Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Control and recalibration of path integration in place cells using optic flow

Abstract

Hippocampal place cells are influenced by both self-motion (idiothetic) signals and external sensory landmarks as an animal navigates its environment. To continuously update a position signal on an internal ‘cognitive map’, the hippocampal system integrates self-motion signals over time, a process that relies on a finely calibrated path integration gain that relates movement in physical space to movement on the cognitive map. It is unclear whether idiothetic cues alone, such as optic flow, exert sufficient influence on the cognitive map to enable recalibration of path integration, or if polarizing position information provided by landmarks is essential for this recalibration. Here, we demonstrate both recalibration of path integration gain and systematic control of place fields by pure optic flow information in freely moving rats. These findings demonstrate that the brain continuously rebalances the influence of conflicting idiothetic cues to fine-tune the neural dynamics of path integration, and that this recalibration process does not require a top-down, unambiguous position signal from landmarks.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Stripe presentation and gain computation.
Fig. 2: Effect of stripe manipulation on place cells.
Fig. 3: Recalibration of landmarks with open-loop optic flow.
Fig. 4: Cognitive clamp of hippocampal gain via optic flow.
Fig. 5: Recalibration of path integration gain via the cognitive clamp.

Similar content being viewed by others

Data availability

Preprocessed data used to perform the analyses and generate the figures in this manuscript are available in the Johns Hopkins Research Data Repository, at https://doi.org/10.7281/T1/THLC8N.

Code availability

Custom code was written to analyze the datasets used in this study, and to generate figures for this manuscript. This codebase is versioned, and uses several third-party packages, the license files for which are included with the respective code. The codes used to perform the analyses and generate the figures in this manuscript are available in the Johns Hopkins Research Data Repository, at https://doi.org/10.7281/T1/THLC8N.

References

  1. Etienne, A. S. & Jeffery, K. J. Path integration in mammals. Hippocampus 14, 180–192 (2004).

    Article  PubMed  Google Scholar 

  2. McNaughton, B. L. et al. Deciphering the hippocampal polyglot: the hippocampus as a path integration system. J. Exp. Biol. 199, 173–185 (1996).

    Article  CAS  PubMed  Google Scholar 

  3. O’Keefe, J. & Conway, D. H. Hippocampal place units in the freely moving rat: why they fire where they fire. Exp. Brain Res. 31, 573–590 (1978).

    PubMed  Google Scholar 

  4. Knierim, J. J., Kudrimoti, H. S. & McNaughton, B. L. Place cells, head direction cells, and the learning of landmark stability. J. Neurosci. 15, 1648–1659 (1995).

    Article  CAS  PubMed  Google Scholar 

  5. Knierim, J. J., Kudrimoti, H. S. & McNaughton, B. L. Interactions between idiothetic cues and external landmarks in the control of place cells and head direction cells. J. Neurophysiol. 80, 425–446 (1998).

    Article  CAS  PubMed  Google Scholar 

  6. Jayakumar, R. P. et al. Recalibration of path integration in hippocampal place cells. Nature 566, 533–537 (2019).

    Article  CAS  PubMed  Google Scholar 

  7. Chen, G., King, J. A., Burgess, N. & O’Keefe, J. How vision and movement combine in the hippocampal place code. Proc. Natl Acad. Sci. USA 110, 378–383 (2013).

    Article  CAS  PubMed  Google Scholar 

  8. Terrazas, A. et al. Self-motion and the hippocampal spatial metric. J. Neurosci. 25, 8085–8096 (2005).

    Article  CAS  PubMed  Google Scholar 

  9. Moser, E. I., Moser, M.-B. & McNaughton, B. L. Spatial representation in the hippocampal formation: a history. Nat. Neurosci. 20, 1448–1464 (2017).

    Article  CAS  PubMed  Google Scholar 

  10. Muller, R. U. & Kubie, J. L. The effects of changes in the environment on the spatial firing of hippocampal complex-spike cells. J. Neurosci. 7, 1951–1968 (1987).

    Article  CAS  PubMed  Google Scholar 

  11. 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, 1245–1279 (2011).

    Article  PubMed  Google Scholar 

  12. Acharya, L., Aghajan, Z. M., Vuong, C., Moore, J. J. & Mehta, M. R. Causal influence of visual cues on hippocampal directional selectivity. Cell 164, 197–207 (2016).

    Article  CAS  PubMed  Google Scholar 

  13. Purandare, C. S. et al. Moving bar of light evokes vectorial spatial selectivity in the immobile rat hippocampus. Nature 602, 461–467 (2022).

    Article  CAS  PubMed  Google Scholar 

  14. 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, 663–678 (2006).

    Article  CAS  PubMed  Google Scholar 

  15. Savelli, F. & Knierim, J. J. Origin and role of path integration in the cognitive representations of the hippocampus: computational insights into open questions. J. Exp. Biol. 222, jeb188912 (2019).

    Article  PubMed  Google Scholar 

  16. Zhang, S., Schönfeld, F., Wiskott, L. & Manahan-Vaughan, D. Spatial representations of place cells in darkness are supported by path integration and border information. Front. Behav. Neurosci. 8, 222 (2014).

    Article  PubMed  Google Scholar 

  17. Madhav, M. S. & Cowan, N. J. The synergy between neuroscience and control theory: the nervous system as inspiration for hard control challenges. Annu. Rev. Control Robot. Auton. Syst. 3, 243–267 (2020).

    Article  Google Scholar 

  18. Cowan, N. J. et al. Feedback control as a framework for understanding tradeoffs in biology. Integr. Comp. Biol. 54, 223–237 (2014).

    Article  PubMed  Google Scholar 

  19. Marken, R. S. & Mansell, W. Perceptual control as a unifying concept in psychology. Rev. Gen. Psychol. 17, 190–195 (2013).

    Article  Google Scholar 

  20. Robinson, D. A. The use of control systems analysis in the neurophysiology of eye movements. Annu. Rev. Neurosci. 4, 463–503 (1981).

    Article  CAS  PubMed  Google Scholar 

  21. McNamee, D. & Wolpert, D. M. Internal models in biological control. Annu. Rev. Control Robot. Auton. Syst. 2, 339–364 (2019).

    Article  PubMed  PubMed Central  Google Scholar 

  22. Wiener, N. Cybernetics or Control and Communication in the Animal and the Machine (MIT, 2019).

  23. Huxley, A. From overshoot to voltage clamp. Trends Neurosci. 25, 553–558 (2002).

    Article  CAS  PubMed  Google Scholar 

  24. Peixoto, D. et al. Decoding and perturbing decision states in real time. Nature 591, 604–609 (2021).

    Article  CAS  PubMed  Google Scholar 

  25. Wright, J., Macefield, V. G., Schaik, Avan. & Tapson, J. C. A review of control strategies in closed-loop neuroprosthetic systems. Front. Neurosci. 10, 312 (2016).

    Article  PubMed  Google Scholar 

  26. O’Doherty, J. E. et al. Active tactile exploration using a brain-machine-brain interface. Nature 479, 228–231 (2011).

    Article  PubMed  Google Scholar 

  27. Ruffini, G. Conscious brain-to-brain communication using noninvasive technologies. in Closed Loop Neuroscience (El Hady, A. ed) 241–256 (Academic Press, 2016).

  28. Roth, E., Sponberg, S. & Cowan, N. J. A comparative approach to closed-loop computation. Curr. Opin. Neurobiol. 25, 54–62 (2014).

    Article  CAS  PubMed  Google Scholar 

  29. Mohler, B. J. et al. Calibration of locomotion resulting from visual motion in a treadmill-based virtual environment. ACM Trans. Appl. Percept. 4, 4-es (2007).

    Article  Google Scholar 

  30. Tcheang, L., Bülthoff, H. H. & Burgess, N. Visual influence on path integration in darkness indicates a multimodal representation of large-scale space. Proc. Natl Acad. Sci. USA 108, 1152–1157 (2011).

    Article  CAS  PubMed  Google Scholar 

  31. Rieser, J. J., Pick, H. L., Ashmead, D. H. & Garing, A. E. Calibration of human locomotion and models of perceptual-motor organization. J. Exp. Psychol. Hum. Percept. Perform. 21, 480–497 (1995).

    Article  CAS  PubMed  Google Scholar 

  32. Madhav, M. S. et al. The Dome: a virtual reality apparatus for freely locomoting rodents. J. Neurosci. Methods 368, 109336 (2022).

    Article  PubMed  Google Scholar 

  33. Kautzky, M. & Thurley, K. Estimation of self-motion duration and distance in rodents. R. Soc. Open Sci. 3, 160118 (2016).

    Article  PubMed  Google Scholar 

  34. O’Connor, S. M. & Donelan, J. M. Fast visual prediction and slow optimization of preferred walking speed. J. Neurophysiol. 107, 2549–2559 (2012).

    Article  PubMed  Google Scholar 

  35. Warren, W. H., Kay, B. A., Zosh, W. D., Duchon, A. P. & Sahuc, S. Optic flow is used to control human walking. Nat. Neurosci. 4, 213–216 (2001).

    Article  CAS  PubMed  Google Scholar 

  36. Bruggeman, H., Zosh, W. & Warren, W. H. Optic flow drives human visuo-locomotor adaptation. Curr. Biol. 17, 2035–2040 (2007).

    Article  CAS  PubMed  Google Scholar 

  37. Srinivasan, M. V., Zhang, S. W., Lehrer, M. & Collett, T. S. Honeybee navigation en route to the goal: visual flight control and odometry. J. Exp. Biol. 199, 237–244 (1996).

    Article  CAS  PubMed  Google Scholar 

  38. Pfeffer, S. E. & Wittlinger, M. Optic flow odometry operates independently of stride integration in carried ants. Science 353, 1155–1157 (2016).

    Article  CAS  PubMed  Google Scholar 

  39. Webb, B. & Wystrach, A. Neural mechanisms of insect navigation. Curr. Opin. Insect Sci. 15, 27–39 (2016).

    Article  PubMed  Google Scholar 

  40. Biswas, D. et al. Closed-loop control of active sensing movements regulates sensory slip. Curr. Biol. 28, 4029–4036.e4 (2018).

    Article  CAS  PubMed  Google Scholar 

  41. Smyth, G., Baliga, V. B., Gaede, A. H., Wylie, D. R. & Altshuler, D. L. Specializations in optic flow encoding in the pretectum of hummingbirds and zebra finches. Curr. Biol. https://doi.org/10.1016/j.cub.2022.04.076 (2022).

  42. Mao, D., Molina, L. A., Bonin, V. & McNaughton, B. L. Vision and locomotion combine to drive path integration sequences in mouse retrosplenial cortex. Curr. Biol. 30, 1680–1688.e4 (2020).

    Article  CAS  PubMed  Google Scholar 

  43. Arleo, A. et al. Optic flow stimuli update anterodorsal thalamus head direction neuronal activity in rats. J. Neurosci. 33, 16790–16795 (2013).

    Article  CAS  PubMed  Google Scholar 

  44. Sharp, P. E., Blair, H. T., Etkin, D. & Tzanetos, D. B. Influences of vestibular and visual motion information on the spatial firing patterns of hippocampal place cells. J. Neurosci. 15, 173–189 (1995).

    Article  CAS  PubMed  Google Scholar 

  45. Gaede, A. H. et al. Response properties of optic flow neurons in the accessory optic system of hummingbirds versus zebra finches and pigeons. J. Neurophysiol. 127, 130–144 (2022).

    Article  PubMed  Google Scholar 

  46. Mertes, M., Dittmar, L., Egelhaaf, M. & Boeddeker, N. Visual motion-sensitive neurons in the bumblebee brain convey information about landmarks during a navigational task. Front. Behav. Neurosci. 8, 335 (2014).

    Article  PubMed  Google Scholar 

  47. Yu, C. P., Page, W. K., Gaborski, R. & Duffy, C. J. Receptive field dynamics underlying MST neuronal optic flow selectivity. J. Neurophysiol. 103, 2794–2807 (2010).

    Article  PubMed  Google Scholar 

  48. Greenlee, M. W. Human cortical areas underlying the perception of optic flow: brain imaging studies. Int. Rev. Neurobiol. 44, 269–292 (2000).

  49. Stangl, M., Kanitscheider, I., Riemer, M., Fiete, I. & Wolbers, T. Sources of path integration error in young and aging humans. Nat. Commun. 11, 2626 (2020).

    Article  CAS  PubMed  Google Scholar 

  50. Seguinot, V., Cattet, J. & Benhamou, S. Path integration in dogs. Anim. Behav. 55, 787–797 (1998).

    Article  CAS  PubMed  Google Scholar 

  51. Campbell, M. G. et al. Principles governing the integration of landmark and self-motion cues in entorhinal cortical codes for navigation. Nat. Neurosci. 21, 1096–1106 (2018).

    Article  CAS  PubMed  Google Scholar 

  52. Raftery, A. E. Bayesian model selection in social research. Sociol. Methodol. 25, 111 (1995).

    Article  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  54. Carver, S., Kiemel, T. & Jeka, J. J. Modeling the dynamics of sensory reweighting. Biol. Cybern. 95, 123–134 (2006).

    Article  PubMed  Google Scholar 

  55. Wang, Q., Gao, E. & Burkhalter, A. Gateways of ventral and dorsal streams in mouse visual cortex. J. Neurosci. 31, 1905–1918 (2011).

    Article  CAS  PubMed  Google Scholar 

  56. Roth, M. M. et al. Thalamic nuclei convey diverse contextual information to layer 1 of visual cortex. Nat. Neurosci. 19, 299–307 (2016).

    Article  CAS  PubMed  Google Scholar 

  57. Blot, A. et al. Visual intracortical and transthalamic pathways carry distinct information to cortical areas. Neuron 109, 1996–2008.e6 (2021).

    Article  CAS  PubMed  Google Scholar 

  58. Fetsch, C. R., DeAngelis, G. C. & Angelaki, D. E. Bridging the gap between theories of sensory cue integration and the physiology of multisensory neurons. Nat. Rev. Neurosci. 14, 429–442 (2013).

    Article  CAS  PubMed  Google Scholar 

  59. Contzen, M. P. Consensus based synchronization of clocks to diminish the effect of clock drifts in microgrids. IFAC Pap OnLine 53, 12980–12985 (2020).

    Article  Google Scholar 

  60. Kloosterman, F., Layton, S. P., Chen, Z. & Wilson, M. S. Bayesian decoding using unsorted spikes in the rat hippocampus. J. Neurophysiol. 111, 217–227 (2014).

    Article  PubMed  Google Scholar 

  61. Hu, S. et al. Real-time readout of large-scale unsorted neural ensemble place codes. Cell Rep. 25, 2635–2642.e5 (2018).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  62. Vagvolgyi, B. P., Jayakumar, R. P., Madhav, M. S., Knierim, J. J. & Cowan, N. J. Wide-angle, monocular head tracking using passive markers. J. Neurosci. Methods 368, 109453 (2022).

    Article  PubMed  Google Scholar 

  63. Quigley, M. et al. ROS: an open-source robot operating system. in ICRA Workshop on Open Source Software vol. 3 p. 5 (IEEE, 2009).

  64. Kennedy, J. P. et al. A direct comparison of theta power and frequency to speed and acceleration. J. Neurosci. 42, 4326–4341 (2022).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  65. Pfeiffer, B. E. & Foster, D. J. Hippocampal place-cell sequences depict future paths to remembered goals. Nature 497, 74–79 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  66. Jeewajee, A., Barry, C., O’Keefe, J. & Burgess, N. Grid cells and theta as oscillatory interference: electrophysiological data from freely moving rats. Hippocampus 18, 1175–1185 (2008).

    Article  CAS  PubMed  Google Scholar 

  67. Csicsvari, J., Hirase, H., Czurkó, A., Mamiya, A. & Buzsáki, G. Oscillatory coupling of hippocampal pyramidal cells and interneurons in the behaving Rat. J. Neurosci. 19, 274–287 (1999).

    Article  CAS  PubMed  Google Scholar 

  68. Branch, A. et al. An optimized tissue clearing protocol for rat brain labeling, imaging, and high throughput analysis. Preprint at bioRxiv https://doi.org/10.1101/639674 (2019).

Download references

Acknowledgements

We thank E. Fortune for providing valuable comments on the manuscript; K. Nnah, A. Branch, M. Ferreyros, B. Krishnan, B. Vagvolgyi and V. Puliyadi for technical assistance; and H. T. Blair for useful discussions. This work was supported by US Public Health Service grant no. R01 NS102537 (N.J.C., J.J.K., F.S.) from the NINDS, a Johns Hopkins University Kavli Neuroscience Discovery Institute Distinguished Postdoctoral Fellowship (M.S.M.), a Johns Hopkins University Provost’s Undergraduate Research Award (B.Y.L.), ARO Grants no. W911NF1810327 (N.J.C., J.J.K.) and a Discovery Award from the Johns Hopkins University (N.J.C., J.J.K.).

Author information

Authors and Affiliations

Authors

Contributions

M.S.M., R.P.J., F.S., J.J.K. and N.J.C. conceived and designed the study. J.J.K. and N.J.C. supervised all aspects of the experiments and analysis. R.P.J. and M.S.M. designed and constructed the apparatus, performed experiments and analyzed the data. B.Y.L. performed experiments and analyzed data. S.G.L. and K.W. performed experiments. M.S.M., R.P.J., B.Y.L., J.J.K. and N.J.C. wrote the paper and F.S. and S.G.L. provided critical feedback.

Corresponding authors

Correspondence to Manu S. Madhav, James J. Knierim or Noah J. Cowan.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Neuroscience thanks Loren Frank, Edvard Moser, Aman Saleem and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Hippocampal gain decoding.

(a) If a unit has a characteristic spatial tuning that repeats once per physical lap, the firing rate of the unit exhibits a spatial frequency of H = 1 per lap. Illustration of the firing of a spatially tuned cell for three values of hippocampal gain, H. (b) Reproduction of data from Fig. 1d, f. The spectrogram of one unit is shown at the bottom, with the color denoting the power at a given position and spatial frequency. Spectrogram peaks emerge at a fundamental frequency starting at ~1.1 and at its harmonics. We use a custom algorithm to trace these peaks (see ‘Spectral Decoding’ in Methods) and estimate the gain for each unit. The hippocampal gain, H, is estimated as the median spatial frequency across all isolated units for a given session. (c) Real-time decoding flowchart. Neural data from each tetrode and rat position data from the camera are acquired (see62 for hardware details). Incoming spike times, as detected by Neuralynx spike detection parameters, and positions are added to a temporal buffer. The following operations are performed every 1 s. The temporal buffer is transferred into a spatial queue buffer that accumulates spike times and positions from the previous 6 laps. Velocities are computed from positions, and spikes and positions with velocities <5 cm/s are eliminated. The remaining spikes and positions are spatially binned (5° width). The spike bins are divided by position bins to create firing rate bins for each tetrode, which are then smoothed and sent to the spectral decoder to estimate H (details in Methods section and Fig. 1d–g). The spectral decoder is able to estimate spatial frequency from the cumulative spatial tuning of all simultaneously recorded cells on a tetrode, extending the success of decoding spatial frequency from cells with such diffuse spatial tuning like interneurons (described in6). Spatial frequencies estimated independently from each tetrode were combined together into \(\hat{H}\), to be robust to noisy estimates on any particular tetrode. (d) Comparison of online (unsorted) decoding vs. offline (sorted) decoding in Epoch 2 (controller on and using online decoded values) of the 25 closed-loop sessions. The mean absolute error between these gains remains close to 0, with a few sessions (3/25) showing deviations greater than 0.1.

Extended Data Fig. 2 Comparison of population coherence of putative pyramidal cells and interneurons.

Here, the data from Fig. 2h is split into (a) putative pyramidal cells (1549 units) and (b) putative interneurons (85 units) that were identified in all data (see Methods). If a unit, i, were part of a coherent population, its gain Hi should equal the population hippocampal gain H. For each 6-lap window we computed a gain ratio error \(|1\mbox{--}Hi/H|\) and computed the average of this value across the session to derive the coherence score for the unit. To avoid bias, for each unit i, Hi was excluded from the computation of population gain H. Most units in both populations have a score very close to zero and very few have values above 0.1 (19/1549 pyramidal, 2/85 interneurons). These populations were thus combined in the other analyses.

Extended Data Fig. 3 Gain dynamics during all open-loop sessions.

Gain dynamics during all open-loop sessions (including sessions illustrated in main text figures). Each plot represents a single session (titled as ‘Rat-Day, Session’, 40 sessions across 5 rats). X axis is number of laps the rat ran on the table and Y axis is gain. The black scale bar in each plot denotes 10 laps. Applied stripe gain (S; blue) plotted with decoded hippocampal gain (H; yellow). Sessions are grouped by the final stripe gain: (a) Up sessions (Sfinal > 1), (b) Down sessions (Sfinal < 1), and (c) Unity sessions (Sfinal = 1). Dashed vertical lines indicate boundaries between Epochs 1, 2a, 2b and 3 for Up and Down sessions, and between Epochs 1 and 3 for Unity sessions. The blips in the S curve in session 791–06, m1 was the result of a momentary software error. In most of the Up sessions, the hippocampal gain increases at a faster rate in Epoch 2a (S ramps up) than in Epoch 1 (S = 1). In many Down sessions, the hippocampal gain appears to decrease slowly, stay stable, and or even increase over laps, even though the stripe gain is decreasing. This may be the result of two effects—high baseline and low influence of stripes when gain is changed in the downward direction. In general, reducing the stripe gain has a lower influence on H than increasing the gain (Fig. 2i). These two factors combine: in the first four sessions of panel b, H rises up to Hbaseline in Epoch 1, but this upward drift is arrested and overcome by larger decreases in S (panel b, sessions 2, 3, and 4) but not quite overcome by a smaller decrease in S (panel b, session 1). For one animal (883), we observed a ‘rebound’ in the hippocampal gain after the stripes were extinguished, resulting in a consistent offset (that is, a negative intercept and low slope in the recalibration line, Fig. 3c, yellow); despite this offset, there was still a linear relationship between HfinalHbaseline and HrecalHbaseline for each rat (Fig. 3c), demonstrating the recalibration phenomenon.

Extended Data Fig. 4 Hippocampal gain drift.

(a) Data from Epoch 1 of all open and closed-loop sessions where the stripe gain was held at 1. Most sessions have a positive slope. (b) Data from Epoch 2b of open-loop sessions where the stripe gain was held constant for 26 laps at a value not equal to 1. Most sessions have a positive slope. The x axis shows slopes of the linear fits of the hippocampal gain in these respective epochs and the y axis shows the session count. Colors indicate individual animals (see key in (f)). (c) Simulation of drift in path integration gain within session. We created a simulation to test the hypothesis that the positive drift might be caused by the asymmetric responses of the hippocampal gain to UP and DOWN manipulations of stripe gain (Fig. 2i, Extended Data Fig. 4a, b). Under the assumption that the velocity inputs are noisy, the asymmetric response would result in any noise deviation in the UP direction having a stronger influence on the updating of position on the hippocampal map than noise deviations in the DOWN direction. If the gain is continually recalibrated, the biased influence of noise and gain recalibration results in a biased random walk toward higher gain values (description in Simulation of biased drift in path integration under Methods). An iterative model was fed a noisy stationary optic flow gain input for 15 laps. As predicted, the output hippocampal gain exhibited a biased drift toward higher gain values. The x axis shows slopes of the linear fits of the hippocampal gain in these 15 laps and the y axis shows the run count for each slope bin. (An alternative explanation reverses the causal relationship between the observed asymmetry and the observed drift. That is, the asymmetry might result from a biased drift inherent in the system, which would need to be counteracted to drive the hippocampal gain down in the DOWN condition. In contrast, this bias would presumably augment the effects of increasing optic flow gain in the UP condition. We currently cannot distinguish between these two possible explanations of the relationship between biased drift and asymmetrical influence of optic flow.) (d) Example of baseline shift across days in one rat. The y axis is hippocampal gain, H, during the first 12 laps of Epoch 1 (stripes stationary) for 9 consecutive sessions. The last point in each curve (square marker) is considered Hbaseline for the session. The x axis denotes laps on the table. For Rat 923, the value of Hbaseline steadily increased across sessions but was relatively stable within a session. (e) Baseline shifts across sessions (typically 1 session/day) for individual rats. Data from each rat is plotted in a different color. The x axis is the session number of each rat and the y axis is Hbaseline for that session. Dots denote open-loop sessions and stars denote closed-loop sessions. 4/5 rats show a significant positive drift of Hbaseline over sessions (Rats= 771,791,883,923: slope = 0.029, 0.029, 0.029, 0.049; r2 = 0.82, 0.93, 0.73, 0.91; two-sided t-test against null hypothesis of slope 0, t-statistic = 5.18, 11.5, 5.88, 11.1, p = 2.05 × 10−3, 4.47 × 10−7, 5.37 × 10−5, 1.13 × 10−7; n = 8, 12, 15, 14 ; df = 6, 10, 13, 12, no adjustment made for multiple comparisons) whereas one rat showed a significant negative drift (Rat 913: slope = −0.006, r2 = 0.44; two-sided t-test, t-statistic = −3.33, p = 4.98 × 10−3; n = 16, df = 14). Because of these shifts, we subtracted Hbaseline from the dependent measures in our analyses of Figs. 2g, 3c, 4h, and 5c. We speculate that the baseline shift across days, shown in panels (d) and (e), may be due to an accumulation of within-session biased drift shown in (a) and (b) and simulated in (c). Future work exploring the question of biased drift may help explain observed behavioral path integration error biases49,50. (f) While there was an overall linear trend in the baseline over all sessions (panel e), it is unclear if, on a day-to-day basis, the baseline shift was influenced by the effect on H from the previous session’s manipulation. Typically, we alternated up and down manipulations in successive sessions, so if there were such a day-to-day influence, the residual around the linear trend should be correlated with the magnitude of the previous day’s manipulation. To examine if there was a systematic influence of the previous session’s manipulation on this residual, we plotted the residual (that is, the change in the baseline on session (n + 1), minus the linear trend from (e)) versus the gain change induced by stripes on the previous session, Hfinal (n) –Hbaseline (n). There was no significant relationship between these variables (r2 = 0.02, two-sided t-test, t-statistic = 1.07, p = 0.29, n = 48, df = 46).

Extended Data Fig. 5 Comparison of open-loop and closed-loop control.

(a) As might be expected, regardless of the control scheme implemented, the nonlinear relationship between change of hippocampal gain from its Epoch 1 baseline value (y-axis) and stripe manipulation (x-axis) is similar in open-loop (green fit) and closed-loop (orange fit) sessions. (b-c) The utility of closed-loop control is to drive the hippocampus to a desired state and hold it there. To demonstrate its effectiveness in this regard, we compared it with how well an open-loop experiment would perform. (b) Neurally open-loop (feedforward) control: The nonlinearity described in panel (a) can be used to predict Hfinal for a given open-loop stripe manipulation, Sfinal. However, rather than using all of the data to fit the model as in panel (a), an individual model fit was made for each open-loop session using the remaining open-loop sessions (leave-one-out). The y-axis shows a 1-lap moving average of the difference between the measured hippocampal gain, H, and the predicted gain from the leave-one-out fit for that session, \({H}_{{\rm{final}}}^{{\rm{predicted}}}\), in the laps (x-axis) leading up to the stripes being turned off (zero point on x-axis). The stripe gain was held at Sfinal for 26 laps prior to the stripes being turned off. Data are shown as mean ± standard deviation, with the dark lines representing mean and shaded region representing standard deviation. DOWN sessions (Sfinal < 1) are shown in blue and UP sessions (Sfinal > 1) are shown in red. The means of both UP and DOWN sessions approached close to zero offset from the predicted value, albeit with a large standard deviation. (c) Neurally closed-loop (feedback) control: in strongly and modestly controlled neurally closed-loop sessions, a target state, Hdesired, was defined prior to each session. The controller was able to achieve close to zero-offset in both UP (Hdesired > Hbaseline) and DOWN (Hdesired < Hbaseline) sessions, but with notably lower standard deviations than in panel (b), demonstrating tighter control of H for neurally closed loop sessions compared to neurally open loop sessions.

Extended Data Fig. 6 Examining time and distance confounds.

Because our manipulations generally require gradually increasing (or decreasing) gain in a monotonic fashion, it was necessary to ensure that the concomitant increase in time and distance were not confounding, critical factors that determined the evolution of the hippocampal gain. (a, b) Evolution of HHbaseline in Epoch 2 for (a) controlled closed-loop sessions for which the target gain was away from 1 and (b) open-loop sessions such that Sfinal was away from 1, plotted as a function of time (top) and distance run (bottom). In closed-loop sessions, the controller moved H either up (Hdesired > Hbaseline, blue, 10 sessions) or down (Hdesired < Hbaseline, red, 9 sessions). In open-loop sessions, the stripe gain was either increased (Sfinal > 1, blue, X sessions) or decreased (Sfinal < 1, red, X sessions). Time and distance only increase (+) in these experiments but the hippocampal gain followed the sign of the manipulation, clearly indicating the strong causal control of our stripe manipulations above any potential confounding influence of time or distance. (c, d) We also examined the influences of distance run and time spent under stripe manipulation to the change in hippocampal gain, HHbaseline, compared to our stripe gain manipulation S. These analyses were run for all open-loop sessions where Sfinal ≠ 1. (c) For these sessions, we computed the minimum distance rats ran in Epoch 1 and 2 (49 laps, the distance run in the Sfinal = 1 ± 2/13 sessions) to equate distance across gain manipulations. At 49 laps after the start of Epoch 1, the change in hippocampal gain HHbaseline is plotted as a function of both time (top) and stripe gain S (bottom) for all sessions. Each data point is from a session and colors denote different rats. We fit a power-law curve to both plots (HHbaseline = a + bxm). There is no obvious relationship between HHbaseline and time (adjusted r2 = −0.26, df = 30), whereas there is a power-law relationship to S (adjusted r2 = 0.69, df = 30) similar to Fig. 2i. (d) For these sessions, we computed the minimum time rats ran in Epochs 1 and 2 (range 13.1–19.9 mins). At 13.1 mins after the start of Epoch 1, the change in hippocampal gain HHbaseline is plotted as a function of both distance run (top) and stripe gain S (bottom). There is no strong relationship between HHbaseline and distance (adjusted r2 = −0.077, df = 30) whereas there is a clear power-law relationship to S (adjusted r2 = 0.72, df = 30), similar to Fig. 2i. From these plots, we conclude that the change in H in these experiments is related to S and not to the correlated variables, time and distance travelled.

Extended Data Fig. 7 Block diagram of closed-loop controller.

Here, s is the Laplace complex frequency variable. Multiplication by s denotes differentiation, whereas dividing by s denotes integration. C is the implementation of our neurally closed-loop controller, namely the transformation from the error \(({H}_{{\rm{desired}}}-\hat{H})\) to the stripe gain S. In control theoretic terminology, the controlled system (hippocampal circuit) is the ‘plant’ P, which transforms the stripe gain S into the output H. The term \(\frac{(1-{e}^{-6s})}{6s}\) in the feedback loop is the transfer function of a 6-lap moving average, capturing the lag introduced by our online gain decoder. The transfer function of the controller is \(C=\frac{{K}_{I}}{s}\) and that of the plant reduces to a constant gain, P = κ.

Extended Data Fig. 8 Gain dynamics during all closed-loop sessions.

Gain dynamics during all closed-loop sessions (including sessions illustrated in main text figures). Each plot represents a single session (titled as ‘Rat-Day, Session’, 25 sessions across 4 rats). X axis is laps the rat ran on the table and Y axis is gain. The black scale bar in each plot denotes 10 laps. Applied stripe gain (S; blue) plotted with offline-decoded hippocampal gain (H; yellow) and hippocampal gain estimated online using unsorted spikes (\(\hat{H}\); brown). This estimated value was driven to a constant desired value during the session (Hdesired; green dashed line). Dashed vertical lines indicate boundaries between Epochs 1, 2 and 3. Data is sorted into three groups based on how closely the final hippocampal gain (\({H}_{{\rm{final}}}\)) matched \({H}_{{\rm{desired}}}\) (see Methods): (a) strongly controlled sessions (\(|{H}_{{\rm{final}}}-{H}_{{\rm{desired}}}| < 0.05\)), (b) modestly controlled sessions (\(0.05\,\le |{H}_{{\rm{final}}}-{H}_{{\rm{desired}}}| < 0.20\)), and (c) uncontrolled sessions (\(|{H}_{{\rm{final}}}-{H}_{{\rm{desired}}}|\,\ge 0.20\)). Note that \(\hat{H}\) is a real-time estimate that depended on neural noise inherent in multi-unit electrophysiology and varied in quality day-to-day. \(\hat{H}\) was utilized only in Epoch 2 and even then, our slow-moving integral controller mitigated the effects of momentary noise in the estimate. For sessions in which \({H}_{{\rm{desired}}} > 1\) (Up sessions), 8 were strongly controlled, 5 were moderately controlled, and 3 were uncontrolled. For sessions in which \({H}_{{\rm{desired}}}\,\le 1\) (Down sessions), 2 were strongly controlled, 4 were moderately controlled, and 2 were uncontrolled. The small numbers of sessions do not provide enough power for statistical testing, but the apparent differences in closed-loop control between Up and Down sessions is discussed in the main text.

Supplementary information

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Madhav, M.S., Jayakumar, R.P., Li, B.Y. et al. Control and recalibration of path integration in place cells using optic flow. Nat Neurosci (2024). https://doi.org/10.1038/s41593-024-01681-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1038/s41593-024-01681-9

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing