A Model for Time Interval Learning in The Purkinje Cell

Recent experimental findings indicate that Purkinje cells in the cerebellum represent time intervals by mechanisms other than conventional synaptic weights. This finding adds to the theoretical and experimental observations suggesting the presence of intra-cellular mechanisms for adaptation and processing. To account for these experimental results we developed a 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 show that the model is able to learn along the 150-1000 ms interval range. Finally, we discuss how this model would allow the cerebellum to detect and generate specific spatio-temporal patterns, a classical theory for cerebellar function.\n\nAuthor SummaryThe prevailing view in neurosciences considers synaptic weights between neurons the determinant factor for learning and processing information in the nervous system. Theoretical considerations [1, 2] and experiments [3, 4] examined some potential limitations of this classical paradigm, pointing out that adaptation and computation might also have to rely on other mechanisms besides the learning of synaptic weights. Recent experimental findings [5-7] indicate that Purkinje cells in the cerebellum represent time intervals by mechanisms other than conventional synaptic weights. We propose here a biologically plausible model which complements the modification of synaptic weights for learning one time interval in one synapse of one Purkinje cell. In the model a calcium signal in a small domain keeps track of time. Several molecules read and modify this calcium signal to learn a time interval. We discuss how this model would allow the cerebellum to detect and generate specific patterns in space and time, a classical theory for cerebellar function proposed by Braitenberg [8, 9].