{"title": "Modeling Interactions of the Rat's Place and Head Direction Systems", "book": "Advances in Neural Information Processing Systems", "page_first": 61, "page_last": 67, "abstract": null, "full_text": "Modeling Interactions of the Rat's Place and \n\nHead Direction Systems \n\nA. David Redish and David S. Touretzky \n\nComputer Science Department & Center for the Neural Basis of Cognition \n\nCarnegie Mellon University, Pittsburgh PA 15213-3891 \n\nInternet: {dredi sh, ds t}@es . emu. edu \n\nAbstract \n\nWe have developed a computational theory of rodent navigation that \nincludes analogs of the place cell system, the head direction system, and \npath integration. In this paper we present simulation results showing how \ninteractions between the place and head direction systems can account for \nrecent observations about hippocampal place cell responses to doubling \nand/or rotation of cue cards in a cylindrical arena (Sharp et at., 1990). \n\nRodents have multiple internal representations of their relationship to their environment. \nThey have, for example, a representation of their location (place cells in the hippocampal \nformation, see Muller et at., 1991), and a location-independent representation of their \nheading (head direction cells in the postsubiculum and the anterior thalamic nuclei, see \nTaube et at., 1990; Taube, 1995). \nIf these representations are to be used for navigation, they must be aligned consistently \nwhenever the animal reenters a familiar environment. This process was examined in a set \nof experiments by Sharp et at. (1990). \n\n1 The Sharp et al., 1990 experiment \n\nRats spent multiple sessions finding food scattered randomly on the floor of a black cylin(cid:173)\ndrical arena with a white cue card along the wall subtending 90\u00b0 of arc. The animals were \nnot disoriented before entering the arena, and they always entered at the same location: the \nnorthwest corner. See Figure 3a. Hippocampal place fields were mapped by single-cell \nrecording. A variety of probe trials were then introduced. When an identical second cue \n\n\f62 \n\nA. D. REDISH, D. S. TOURETZKY \n\nHead \n\nr-----~ Direction \n~ \n\nLocal \nView \n(T~ 'I' .;) \n\nPath \n\nr-----'--~ Integral_.I.o ........ .J \n\n(xp,Y,,> \n\nPlace \nCOde \nA (It) \n\nGoal \n\nMemory \n\nFigure 1: Organization of the rodent navigation model. \n\ncard was added opposite the first (Figure 3c), most place fields did not double. J Instead, \nthe cells continued to fire at their original locations. However, if the rat was introduced into \nthe double-card environment at the southeast corner (Figure 3d), the place fields rotated \nby 1800 \u2022 But rotation did not occur in single-card probe trials with a southeast entry point \n(Figure 3b). When tested with cue cards rotated by \u00b130\u00b0, Sharp et al. observed that place \nfield locations were controlled by an interaction of the choice of entry point with the cue \ncard positions (Figure 3f.) \n\n2 The CRAWL model \n\nIn earlier work (Wan et al., 1994a; Wan et al., 1994b; Redish and Touretzky, 1996) we \ndescribed a model of rodent navigation that includes analogs of both place cells and the head \ndirection system. This model also includes a local view module representing egocentric \nspatial information about landmarks, and a separate metric representation of location which \nserves as a substrate for path integration. The existence of a path integration faculty in \nrodents is strongly supported by behavioral data; see Maurer and Seguinot (1995) for \na discussion. Hypotheses about the underyling neural mechanismss are presently being \nexplored by several researchers, including us. \n\nThe structure of our model is shown in Figure 1. Visual inputs are represented as triples of \nform (Ti, 'i, (Ji), each denoting the type, distance, and egocentric bearing ofa landmark. The \nexperiments reported here used two point-type landmarks representing the left and right \nedges of the cue card, and one surface-type landmark representing the arena wall. For the \nlatter, 'i and (Ji define the normal vector between the rat and the surface. In the local view \nmodule, egocentric bearings (Ji are converted to allocentric form .) \n} 1 1 \n\nFigure 2: Spatial variables used in tuning a place cell to two landmarks i and j when the \nanimal is at path integrator coordinates (xl\" Yl') . \n\nOur simulated place units are radial basis functions tuned to combinations of individual \nlandmark bearings and distances, visual angles between landmark pairs, and path integrator \ncoordinates. Place units can be driven by visual input alone when the animal is trying \nto localize itself upon initial entry at a random spot in the environment, or by the path \nintegrator alone when navigating in the dark. But normally they are driven by both \nsources simultaneously. A key role of the place system is to maintain associations between \nthe two representations, so that either can be reconstructed from the other. The place \nsystem also maintains a record of allocentric bearings of landmarks when viewed from the \ncurrent position; this enables the local view module to compare perceived with remembered \nlandmark bearings, so that drift in the head direction system can be detected and corrected. \n\nIn computer simulations using a single parameter set, the model reproduces a variety \nof behavioral and neurophysiological results including control of place fields by visual \nlandmarks, persistence of place fields in the dark, and place fields drifting in synchrony \nwith drift in the head direction system. \nIts predictions for open-field landmark-based \nnavigation behavior match many of the experimental results of Collett et al. (1986) for \ngerbils. \n\n2.1 Entering a familiar environment \n\nUpon entering a familiar environment, the model's four spatial representations (local view, \nhead direction, place code, and path integrator coordinates) must be aligned with the \ncurrent sensory input and with each other. Note that local view information is completely \ndetermined given the visual input and head direction, and place cell activity is completely \ndetermined given the local view and path integrator representations. Thus, the alignment \nprocess manipulates just two variables: head direction and path integrator coordinates. \nWhen the animal enters the environment with initial estimates for them, the alignment \nprocess can produce four possible outcomes: (1) Retain the initial values of both variables, \n(2) Reset the head direction, (3) Reset the path integrator, or (4) Reset both head direction \nand the path integrator. \n\n2.2 Prioritizing the outcomes \n\nWhen the animal was placed at the northwest entry point and there were two cue cards \n(Figure 3c), we note that the orientation of the wall segment adjacent to the place field \nis identical with that in the training case. This suggests that the animal's head direction \n\n\f64 \n\nA. D. REDISH, D. S. TOURETZKY \n\ndid not change. The spatial relationship between the entry point and place field was also \nunchanged: notice that the distance from the entry point to the center of the field is the \nsame as in Figure 3a. Therefore, we conclude that the initially estimated path integrator \ncoordinates were retained. Alternatively, the animal could have changed both its head \ndirection (by 180\u00b0) and its path integrator coordinates (to those of the southeast comer) and \nproduced consistent results, but to the experimenter the place field would appear to have \nflipped to the other card. Because no flip was observed, the first outcome must have priority \nover the fourth. \n\nIn panel d, where the place field has flipped to the northwest comer, the orientation of the \nsegment of wall adjacent to the field has changed, but the spatial relationship between the \nentry point and field center has not. Resetting the path integrator and not the head direction \nwould also give a solution consistent with this local view, but with the place field unflipped \n(as in panel b). We conclude that the second outcome (reset head direction) must have \npriority over the third (reset the path integrator). \n\nThe third and fourth outcomes are demonstrated in Figures 3b and 3f. In panel b, the \norientation of the wall adjacent to the place field is unchanged from panel a, but the spatial \nrelationship between the entry point and the place field center is different, as evidenced by \nthe fact that the distance between them is much reduced. This is outcome 3. In panel f, \nboth variables have changed (outcome 4). \n\nFinally, the fact that place fields are stable over an entire session, even when there are \nmultiple cue cards (and therefore multiple consistent pairings of head directions and path \nintegrator coordinates) implies that animals do not reset their head direction or path in(cid:173)\ntegrator in visually ambiguous environments as long as the current values are reasonably \nconsistent with the local view. We therefore assume that outcome 1 is preferred over the \nothers. \n\nThis analysis establishes a partial ordering over the four outcomes: 1 is preferred over 4 by \nFigure 3c, and over the others by the stability of place fields, and outcome 2 is preferred \nover 3 by Figure 3d. This leaves open the question of whether outcome 3 or 4 has priority \nover the other. In this experiment, after resetting the path integrator it's always safe for the \nanimal to attempt to reset its head direction. If the head direction does not change by more \nthan a few degrees, as in panel b, we observe outcome 3; if it does change substantially, as \nin panel f, we observe outcome 4. \n\n2.3 Consistency \n\nThe viability of an outcome is a function of the consistency between the local view and \npath integrator representations. The place system maintains the association between the \ntwo representations and mediates the comparison between them. \n\nThe activity A(u) of a place unit is the product of a local view term LV(u) and a path \nintegrator term C(u). LV(u) is in turn a product of five Gaussians: two tuned to bearings \nand two to distances (for the same' pair of landmarks), and one tuned to the retinal angle \nbetween a pair of landmarks. C(u) is a Gaussian tuned to the path integrator coordinates of \nthe center of the place field. \n\nIf the two representations agree, then the place units activated by path integrator input will \nbe the same as those activated by the local view module, so the product A(u) computed \nby those units will be significantly greater than zero. The consistency K, of the association \n\n\fModeling Interactions of the Rat's Place and Head Direction Systems \n\n65 \n\nbetween path integrator and local view representations is given by: K, = Lu A(u)/ Lu C(u). \nBecause A(u) < C(u) for all place units, K, ranges between 0 and 1. When the current local \nview is compatible with that predicted by the current path integrator coordinates, K, will be \nhigh; when the two are not compatible, K, will be low. \n\nEarlier we showed that the navigation system should choose the highest priority viable \noutcome. If the consistency of an outcome is more than K, * better than all higher-priority \noutcomes, that outcome is a viable choice and higher-priority ones are not. \nK,* is an \nempirically derived constant that we have set equal to 0.04. \n\n3 Discussion \n\nOur results match all of the cases already discussed. (See Figure 3, panels a through d \nas well as f and h.) Sharp et al. (1990) did not actually test the rotated cue cards with a \nnorthwest entry point, so our result in panel e is a prediction. \n\nWhen the animals entered from the northwest, but only one cue card was available at 1800 , \nSharp et al. report that the place field did not rotate. In our model the place field does \nrotate, as a result of outcome 4. This discrepancy can be explained by the fact that this \nparticular manipulation was the last one in the sequence done by Sharp et at. McNaughton \net al. (1994) and Knierim et al. (1995) have shown that if rats experience the cue card \nmoving over a number of sessions, they eventually come to ignore it and it loses control \nover place fields . When we tested our model without a cue card (equivalent to a card being \npresent but ignored), the resulting place field was more diffuse than normal but showed no \nrotation; see Figure 3g. We thus predict that if this experiment had been done before the \nother manipulations rather than after, the place field would have foIlowed the cue card. \nIn the Sharp et al. experiment, the animals were always placed in the environment at the \nsame location during training. Therefore, they could reliably estimate their initial path \nintegrator coordinates. They also had a reliable head direction estimate because they were \nnot disoriented. We predict that were the rats trained with a variety of entry points instead \nof just one, using an environment with a single cue card at 00 (the training environment \nused by Sharp et al.), and then tested with two cue cards at 0 0 and 1800 , the place field \nwould not rotate no matter what entry point was used. This is because when trained with a \nvariable entry point, the animal would not learn to anticipate its path integrator coordinates \nupon entry; a path integratorreset would have to be done every time in order to establish the \nanimal's coordinates. The reset mechanism uses allocentric bearing information derived \nfrom the head direction estimate, and in this task the resulting path integrator coordinates \nwill be consistent with the initial head direction estimate. Hence, outcome 3 will always \nprevail. \n\nIf the animal is disoriented, however, then both the path integrator and the head direction \nsystem must be reset upon entry (because consistency will be low with a faulty head \ndirection), and the animal must choose one cue card or the other to match against its \nmemory. So with disorientation and a variable entry point, the place field will be controlled \nby one or the other cue card with a 50/50 probability. This was found to be true in a related \nbehavioral experiment by Cheng (1986). \n\nOur model shows how interactions between the place and head direction systems handle the \nvarious combinations of entry point, number of cue cards, and amount of cue card rotation. \nIt predicts that head direction reset will be observed in certain tasks and not in others. In \n\n\f66 \n\nA. D. REDISH, D. S. TOURETZKY \n\nexperiments such as the single cue card task with an entry in the southeast, it predicts the \nplace code will shift from an initial value corresponding to the northwest entry point to the \nvalue for the southeast entry point, but the head direction will not change. This could be \ntested by recording simultaneously from place cells and head direction cells. \n\nReferences \n\nCheng, K. (1986). A purely geometric module in the rat's spatial representation. Cog(cid:173)\nnition, 23: 149-178. \n\nCollett, T., Cartwright, B. A., and Smith, B. A. (1986). Landmark learning and visuo(cid:173)\nspatial memories in gerbils. Journal of Comparative Physiology A, 158:835-851. \n\nKnierim, J. J., Kudrimoti, H. 5., and McNaughton, B. L. (1995). Place cells, head \ndirection cells, and the learning of landmark stability. Journal of Neuroscience, 15: 1648-\n59. \n\nMaurer, R. and Seguinot, V. (1995). What is modelling for? A critical review of the \nmodels of path integration. Journal of Theoretical Biology, 175:457-475. \n\nMcNaughton, B. L., Mizumori, S. J. Y., Barnes, C. A., Leonard, B. 1., Marquis, M., \nand Green, E. J. (1994). Cortical rpresentation of motion during unrestrained spatial \nnavigation in the rat. Cerebral Cortex, 4(1):27-39. \n\nMuller, R. U., Kubie, 1. L., Bostock, E. M., Taube, J. 5., and Quirk, G. 1. (1991). \nSpatial firing correlates of neurons in the hippocampal formation of freely moving rats. \nIn Paillard, J., editor, Brain and Space, chapter 17, pages 296-333. Oxford University \nPress, New York. \nRedish, A. D. and Touretzky, D. s. (1996). Navigating with landmarks: Computing \ngoal locations from place codes. In Ikeuchi, K. and Veloso, M., editors, Symbolic Visual \nLearning. Oxford University Press. In press. \n\nSharp, P. E., Kubie, J. L., and Muller, R. U. (1990). Firing properties of hippocampal \nneurons in a visually symmetrical environment: Contributions of multiple sensory cues \nand mnemonic processes. Journal of Neuroscience, 10(9):3093-3105. \nTaube, 1. s. (1995). Head direction cells recorded in the anterior thalamic nuclei of freely \nmoving rats. Journal of Neuroscience, 15(1): 1953-1971. \n\nTaube, J. 5., Muller, R. I., and Ranck, Jr., J. B. (1990). Head direction cells recorded \nfrom the postsubiculum in freely moving rats. I. Description and quantitative analysis. \nJournal of Neuroscience, 10:420-435. \n\nWan, H. 5., Touretzky, D. 5., and Redish, A. D. (1994a). Computing goal locations \nfrom place codes. In Proceedings of the 16th annual conference of the Cognitive Science \nsociety, pages 922-927. Lawrence Earlbaum Associates, Hillsdale N1. \n\nWan, H. 5., Touretzky, D. 5., and Redish, A. D. (1994b). Towards a computational \ntheory of rat navigation. In Mozer, M., Smolen sky, P., Touretzky, D., Elman, J., and \nWeigend, A., editors, Proceedings of the 1993 Connectionist Models Summer School, \npages 11-19. Lawrence Earlbaum Associates, Hillsdale NJ. \n\n\fModeling Interactions of the Rat's Place and Head Direction Systems \n\n67 \n\n(a) 1 cue card at 0\u00b0 (East) \nentry in Northwest comer \nangle of rotation (Sharp et al.) = 2.7\u00b0 \nprecession of HD system = 0 0 \n\n(b) 1 cue card at 0 0 \nentry in Southeast comer \nangle of rotation (Sharp et al.) = -6.0 0 \nprecession of HD system = 2\u00b0 \n\n(c) 2 cue cards at 0 0 (East) & 180 0 (West) \nentry in Northwest comer \nangle of rotation (Sharp et al.) = -2.3\u00b0 \nprecession of HD system = 0 0 \n\n(d) 2 cue cards at 0 0 & 180 0 \nentry in Southeast comer \nangle of rotation (Sharp et al.) = 182.5 0 \nprecession of HD system::: 178 0 \n\n(e) 2 cue cards at 330 0 & 150 0 \nentry in Northwest comer \nnot done by Sharp et al. \nprecession of HD system = 331 0 \n\n(f) 2 cue cards at 330 0 & 150 0 \nentry in Southeast comer \nangle of rotation (Sharp et al.) = 158.3\u00b0 \nprecession of HD system = 151 \u00b0 \n\n(g) I cue card at 180 0 (West) \nentry in Northwest comer \nangle of rotation (Sharp et al.) ::: -5.5 0 \nprecession of HD system = 0 0 \n\n(h) 1 cue card at 180 0 \nentry in Southeast comer \nangle of rotation (Sharp et al.) = 182.2\u00b0 \nprecession of HD system = 179 0 \n\nFigure 3: Computer simulations of the Sharp et al. (1990) experiment showing that place \nfields are controlled by both cue cards (thick arcs) and entry point (arrowhead). \"Angle of \nrotation\" is the angle at which the correlation between the probe and training case place \nfields is maximal. Because head direction and place code are tightly coupled in our model, \nprecession of HD is an equivalent measure in our model. \n\n\f", "award": [], "sourceid": 1078, "authors": [{"given_name": "A.", "family_name": "Redish", "institution": null}, {"given_name": "David", "family_name": "Touretzky", "institution": null}]}