and retrospective memory coding in the hippocampus”, Neuron, 40 (2003), 1227–1239 | DOI

[84] O'Keefe J., Recce M. L., “Phase relationship between hippocampal place units and the EEG theta rhythm”, Hippocampus, 3 (1993), 317–330 | DOI

[85] Skaggs W. E., McNaughton B. L. Wilson M. A., Barnes C. A., “Theta phase precession in hippocampal neuronal populations and the compression of temporal sequences”, Hippocampus, 6 (1996), 149–172 | 3.0.CO;2-K class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI

[86] Foster D. J., Wilson M. A., “Hippocampal theta sequences”, Hippocampus, 17 (2007), 1093–1099 | DOI

[87] Johnson A., Redish A. D., “Neural ensembles in CA3 transiently encode paths forward of the animal at a decision point”, J. Neurosci., 27 (2007), 12176–12189 | DOI

[88] Dragoi G., Buzsaki G., “Temporal encoding of place sequences by hippocampal cell assemblies”, Neuron, 50 (2006), 145–157 | DOI

[89] Lisman J., Redish A. D., “Prediction, sequences and the hippocampus”, Phil. Trans. R. Soc. B, 364 (2009), 1193–1201 | DOI

[90] Lee A. K., Wilson M. A., “Memory of sequential experience in the hippocampus during slow wave sleep”, Neuron, 36 (2002), 1183–1194 | DOI

[91] Foster D. J., Wilson M. A., “Reverse replay of behavioural sequences in hippocampal place cells during the awake state”, Nature, 440 (2006), 680–683 | DOI

[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., 26 (2007), 704–716 | DOI

[93] Diba K., Buzsaki G., “Forward and reverse hippocampal place-cell sequences during ripples”, Nat. Neurosci., 10 (2007), 1241–1242 | DOI

[94] Davidson T. J., Kloosterman F., Wilson M. A., “Hippocampal replay of extended experience”, Neuron, 63 (2009), 497–507 | DOI

[95] Karlsson M. P., Frank L. M., “Awake replay of remote experiences in the hippocampus”, Nat. Neurosci., 12 (2009), 913–918 | DOI

[96] Gupta A. S., van der Meer M. A., Touretzky D. S., Redish A. D., “Hippocampal replay is not a simple function of experience”, Neuron, 65 (2010), 695–705 | DOI

[97] Packard M. G., Knowlton B. J., “Learning and memory functions of the basal ganglia”, Annu. Rev. Neurosci., 25 (2002), 563–593 | DOI

[98] Igloi K., Doeller C. F., Berthoz A., Rondi-Reig L., Burgess N., “Lateralized human hippocampal activity predicts navigation based on sequence or place memory”, PNAS USA, 107 (2010), 14466–14471 | DOI