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Allothetic and idiothetic spatial cues control the multiplexed theta phase coding of place cells

Nature Neuroscience volume 28, pages 2106–2117 (2025)Cite this article

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Abstract

Theta oscillation is considered a temporal scaffold for hippocampal computations that organizes the activity of spatially tuned cells known as place cells. Late phases of theta support prospective spatial representation via phase ‘precession’. In contrast, some studies have hypothesized that early phases of theta may subserve both retrospective spatial representation via phase ‘procession’ and the encoding of new associations. Here, combining virtual reality, electrophysiology and computational modeling, we provide experimental evidence for such a functionally multiplexed phase code and describe how distinct spatial inputs control its manifestation. Specifically, when rats continuously learned new associations between external landmark (allothetic) cues and self-motion (idiothetic) cues, phase ‘precession’ remained intact, allowing continuous prediction of future positions. Conversely, phase ‘procession’ was diminished, matching the putative role in encoding at the early theta phase. This multiplexed phase code may serve as a general circuit logic for alternating different computations at a sub-second scale.

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Fig. 1: Place cells are locked to allothetic spatial cues inside the Dome.
Fig. 2: Phase precession is maintained in the landmark frame of reference.
Fig. 3: Place cells scale their theta-modulated bursting frequency in response to the experimental gain.
Fig. 4: Phase precession is controlled by the hippocampal map when allothetic cues are weak or absent.
Fig. 5: Single-traversal analysis reveals the two-lobe structure of phase coding.
Fig. 6: Phase procession is diminished under incoherent allothetic and idiothetic inputs.
Fig. 7: CAN model explains the selective diminishment of phase procession.

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Data availability

Preprocessed data used to perform the analyses and generate the figures in this paper are available via OSF at https://osf.io/nq65k/?. Source data are provided with this paper.

Code availability

The code is available via OSF at https://osf.io/nq65k/?.

References

  1. Tolman, E. C. Cognitive maps in rats and men. Psychol. Rev. 55, 189–208 (1948).

    Article  CAS  PubMed  Google Scholar 

  2. Tulving, E. & Donaldson, W. Organization of Memory (Academic Press, 1972).

  3. O’Keefe, J. & Dostrovsky, J. The hippocampus as a spatial map: preliminary evidence from unit activity in the freely-moving rat. Brain Res. 34, 171–175 (1971).

    Article  PubMed  Google Scholar 

  4. O’Keefe, J. Place units in the hippocampus of the freely moving rat. Exp. Neurol. 51, 78–109 (1976).

    Article  PubMed  Google Scholar 

  5. O’Keefe, J. & Nadel, L. The Hippocampus as a Cognitive Map (Oxford Univ. Press, 1978).

  6. Robinson, N. T. M. et al. Targeted activation of hippocampal place cells drives memory-guided spatial behavior. Cell 183, 1586–1599 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  7. Vanderwolf, C. H. Hippocampal electrical activity and voluntary movement in the rat. Electroencephalogr. Clin. Neurophysiol. 26, 407–418 (1969).

    Article  CAS  PubMed  Google Scholar 

  8. Buzsáki, G. Theta oscillations in the hippocampus. Neuron 33, 325–340 (2002).

    Article  PubMed  Google Scholar 

  9. Hasselmo, M. E. What is the function of hippocampal theta rhythm?—Linking behavioral data to phasic properties of field potential and unit recording data. Hippocampus 15, 936–949 (2005).

    Article  PubMed  Google Scholar 

  10. O’Keefe, J. & Recce, M. L. Phase relationship between hippocampal place units and the EEG theta rhythm. Hippocampus 3, 317–330 (1993).

    Article  PubMed  Google Scholar 

  11. 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, 149–172 (1996).

    Article  CAS  PubMed  Google Scholar 

  12. Jensen, O. & Lisman, J. E. Position reconstruction from an ensemble of hippocampal place cells: contribution of theta phase coding. J. Neurophysiol. 83, 2602–2609 (2000).

    Article  CAS  PubMed  Google Scholar 

  13. Mehta, M. R., Lee, A. K. & Wilson, M. A. Role of experience and oscillations in transforming a rate code into a temporal code. Nature 417, 741–746 (2002).

  14. Huxter, J., Burgess, N. & O’Keefe, J. Independent rate and temporal coding in hippocampal pyramidal cells. Nature 425, 828–832 (2003).

  15. O’Keefe, J. & Burgess, N. Dual phase and rate coding in hippocampal place cells: theoretical significance and relationship to entorhinal grid cells. Hippocampus 15, 853–866 (2005).

    Article  PubMed  PubMed Central  Google Scholar 

  16. Geisler, C., Robbe, D., Zugaro, M., Sirota, A. & Buzsáki, G. Hippocampal place cell assemblies are speed-controlled oscillators. Proc. Natl Acad. Sci. USA 104, 8149–8154 (2007).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  17. Huxter, J. R., Senior, T. J., Allen, K. & Csicsvari, J. Theta phase–specific codes for two-dimensional position, trajectory and heading in the hippocampus. Nat. Neurosci. 11, 587–594 (2008).

  18. Harvey, C. D., Collman, F., Dombeck, D. A., & Tank, D. W. Intracellular dynamics of hippocampal place cells during virtual navigation. Nature 461, 941–946 (2009).

  19. Dragoi, G. & Buzsáki, G. Temporal encoding of place sequences by hippocampal cell assemblies. Neuron 50, 145–157 (2006).

    Article  CAS  PubMed  Google Scholar 

  20. Foster, D. J. & Wilson, M. A. Hippocampal theta sequences. Hippocampus 17, 1093–1099 (2007).

    Article  PubMed  Google Scholar 

  21. Foster, D. J. & Knierim, J. J. Sequence learning and the role of the hippocampus in rodent navigation. Curr. Opin. Neurobiol. 22, 294–300 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  22. Johnson, A. & Redish, A. D. Neural ensembles in CA3 transiently encode paths forward of the animal at a decision point. J. Neurosci. 27, 12176–12189 (2007).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  23. Wikenheiser, A. M. & Redish, A. D. Hippocampal theta sequences reflect current goals. Nat. Neurosci. 18, 289–294 (2005).

  24. Kay, K. et al. Constant sub-second cycling between representations of possible futures in the hippocampus. Cell 180, 552–567 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  25. Zheng, C., Hwaun, E., Loza, C. A. & Colgin, L. L. Hippocampal place cell sequences differ during correct and error trials in a spatial memory task. Nat. Commun. 12, 3373 (2021).

  26. Eliav, T. et al. Nonoscillatory phase coding and synchronization in the bat hippocampal formation. Cell 175, 1119–1130 (2018).

    Article  CAS  PubMed  Google Scholar 

  27. Qasim, S. E., Fried, I. & Jacobs, J. Phase precession in the human hippocampus and entorhinal cortex. Cell 184, 3242–3255 (2021).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  28. Hopfield, J. J. Pattern recognition computation using action potential timing for stimulus representation. Nature 376, 33–36 (1995).

  29. Lisman, J. The theta/gamma discrete phase code occuring during the hippocampal phase precession may be a more general brain coding scheme. Hippocampus 15, 913–922 (2005).

    Article  PubMed  Google Scholar 

  30. Yamaguchi, Y., Aota, Y., McNaughton, B. L. & Lipa, P. Bimodality of theta phase precession in hippocampal place cells in freely running rats. J. Neurophysiol. 87, 2629–2642 (2002).

    Article  PubMed  Google Scholar 

  31. Hasselmo, M. E., Bodelón, C. & Wyble, B. P. A proposed function for hippocampal theta rhythm: separate phases of encoding and retrieval enhance reversal of prior learning. Neural Comput. 14, 793–817 (2002).

    Article  PubMed  Google Scholar 

  32. Huerta, P. T. & Lisman, J. E. Heightened synaptic plasticity of hippocampal CA1 neurons during a cholinergically induced rhythmic state. Nature 364, 723–725 (1993).

    Article  CAS  PubMed  Google Scholar 

  33. Hölscher, C., Anwyl, R. & Rowan, M. J. Stimulation on the positive phase of hippocampal theta rhythm induces long-term potentiation that can be depotentiated by stimulation on the negative phase in area CA1 in vivo. J. Neurosci. 17, 6470–6477 (1997).

    Article  PubMed  PubMed Central  Google Scholar 

  34. Golding, N. L., Staff, N. P. & Spruston, N. Dendritic spikes as a mechanism for cooperative long-term potentiation. Nature 418, 326–331 (2002).

    Article  CAS  PubMed  Google Scholar 

  35. Sheffield, M. E. J. & Dombeck, D. A. Calcium transient prevalence across the dendritic arbour predicts place field properties. Nature 517, 200–204 (2015).

    Article  CAS  PubMed  Google Scholar 

  36. Sheffield, M. E. J., Adoff, M. D. & Dombeck, D. A. Increased prevalence of calcium transients across the dendritic arbor during place field formation. Neuron 96, 490–504 (2017).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  37. Wang, M., Foster, D. J. & Pfeiffer, B. E. Alternating sequences of future and past behavior encoded within hippocampal theta oscillations. Science 370, 247–250 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  38. Chu, T. et al. Firing rate adaptation affords place cell theta sweeps, phase precession and procession. eLife 12, RP87055 (2024).

  39. 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 

  40. 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 

  41. Cabral, H. O. et al. Oscillatory dynamics and place field maps reflect hippocampal ensemble processing of sequence and place memory under NMDA receptor control. Neuron 81, 402–415 (2014).

    Article  CAS  PubMed  Google Scholar 

  42. Wang, Y., Romani, S., Lustig, B., Leonardo, A. & Pastalkova, E. Theta sequences are essential for internally generated hippocampal firing fields. Nat. Neurosci. 18, 282–288 (2015).

  43. Fattahi, M., Sharif, F., Geiller, T. & Royer, S. Differential representation of landmark and self-motion information along the CA1 radial axis: self-motion generated place fields shift toward landmarks during septal inactivation. J. Neurosci. 38, 6766–6778 (2018).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  44. 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 

  45. 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  PubMed Central  Google Scholar 

  46. 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 

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

  48. Mittelstaedt, M.-L. & Mittelstaedt, H. Homing by path integration in a mammal. Naturwissenschaften 67, 566–567 (1980).

    Article  Google Scholar 

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

    Article  PubMed  Google Scholar 

  50. 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 

  51. Secer, G., Knierim, J. J. & Cowan, N. J. Continuous bump attractor networks require explicit error coding for gain recalibration. Preprint at bioRxiv https://doi.org/10.1101/2024.02.12.579874 (2024).

  52. Maurer, A. P., Cowen, S. L., Burke, S. N., Barnes, C. A. & McNaughton, B. L. Organization of hippocampal cell assemblies based on theta phase precession. Hippocampus 16, 785–794 (2006).

    Article  PubMed  Google Scholar 

  53. Kempter, R., Leibold, C., Buzsáki, G., Diba, K. & Schmidt, R. Quantifying circular–linear associations: hippocampal phase precession. J. Neurosci. Methods 207, 113–124 (2012).

    Article  PubMed  Google Scholar 

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

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  55. Diba, K. & Buzsáki, G. Hippocampal network dynamics constrain the time lag between pyramidal cells across modified environments. J. Neurosci. 28, 13448–13456 (2008).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  56. Ormond, J. & McNaughton, B. L. Place field expansion after focal MEC inactivations is consistent with loss of Fourier components and path integrator gain reduction. Proc. Natl Acad. Sci. USA 112, 4116–4121 (2015).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  57. Mizuseki, K., Sirota, A., Pastalkova, E. & Buzsáki, G. Theta oscillations provide temporal windows for local circuit computation in the entorhinal-hippocampal loop. Neuron 64, 267–280 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  58. King, C., Recce, M. & O’Keefe, J. The rhythmicity of cells of the medial septum/diagonal band of Broca in the awake freely moving rat: relationships with behaviour and hippocampal theta. Eur. J. Neurosci. 10, 464–477 (1998).

    Article  CAS  PubMed  Google Scholar 

  59. Deshmukh, S. S., Yoganarasimha, D., Voicu, H. & Knierim, J. J. Theta modulation in the medial and the lateral entorhinal cortices. J. Neurophysiol. 104, 994–1006 (2010).

    Article  PubMed  PubMed Central  Google Scholar 

  60. Brandon, M. P., Bogaard, A. R., Schultheiss, N. W. & Hasselmo, M. E. Segregation of cortical head direction cell assemblies on alternating theta cycles. Nat. Neurosci. 16, 739–748 (2013).

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

  62. 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  PubMed Central  Google Scholar 

  63. Rotenberg, A. & Muller, R. U. Variable place–cell coupling to a continuously viewed stimulus: evidence that the hippocampus is part of a perceptual system. Philos. Trans. R. Soc. Lond. Ser. B 352, 1505–1513 (1997).

    Article  CAS  Google Scholar 

  64. 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 

  65. Schmidt, R. et al. Single-trial phase precession in the hippocampus. J. Neurosci. 29, 13232–13241 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  66. Feng, T., Silva, D. & Foster, D. J. Dissociation between the experience-dependent development of hippocampal theta sequences and single-trial phase precession. J. Neurosci. 35, 4890–4902 (2015).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  67. Colgin, L. L. et al. Frequency of gamma oscillations routes flow of information in the hippocampus. Nature 462, 353–357 (2009).

  68. Schomburg, E. W. et al. Theta phase segregation of input-specific gamma patterns in entorhinal-hippocampal networks. Neuron 84, 470–485 (2014).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  69. Fernández-Ruiz, A. et al. Entorhinal–CA3 dual-input control of spike timing in the hippocampus by theta-gamma coupling. Neuron 93, 1213–1226 (2017).

    Article  PubMed  PubMed Central  Google Scholar 

  70. Palmigiano, A., Geisel, T., Wolf, F. & Battaglia, D. Flexible information routing by transient synchrony. Nat. Neurosci. 20, 1014–1022 (2017).

  71. Zhou, Y. et al. Theta dominates cross-frequency coupling in hippocampal-medial entorhinal circuit during awake-behavior in rats. iScience 25, 105457 (2022).

    Article  PubMed  PubMed Central  Google Scholar 

  72. Douchamps, V., di Volo, M., Torcini, A., Battaglia, D. & Goutagny, R. Gamma oscillatory complexity conveys behavioral information in hippocampal networks. Nat. Commun. 15, 1849 (2024).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  73. Zheng, C., Bieri, K. W., Hsiao, Y.-T. & Colgin, L. L. Spatial sequence coding differs during slow and fast gamma rhythms in the hippocampus. Neuron 89, 398–408 (2016).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  74. McNaughton, B. L., Chen, L. L. & Markus, E. J. ‘Dead reckoning,’ landmark learning, and the sense of direction: a neurophysiological and computational hypothesis. J. Cogn. Neurosci. 3, 190–202 (1991).

    Article  CAS  PubMed  Google Scholar 

  75. Redish, A. D. & Touretzky, D. S. Cognitive maps beyond the hippocampus. Hippocampus 7, 15–35 (1997).

    Article  CAS  PubMed  Google Scholar 

  76. Hardcastle, K., Ganguli, S. & Giocomo, L. M. Environmental boundaries as an error correction mechanism for grid cells. Neuron 86, 827–839 (2015).

    Article  CAS  PubMed  Google Scholar 

  77. Pastalkova, E., Itskov, V., Amarasingham, A. & Buzsáki, G. Internally generated cell assembly sequences in the rat hippocampus. Science 321, 1322–1327 (2008).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  78. Bieri, K. W., Bobbitt, K. N. & Colgin, L. L. Slow and fast γ rhythms coordinate different spatial coding modes in hippocampal place cells. Neuron 82, 670–681 (2014).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  79. Guardamagna, M., Stella, F. & Battaglia, F. P. Heterogeneity of network and coding states in mouse CA1 place cells. Cell Rep. 42, 112022 (2023).

    Article  CAS  PubMed  Google Scholar 

  80. Aghajan, Z. M. et al. Impaired spatial selectivity and intact phase precession in two-dimensional virtual reality. Nat. Neurosci. 18, 121–128 (2015).

  81. Gupta, A. S., van der Meer, M. A. A., Touretzky, D. S. & Redish, A. D. Segmentation of spatial experience by hippocampal theta sequences. Nat. Neurosci. 15, 1032–1039 (2012).

  82. Maurer, A. P., Burke, S. N., Lipa, P., Skaggs, W. E. & Barnes, C. A. Greater running speeds result in altered hippocampal phase sequence dynamics. Hippocampus 22, 737–747 (2012).

    Article  PubMed  Google Scholar 

  83. Ambrose, R. E., Pfeiffer, B. E. & Foster, D. J. Reverse replay of hippocampal place cells is uniquely modulated by changing reward. Neuron 91, 1124–1136 (2016).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  84. Harris, K. D. et al. Spike train dynamics predicts theta-related phase precession in hippocampal pyramidal cells. Nature 417, 738–741 (2022).

  85. Takahashi, M., Nishida, H., David Redish, A. & Lauwereyns, J. Theta phase shift in spike timing and modulation of gamma oscillation: a dynamic code for spatial alternation during fixation in rat hippocampal area CA1. J. Neurophysiol. 111, 1601–1614 (2014).

    Article  PubMed  PubMed Central  Google Scholar 

  86. Robinson, N. T. M. et al. Medial entorhinal cortex selectively supports temporal coding by hippocampal neurons. Neuron 94, 677–688 (2017).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  87. Terada, S., Sakurai, Y., Nakahara, H. & Fujisawa, S. Temporal and rate coding for discrete event sequences in the hippocampus. Neuron 94, 1248–1262 (2017).

    Article  CAS  PubMed  Google Scholar 

  88. Shimbo, A., Izawa, E.-I. & Fujisawa, S. Scalable representation of time in the hippocampus. Sci. Adv. 7, eabd7013 (2021).

    Article  PubMed  PubMed Central  Google Scholar 

  89. Jones, M. W. & Wilson, M. A. Phase precession of medial prefrontal cortical activity relative to the hippocampal theta rhythm. Hippocampus 15, 867–873 (2005).

    Article  PubMed  Google Scholar 

  90. Hafting, T., Fyhn, M., Bonnevie, T., Moser, M.-B. & Moser, E. I. Hippocampus-independent phase precession in entorhinal grid cells. Nature 453, 1248–1252 (2008).

    Article  CAS  PubMed  Google Scholar 

  91. van der Meer, M. A. A. & Redish, A. D. Theta phase precession in rat ventral striatum links place and reward information. J. Neurosci. 31, 2843–2854 (2011).

    Article  PubMed  PubMed Central  Google Scholar 

  92. Kim, S. M., Ganguli, S. & Frank, L. M. Spatial information outflow from the hippocampal circuit: distributed spatial coding and phase precession in the subiculum. J. Neurosci. 32, 11539–11558 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  93. Asiminas, A. Adult_Hooded_Rat_Running. Zenodo https://doi.org/10.5281/zenodo.3926277 (2020).

  94. 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  PubMed Central  Google Scholar 

  95. Skaggs, W., McNaughton, B. & Gothard, K. An information-theoretic approach to deciphering the hippocampal code. In Advances in Neural Information Processing Systems 5 (1992); https://proceedings.neurips.cc/paper_files/paper/1992/hash/5dd9db5e033da9c6fb5ba83c7a7ebea9-Abstract.html

  96. Monaco, J. D., Rao, G., Roth, E. D. & Knierim, J. J. Attentive scanning behavior drives one-trial potentiation of hippocampal place fields. Nat. Neurosci. 17, 725–731 (2014).

  97. Mehta, M. R., Barnes, C. A. & McNaughton, B. L. Experience-dependent, asymmetric expansion of hippocampal place fields. Proc. Natl Acad. Sci. USA 94, 8918–8921 (1997).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  98. Lee, I. & Knierim, J. J. The relationship between the field-shifting phenomenon and representational coherence of place cells in CA1 and CA3 in a cue-altered environment. Learn. Mem. 14, 807–815 (2007).

    Article  PubMed  PubMed Central  Google Scholar 

  99. Lubenov, E. V. & Siapas, A. G. Hippocampal theta oscillations are travelling waves. Nature 459, 534–539 (2009).

  100. Mizuseki, K., Diba, K., Pastalkova, E. & Buzsáki, G. Hippocampal CA1 pyramidal cells form functionally distinct sublayers. Nat. Neurosci. 14, 1174–1181 (2011).

  101. Landler, L., Ruxton, G. D. & Malkemper, E. P. Circular data in biology: advice for effectively implementing statistical procedures. Behav. Ecol. Sociobiol. 72, 128 (2018).

    Article  PubMed  PubMed Central  Google Scholar 

  102. Ranck, J. B. Studies on single neurons in dorsal hippocampal formation and septum in unrestrained rats: part I. Behavioral correlates and firing repertoires. Exp. Neurol. 41, 462–531 (1973).

    Article  Google Scholar 

  103. Zhang, L., Lee, J., Rozell, C. & Singer, A. C. Sub-second dynamics of theta-gamma coupling in hippocampal CA1. eLife 8, e44320 (2019).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  104. Igarashi, K. M., Lu, L., Colgin, L. L., Moser, M.-B. & Moser, E. I. Coordination of entorhinal–hippocampal ensemble activity during associative learning. Nature 510, 143–147 (2014).

  105. Liu, J. & Newsome, W. T. Local field potential in cortical area MT: stimulus tuning and behavioral correlations. J. Neurosci. 26, 7779–7790 (2006).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  106. Ray, S., Crone, N. E., Niebur, E., Franaszczuk, P. J. & Hsiao, S. S. Neural correlates of high-gamma oscillations (60–200 Hz) in macaque local field potentials and their potential implications in electrocorticography. J. Neurosci. 28, 11526–11536 (2008).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  107. Scheffer-Teixeira, R., Belchior, H., Leão, R. N., Ribeiro, S. & Tort, A. B. L. On high-frequency field oscillations (>100 Hz) and the spectral leakage of spiking activity. J. Neurosci. 33, 1535–1539 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  108. Vinck, M., van Wingerden, M., Womelsdorf, T., Fries, P. & Pennartz, C. M. A. The pairwise phase consistency: a bias-free measure of rhythmic neuronal synchronization. Neuroimage 51, 112–122 (2010).

    Article  PubMed  Google Scholar 

  109. Folias, S. E. & Bressloff, P. C. Breathing pulses in an excitatory neural network. SIAM J. Appl. Dyn. Syst. 3, 378–407 (2004).

    Article  Google Scholar 

  110. Folias, S. E. Nonlinear analysis of breathing pulses in a synaptically coupled neural network. SIAM J. Appl. Dyn. Syst. 10, 744–787 (2011).

    Article  Google Scholar 

  111. Fenton, A. A. & Muller, R. U. Place cell discharge is extremely variable during individual passes of the rat through the firing field. Proc. Natl Acad. Sci. USA 95, 3182–3187 (1998).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  112. Madhav, M. S. et al. Control and recalibration of path integration in place cells using optic flow. Nat. Neurosci. 27, 1599–1608 (2024).

  113. Lopes-Dos-Santos, V. et al. Parsing hippocampal theta oscillations by nested spectral components during spatial exploration and memory-guided behavior. Neuron 100, 940–952 (2018).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

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Acknowledgements

We thank F. P. Battaglia for feedback on an earlier version of the paper, S. Zeger for statistical consultation and H. T. Blair and the members of the Cowan and Knierim laboratories for helpful comments. This research was supported in part by National Institutes of Health grants R01 NS102537 (J.J.K., N.J.C. and F.S.), R01 MH118926 (J.J.K. and N.J.C.) and R21 NS095075 (J.J.K. and N.J.C.); the Johns Hopkins Kavli Neuroscience Discovery Institute (M.S.M.); the Masason Foundation (Y.S.); the Ezoe Memorial Recruit Foundation (Y.S.); the Quad Fellowship (Y.S.); and the Honjo International Scholarship Foundation (Y.S.).

Author information

Author notes

  1. Manu S. Madhav

    Present address: School of Biomedical Engineering, University of British Columbia, Vancouver, BC, Canada

  2. Francesco Savelli

    Present address: Department of Neuroscience, Developmental and Regenerative Biology, The University of Texas at San Antonio, San Antonio, TX, USA

Authors and Affiliations

  1. Solomon H. Snyder Department of Neuroscience, Johns Hopkins University, Baltimore, MD, USA

    Yotaro Sueoka & James J. Knierim

  2. Zanvyl Krieger Mind/Brain Institute, Johns Hopkins University, Baltimore, MD, USA

    Yotaro Sueoka, Ravikrishnan P. Jayakumar, Manu S. Madhav, Francesco Savelli & James J. Knierim

  3. Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD, USA

    Ravikrishnan P. Jayakumar & Noah J. Cowan

  4. Laboratory for Computational Sensing and Robotics, Johns Hopkins University, Baltimore, MD, USA

    Ravikrishnan P. Jayakumar, Manu S. Madhav & Noah J. Cowan

  5. Kavli Neuroscience Discovery Institute, Johns Hopkins University, Baltimore, MD, USA

    Manu S. Madhav, Noah J. Cowan & James J. Knierim

Authors
  1. Yotaro Sueoka
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  2. Ravikrishnan P. Jayakumar
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  3. Manu S. Madhav
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  4. Francesco Savelli
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  5. Noah J. Cowan
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  6. James J. Knierim
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Contributions

R.P.J., M.S.M., F.S., N.J.C. and J.J.K. conceived of the study. All authors designed the analyses. Y.S. performed the formal analysis. Y.S. and J.J.K. wrote the paper, with input from all authors. N.J.C. and J.J.K. supervised the project.

Corresponding author

Correspondence to James J. Knierim.

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Nature Neuroscience thanks Michael Hasselmo and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Characterization of phase precession inside the Dome.

a, Example position–phase plots in landmark frame with different values of G. Red lines indicate the best-fit lines of the precession, computed using circular-linear regression. Place fields that contained double precessions are indicated by daggers and were excluded from further analyses. b, Comparison of precession statistics in epoch-based vs. lap-based fields. Epoch-based fields were defined from the tuning curve of the place cell during the entire epoch, while lap-based fields were defined as the range within the epoch-based field that the cell fired in a given lap. The lap-based field accounts for the lap-to-lap variability of the firing field locations111. This is especially important in this dataset, since the gain manipulation often caused a slight but continuous drift of the field locations throughout the session, making the epoch-based field larger than typical individual passes through the field. To test that our definition of lap-based fields produced a position–phase plot consistent with a more standard epoch-based field definition when fields did not have a biased drift, we compared the statistics of precession using data from epoch 1. Lap-based definition of place fields did not affect the correlational structure of phase coding but shallowed the slope estimate. Left, Precession slope. Best fit line: y = 0.622x + 6.33 (rho = 0.753, P = 1.00 ×10−16). Middle, Correlation coefficient. Best fit line: y = 0.919x - 0.0189 (rho = 0.935, P = 4.44 ×10−39). Right, Phase offset. Best fit line: y = 1.04x −26.5 (rho = 0.709, P = 8.64 ×10−9). Since the phase offset is a circular variable, the best fit line was found after wrapping around each lap-based phase offset such that the difference with its epoch-based counterpart was less than 180 degrees. Moreover, the correlation coefficient and the P value were computed using a circular-circular regression.

Source data

Extended Data Fig. 2 Scaling in the theta-modulated bursting frequency is accompanied by changes in other theta-modulated firing properties.

a–b, Change in NPR is predicted by the unit’s initial NPR. a, Histogram of the y-coordinate distance between each unit’s NPR in epoch 3 and the y = x line. A distance of 0 means that the unit scaled its theta-modulated firing frequency perfectly with gain. The units that formed fields in both epochs 1 and 3 were classified as having NPRs close to (distance < median) or further from (distance > median) the theoretical value. b, NPR of the two groups in epoch 1 (n = 33 units). Units that scaled their theta-modulated firing frequencies more faithfully in epoch 3 tended to have higher NPRs in epoch 1. β = 0.461, s.e. = 0.174, t(31) = 2.65, P = 0.0125; t-statistics/two-sided P value from the LMEM. Each violin plot shows the median (white circle), IQR (gray line), and distribution outline. c, Bursting rate was invariant to gain (n = 246 units). Overall: W(3) = 5.25, P = 0.154 (two-sided); Wald test on the LMEM. d, Theta-missing index was invariant to gain (n = 246 units). Overall: W(3) = 2.75, P = 0.432 (two-sided); Wald test on the LMEM. e–g, Quantification of theta-skipping24,58,59,60. e, Autocorrelogram (ACG) of an example unit without theta-skipping. f, Top, ACG of an example unit with theta-skipping. Note the disappearance of peak 1. Bottom, spiking of this unit relative to theta. g, Theta-skipping index was higher (less theta-skipping) in high gain condition compared to mid gain and G = 1 conditions (n = 242 units). Overall: W(3) = 14.6, P = 2.17 ×10−3 (two-sided); Epoch 1 vs. Low: β = −0.0808, s.e. = 0.0500, t(238) = −1.62, P = 0.107, Epoch 1 vs. Mid: β = −0.0438, s.e. = 0.0304, t(238) = −1.44, P = 0.150, Epoch 1 vs. High: β = −0.146, s.e. = 0.0408, t(238) = −3.59, P = 3.98 ×10−4, Low vs. Mid: β = 0.0370, s.e. = 0.0552, t(238) = 0.671, P = 0.503, Low vs. High: β = −0.0656, s.e. = 0.0601, t(238) = −1.09, P = 0.276, Mid vs. High: β = −0.103, s.e. = 0.0458, t(238) = −2.24, P = 0.0259; Wald test followed by t-statistics/two-sided P values from the LMEM. *: P < 0.05, ***: P < 0.001.

Source data

Extended Data Fig. 3 Quantification of theta phase coding in the absence of landmarks and under conditions of failure of landmark control.

a, Schematic of the hippocampal gain. When the pattern of place cell firing repeats every physical lap, the hippocampal map is locked to the lab frame (H = 1). Under gain manipulation, the same pattern repeats every n laps (n ≠ 1), which is defined as a hippocampal gain of 1/n. Reproduced from112. b, Example gain traces for epochs 1 through 4 and respective position–phase plots in epoch 4. The black (G) and blue (H) lines overlap during epochs 1–3, demonstrating the strong control of the hippocampal map by the landmarks. In epoch 4, the blue traces were maintained at values different from 1, demonstrating path integration gain recalibration47. c, Circular-linear correlation coefficients for epochs 1 and 4 (n = 233 units). β = 0.0148, s.e. = 0.0305, t(231) = 0.485, P = 0.628; t-statistics/two-sided p-value from the LMEM. Each violin plot shows the median (white circle), IQR (gray line), and distribution outline. d, Phase offsets for epochs 1 and 4 (n = 233 units). P = 0.556 (two-sided); hierarchical bootstrap test. e, Example gain traces of landmark failure (LMF) sessions and respective position–phase plots during LMF. The blue line (H) dissociated from the black line (G) during epochs 2 and 3. f, Example gain traces of an LMF session from individual place cells. The thick blue line (H) and the red lines (unit gains) overlap, demonstrating the coherence of the hippocampal map. g, Coherence error score of all place cells recorded during LMF as reported in Fig. 2g of47. The dashed line indicates a coherence error score of 0.1, analogous to the threshold defining landmark control. Most place cells (69/85) exhibited error scores < 0.1, indicating the coherence of the hippocampal population. Units with coherence error scores > 0.5 were grouped into a single bin. h, Circular-linear correlation coefficients for epoch 1 and LMF (n = 137 units). β = 0.0816, s.e. = 0.0397, t(135) = 2.05, P = 0.0419; t-statistic/two-sided P value from the LMEM. i, Phase offsets for epoch 1 and LMF (n = 137 units). P = 0.802 (two-sided); hierarchical bootstrap test. *: P < 0.05.

Source data

Extended Data Fig. 4 Quantification of single-traversal phase coding.

a, Distribution of single-traversal correlation coefficients. b, Distribution of single-traversal phase offsets. c, Constant precession can still be fit by a positive slope (red line). The blue-shaded region indicates one theta cycle, with a drop in firing rate in the middle of the field. d, Example single-traversal phase coding, fit with half-field slopes. e, Proportion of half-field slopes shows the nonmonotonic nature of many single-traversal phase coding. f, Proportion of positive half-field slopes. The second half of the field shows increased positive-slope traversals, suggestive of bona fide procession. χ2(1) = 91.97, P = 8.79 ×10−22; chi-squared test. g, Proportion of positive single-traversal slopes using traversals with strong firing (>= 25 spikes). Overall: χ2(3) = 29.13, P = 2.10 ×10−6; Epoch 1 vs. Low: χ2(1) = 18.64, P = 9.46 ×10−5, Epoch 1 vs. Mid: χ2(1) = 1.37, P = 0.242, Epoch 1 vs. High: χ2(1) = 13.66, P = 4.39 ×10−4, Low vs. Mid: χ2(1) = 15.45, P = 2.54 ×10−4, Low vs. High: χ2(1) = 2.13, P = 0.173, Mid vs. High: χ2(1) = 10.53, P = 1.76 ×10−3; chi-squared test followed by FDR correction. h, Proportion of positive single-traversal correlation coefficients. Overall: χ2(3) = 41.53, P = 5.05 ×10−9; Epoch 1 vs. Low: χ2(1) = 15.54, P = 1.61 ×10−4, Epoch 1 vs. Mid: χ2(1) = 2.53, P = 0.112, Epoch 1 vs. High: χ2(1) = 4.24, P = 0.0474, Low vs. Mid: χ2(1) = 26.90, P = 1.29 ×10−6, Low vs. High: χ2(1) = 8.77, P = 4.59 ×10−3, Mid vs. High: χ2(1) = 22.80, P = 5.40 ×10−6; chi-squared test followed by FDR correction. i, Phase offsets of single-traversal phase coding for each gain group. Epoch 1 vs. Low: k(1) = 3.09 ×104, P = 6.00 ×10−3, Epoch 1 vs. Mid: k(1) = 1.66 ×105, P = 1.50 ×10−3, Epoch 1 vs. High: k(1) = 9.12 ×104, P = 1, Low vs. Mid: k(1) = 1.04 ×105, P = 1.50 ×10−3, Low vs. High: k(1) = 7.56 ×104, P = 1.50 ×10−3, Mid vs. High: k(1) = 5.78 ×105, P = 1.50 ×10−3; two-sample Kuiper test (two-sided) followed by FDR correction. j, Phase occupancy histograms in epoch 4, similar to Fig. 6b. *: P < 0.05, **: P < 0.01, ***: P < 0.001.

Source data

Extended Data Fig. 5 Differences in SLIs cannot be explained by other experimental variables.

a, Schematic of the shuffling test based on theta frequency. SLIs in the same theta frequency bins (same color) were shuffled to create a null distribution of SLIs for each gain group. The same procedure was done for the shuffling based on the other parameters. b, Shuffling analysis to test if the difference in theta frequency (Fig. 3a) can explain the observed SLIs. The difference in the median SLI compared to epoch 1 was computed and tested against the null distribution. The differences in SLI between epoch 1 and the low and high gain groups were larger than the null distribution, demonstrating that the difference in theta frequency cannot explain the observed effect of SLI. Low: P <= 1.00 ×10−3, Mid: P = 0.249, High: P <= 1.00 ×10−3. c, Shuffling analysis to test if the difference in distance traveled by the rat to pass through the field in the lab frame can explain the observed SLIs. The decrease in SLIs in the low and high gain conditions was greater than the null distribution. Low: P <= 1.00 ×10−3, Mid: P = 0.0870, High: P <= 1.00 ×10−3. d, Shuffling analysis to test if the difference in the animal’s speed can explain the observed SLIs. The decrease in SLIs in the low and high gain conditions was greater than the null distribution. Low: P <= 1.00 ×10−3, Mid: P = 0.127, High: P <= 1.00 ×10−3. e, Shuffling analysis to test if the difference in time since the start of the experiment can explain the observed SLIs. Because epoch 1 is temporally segregated from epoch 3 by definition, shuffling was performed only using epoch 3 data. The decrease in SLIs in the low and high gain conditions compared to the mid gain condition was greater than the null distribution. Low: P <= 1.00 ×10−3, Mid: P = 8.00 ×10−3, High: P <= 1.00 ×10−3. Multiple comparisons correction was not applied for these shuffling analyses. **: P < 0.01, ***: P < 0.001.

Source data

Extended Data Fig. 6 Differences in SLIs cannot be explained by a biased sample of bimodal units.

a, Histograms of theta phase preference for example units classified as unimodal, bimodal, and unclassified ( > 2 peaks) units. Pyramidal cells in the deep layer of CA1 tend to exhibit strong firing in both the early and late phases of theta (bimodal cells), while cells in the superficial cell layer tend to fire only in the late phases of theta37,100 (unimodal cells). X-axis shows the theta phase repeated for two cycles. b, Number of units classified in each category. No significant difference in the distribution was observed among gain groups. This finding suggests that gain manipulation affects the relative size of the second lobe while sparing the modality of theta phase preference; for instance, bimodal units maintain their bimodality despite a smaller second lobe during gain manipulation. χ2(6) = 4.45, P = 0.616; chi-squared test. c, Smoothed phase coding plots for units classified as unimodal and bimodal cells. The plot for the bimodal cells showed a larger second lobe. d, Shuffling analysis to test if the difference in the sampling of unit modality can explain the observed SLIs. The decrease in SLIs in the low and high gain conditions was greater than the null distribution. The finding complements that of b, together demonstrating that the effect of gain on the size of the second lobe is not due to the change in the theta modality of the units or a biased sampling of unimodal/bimodal units across gain groups. Low: P <= 1.00 ×10−3, Mid: P = 0.229, High: P <= 1.00 ×10−3. Multiple comparisons correction was not applied. ***: P < 0.001.

Source data

Extended Data Fig. 7 Further characterization of the diminishment of the second lobe.

a, Slow, medium, and two fast gamma components averaged across sessions. Gamma components were extracted using the unsupervised clustering method of Zhang et al.103. The algorithm computed the frequency and the phase power matrix (FPP) for each theta cycle and obtained the groups of pixels in this theta phase–frequency space whose power co-fluctuates across theta cycles using k-mean clustering. The gamma components are coupled to theta phases that match previous studies68,103,113. We observed a slow gamma component at a frequency range of ~20–60 Hz associated with CA3 inputs (first column) and a medium gamma component at a frequency range of ~70–140 Hz associated with MECIII inputs67,68 (second column). The two fast gamma components (last 2 columns; > ~100 Hz) may include spiking artifacts107 and were not used for further analyses. b, Spike–medium gamma coupling comparison between gains, limited to the lower half of the medium gamma range ( ~ 70–105 Hz) to minimize the overlap in frequency with fast gamma (n = 151 units). Overall: W(2) = 8.78, P = 0.0124 (two-sided); Low vs. Mid: β = 0.0131, s.e. = 4.49 ×10−3, t(148) = 2.92, P = 4.01 ×10−3, Low vs. High: β = 8.07 ×10−3, s.e. = 4.85 ×10−3, t(148) = 1.66, P = 0.0985, Mid vs. High: β = −5.07 ×10−3, s.e. = 3.70 ×10−3, t(148) = −1.37, P = 0.172; Wald test followed by t-statistics/two-sided P values from the LMEM. Each violin plot shows the median (white circle), IQR (gray line), and distribution outline. c, Conceptual schematics of the network dynamics during epoch 4. In epoch 4, allothetic input is ablated. Note that the idiothetic Gaussian is assigned the larger amplitude (assigned to the allothetic Gaussian in epoch 1), since idiothetic input has the primary control over the hippocampal map in this condition. d, Position–phase plots of model neurons in epochs 1 and 4. The processing lobe diminished in epoch 4 compared to epoch 1 (same as the middle panel of Fig. 7c).

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Sueoka, Y., Jayakumar, R.P., Madhav, M.S. et al. Allothetic and idiothetic spatial cues control the multiplexed theta phase coding of place cells. Nat Neurosci 28, 2106–2117 (2025). https://doi.org/10.1038/s41593-025-02038-6

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