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Recent studies have shown that multiple internal models are acquired in the cerebellum and that these can be switched under a given context of behavior. It has been proposed that long-term depression (LTD) of parallel fiber (PF)-Purkinje cell (PC) synapses forms the cellular basis of cerebellar learning, and that the presynaptically synthesized messenger nitric oxide (NO) is a crucial "gatekeeper" for LTD. Because NO diffuses freely to neighboring synapses, this volume learning is not input-specific and brings into question the biological significance of LTD as the basic mechanism for efficient supervised learning. To better characterize the role of NO in cerebellar learning, we simulated the sequence of electrophysiological and biochemical events in PF-PC LTD by combining established simulation models of the electrophysiology, calcium dynamics, and signaling pathways of the PC. The results demonstrate that the local NO concentration is critical for induction of LTD and for its input specificity. Pre- and postsynaptic coincident firing is not sufficient for a PF-PC synapse to undergo LTD, and LTD is induced only when a sufficient amount of NO is provided by activation of the surrounding PFs. On the other hand, above-adequate levels of activity in nearby PFs cause accumulation of NO, which also allows LTD in neighboring synapses that were not directly stimulated, ruining input specificity. These findings lead us to propose the hypothesis that NO represents the relevance of a given context and enables context-dependent selection of internal models to be updated. We also predict sparse PF activity in vivo because, otherwise, input specificity would be lost.

Large Ca2+ signals essential for cerebellar long-term depression (LTD) at parallel fiber (PF)-Purkinje cell synapses are known to be induced when PF activation precedes climbing fiber (CF) activation by 50-200 ms, consistent with cerebellar learning theories. However, large Ca2+ signals and/or LTD can also be induced by massive PF stimulation alone or by photolysis of caged Ca2+ or inositol 1,4,5-trisphosphate (IP3). To understand the spike-timing detection mechanisms in cerebellar LTD, we developed a kinetic model of Ca2+ dynamics within a Purkinje dendritic spine. In our kinetic simulation, IP3 was first produced via the metabotropic pathway of PF inputs, and the Ca2+ influx in response to the CF input triggered regenerative Ca2+-induced Ca2+ release from the internal stores via the IP3 receptors activated by the increased IP3. The delay in IP3 increase caused by the PF metabotropic pathway generated the optimal PF-CF interval. The Ca2+ dynamics revealed a threshold for large Ca2+ release that decreased as IP3 increased, and it coherently explained the different forms of LTD. At 2.5 microM IP3, CF activation after PF activation was essential to reach the threshold for the regenerative Ca2+ release. At 10 microM IP3, the same as achieved experimentally by strong IP3 photolysis, the threshold was lower, and thus large Ca2+ release was generated even without CF stimulation. In contrast, the basal 0.1 microM IP3 level resulted in an extremely high Ca2+ threshold for regenerative Ca2+ release. Thus, the results demonstrated that Ca2+ dynamics can detect spike timing under physiological conditions, which supports cerebellar learning theories.

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