Abstract
During periods of immobility and sleep, the hippocampus generates diverse self-sustaining sequences of “replay” activity, which exhibit stationary, diffusive, and super-diffusive dynamical patterns. However, the neural mechanisms underlying this diversity in hippocampal sequential dynamics remain largely unknown. Here, we propose a unifying mechanism by showing that modulation of firing-rate adaptation strength within a continuous attractor model of place cells gives rise to these distinct forms of replay. Our model accounts for empirical data and yields several testable predictions. First, more diffusive replay sequences should positively correlate with longer theta sequences, both reflecting stronger adaptation. Second, increased neural activity combined with firing-rate adaptation should reduce the step size of decoded trajectories during replay. Third, the framework is consistent with previous work showing that replay diffusivity can vary within an animal across behavioural states that may influence adaptation (such as wake and sleep). Together, these results suggest that the diverse replay dynamics observed in the hippocampus can be understood through a simple yet powerful neural mechanism, providing insight into the computational role of replay in hippocampal-dependent cognition and its relationship to other electrophysiological phenomena.
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Data availability
All experimental data are taken from the Collaborative Research in Computational Neuroscience (CRCNS) hc-6 dataset contributed by Loren Frank and colleagues61. They are publicly available at: https://crcns.org/data-sets/hc/hc-6. Source data are provided with this paper.
Code availability
Code for reproducing all the results in the main text is available at https://doi.org/10.5281/zenodo.17488344.
References
O’Keefe, J. & Nadel, L. The Hippocampus as A Cognitive Map (Clarendon Press, 1978).
Morris, R. G., Garrud, P., Rawlins, J. A. & O’Keefe, J. Place navigation impaired in rats with hippocampal lesions. Nature 297, 681–683 (1982).
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).
Wikenheiser, A. M. & Redish, A. D. Hippocampal theta sequences reflect current goals. Nat. Neurosci. 18, 289–294 (2015).
Kay, K. et al. Constant sub-second cycling between representations of possible futures in the hippocampus. Cell 180, 552–567 (2020).
Scoville, W. B. & Milner, B. Loss of recent memory after bilateral hippocampal lesions. J. Neurol. Neurosurg. Psychiatry 20, 11 (1957).
Olton, D. S. & Samuelson, R. J. Remembrance of places passed: spatial memory in rats. J. Exp. Psychol.: Anim. Behav. Process. 2, 97 (1976).
Steele, R. & Morris, R. Delay-dependent impairment of a matching-to-place task with chronic and intrahippocampal infusion of the NMDA-antagonist D-AP5. Hippocampus 9, 118–136 (1999).
Wilson, M. A. & McNaughton, B. L. Reactivation of hippocampal ensemble memories during sleep. Science 265, 676–679 (1994).
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).
Foster, D. J. & Wilson, M. A. Hippocampal theta sequences. Hippocampus 17, 1093–1099 (2007).
Diba, K. & Buzsáki, G. Forward and reverse hippocampal place-cell sequences during ripples. Nat. Neurosci. 10, 1241–1242 (2007).
Karlsson, M. P. & Frank, L. M. Awake replay of remote experiences in the hippocampus. Nat. Neurosci. 12, 913–918 (2009).
Gupta, A. S., Van Der Meer, M. A., Touretzky, D. S. & Redish, A. D. Hippocampal replay is not a simple function of experience. Neuron 65, 695–705 (2010).
Dragoi, G. & Buzsáki, G. Temporal encoding of place sequences by hippocampal cell assemblies. Neuron 50, 145–157 (2006).
O’Keefe, J. & Recce, M. L. Phase relationship between hippocampal place units and the EEG theta rhythm. Hippocampus 3, 317–330 (1993).
Jensen, O. & Lisman, J. E. Hippocampal CA3 region predicts memory sequences: accounting for the phase precession of place cells. Learn. Mem. 3, 279–287 (1996).
Magee, J. C. & Johnston, D. A synaptically controlled, associative signal for Hebbian plasticity in hippocampal neurons. Science 275, 209–213 (1997).
Drieu, C., Todorova, R. & Zugaro, M. Nested sequences of hippocampal assemblies during behavior support subsequent sleep replay. Science 362, 675–679 (2018).
Muessig, L., Lasek, M., Varsavsky, I., Cacucci, F. & Wills, T. J. Coordinated emergence of hippocampal replay and theta sequences during post-natal development. Curr. Biol. 29, 834–840 (2019).
Drieu, C. & Zugaro, M. Hippocampal sequences during exploration: mechanisms and functions. Front. Cell. Neurosci. 13, 232 (2019).
Yu, C., Ji, Z., Ormond, J., O’Keefe, J. & Burgess, N. Hippocampal theta sweeps indicate goal direction. Preprint at https://www.biorxiv.org/content/10.1101/2025.08.21.671551v1 (2025).
Tang, W. et al. Goal-directed hippocampal theta sweeps during memory-guided navigation. Preprint at https://www.biorxiv.org/content/10.1101/2025.08.26.672489v1 (2025).
Vollan, A. Z., Gardner, R. J., Moser, M.-B. & Moser, E. I. Left–right-alternating theta sweeps in entorhinal–hippocampal maps of space. Nature 639, 995–1005 (2025).
Ji, Z., Chu, T., Wu, S. & Burgess, N. A systems model of alternating theta sweeps via firing rate adaptation. Curr. Biol. 35, 709–722 (2025).
Widloski, J., Theurel, D. & Foster, D. J. Spontaneous alternation of place-cell sequences in the open field through spike frequency adaptation. Cell Rep. 44, 115475 (2025).
Lee, A. K. & Wilson, M. A. Memory of sequential experience in the hippocampus during slow wave sleep. Neuron 36, 1183–1194 (2002).
Foster, D. J. & Wilson, M. A. Reverse replay of behavioural sequences in hippocampal place cells during the awake state. Nature 440, 680–683 (2006).
Dragoi, G. & Tonegawa, S. Preplay of future place cell sequences by hippocampal cellular assemblies. Nature 469, 397–401 (2011).
Girardeau, G., Benchenane, K., Wiener, S. I., Buzsáki, G. & Zugaro, M. B. Selective suppression of hippocampal ripples impairs spatial memory. Nat. Neurosci. 12, 1222–1223 (2009).
Pfeiffer, B. E. & Foster, D. J. Hippocampal place-cell sequences depict future paths to remembered goals. Nature 497, 74–79 (2013).
Yu, J. Y. et al. Distinct hippocampal-cortical memory representations for experiences associated with movement versus immobility. eLife 6, e27621 (2017).
Pfeiffer, B. E. & Foster, D. J. Autoassociative dynamics in the generation of sequences of hippocampal place cells. Science 349, 180–183 (2015).
Stella, F., Baracskay, P., O’Neill, J. & Csicsvari, J. Hippocampal reactivation of random trajectories resembling Brownian diffusion. Neuron 102, 450–461 (2019).
Farooq, U. & Dragoi, G. Emergence of preconfigured and plastic time-compressed sequences in early postnatal development. Science 363, 168–173 (2019).
Azizi, A. H., Wiskott, L. & Cheng, S. A computational model for preplay in the hippocampus. Front. Comput. Neurosci. 7, 161 (2013).
Romani, S. & Tsodyks, M. Short-term plasticity based network model of place cells dynamics. Hippocampus 25, 94–105 (2015).
Chu, T. et al. Firing rate adaptation affords place cell theta sweeps, phase precession, and procession. eLife 12, RP87055 (2024).
Granit, R., Kernell, D. & Shortess, G. Quantitative aspects of repetitive firing of mammalian motoneurones, caused by injected currents. J. Physiol. 168, 911 (1963).
Lancaster, B. & Nicoll, R. Properties of two calcium-activated hyperpolarizations in rat hippocampal neurones. J. Physiol. 389, 187–203 (1987).
Barkai, E. & Hasselmo, M. E. Modulation of the input/output function of rat piriform cortex pyramidal cells. J. Neurophysiol. 72, 644–658 (1994).
Connors, B. W. & Gutnick, M. J. Intrinsic firing patterns of diverse neocortical neurons. Trends Neurosci. 13, 99–104 (1990).
Madison, D. & Nicoll, R. Control of the repetitive discharge of rat CA1 pyramidal neurones in vitro. J. Physiol. 354, 319–331 (1984).
Zucker, R. S. Short-term synaptic plasticity. Annu. Rev. Neurosci. 12, 13–31 (1989).
Liljenström, H. & Hasselmo, M. E. Acetylcholine and cortical oscillatory dynamics. In Computation and Neural Systems pp. 523–530 (Springer US, Boston, MA, 1993).
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).
Zhang, K. Representation of spatial orientation by the intrinsic dynamics of the head-direction cell ensemble: a theory. J. Neurosci. 16, 2112–2126 (1996).
Tsodyks, M. Attractor neural network models of spatial maps in hippocampus. Hippocampus 9, 481–489 (1999).
Burak, Y. & Fiete, I. R. Accurate path integration in continuous attractor network models of grid cells. PLoS Comput. Biol. 5, e1000291 (2009).
McNamee, D. C., Stachenfeld, K. L., Botvinick, M. M. & Gershman, S. J. Flexible modulation of sequence generation in the entorhinal–hippocampal system. Nat. Neurosci. 24, 851–862 (2021).
Stachenfeld, K. L., Botvinick, M. M. & Gershman, S. J. The hippocampus as a predictive map. Nat. Neurosci. 20, 1643–1653 (2017).
Yu, C., Behrens, T. E. & Burgess, N. Prediction and generalisation over directed actions by grid cells. In ICLR 2021-9th International Conference on Learning Representations. https://arxiv.org/abs/2006.03355 (2021).
Hopfield, J. J. Neurodynamics of mental exploration. Proc. Natl. Acad. Sci. USA 107, 1648–1653 (2010).
Itskov, V., Curto, C., Pastalkova, E. & Buzsáki, G. Cell assembly sequences arising from spike threshold adaptation keep track of time in the hippocampus. J. Neurosci. 31, 2828–2834 (2011).
Fuhrmann, G., Markram, H. & Tsodyks, M. Spike frequency adaptation and neocortical rhythms. J. Neurophysiol. 88, 761–770 (2002).
Benda, J. & Herz, A. V. A universal model for spike-frequency adaptation. Neural Comput. 15, 2523–2564 (2003).
Mi, Y., Fung, C., Wong, K. & Wu, S. Spike frequency adaptation implements anticipative tracking in continuous attractor neural networks. Adv. Neural Inf. Process. Syst. 27 (2014).
Krause, E. L. & Drugowitsch, J. A large majority of awake hippocampal sharp-wave ripples feature spatial trajectories with momentum. Neuron 110, 722–733 (2022).
Denovellis, E. L. et al. Hippocampal replay of experience at real-world speeds. eLife 10, e64505 (2021).
Bracewell, R. N. The Fourier Transform and its Applications Vol. 31999 (McGraw-Hill New York, 1986).
Karlsson, M., Carr, M. & Frank, L. Simultaneous extracellular recordings from hippocampal areas CA1 and CA3 (or MEC and CA1) from rats performing an alternation task in two W-shapped tracks that are geometrically identically but visually distinct. CRCNS https://doi.org/10.6080/K0NK3BZJ (2015).
Deng, X., Liu, D. F., Kay, K., Frank, L. M. & Eden, U. T. Clusterless decoding of position from multiunit activity using a marked point process filter. Neural Comput. 27, 1438–1460 (2015).
Battaglia, F. P., Sutherland, G. R. & McNaughton, B. L. Local sensory cues and place cell directionality: additional evidence of prospective coding in the hippocampus. J. Neurosci. 24, 4541–4550 (2004).
Parra-Barrero, E., Diba, K. & Cheng, S. Neuronal sequences during theta rely on behavior-dependent spatial maps. eLife 10, e70296 (2021).
Tsodyks, M. V., Skaggs, W. E., Sejnowski, T. J. & McNaughton, B. L. Population dynamics and theta rhythm phase precession of hippocampal place cell firing: a spiking neuron model. Hippocampus 6, 271–280 (1996).
Hasselmo, M. E., Schnell, E. & Barkai, E. Dynamics of learning and recall at excitatory recurrent synapses and cholinergic modulation in rat hippocampal region CA3. J. Neurosci. 15, 5249–5262 (1995).
Saravanan, V. et al. Transition between encoding and consolidation/replay dynamics via cholinergic modulation of can current: a modeling study. Hippocampus 25, 1052–1070 (2015).
Pietras, B., Schmutz, V. & Schwalger, T. Mesoscopic description of hippocampal replay and metastability in spiking neural networks with short-term plasticity. PLoS Comput. Biol. 18, e1010809 (2022).
Singh, D., Norman, K. A. & Schapiro, A. C. A model of autonomous interactions between hippocampus and neocortex driving sleep-dependent memory consolidation. Proc. Natl. Acad. Sci. USA 119, e2123432119 (2022).
McNamee, D. C. The generative neural microdynamics of cognitive processing. Curr. Opin. Neurobiol. 85, 102855 (2024).
Schlesiger, M. I. et al. The medial entorhinal cortex is necessary for temporal organization of hippocampal neuronal activity. Nat. Neurosci. 18, 1123–1132 (2015).
Yamamoto, J. & Tonegawa, S. Direct medial entorhinal cortex input to hippocampal CA1 is crucial for extended quiet awake replay. Neuron 96, 217–227 (2017).
Wills, T. J., Lever, C., Cacucci, F., Burgess, N. & O’Keefe, J. Attractor dynamics in the hippocampal representation of the local environment. Science 308, 873–876 (2005).
Sato, N. & Yamaguchi, Y. Memory encoding by theta phase precession in the hippocampal network. Neural Comput. 15, 2379–2397 (2003).
Van de Ven, G. M., Trouche, S., McNamara, C. G., Allen, K. & Dupret, D. Hippocampal offline reactivation consolidates recently formed cell assembly patterns during sharp wave-ripples. Neuron 92, 968–974 (2016).
Mallory, C. S., Widloski, J. & Foster, D. J. The time course and organization of hippocampal replay. Science 387, 541–548 (2025).
Dong, X. et al. Adaptation accelerating sampling-based Bayesian inference in attractor neural networks. Adv. Neural Inf. Process. Syst. 35, 21534–21547 (2022).
Benda, J., Longtin, A. & Maler, L. Spike-frequency adaptation separates transient communication signals from background oscillations. J. Neurosci. 25, 2312–2321 (2005).
Karlsson, M. P. & Frank, L. M. Network dynamics underlying the formation of sparse, informative representations in the hippocampus. J. Neurosci. 28, 14271–14281 (2008).
Kay, K. et al. A hippocampal network for spatial coding during immobility and sleep. Nature 531, 185–190 (2016).
Mizuseki, K., Diba, K., Pastalkova, E. & Buzsáki, G. Hippocampal CA1 pyramidal cells form functionally distinct sublayers. Nat. Neurosci. 14, 1174–1181 (2011).
Davidson, T. J., Kloosterman, F. & Wilson, M. A. Hippocampal replay of extended experience. Neuron 63, 497–507 (2009).
Dong, X., Chu, T., Huang, T., Ji, Z. & Wu, S. Noisy adaptation generates lévy flights in attractor neural networks. Adv. Neural Inf. Process. Syst. 34, 16791–16804 (2021).
Fung, C. A., Wong, K. M. & Wu, S. Dynamics of neural networks with continuous attractors. Europhys. Lett. 84, 18002 (2008).
Fung, C. A., Wong, K. M. & Wu, S. A moving bump in a continuous manifold: a comprehensive study of the tracking dynamics of continuous attractor neural networks. Neural Comput. 22, 752–792 (2010).
Acknowledgements
We thank Eric Denovellis for sharing the code of the state space decoder. We thank Loren Frank and colleagues for making the experimental data available online. We thank Kenneth Kay, Thomas Wills, Mattias Horan, Wentao Qiu, and Wenhao Zhang for valuable discussions. This work was supported by: a National Key Research and Development Program of China (2024YFF1206500, S.W.), a Wellcome Principal Research Fellowship (NB), a UKRI Frontier Research Grant (EP/X023060/1, D.B.), and an International Postdoctoral Exchange Fellowship Program (PC2021005, Z.J.).
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Z.J., T.C., X.D., N.B., and S.W. conceptualised and designed the research. Z.J. analysed the experimental data with the input from N.B. Z.J., T.C., X.D., and C.Y. performed theoretical analysis and simulations. D.B. and N.B. supervised the analysis of experimental data, and S.W. supervised the analysis of theoretical modelling. Z.J., N.B., and S.W. wrote the manuscript with the input from all the other authors.
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Ji, Z., Chu, T., Dong, X. et al. Dynamical modulation of hippocampal replay through firing rate adaptation. Nat Commun (2026). https://doi.org/10.1038/s41467-025-68042-3
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DOI: https://doi.org/10.1038/s41467-025-68042-3
