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.

  • Review Article
  • Published:

A neural manifold view of the brain

Nature Neuroscience volume 28, pages 1582–1597 (2025)Cite this article

Subjects

Abstract

Animal behavior arises from the coordinated activity of neural populations that span the entire brain. The activity of large neural populations from an increasing number of brain regions, behaviors and species shows low-dimensional structure. We posit that this structure arises as a result of neural manifolds. Neural manifolds are mathematical descriptions of a meaningful biological entity: the possible collective states of a population of neurons given the constraints, both intrinsic (for example, connectivity) and extrinsic (for example, behavior), to the neural circuit. Here, we explore the link between neural manifolds and behavior, and discuss the insights that the neural manifold framework can provide into brain function. To conclude, we explore existing conceptual gaps in this framework and discuss their implications when building an integrative view of brain function. We thus position neural manifolds as a crucial framework with which to describe how the brain generates behavior.

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

Access options

Buy this article

  • Purchase on SpringerLink
  • Instant access to the full article PDF.

USD 39.95

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

Fig. 1: Neural manifolds underlying the generation of behavior by the brain.
Fig. 2: Examples of neural manifolds estimated from behaving animals.
Fig. 3: Factors shaping the emergence of neural manifolds.
Fig. 4: Neural manifolds are shaped over various timescales.
Fig. 5: Using causal manipulations to characterize neural manifolds.

Similar content being viewed by others

References

  1. Ramón y Cajal, S. Textura del sistema nervioso del hombre y de los vertebrados: estudios sobre el plan estructural y composición histológica de los centros nerviosos adicionados de consideraciones fisiológicas fundadas en los nuevos descubrimientos (N. Moya, 1899).

  2. Georgopoulos, A. P., Kalaska, J. F., Caminiti, R. & Massey, J. T. On the relations between the direction of two-dimensional arm movements and cell discharge in primate motor cortex. J. Neurosci. 2, 1527–1537 (1982).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  3. Humphrey, D. R., Schmidt, E. M. & Thompson, W. D. Predicting measures of motor performance from multiple cortical spike trains. Science 170, 758–762 (1970).

    Article  CAS  PubMed  Google Scholar 

  4. Hubel, D. H. & Wiesel, T. N. Receptive fields, binocular interaction and functional architecture in the cat’s visual cortex. J. Physiol. 160, 106–154 (1962).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  5. 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 

  6. Brodmann, K. Vergleichende Lokalisationslehre der Grosshirnrinde in ihren Prinzipien dargestellt auf Grund des Zellenbaues (Barth, 1909).

  7. Gallego, J. A., Perich, M. G., Miller, L. E. & Solla, S. A. Neural manifolds for the control of movement. Neuron 94, 978–984 (2017).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  8. Perich, M. G. & Rajan, K. Rethinking brain-wide interactions through multi-region ‘network of networks’ models. Curr. Opin. Neurobiol. 65, 146–151 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  9. Vyas, S., Golub, M. D., Sussillo, D. & Shenoy, K. V. Computation through neural population dynamics. Annu. Rev. Neurosci. 43, 249–275 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  10. Mante, V., Sussillo, D., Shenoy, K. V. & Newsome, W. T. Context-dependent computation by recurrent dynamics in prefrontal cortex. Nature 503, 78–84 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  11. Churchland, M. M. & Shenoy, K. V. Temporal complexity and heterogeneity of single-neuron activity in premotor and motor cortex. J. Neurophysiol. 97, 4235–4257 (2007).

    Article  PubMed  Google Scholar 

  12. Machens, C. K., Romo, R. & Brody, C. D. Functional, but not anatomical, separation of ‘what’ and ‘when’ in prefrontal cortex. J. Neurosci. 30, 350–360 (2010).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  13. Stevenson, I. H. & Kording, K. P. How advances in neural recording affect data analysis. Nat. Neurosci. 14, 139–142 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  14. Jun, J. J. et al. Fully integrated silicon probes for high-density recording of neural activity. Nature 551, 232–236 (2017).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  15. Ahrens, M. B., Orger, M. B., Robson, D. N., Li, J. M. & Keller, P. J. Whole-brain functional imaging at cellular resolution using light-sheet microscopy. Nat. Methods 10, 413–420 (2013).

    Article  CAS  PubMed  Google Scholar 

  16. Chen, T. -W. et al. Ultrasensitive fluorescent proteins for imaging neuronal activity. Nature 499, 295–300 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  17. Cunningham, J. P. & Yu, B. M. Dimensionality reduction for large-scale neural recordings. Nat. Neurosci. 17, 1500–1509 (2014).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  18. Saxena, S. & Cunningham, J. P. Towards the neural population doctrine. Curr. Opin. Neurobiol. 55, 103–111 (2019).

    Article  CAS  PubMed  Google Scholar 

  19. Wang, J., Narain, D., Hosseini, E. A. & Jazayeri, M. Flexible timing by temporal scaling of cortical responses. Nat. Neurosci. 21, 102–110 (2018).

    Article  CAS  PubMed  Google Scholar 

  20. Wang, Y. et al. Heterogeneity in the pyramidal network of the medial prefrontal cortex. Nat. Neurosci. 9, 534–542 (2006).

    Article  CAS  PubMed  Google Scholar 

  21. Riemann, B. On the Hypotheses Which Lie at the Bases of Geometry (Birkhäuser, 2016).

  22. Dubrovin, B. A., Fomenko, A. T. & Novikov, S. P. Modern Geometry—Methods and Applications: Part II: The Geometry and Topology of Manifolds (Springer Science & Business Media, 2012).

  23. Sadtler, P. T. et al. Neural constraints on learning. Nature 512, 423–426 (2014).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  24. Mitchell-Heggs, R., Prado, S., Gava, G. P., Go, M. A. & Schultz, S. R. Neural manifold analysis of brain circuit dynamics in health and disease. J. Comput. Neurosci. 51, 1–21 (2023).

    Article  PubMed  Google Scholar 

  25. Stopfer, M., Jayaraman, V. & Laurent, G. Intensity versus identity coding in an olfactory system. Neuron 39, 991–1004 (2003).

    Article  CAS  PubMed  Google Scholar 

  26. Briggman, K. L., Abarbanel, H. D. I. & Kristan, W. B. Jr. Optical imaging of neuronal populations during decision-making. Science 307, 896–901 (2005).

    Article  CAS  PubMed  Google Scholar 

  27. Kato, S. et al. Global brain dynamics embed the motor command sequence of Caenorhabditis elegans. Cell 163, 656–669 (2015).

    Article  CAS  PubMed  Google Scholar 

  28. Bruno, A. M., Frost, W. N. & Humphries, M. D. A spiral attractor network drives rhythmic locomotion. Elife 6, e27342 (2017).

    Article  PubMed  PubMed Central  Google Scholar 

  29. Ahrens, M. B. et al. Brain-wide neuronal dynamics during motor adaptation in zebrafish. Nature 485, 471–477 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  30. Andalman, A. S. et al. Neuronal dynamics regulating brain and behavioral state transitions. Cell 177, 970–985 (2019).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  31. Petrucco, L. et al. Neural dynamics and architecture of the heading direction circuit in zebrafish. Nat. Neurosci. 26, 765–773 (2023).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  32. Churchland, M. M. et al. Neural population dynamics during reaching. Nature 487, 51–56 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  33. Raposo, D., Kaufman, M. T. & Churchland, A. K. A category-free neural population supports evolving demands during decision-making. Nat. Neurosci. 17, 1784–1792 (2014).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  34. Sauerbrei, B. A. et al. Cortical pattern generation during dexterous movement is input-driven. Nature 577, 386–391 (2020).

    Article  CAS  PubMed  Google Scholar 

  35. Stringer, C. et al. Spontaneous behaviors drive multidimensional, brainwide activity. Science 364, 255 (2019).

    Article  PubMed  PubMed Central  Google Scholar 

  36. Miri, A. et al. Behaviorally selective engagement of short-latency effector pathways by motor cortex. Neuron 95, 683–696 (2017).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  37. Rubin, A. et al. Revealing neural correlates of behavior without behavioral measurements. Nat. Commun. 10, 4745 (2019).

    Article  PubMed  PubMed Central  Google Scholar 

  38. Chen, H. -T., Manning, J. R. & van der Meer, M. A. A. Between-subject prediction reveals a shared representational geometry in the rodent hippocampus. Curr. Biol. 31, 4293–4304 (2021).

    Article  CAS  PubMed  Google Scholar 

  39. Yoo, S. B. M. & Hayden, B. Y. The transition from evaluation to selection involves neural subspace reorganization in core reward regions. Neuron 105, 712–724 (2020).

    Article  CAS  PubMed  Google Scholar 

  40. Cueva, C. J. et al. Low-dimensional dynamics for working memory and time encoding. Proc. Natl Acad. Sci. USA 117, 23021–23032 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  41. Sohn, H., Narain, D., Meirhaeghe, N. & Jazayeri, M. Bayesian computation through cortical latent dynamics. Neuron 103, 934–947 (2019).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  42. Hennig, J. A. et al. Learning is shaped by abrupt changes in neural engagement. Nat. Neurosci. 24, 727–736 (2021).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  43. Gallego, J. A. et al. Cortical population activity within a preserved neural manifold underlies multiple motor behaviors. Nat. Commun. 9, 4233 (2018).

    Article  PubMed  PubMed Central  Google Scholar 

  44. Stavisky, S. D. et al. Neural ensemble dynamics in dorsal motor cortex during speech in people with paralysis. Elife 8, e46015 (2019).

    Article  PubMed  PubMed Central  Google Scholar 

  45. Pandarinath, C. et al. Neural population dynamics in human motor cortex during movements in people with ALS. Elife 4, e07436 (2015).

    Article  PubMed  PubMed Central  Google Scholar 

  46. Minxha, J., Adolphs, R., Fusi, S., Mamelak, A. N. & Rutishauser, U. Flexible recruitment of memory-based choice representations by the human medial frontal cortex. Science 368, eaba3313 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  47. Dekleva, B. M. et al. Motor cortex retains and reorients neural dynamics during motor imagery. Nat. Hum. Behav. 8, 729–742 (2024).

    Article  PubMed  PubMed Central  Google Scholar 

  48. Perich, M. G. et al. Motor cortical dynamics are shaped by multiple distinct subspaces during naturalistic behavior. Preprint at bioRxiv https://doi.org/10.1101/2020.07.30.228767 (2020).

  49. Kobak, D., Pardo-Vazquez, J. L., Valente, M., Machens, C. K. & Renart, A. State-dependent geometry of population activity in rat auditory cortex. Elife 8, e44526 (2019).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  50. Gardner, R. J. et al. Toroidal topology of population activity in grid cells. Nature 602, 123–128 (2022).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  51. Ebitz, R. B. & Hayden, B. Y. The population doctrine in cognitive neuroscience. Neuron 109, 3055–3068 (2021).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  52. Jurewicz, K., Sleezer, B. J., Mehta, P. S., Hayden, B. Y. & Ebitz, R. B. Irrational choices via a curvilinear representational geometry for value. Nat. Commun. 15, 6424 (2024).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  53. Gallego, J. A., Perich, M. G., Chowdhury, R. H., Solla, S. A. & Miller, L. E. Long-term stability of cortical population dynamics underlying consistent behavior. Nat. Neurosci. 23, 260–270 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  54. Russo, A. A. et al. Motor cortex embeds muscle-like commands in an untangled population response. Neuron 97, 953–966 (2018).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  55. Chaudhuri, R., Gerçek, B., Pandey, B., Peyrache, A. & Fiete, I. The intrinsic attractor manifold and population dynamics of a canonical cognitive circuit across waking and sleep. Nat. Neurosci. 22, 1512–1520 (2019).

    Article  CAS  PubMed  Google Scholar 

  56. Lindén, H., Petersen, P. C., Vestergaard, M. & Berg, R. W. Movement is governed by rotational neural dynamics in spinal motor networks. Nature 610, 526–531 (2022).

    Article  PubMed  Google Scholar 

  57. Gmaz, J. M. & van der Meer, M. A. A. Context coding in the mouse nucleus accumbens modulates motivationally relevant information. PLoS Biol. 20, e3001338 (2022).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  58. Lanore, F., Cayco-Gajic, N. A., Gurnani, H., Coyle, D. & Silver, R. A. Cerebellar granule cell axons support high-dimensional representations. Nat. Neurosci. 24, 1142–1150 (2021).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  59. Safaie, M. et al. Preserved neural dynamics across animals performing similar behaviour. Nature https://doi.org/10.1038/s41586-023-06714-0 (2023).

    Article  PubMed  PubMed Central  Google Scholar 

  60. Ayar, E. C., Heusser, M. R., Bourrelly, C. & Gandhi, N. J. Distinct context- and content-dependent population codes in superior colliculus during sensation and action. Proc. Natl Acad. Sci. USA 120, e2303523120 (2023).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  61. Allsop, S. A. et al. Corticoamygdala transfer of socially derived information gates observational learning. Cell 173, 1329–1342 (2018).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  62. Nair, A. et al. An approximate line attractor in the hypothalamus encodes an aggressive state. Cell 186, 178–193 (2023).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  63. Jahn, C. I. et al. Learning attentional templates for value-based decision-making. Cell 187, 1476–1489 (2024).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  64. Markanday, A., Hong, S., Inoue, J., De Schutter, E. & Thier, P. Multidimensional cerebellar computations for flexible kinematic control of movements. Nat. Commun. 14, 2548 (2023).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  65. Vinograd, A., Nair, A., Kim, J. H., Linderman, S. W. & Anderson, D. J. Causal evidence of a line attractor encoding an affective state. Nature 634, 910–918 (2024).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  66. Talpir, I. & Livneh, Y. Stereotyped goal-directed manifold dynamics in the insular cortex. Cell Rep. 43, 114027 (2024).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  67. Bush, N. E. & Ramirez, J. -M. Latent neural population dynamics underlying breathing, opioid-induced respiratory depression and gasping. Nat. Neurosci. 27, 259–271 (2024).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  68. Nieh, E. H. et al. Geometry of abstract learned knowledge in the hippocampus. Nature 595, 80–84 (2021).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  69. Schneider, S., Lee, J. H. & Mathis, M. W. Learnable latent embeddings for joint behavioural and neural analysis. Nature 617, 360–368 (2023).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  70. Sun, X. et al. Cortical preparatory activity indexes learned motor memories. Nature 602, 274–279 (2022).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  71. Perich, M. G., Gallego, J. A. & Miller, L. E. A neural population mechanism for rapid learning. Neuron 100, 964–976 (2018).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  72. Cowley, B. R. et al. Slow drift of neural activity as a signature of impulsivity in macaque visual and prefrontal cortex. Neuron 108, 551–567 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  73. Churchland, M. M. & Shenoy, K. V. Preparatory activity and the expansive null-space. Nat. Rev. Neurosci. 25, 213–236 (2024).

    Article  CAS  PubMed  Google Scholar 

  74. Vyas, S. et al. Neural population dynamics underlying motor learning transfer. Neuron 97, 1177–1186 (2018).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  75. Kaufman, M. T., Churchland, M. M., Ryu, S. I. & Shenoy, K. V. Cortical activity in the null space: permitting preparation without movement. Nat. Neurosci. 17, 440–448 (2014).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  76. Elsayed, G. F., Lara, A. H., Kaufman, M. T., Churchland, M. M. & Cunningham, J. P. Reorganization between preparatory and movement population responses in motor cortex. Nat. Commun. 7, 13239 (2016).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  77. Javadzadeh, M. & Hofer, S. B. Dynamic causal communication channels between neocortical areas. Neuron 110, 2470–2483 (2022).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  78. Semedo, J. D., Zandvakili, A., Machens, C. K., Yu, B. M. & Kohn, A. Cortical areas interact through a communication subspace. Neuron 102, 249–259 (2019).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  79. Veuthey, T. L., Derosier, K., Kondapavulur, S. & Ganguly, K. Single-trial cross-area neural population dynamics during long-term skill learning. Nat. Commun. 11, 4057 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  80. Semedo, J. D. et al. Feedforward and feedback interactions between visual cortical areas use different population activity patterns. Nat. Commun. 13, 1099 (2022).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  81. Jazayeri, M. & Afraz, A. Navigating the neural space in search of the neural code. Neuron 93, 1003–1014 (2017).

    Article  CAS  PubMed  Google Scholar 

  82. Oby, E. R. et al. New neural activity patterns emerge with long-term learning. Proc. Natl Acad. Sci. USA 116, 15210–15215 (2019).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  83. Brennan, C. & Proekt, A. A quantitative model of conserved macroscopic dynamics predicts future motor commands. Elife 8, e46814 (2019).

    Article  PubMed  PubMed Central  Google Scholar 

  84. Hermansen, E., Klindt, D. A. & Dunn, B. A. Uncovering 2-D toroidal representations in grid cell ensemble activity during 1-D behavior. Nat. Commun. 15, 5429 (2024).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  85. Fortunato, C. et al. Nonlinear manifolds underlie neural population activity during behaviour. Preprint at bioRxiv https://doi.org/10.1101/2023.07.18.549575 (2023).

  86. Guo, W., Zhang, J. J., Newman, J. P. & Wilson, M. A. Latent learning drives sleep-dependent plasticity in distinct CA1 subpopulations. Cell Rep. 43, 115028 (2024).

    Article  CAS  PubMed  Google Scholar 

  87. Remington, E. D., Narain, D., Hosseini, E. A. & Jazayeri, M. Flexible sensorimotor computations through rapid reconfiguration of cortical dynamics. Neuron 98, 1005–1019 (2018).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  88. Okazawa, G., Hatch, C. E., Mancoo, A., Machens, C. K. & Kiani, R. Representational geometry of perceptual decisions in the monkey parietal cortex. Cell 184, 3748–3768 (2021).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  89. Langdon, C., Genkin, M. & Engel, T. A. A unifying perspective on neural manifolds and circuits for cognition. Nat. Rev. Neurosci. 24, 363–377 (2023).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  90. Tsodyks, M., Kenet, T., Grinvald, A. & Arieli, A. Linking spontaneous activity of single cortical neurons and the underlying functional architecture. Science 286, 1943–1946 (1999).

    Article  CAS  PubMed  Google Scholar 

  91. Okun, M. et al. Diverse coupling of neurons to populations in sensory cortex. Nature 521, 511–515 (2015).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  92. Marshel, J. H. et al. Cortical layer-specific critical dynamics triggering perception. Science 365, eaaw5202 (2019).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  93. Dahmen, D. et al. Strong and localized recurrence controls dimensionality of neural activity across brain areas. Preprint at bioRxiv https://doi.org/10.1101/2020.11.02.365072 (2023).

  94. Harris, K. D. & Shepherd, G. M. G. The neocortical circuit: themes and variations. Nat. Neurosci. 18, 170–181 (2015).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  95. Park, J. et al. Motor cortical output for skilled forelimb movement is selectively distributed across projection neuron classes. Sci. Adv. 8, eabj5167 (2022).

    Article  PubMed  PubMed Central  Google Scholar 

  96. Azcorra, M. et al. Unique functional responses differentially map onto genetic subtypes of dopamine neurons. Nat. Neurosci. 26, 1762–1774 (2023).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  97. Musall, S. et al. Pyramidal cell types drive functionally distinct cortical activity patterns during decision-making. Nat. Neurosci. 26, 495–505 (2023).

    CAS  PubMed  PubMed Central  Google Scholar 

  98. Bugeon, S. et al. A transcriptomic axis predicts state modulation of cortical interneurons. Nature 607, 330–338 (2022).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  99. Nakai, S., Kitanishi, T. & Mizuseki, K. Distinct manifold encoding of navigational information in the subiculum and hippocampus. Sci. Adv. 10, eadi4471 (2024).

    Article  PubMed  PubMed Central  Google Scholar 

  100. Lara, A. H., Cunningham, J. P. & Churchland, M. M. Different population dynamics in the supplementary motor area and motor cortex during reaching. Nat. Commun. 9, 2754 (2018).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  101. Stringer, C., Pachitariu, M., Steinmetz, N., Carandini, M. & Harris, K. D. High-dimensional geometry of population responses in visual cortex. Nature 571, 361–365 (2019).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  102. Recanatesi, S., Bradde, S., Balasubramanian, V., Steinmetz, N. A. & Shea-Brown, E. A scale-dependent measure of system dimensionality. Patterns 3, 100555 (2022).

    Article  PubMed  PubMed Central  Google Scholar 

  103. Park, J. et al. Conjoint specification of action by neocortex and striatum. Neuron 113, 620–636 (2025).

    Article  CAS  PubMed  Google Scholar 

  104. Kutsuwada, T. et al. Molecular diversity of the NMDA receptor channel. Nature 358, 36–41 (1992).

    Article  CAS  PubMed  Google Scholar 

  105. Nakanishi, S. Molecular diversity of glutamate receptors and implications for brain function. Science 258, 597–603 (1992).

    Article  CAS  PubMed  Google Scholar 

  106. Fişek, M. et al. Cortico-cortical feedback engages active dendrites in visual cortex. Nature https://doi.org/10.1038/s41586-023-06007-6 (2023).

    Article  PubMed  PubMed Central  Google Scholar 

  107. Srivastava, K. H. et al. Motor control by precisely timed spike patterns. Proc. Natl Acad. Sci. USA 114, 1171–1176 (2017).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  108. Riehle, A., Grün, S., Diesmann, M. & Aertsen, A. Spike synchronization and rate modulation differentially involved in motor cortical function. Science 278, 1950–1953 (1997).

    Article  CAS  PubMed  Google Scholar 

  109. Perea, G. et al. Activity-dependent switch of GABAergic inhibition into glutamatergic excitation in astrocyte-neuron networks. Elife 5, e20362 (2016).

    Article  PubMed  PubMed Central  Google Scholar 

  110. Mu, Y. et al. Glia accumulate evidence that actions are futile and suppress unsuccessful behavior. Cell 178, 27–43 (2019).

    Article  CAS  PubMed  Google Scholar 

  111. Hsueh, B. et al. Cardiogenic control of affective behavioural state. Nature 615, 292–299 (2023).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  112. Cahill, M. K. et al. Network-level encoding of local neurotransmitters in cortical astrocytes. Nature 629, 146–153 (2024).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  113. Gao, P. et al. A theory of multineuronal dimensionality, dynamics and measurement. Preprint at bioRxiv https://doi.org/10.1101/214262 (2017).

  114. Chung, S. & Abbott, L. F. Neural population geometry: an approach for understanding biological and artificial neural networks. Curr. Opin. Neurobiol. 70, 137–144 (2021).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  115. Zhou, J. et al. Evolving schema representations in orbitofrontal ensembles during learning. Nature 590, 606–611 (2021).

    Article  CAS  PubMed  Google Scholar 

  116. Shuvaev, S., Lachi, D., Koulakov, A. & Zador, A. Encoding innate ability through a genomic bottleneck. Proc. Natl Acad. Sci. USA 121, e2409160121 (2024).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  117. Driscoll, L. N., Shenoy, K. & Sussillo, D. Flexible multitask computation in recurrent networks utilizes shared dynamical motifs. Nat. Neurosci. 27, 1349–1363 (2024).

    Article  PubMed  PubMed Central  Google Scholar 

  118. Feulner, B. & Clopath, C. Neural manifold under plasticity in a goal driven learning behaviour. PLoS Comput. Biol. 17, e1008621 (2021).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  119. Simpson, G. G. The Baldwin effect. Evolution 7, 110–117 (1953).

    Article  Google Scholar 

  120. Hiesinger, P. R. The Self-Assembling Brain: How Neural Networks Grow Smarter (Princeton University Press, 2022).

  121. Mitchell, K. J. Innate: How the Wiring of Our Brains Shapes Who We Are (Princeton University Press, 2020).

  122. Martini, F. J., Guillamón-Vivancos, T., Moreno-Juan, V., Valdeolmillos, M. & López-Bendito, G. Spontaneous activity in developing thalamic and cortical sensory networks. Neuron 109, 2519–2534 (2021).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  123. Glanz, R. M., Sokoloff, G. & Blumberg, M. S. Neural decoding reveals specialized kinematic tuning after an abrupt cortical transition. Cell Rep. 42, 113119 (2023).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  124. Maimon-Mor, R. O., Schone, H. R., Henderson Slater, D., Faisal, A. A. & Makin, T. R. Early life experience sets hard limits on motor learning as evidenced from artificial arm use. Elife 10, e66320 (2021).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  125. Seelig, J. D. & Jayaraman, V. Neural dynamics for landmark orientation and angular path integration. Nature 521, 186–191 (2015).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  126. O’Shea, D. J. et al. Direct neural perturbations reveal a dynamical mechanism for robust computation. Preprint at bioRxiv https://doi.org/10.1101/2022.12.16.520768 (2022).

  127. Dowling, M., Zhao, Y. & Park, I. M. eXponential FAmily Dynamical Systems (XFADS): large-scale nonlinear Gaussian state-space modeling. In Advances in Neural Information Processing Systems 38 (2024).

  128. Zhang, F. et al. Multimodal fast optical interrogation of neural circuitry. Nature 446, 633–639 (2007).

    Article  CAS  PubMed  Google Scholar 

  129. Lovett-Barron, M. et al. Ancestral circuits for the coordinated modulation of brain state. Cell 171, 1411–1423 (2017).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  130. Sylwestrak, E. L. et al. Cell-type-specific population dynamics of diverse reward computations. Cell 185, 3568–3587 (2022).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  131. Esparza, J. et al. Cell-type-specific manifold analysis discloses independent geometric transformations in the hippocampal spatial code. Neuron https://doi.org/10.1016/j.neuron.2025.01.022 (2025).

    Article  PubMed  Google Scholar 

  132. Chan, K. Y. et al. Engineered AAVs for efficient noninvasive gene delivery to the central and peripheral nervous systems. Nat. Neurosci. 20, 1172–1179 (2017).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  133. Cardin, J. A. et al. Targeted optogenetic stimulation and recording of neurons in vivo using cell-type-specific expression of Channelrhodopsin-2. Nat. Protoc. 5, 247–254 (2010).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  134. Economo, M. N. et al. A platform for brain-wide imaging and reconstruction of individual neurons. Elife 5, e10566 (2016).

    Article  PubMed  PubMed Central  Google Scholar 

  135. Prinz, A. A., Bucher, D. & Marder, E. Similar network activity from disparate circuit parameters. Nat. Neurosci. 7, 1345–1352 (2004).

    Article  CAS  PubMed  Google Scholar 

  136. Randi, F., Sharma, A. K., Dvali, S. & Leifer, A. M. Neural signal propagation atlas of Caenorhabditis elegans. Nature 623, 406–414 (2023).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  137. Pospisil, D. A. et al. The fly connectome reveals a path to the effectome. Nature 634, 201–209 (2024).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  138. Roth, B. L. DREADDs for neuroscientists. Neuron 89, 683–694 (2016).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  139. Krakauer, J. W., Ghazanfar, A. A., Gomez-Marin, A., MacIver, M. A. & Poeppel, D. Neuroscience needs behavior: correcting a reductionist bias. Neuron 93, 480–490 (2017).

    Article  CAS  PubMed  Google Scholar 

  140. Gomez-Marin, A. & Ghazanfar, A. A. The life of behavior. Neuron 104, 25–36 (2019).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  141. Gmaz, J. M., Keller, J. A., Dudman, J. T. & Gallego, J. A. Integrating across behaviors and timescales to understand the neural control of movement. Curr. Opin. Neurobiol. 85, 102843 (2024).

    Article  CAS  PubMed  Google Scholar 

  142. Mizes, K. G. C., Lindsey, J., Escola, G. S. & Ölveczky, B. P. Dissociating the contributions of sensorimotor striatum to automatic and visually guided motor sequences. Nat. Neurosci. 26, 1791–1804 (2023).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  143. Ganguly, K. & Carmena, J. M. Emergence of a stable cortical map for neuroprosthetic control. PLoS Biol. 7, e1000153 (2009).

    Article  PubMed  PubMed Central  Google Scholar 

  144. Lai, C., Tanaka, S., Harris, T. D. & Lee, A. K. Volitional activation of remote place representations with a hippocampal brain-machine interface. Science 382, 566–573 (2023).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  145. Barack, D. L. & Krakauer, J. W. Two views on the cognitive brain. Nat. Rev. Neurosci. 22, 359–371 (2021).

    Article  CAS  PubMed  Google Scholar 

  146. Humphreys, P. Emergence: a Philosophical Account (Oxford University Press, 2016).

  147. Kim, J. Emergence: core ideas and issues. Synthese 151, 547–559 (2006).

    Article  Google Scholar 

  148. Anderson, P. W. More is different. Science https://doi.org/10.1126/science.177.4047.393 (1972).

    Article  PubMed  Google Scholar 

  149. Marder, E. & Goaillard, J. -M. Variability, compensation and homeostasis in neuron and network function. Nat. Rev. Neurosci. 7, 563–574 (2006).

    Article  CAS  PubMed  Google Scholar 

  150. Kilgard, M. P. et al. Sensory input directs spatial and temporal plasticity in primary auditory cortex. J. Neurophysiol. 86, 326–338 (2001).

    Article  CAS  PubMed  Google Scholar 

  151. Chang, J. C., Perich, M. G., Miller, L. E., Gallego, J. A. & Clopath, C. De novo motor learning creates structure in neural activity that shapes adaptation. Nat. Commun. 15, 4084 (2024).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  152. Degenhart, A. D. et al. Stabilization of a brain-computer interface via the alignment of low-dimensional spaces of neural activity. Nat. Biomed. Eng. 4, 672–685 (2020).

    Article  PubMed  PubMed Central  Google Scholar 

  153. Lee, J. Introduction to Topological Manifolds (Springer Science & Business Media, 2010).

  154. Dijkstra, J. J. & van Mill, J. Erdos Space and Homeomorphism Groups of Manifolds (American Mathematical Society, 2010).

  155. Jazayeri, M. & Ostojic, S. Interpreting neural computations by examining intrinsic and embedding dimensionality of neural activity. Curr. Opin. Neurobiol. 70, 113–120 (2021).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  156. Manley, J. et al. Simultaneous, cortex-wide dynamics of up to 1 million neurons reveal unbounded scaling of dimensionality with neuron number. Neuron 112, 1694–1709 (2024).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  157. Marshall, N. J. et al. Flexible neural control of motor units. Nat. Neurosci. 25, 1492–1504 (2022).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  158. Trautmann, E. M. et al. Accurate estimation of neural population dynamics without spike sorting. Neuron 103, 292–308 (2019).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  159. DePasquale, B., Sussillo, D., Abbott, L. F. & Churchland, M. M. The centrality of population-level factors to network computation is demonstrated by a versatile approach for training spiking networks. Neuron 111, 631–649 (2023).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  160. Kobak, D. et al. Demixed principal component analysis of neural population data. Elife 5, e10989 (2016).

    Article  PubMed  PubMed Central  Google Scholar 

  161. Aoi, M. C., Mante, V. & Pillow, J. W. Prefrontal cortex exhibits multidimensional dynamic encoding during decision-making. Nat. Neurosci. 23, 1410–1420 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  162. Pandarinath, C. et al. Inferring single-trial neural population dynamics using sequential auto-encoders. Nat. Methods 15, 805–815 (2018).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  163. Hurwitz, C. et al. Targeted neural dynamical modeling. Adv. Neural Inf. Process. Syst. 34, 29379–29392 (2021).

    Google Scholar 

  164. Gosztolai, A., Peach, R. L., Arnaudon, A., Barahona, M. & Vandergheynst, P. MARBLE: interpretable representations of neural population dynamics using geometric deep learning. Nat. Methods 22, 612–620 (2025).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  165. Tenenbaum, J. B., de Silva, V. & Langford, J. C. A global geometric framework for nonlinear dimensionality reduction. Science 290, 2319–2323 (2000).

    Article  CAS  PubMed  Google Scholar 

  166. Balasubramanian, M. & Schwartz, E. L. The isomap algorithm and topological stability. Science 295, 7 (2002).

    Article  PubMed  Google Scholar 

  167. Roweis, S. T. & Saul, L. K. Nonlinear dimensionality reduction by locally linear embedding. Science 290, 2323–2326 (2000).

    Article  CAS  PubMed  Google Scholar 

  168. Lafon, S., Keller, Y. & Coifman, R. R. Data fusion and multicue data matching by diffusion maps. IEEE Trans. Pattern Anal. Mach. Intell. 28, 1784–1797 (2006).

    Article  PubMed  Google Scholar 

  169. Belkin, M. & Niyogi, P. Laplacian eigenmaps for dimensionality reduction and data representation. Neural Comput. 15, 1373–1396 (2003).

    Article  Google Scholar 

  170. van der Maaten, L. & Hinton, G. Visualizing data using t-SNE. J. Machine Learn. Res. 9, 2579–2605 (2008).

  171. McInnes, L., Healy, J. & Melville, J. UMAP: uniform manifold approximation and projection for dimension reduction. Preprint at https://arxiv.org/abs/1802.03426 (2018).

  172. Zhang, Z. & Zha, H. Principal manifolds and nonlinear dimensionality reduction via tangent space alignment. SIAM J. Sci. Comput. 26, 313–338 (2004).

    Article  Google Scholar 

  173. Kohli, D., Cloninger, A. & Mishne, G. LDLE: Low distortion local eigenmaps. J. Mach. Learn. Res. 22, 1–64 (2021).

    Google Scholar 

  174. Kohli, D., Nieuwenhuis, J., S., Cloninger, A., Mishne, G. & Narain, D. RATS: Unsupervised manifold learning using low-distortion alignment of tangent spaces. Preprint at bioRxiv https://doi.org/10.1101/2024.10.31.621292 (2024).

  175. Rajan, K., Abbott, L. F. & Sompolinsky, H. Stimulus-dependent suppression of chaos in recurrent neural networks. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 82, 011903 (2010).

    Article  PubMed  PubMed Central  Google Scholar 

  176. Mastrogiuseppe, F. & Ostojic, S. Linking connectivity, dynamics, and computations in low-rank recurrent neural networks. Neuron 99, 609–623 (2018).

  177. Rajan, K., Harvey, C. D. & Tank, D. W. Recurrent network models of sequence generation and memory. Neuron 90, 128–142 (2016).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  178. Perich, M. G. et al. Inferring brain-wide interactions using data-constrained recurrent neural network models. Preprint at bioRxiv https://doi.org/10.1101/2020.12.18.423348 (2021).

  179. Fisher, D., Olasagasti, I., Tank, D. W., Aksay, E. R. F. & Goldman, M. S. A modeling framework for deriving the structural and functional architecture of a short-term memory microcircuit. Neuron 79, 987–1000 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  180. Dinc, F., Shai, A., Schnitzer, M. & Tanaka, H. CORNN: convex optimization of recurrent neural networks for rapid inference of neural dynamics. In Advances in Neural Information Processing Systems 36 https://proceedings.neurips.cc/paper_files/paper/2023/file/a103529738706979331778377f2d5864-Paper-Conference.pdf (2023).

  181. Laje, R. & Buonomano, D. V. Robust timing and motor patterns by taming chaos in recurrent neural networks. Nat. Neurosci. 16, 925–933 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  182. Sussillo, D. & Abbott, L. F. Generating coherent patterns of activity from chaotic neural networks. Neuron 63, 544–557 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  183. Sussillo, D., Churchland, M. M., Kaufman, M. T. & Shenoy, K. V. A neural network that finds a naturalistic solution for the production of muscle activity. Nat. Neurosci. 18, 1025–1033 (2015).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  184. Sussillo, D. & Barak, O. Opening the black box: low-dimensional dynamics in high-dimensional recurrent neural networks. Neural Comput. 25, 626–649 (2013).

    Article  PubMed  Google Scholar 

  185. Beiran, M., Meirhaeghe, N., Sohn, H., Jazayeri, M. & Ostojic, S. Parametric control of flexible timing through low-dimensional neural manifolds. Neuron 111, 739–753 (2023).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  186. Valente, A., Ostojic, S. & Pillow, J. W. Probing the relationship between latent linear dynamical systems and low-rank recurrent neural network models. Neural Comput. 34, 1871–1892 (2022).

    Article  PubMed  Google Scholar 

  187. Pollock, E. & Jazayeri, M. Engineering recurrent neural networks from task-relevant manifolds and dynamics. PLoS Comput. Biol. 16, e1008128 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  188. Enel, P., Procyk, E., Quilodran, R. & Dominey, P. F. Reservoir computing properties of neural dynamics in prefrontal cortex. PLoS Comput. Biol. 12, e1004967 (2016).

    Article  PubMed  PubMed Central  Google Scholar 

  189. Schuessler, F., Dubreuil, A., Mastrogiuseppe, F., Ostojic, S. & Barak, O. Dynamics of random recurrent networks with correlated low-rank structure. Phys. Rev. Res. 2, 013111 (2020).

    Article  CAS  Google Scholar 

  190. Burak, Y. & Fiete, I. R. Accurate path integration in continuous attractor network models of grid cells. PLoS Comput. Biol. 5, e1000291 (2009).

    Article  PubMed  PubMed Central  Google Scholar 

  191. Michaels, J. A., Schaffelhofer, S., Agudelo-Toro, A. & Scherberger, H. A goal-driven modular neural network predicts parietofrontal neural dynamics during grasping. Proc. Natl Acad. Sci. USA 117, 32124–32135 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  192. Yang, G. R., Joglekar, M. R., Song, H. F., Newsome, W. T. & Wang, X. -J. Task representations in neural networks trained to perform many cognitive tasks. Nat. Neurosci. 22, 297–306 (2019).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  193. Litwin-Kumar, A. & Doiron, B. Slow dynamics and high variability in balanced cortical networks with clustered connections. Nat. Neurosci. 15, 1498–1505 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  194. Feulner, B. et al. Small, correlated changes in synaptic connectivity may facilitate rapid motor learning. Nat. Commun. 13, 5163 (2022).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  195. Feulner, B., Perich, M. G., Miller, L. E., Clopath, C. & Gallego, J. A. A neural implementation model of feedback-based motor learning. Nat. Commun. 16, 1805 (2025).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  196. Darshan, R. & Rivkind, A. Learning to represent continuous variables in heterogeneous neural networks. Cell Rep. 39, 110612 (2022).

  197. Pezon, L., Schmutz, V. & Gerstner, W. Linking neural manifolds to circuit structure in recurrent networks. Preprint at bioRxiv https://doi.org/10.1101/2024.02.28.582565 (2024).

  198. Dubreuil, A., Valente, A., Beiran, M., Mastrogiuseppe, F. & Ostojic, S. The role of population structure in computations through neural dynamics. Nat. Neurosci. 25, 783–794 (2022).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  199. Hennequin, G., Vogels, T. P. & Gerstner, W. Optimal control of transient dynamics in balanced networks supports generation of complex movements. Neuron 82, 1394–1406 (2014).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  200. Fuhs, M. C. & Touretzky, D. S. A spin glass model of path integration in rat medial entorhinal cortex. J. Neurosci. 26, 4266–4276 (2006).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

Download references

Acknowledgements

We thank J. W. Krakauer for the movie analogy, Carolina Massumoto for her input during figure conceptualisation, and R. H. Chowdhury and G. Mishne for comments on this manuscript. M.G.P. received funding (chercheurs-boursiers en intelligence artificielle) from the Fonds de recherche du Québec Santé. D.N. received funding from the Netherlands Organisation for Scientific Research (NWO Vidi - VI.Vidi.193.076, Aspasia 015.016.012 and Gravitation - DBI2 - 024.005.022) and the Nationaal Groeifonds NGF.1609.241.021. J.A.G. received funding from the EPSRC (EP/T020970/1), Advanced Research + Invention Agency (Scalable neural interfaces SCNI-PR01-P09) and the European Research Council (ERC-2020-StG-949660).

Author information

Authors and Affiliations

  1. Département de neurosciences, Faculté de médecine, Université de Montréal, Montreal, Quebec, Canada

    Matthew G. Perich

  2. Mila - Quebec Artificial Intelligence Institute, Montreal, Quebec, Canada

    Matthew G. Perich

  3. Department of Neuroscience, Erasmus Medical Center, Rotterdam, the Netherlands

    Devika Narain

  4. Department of Bioengineering, Imperial College London, London, UK

    Juan A. Gallego

Authors
  1. Matthew G. Perich
    View author publications

    Search author on:PubMed Google Scholar

  2. Devika Narain
    View author publications

    Search author on:PubMed Google Scholar

  3. Juan A. Gallego
    View author publications

    Search author on:PubMed Google Scholar

Contributions

M.G.P. and J.A.G. conceived of the overall concept for the manuscript. M.G.P., D.N. and J.A.G. wrote and edited the manuscript.

Corresponding authors

Correspondence to Matthew G. Perich or Juan A. Gallego.

Ethics declarations

Competing interests

J.A.G. receives funding from Meta Platform Technologies and InBrain Neuroelectronics. M.G.P. and D.N. declare no competing interests.

Peer review

Peer review information

Nature Neuroscience thanks Joao Barbosa and Srdjan Ostojic 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.

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

Perich, M.G., Narain, D. & Gallego, J.A. A neural manifold view of the brain. Nat Neurosci 28, 1582–1597 (2025). https://doi.org/10.1038/s41593-025-02031-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Version of record:

  • Issue date:

  • DOI: https://doi.org/10.1038/s41593-025-02031-z

This article is cited by

Search

Advanced 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