{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T00:10:31Z","timestamp":1777507831590,"version":"3.51.4"},"reference-count":51,"publisher":"Frontiers Media SA","license":[{"start":{"date-parts":[[2023,3,6]],"date-time":"2023-03-06T00:00:00Z","timestamp":1678060800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004359","name":"Vetenskapsr\u00e5det","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004359","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003792","name":"Hj\u00e4rnfonden","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100003792","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003173","name":"Crafoordska Stiftelsen","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100003173","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["frontiersin.org"],"crossmark-restriction":true},"short-container-title":["Front. Comput. Neurosci."],"abstract":"<jats:p>The cerebellar Purkinje cell controlling eyeblinks can learn, remember, and reproduce the interstimulus interval in a classical conditioning paradigm. Given temporally separated inputs, the cerebellar Purkinje cell learns to pause its tonic inhibition of a motor pathway with high temporal precision so that an overt blink occurs at the right time. Most models place the passage-of-time representation in upstream network effects. Yet, bypassing the upstream network and directly stimulating the Purkinje cell's pre-synaptic fibers during conditioning still causes acquisition of a well-timed response. Additionally, while network models are sensitive to variance in the temporal structure of probe stimulation, <jats:italic>in vivo<\/jats:italic> findings suggest that the acquired Purkinje cell response is not. Such findings motivate alternative approaches to modeling neural function. Here, we present a proof-of-principle model of the passage-of-time which is internal to the Purkinje cell and is invariant to probe structure. The model is consistent with puzzling findings, accurately recapitulates Purkinje cell firing during classical conditioning and makes testable electrophysiological predictions.<jats:xref><jats:sup>1<\/jats:sup><\/jats:xref><\/jats:p>","DOI":"10.3389\/fncom.2023.1108346","type":"journal-article","created":{"date-parts":[[2023,3,6]],"date-time":"2023-03-06T05:32:10Z","timestamp":1678080730000},"update-policy":"https:\/\/doi.org\/10.3389\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["A computational passage-of-time model of the cerebellar Purkinje cell in eyeblink conditioning"],"prefix":"10.3389","volume":"17","author":[{"given":"Matthew","family":"Ricci","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Junkyung","family":"Kim","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fredrik","family":"Johansson","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1965","published-online":{"date-parts":[[2023,3,6]]},"reference":[{"key":"B1","doi-asserted-by":"publisher","first-page":"2748","DOI":"10.1109\/TNNLS.2016.2598190","article-title":"Model-driven analysis of eyeblink classical conditioning reveals the underlying structure of cerebellar plasticity and neuronal activity","volume":"28","author":"Antonietti","year":"2017","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"B2","doi-asserted-by":"publisher","first-page":"599","DOI":"10.1126\/science.1232758","article-title":"Amplifying genetic logic gates","volume":"340","author":"Bonnet","year":"2013","journal-title":"Science"},{"key":"B3","doi-asserted-by":"publisher","first-page":"1101","DOI":"10.1016\/S0893-6080(05)80161-3","article-title":"A neural model of timed response learning in the cerebellum","volume":"7","author":"Bullock","year":"1994","journal-title":"Neural Netw."},{"key":"B4","doi-asserted-by":"publisher","first-page":"38","DOI":"10.1162\/neco.1994.6.1.38","article-title":"Neural network model of the cerebellum: temporal discrimination and the timing of motor responses","volume":"6","author":"Buonomano","year":"1994","journal-title":"Neural Comput."},{"key":"B5","doi-asserted-by":"publisher","first-page":"4510","DOI":"10.1523\/JNEUROSCI.4530-03.2004","article-title":"Evidence that climbing fibers control an intrinsic spike generator in cerebellar Purkinje cells","volume":"24","author":"Cerminara","year":"2004","journal-title":"J. Neurosci."},{"key":"B6","doi-asserted-by":"publisher","first-page":"e03896","DOI":"10.7554\/eLife.03896","article-title":"Reinstatement of long-term memory following erasure of its behavioral and synaptic expression in Aplysia","volume":"3","author":"Chen","year":"2014","journal-title":"Elife"},{"key":"B7","doi-asserted-by":"publisher","first-page":"98","DOI":"10.1038\/s41586-022-04922-8","article-title":"A time-resolved, multi-symbol molecular recorder via sequential genome editing","volume":"608","author":"Choi","year":"2022","journal-title":"Nature"},{"key":"B8","doi-asserted-by":"publisher","first-page":"551","DOI":"10.1016\/S0898-6568(97)00095-8","article-title":"Signalling via the G protein-activated K+ channels","volume":"9","author":"Dascal","year":"1997","journal-title":"Cell Signal."},{"key":"B9","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-13147-3","author":"Eccles","year":"1967","journal-title":"The Cerebellum as a Neuronal Machine"},{"key":"B10","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1037\/0033-295X.107.2.289","article-title":"Time, rate, and conditioning","volume":"107","author":"Gallistel","year":"2000","journal-title":"Psychol. Rev"},{"key":"B11","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1037\/0033-295X.84.3.279","article-title":"Scalar expectancy theory and Weber's law in animal timing","volume":"84","author":"Gibbon","year":"1977","journal-title":"Psychol. Rev."},{"key":"B12","first-page":"121","article-title":"\u201cClassical conditioning,\u201d","author":"Gormezano","year":"1969","journal-title":"Learning Processes"},{"key":"B13","doi-asserted-by":"publisher","first-page":"7813","DOI":"10.1523\/JNEUROSCI.3663-14.2015","article-title":"Relating cerebellar purkinje cell activity to the timing and amplitude of conditioned eyelid responses","volume":"35","author":"Halverson","year":"2015","journal-title":"J. Neurosci."},{"key":"B14","doi-asserted-by":"publisher","first-page":"467","DOI":"10.1038\/87419","article-title":"Beyond parallel fiber LTD: the diversity of synaptic and non-synaptic plasticity in the cerebellum","volume":"4","author":"Hansel","year":"2001","journal-title":"Nat. Neurosci."},{"key":"B15","doi-asserted-by":"publisher","first-page":"437","DOI":"10.1016\/0301-0082(91)90012-P","article-title":"Quantitative studies on the mammalian cerebellum","volume":"36","author":"Harvey","year":"1991","journal-title":"Prog. Neurobiol"},{"key":"B16","doi-asserted-by":"publisher","first-page":"2321","DOI":"10.1523\/JNEUROSCI.4547-13.2014","article-title":"Precise control of movement kinematics by optogenetic inhibition of Purkinje cell activity","volume":"34","author":"Heiney","year":"2014","journal-title":"J. Neurosci."},{"key":"B17","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1113\/jphysiol.1994.sp020126","article-title":"Correspondence between climbing fibre input and motor output in eyeblink-related areas in cat cerebellar cortex","volume":"476","author":"Hesslow","year":"","journal-title":"J. Physiol."},{"key":"B18","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1113\/jphysiol.1994.sp020127","article-title":"Inhibition of classically conditioned eyeblink responses by stimulation of the cerebellar cortex in the decerebrate cat","volume":"476","author":"Hesslow","year":"","journal-title":"J. Physiol."},{"key":"B19","doi-asserted-by":"publisher","first-page":"649","DOI":"10.1097\/00001756-199401000-00030","article-title":"Suppression of cerebellar Purkinje cells during conditioned responses in ferrets","volume":"5","author":"Hesslow","year":"1994","journal-title":"Neuroreport"},{"key":"B20","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1007\/978-1-4419-8558-3_4","article-title":"\u201cThe functional anatomy of skeletal conditioning,\u201d","author":"Hesslow","year":"2002","journal-title":"A Neuroscience Guide to Classical Conditioning"},{"key":"B21","doi-asserted-by":"publisher","first-page":"2493","DOI":"10.1523\/JNEUROSCI.4202-06.2007","article-title":"Acquisition, extinction, and reacquisition of a cerebellar cortical memory trace","volume":"27","author":"Jirenhed","year":"2007","journal-title":"J. Neurosci."},{"key":"B22","doi-asserted-by":"publisher","first-page":"523","DOI":"10.1007\/s12311-011-0264-3","article-title":"Learning stimulus intervals-adaptive timing of conditioned purkinje cell responses","volume":"10","author":"Jirenhed","year":"","journal-title":"Cerebellum"},{"key":"B23","doi-asserted-by":"publisher","first-page":"9070","DOI":"10.1523\/JNEUROSCI.1653-11.2011","article-title":"Time course of classically conditioned Purkinje cell response is determined by initial part of conditioned stimulus","volume":"31","author":"Jirenhed","year":"","journal-title":"J. Neurosci."},{"key":"B24","doi-asserted-by":"publisher","first-page":"6127","DOI":"10.1073\/pnas.1621132114","article-title":"Learned response sequences in cerebellar Purkinje cells","volume":"114","author":"Jirenhed","year":"2017","journal-title":"Proc. Natl. Acad. Sci. U.S.A."},{"key":"B25","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.celrep.2015.10.047","article-title":"Activation of a temporal memory in Purkinje cells by the mGluR7 receptor","volume":"13","author":"Johansson","year":"2015","journal-title":"Cell Rep."},{"key":"B26","doi-asserted-by":"publisher","first-page":"e994376","DOI":"10.4161\/19420889.2014.994376","article-title":"Theoretical considerations for understanding a Purkinje cell timing mechanism","volume":"7","author":"Johansson","year":"2014","journal-title":"Commun. Integr. Biol."},{"key":"B27","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1016\/j.cobeha.2016.01.013","article-title":"Mechanisms for motor timing in the cerebellar cortex","volume":"8","author":"Johansson","year":"2016","journal-title":"Curr. Opin. Behav. Sci."},{"key":"B28","doi-asserted-by":"publisher","first-page":"14930","DOI":"10.1073\/pnas.1415371111","article-title":"Memory trace and timing mechanism localized to cerebellar Purkinje cells","volume":"111","author":"Johansson","year":"2014","journal-title":"Proc. Natl. Acad. Sci. U. S. A"},{"key":"B29","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1007\/978-1-4419-8558-3_6","article-title":"\u201cFundamental behavioral methods and findings in classical conditioning,\u201d","author":"Kehoe","year":"2002","journal-title":"A Neuroscience Guidance to Classical Conditioning"},{"key":"B30","doi-asserted-by":"publisher","first-page":"e0217364","DOI":"10.1371\/journal.pone.0217364","article-title":"Encoding information in synthetic metabolomes","volume":"14","author":"Kennedy","year":"2019","journal-title":"PLoS ONE"},{"key":"B31","doi-asserted-by":"publisher","first-page":"e1002291","DOI":"10.1371\/journal.pcbi.1002291","article-title":"Of toasters and molecular ticker tapes","volume":"7","year":"2011","journal-title":"PLoS Comput. Biol"},{"key":"B32","doi-asserted-by":"publisher","first-page":"409","DOI":"10.1016\/j.neuron.2006.07.010","article-title":"RGS expression rate-limits recovery of rod photoresponses","volume":"51","author":"Krispel","year":"2006","journal-title":"Neuron"},{"key":"B33","doi-asserted-by":"publisher","first-page":"140","DOI":"10.3389\/fncom.2010.00140","article-title":"Sensory prediction or motor control? Application of marr-albus type models of cerebellar function to classical conditioning","volume":"4","author":"Lepora","year":"2010","journal-title":"Front. Comput. Neurosci."},{"key":"B34","doi-asserted-by":"publisher","first-page":"e1007601","DOI":"10.1371\/journal.pcbi.1007601","article-title":"A model for time interval learning in the Purkinje cell","volume":"16","author":"Majoral","year":"2020","journal-title":"PLoS Comput. Biol."},{"key":"B35","doi-asserted-by":"publisher","first-page":"e0251172","DOI":"10.1371\/journal.pone.0251172","article-title":"A biochemical mechanism for time-encoding memory formation within individual synapses of Purkinje cells","volume":"16","author":"Mandwal","year":"2021","journal-title":"PLoS ONE"},{"key":"B36","doi-asserted-by":"publisher","first-page":"5349","DOI":"10.1073\/pnas.83.14.5349","article-title":"Classical conditioning using stimulation of the inferior olive as the unconditioned stimulus","volume":"83","author":"Mauk","year":"1986","journal-title":"Proc. Natl. Acad. Sci. U.S.A."},{"key":"B37","doi-asserted-by":"publisher","first-page":"1205","DOI":"10.1038\/81486","article-title":"Computer simulation of cerebellar information processing","volume":"3","author":"Medina","year":"2000","journal-title":"Nat. Neurosci."},{"key":"B38","doi-asserted-by":"publisher","first-page":"8920","DOI":"10.1523\/JNEUROSCI.6117-09.2010","article-title":"Electrophysiological localiza- tion of eyeblink-related microzones in rabbit cerebellar cortex","volume":"30","author":"Mostofi","year":"2010","journal-title":"J. Neurosci."},{"key":"B39","doi-asserted-by":"publisher","first-page":"1007","DOI":"10.1126\/science.aaa5542","article-title":"Engram cells retain memory under retrograde amnesia","volume":"348","author":"Ryan","year":"2015","journal-title":"Science"},{"key":"B40","doi-asserted-by":"publisher","first-page":"85","DOI":"10.3758\/BF03209734","article-title":"Rabbit nictitating membrane conditioning: lower limit of the effective inter- stimulus interval","volume":"8","author":"Salafia","year":"1980","journal-title":"Anim. Learn. Behav."},{"key":"B41","doi-asserted-by":"publisher","first-page":"226","DOI":"10.1037\/h0028212","article-title":"Classical conditioning of the rabbit's nictitating membrane response at backward, simultaneous, and forward CS-US intervals","volume":"69","author":"Smith","year":"1969","journal-title":"J. Comp. Physiol. Psychol."},{"key":"B42","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1002\/syn.890030308","article-title":"Classical conditioning in rabbits using pontine nucleus stimulation as a conditioned stimulus and inferior olive stimulation as an unconditioned stimulus","volume":"3","author":"Steinmetz","year":"1989","journal-title":"Synapse"},{"key":"B43","doi-asserted-by":"publisher","first-page":"4333","DOI":"10.1046\/j.1460-9568.1999.00862.x","article-title":"Short-lasting conditioned stimulus applied to the middle cerebellar peduncle elicits delayed conditioned eye blink responses in the decerebrate ferret","volume":"11","author":"Svensson","year":"1999","journal-title":"Eur. J. Neurosci."},{"key":"B44","doi-asserted-by":"publisher","first-page":"1977","DOI":"10.1016\/j.celrep.2015.10.057","article-title":"Evolving models of pavlovian conditioning: cerebellar cortical dynamics in awake behaving mice","volume":"13","author":"Ten Brinke","year":"2015","journal-title":"Cell Rep."},{"key":"B45","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1016\/j.beproc.2013.01.005","volume":"95","author":"Ward","year":"2013"},{"key":"B46","doi-asserted-by":"publisher","first-page":"1731","DOI":"10.1523\/JNEUROSCI.2883-13.2014","article-title":"Bidirectional plasticity of Purkinje cells matches temporal features of learning","volume":"34","author":"Wetmore","year":"2014","journal-title":"J. Neurosci."},{"key":"B47","doi-asserted-by":"publisher","first-page":"190","DOI":"10.1038\/nature12241","article-title":"X-ray structure of the mammalian GIRK2-\u03b2\u03b3 G-protein complex","volume":"498","author":"Whorton","year":"2013","journal-title":"Nature"},{"key":"B48","doi-asserted-by":"publisher","first-page":"661","DOI":"10.1038\/nn.2549","article-title":"Gbeta5 recruits R7 RGS proteins to GIRK channels to regulate the timing of neuronal inhibitory signaling","volume":"13","author":"Xie","year":"2010","journal-title":"Nat. Neurosci."},{"key":"B49","doi-asserted-by":"publisher","first-page":"423","DOI":"10.1007\/s12311-009-0115-7","article-title":"Computational models of timing mechanisms in the cerebellar granular layer","volume":"8","author":"Yamazaki","year":"2009","journal-title":"Cerebellum"},{"key":"B50","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1007\/BF00237023","article-title":"Classical conditioning of the nictitating membrane response of the rabbit. II. Lesions of the cerebellar cortex","volume":"60","author":"Yeo","year":"","journal-title":"Exp. Brain Res."},{"key":"B51","doi-asserted-by":"publisher","first-page":"114","DOI":"10.1007\/BF00237024","article-title":"Classical conditioning of the nictitating membrane response of the rabbit. III. Connections of cerebellar lobule HVI","volume":"60","author":"Yeo","year":"","journal-title":"Exp. Brain Res."}],"container-title":["Frontiers in Computational Neuroscience"],"original-title":[],"link":[{"URL":"https:\/\/www.frontiersin.org\/articles\/10.3389\/fncom.2023.1108346\/full","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,6]],"date-time":"2023-03-06T05:32:15Z","timestamp":1678080735000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.frontiersin.org\/articles\/10.3389\/fncom.2023.1108346\/full"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,3,6]]},"references-count":51,"alternative-id":["10.3389\/fncom.2023.1108346"],"URL":"https:\/\/doi.org\/10.3389\/fncom.2023.1108346","relation":{},"ISSN":["1662-5188"],"issn-type":[{"value":"1662-5188","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,3,6]]},"article-number":"1108346"}}