{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T05:33:07Z","timestamp":1775626387884,"version":"3.50.1"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1012776","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2025,6,13]],"date-time":"2025-06-13T00:00:00Z","timestamp":1749772800000}}],"reference-count":65,"publisher":"Public Library of Science (PLoS)","issue":"1","license":[{"start":{"date-parts":[[2025,1,29]],"date-time":"2025-01-29T00:00:00Z","timestamp":1738108800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100005416","name":"Norges Forskningsr\u00e5d","doi-asserted-by":"publisher","award":["223262"],"award-info":[{"award-number":["223262"]}],"id":[{"id":"10.13039\/501100005416","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Research Council of Norway Centre Centre of Algorithms in the Cortex","award":["332640"],"award-info":[{"award-number":["332640"]}]},{"DOI":"10.13039\/501100005416","name":"Norges Forskningsr\u00e5d","doi-asserted-by":"publisher","award":["295721"],"award-info":[{"award-number":["295721"]}],"id":[{"id":"10.13039\/501100005416","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100001201","name":"The Kavli Foundation","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100001201","id-type":"DOI","asserted-by":"crossref"}]},{"name":"UCLA graduate fellowship"}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>Persistent homology applied to the activity of grid cells in the Medial Entorhinal Cortex suggests that this activity lies on a toroidal manifold. By analyzing real data and a simple model, we show that neural oscillations play a key role in the appearance of this toroidal topology. To quantitatively monitor how changes in spike trains influence the topology of the data, we first define a robust measure for the degree of toroidality of a dataset. Using this measure, we find that small perturbations (<jats:inline-formula id=\"pcbi.1012776.e001\"><jats:alternatives><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" id=\"pcbi.1012776.e001g\" mimetype=\"image\" position=\"anchor\" xlink:href=\"info:doi\/10.1371\/journal.pcbi.1012776.e001\" xlink:type=\"simple\"\/><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\" id=\"M1\"><mml:mrow><mml:mi>~<\/mml:mi><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>100\u2009ms) of spike times have little influence on both the toroidality and the hexagonality of the ratemaps. Jittering spikes by <jats:inline-formula id=\"pcbi.1012776.e002\"><jats:alternatives><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" id=\"pcbi.1012776.e002g\" mimetype=\"image\" position=\"anchor\" xlink:href=\"info:doi\/10.1371\/journal.pcbi.1012776.e002\" xlink:type=\"simple\"\/><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\" id=\"M2\"><mml:mrow><mml:mi>~<\/mml:mi><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>100-500\u2009ms, however, destroys the toroidal topology, while still having little impact on grid scores. These critical jittering time scales fall in the range of the periods of oscillations between the theta and eta bands. We thus hypothesized that these oscillatory modulations of neuronal spiking play a key role in the appearance and robustness of toroidal topology and the hexagonal spatial selectivity is not sufficient. We confirmed this hypothesis using a simple model for the activity of grid cells, consisting of an ensemble of independent rate-modulated Poisson processes. When these rates were modulated by oscillations, the network behaved similarly to the real data in exhibiting toroidal topology, even when the position of the fields were perturbed. In the absence of oscillations, this similarity was substantially lower. Furthermore, we find that the experimentally recorded spike trains indeed exhibit temporal modulations at the eta and theta bands, and that the ratio of the power in the eta band to that of the theta band, <jats:inline-formula id=\"pcbi.1012776.e003\"><jats:alternatives><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" id=\"pcbi.1012776.e003g\" mimetype=\"image\" position=\"anchor\" xlink:href=\"info:doi\/10.1371\/journal.pcbi.1012776.e003\" xlink:type=\"simple\"\/><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\" id=\"M3\"><mml:mrow><mml:msub><mml:mi>A<\/mml:mi><mml:mrow><mml:mi>\u03b7<\/mml:mi><\/mml:mrow><\/mml:msub><mml:mo>\/<\/mml:mo><mml:msub><mml:mi>A<\/mml:mi><mml:mrow><mml:mi>\u03b8<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>, correlates with the critical jittering time at which the toroidal topology disappears.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1012776","type":"journal-article","created":{"date-parts":[[2025,1,29]],"date-time":"2025-01-29T18:39:34Z","timestamp":1738175974000},"page":"e1012776","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":3,"title":["The role of oscillations in grid cells\u2019 toroidal topology"],"prefix":"10.1371","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-8561-1153","authenticated-orcid":true,"given":"Giovanni","family":"di 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preprint"},{"issue":"1","key":"pcbi.1012776.ref027","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/j.neuron.2017.03.004","article-title":"Grid and nongrid cells in medial entorhinal cortex represent spatial location and environmental features with complementary coding schemes","volume":"94","author":"GW Diehl","year":"2017","journal-title":"Neuron"},{"issue":"15","key":"pcbi.1012776.ref028","doi-asserted-by":"crossref","first-page":"2337","DOI":"10.1016\/j.cub.2017.06.034","article-title":"Grid cells encode local positional information","volume":"27","author":"R Ismakov","year":"2017","journal-title":"Curr Biol"},{"issue":"10","key":"pcbi.1012776.ref029","doi-asserted-by":"crossref","first-page":"1128","DOI":"10.1002\/hipo.23378","article-title":"Burst activity plays no role in the field-to-field variability and rate remapping of grid cells","volume":"31","author":"M Poth","year":"2021","journal-title":"Hippocampus"},{"key":"pcbi.1012776.ref030","unstructured":"Chazal F, Fasy B, Lecci F, Michel B, Rinaldo A, Wasserman L. Subsampling methods for persistent homology. Proceedings of the International Conference on Machine Learning; 2015. p. 2143\u201351."},{"key":"pcbi.1012776.ref031","article-title":"Approximating persistent homology for large datasets","author":"Y Cao","year":"2022","journal-title":"arXiv preprint arXiv:220409155"},{"issue":"90","key":"pcbi.1012776.ref032","first-page":"1","article-title":"Outlier-robust subsampling techniques for persistent homology","volume":"24","author":"BJ Stolz","year":"2023","journal-title":"J Mach Learn Res"},{"issue":"1","key":"pcbi.1012776.ref033","doi-asserted-by":"crossref","first-page":"12274","DOI":"10.1038\/s41598-023-37842-2","article-title":"A universal null-distribution for topological data analysis","volume":"13","author":"O Bobrowski","year":"2023","journal-title":"Sci Rep"},{"key":"pcbi.1012776.ref034","article-title":"Weak universality in random persistent homology and scale-invariant functionals","author":"O Bobrowski","year":"2024","journal-title":"arXiv 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Cao","year":"2023","journal-title":"Inf Inference"},{"issue":"4","key":"pcbi.1012776.ref039","first-page":"1486","article-title":"A normalized bottleneck distance on persistence diagrams and homology preservation under dimension reduction","volume":"3","author":"NH May","year":"2024","journal-title":"LaMa"},{"issue":"6890","key":"pcbi.1012776.ref040","doi-asserted-by":"crossref","first-page":"741","DOI":"10.1038\/nature00807","article-title":"Role of experience and oscillations in transforming a rate code into a temporal code","volume":"417","author":"MR Mehta","year":"2002","journal-title":"Nature"},{"key":"pcbi.1012776.ref041","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1113\/jphysiol.2002.031245","article-title":"Theta oscillation coupled spike latencies yield computational vigour in a mammalian sensory system","volume":"546","author":"TW Margrie","year":"2003","journal-title":"J 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