A model for time interval learning in the Purkinje cell

Abstract

Recent experimental findings indicate that Purkinje cells in the cerebellum represent time intervals by mechanisms other than conventional synaptic weights. These findings add to the theoretical and experimental observations suggesting the presence of intra-cellular mechanisms for adaptation and processing. To account for these experimental results we propose a new biophysical model for time interval learning in a Purkinje cell. The numerical model focuses on a classical delay conditioning task (e.g. eyeblink conditioning) and relies on a few computational steps. In particular, the model posits the activation by the parallel fiber input of a local intra-cellular calcium store which can be modulated by intra-cellular pathways. The reciprocal interaction of the calcium signal with several proteins forming negative and positive feedback loops ensures that the timing of inhibition in the Purkinje cell anticipates the interval between parallel and climbing fiber inputs during training. We systematically test the model ability to learn time intervals at the 150-1000 ms time scale, while observing that learning can also extend to the multiple seconds scale. In agreement with experimental observations we also show that the number of pairings required to learn increases with inter-stimulus interval. Finally, we discuss how this model would allow the cerebellum to detect and generate specific spatio-temporal patterns, a classical theory for cerebellar function.

Periodicity Pitch Perception

“…The complex temporal interplay of ON/OFF excitation and ON inhibition makes the timer unit selective for interval durations (Wehr and Zador, 2003;Edwards et al, 2008;Simen et al, 2011;Takizawa et al, 2012;Naud et al, 2015;Majoral et al, 2018;Rajaram et al, 2019). At the start, the IC soma is charged by mini EPSCs by MSO neurons and discharged by IPSCs by DNLL neurons.…”

Discrimination and learning of temporal input sequences in a cerebellar Purkinje cell model

“…Those studies, however, have assumed that individual neurons are simple elements that cannot perform complex functions by dendritic computation. In contrast, a few studies have proposed other types of timing mechanisms on single PCs rather than network mechanisms (Fiala et al, 1996 ; Majoral et al, 2020 ). The present study seems consistent with a view that single PCs might be sufficient for temporal information processing in the cerebellum (Johansson et al, 2014 ).…”

A computational passage-of-time model of the cerebellar Purkinje cell in eyeblink conditioning

“…The time course could be regulated over hundreds of ms by regulators of G-protein signaling (RGS proteins) as in the temporal regulation of photoreceptors returning to resting state (Krispel et al, 2006 ) and prolonged inhibition in hippocampal neurons (Xie et al, 2010 ). Purkinje cell modeling by Majoral et al ( 2020 ) and Mandwal et al ( 2021 ) incorporate these components in biochemical cascades, showing that they could replicate part of the phenomena. Until there are more empirical findings on the involved mechanisms, we here aimed at presenting a general model, exploring what is computationally feasible.…”

“…Biochemical models that present possible mechanisms for parts of the phenomena have recently been proposed (Majoral et al, 2020 ; Mandwal et al, 2021 ). Given that the currents and molecules involved are yet to be elucidated, here we explore a conceptual and mathematical model of what kind of mechanism could explain all the phenomena described above.…”