Ca²⁺ Requirements for Long-Term Depression Are Frequency Sensitive in Purkinje Cells

Cerebellar long-term depression (LTD) is a form of synaptic plasticity dependent on postsynaptic Ca²⁺ changes. One fundamental question is how LTD is selectively induced by specific numbers of Ca²⁺ pulses and which are the frequency and duration of this train of pulses required for LTD induction. The molecular mechanism which leads the integration of postsynaptic Ca²⁺ pulses in the LTD signaling network has not been elucidated either. Recent publications have shown that Ca²⁺/calmodulin-dependent protein kinase II (CaMKII) is required for LTD induction. Additionally, protein kinase C (PKC), CaMKII, and MAPK play an important role to transduce the frequency of Ca²⁺ pulses into their enzymatic activity levels; however, it is still unknown which enzymes are involved in decoding Ca²⁺ pulses in LTD. We have extended a stochastic model of LTD by adding the molecular network regulating CaMKII activity and its activation. We solved this model with stochastic engine for pathway simulation to include the effect of biochemical noise in LTD. We systematically investigated the dependence of LTD induction on stimulus frequencies, and we found that LTD is selectively induced by a specific number of Ca²⁺ spikes at different frequencies. We observed that CaMKII is essential to induce LTD, and LTD is only weakly induced when its Thr286 phosphorylation site has been deleted. We found that CaMKII decodes the frequency of Ca²⁺ spikes into different amounts of kinase activity during LTD induction. In addition, PKC and ERK enzyme activity is highly sensitive to the frequency and the number of Ca²⁺ pulses and this sensitivity has an important effect on LTD activation. This research predicts the postsynaptic Ca²⁺ requirements to induce LTD using a typical synaptic activation sequence and explains how LTD is selectively induced by specific number of Ca²⁺ pulses at different frequencies.