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, IP3was 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 IP3receptors activated by the increased IP3. The delay in IP3increase 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 IP3increased, and it coherently explained the different forms of LTD. At 2.5 μmIP3, CF activation after PF activation was essential to reach the threshold for the regenerative Ca2+release. At 10 μmIP3, the same as achieved experimentally by strong IP3photolysis, the threshold was lower, and thus large Ca2+release was generated even without CF stimulation. In contrast, the basal 0.1 μmIP3level 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.

Photolysis of a caged Ca(2+) compound was used to characterize the dependence of cerebellar long-term synaptic depression (LTD) on postsynaptic Ca(2+) concentration ([Ca(2+)](i)). Elevating [Ca(2+)](i) was sufficient to induce LTD without requiring any of the other signals produced by synaptic activity. A sigmoidal relationship between [Ca(2+)](i) and LTD indicated a highly cooperative triggering of LTD by Ca(2+). The duration of the rise in [Ca(2+)](i) influenced the apparent Ca(2+) affinity of LTD, and this time-dependent behavior could be described by a leaky integrator process with a time constant of 0.6 s. A computational model, based on a positive-feedback cycle that includes protein kinase C and MAP kinase, was capable of simulating these properties of Ca(2+)-triggered LTD. Disrupting this cycle experimentally also produced the predicted changes in the Ca(2+) dependence of LTD. We conclude that LTD arises from a mechanism that integrates postsynaptic Ca(2+) signals and that this integration may be produced by the positive-feedback cycle.

Corticostriatal synapse plasticity of medium spiny neurons is regulated by glutamate input from the cortex and dopamine input from the substantia nigra. While cortical stimulation alone results in long-term depression (LTD), the combination with dopamine switches LTD to long-term potentiation (LTP), which is known as dopamine-dependent plasticity. LTP is also induced by cortical stimulation in magnesium-free solution, which leads to massive calcium influx through NMDA-type receptors and is regarded as calcium-dependent plasticity. Signaling cascades in the corticostriatal spines are currently under investigation. However, because of the existence of multiple excitatory and inhibitory pathways with loops, the mechanisms regulating the two types of plasticity remain poorly understood. A signaling pathway model of spines that express D1-type dopamine receptors was constructed to analyze the dynamic mechanisms of dopamine- and calcium-dependent plasticity. The model incorporated all major signaling molecules, including dopamine- and cyclic AMP-regulated phosphoprotein with a molecular weight of 32 kDa (DARPP32), as well as AMPA receptor trafficking in the post-synaptic membrane. Simulations with dopamine and calcium inputs reproduced dopamine- and calcium-dependent plasticity. Further in silico experiments revealed that the positive feedback loop consisted of protein kinase A (PKA), protein phosphatase 2A (PP2A), and the phosphorylation site at threonine 75 of DARPP-32 (Thr75) served as the major switch for inducing LTD and LTP. Calcium input modulated this loop through the PP2B (phosphatase 2B)-CK1 (casein kinase 1)-Cdk5 (cyclin-dependent kinase 5)-Thr75 pathway and PP2A, whereas calcium and dopamine input activated the loop via PKA activation by cyclic AMP (cAMP). The positive feedback loop displayed robust bi-stable responses following changes in the reaction parameters. Increased basal dopamine levels disrupted this dopamine-dependent plasticity. The present model elucidated the mechanisms involved in bidirectional regulation of corticostriatal synapses and will allow for further exploration into causes and therapies for dysfunctions such as drug addiction.

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.