Abstract
How can synaptic efficacies be maintained despite the fast turnover of proteins at synapses? Partially, we know that the synthesis of new proteins is essential for the induction of the late, long-lasting phase of long-term potentiation (L-LTP). Recent experiments suggest that the concentration of protein kinase Mζ (PKMζ) is increased during L-LTP and that inhibiting the PKMζ activity during the maintenance phase can effectively reverse L-LTP. Experiments have also shown that phosphorylation is necessary for the activation of PKMζ. However, it is not clear what mechanism maintains the level and activity of PKMζ despite protein turnover and phosphatase activity. Using a mathematical modeling framework, I examine the hypothesis that the activity of PKMζ is sustained through a local switching mechanism. The model for the switching mechanism is motivated by several experimental observations: 1) PKMζ has two phosphorylation sites; one is mediated by another constitutively active kinase, Phosphoinositide-dependent kinase 1 PDK1 (T410) and is essential for its activity, and another is an autophosphorylation site, T560. 2) The phosphorylation of PKMζ increases its stability and the doubly phosphorylated PKMζ has a significantly longer lifetime than the unphosphorylated and singly phosphorylated states of PKMζ. 3) The doubly phosphorylated PKMζ also regulates the new synthesis of PKMζ through a translation feedback loop. The present study implemented a mass action model consistent with these observations. The results show that such a model can be bistable and that L-LTP induction produces an increase in the total amount of PKMζ at active synapses. The increase in PKMζ concentration was maintained through the regulation of new protein synthesis by PKMζ. The results also show that blocking the activity of PKMζ in a dose-dependent manner can effectively abolish the increase in the total amount of PKMζ, which is consistent with the effect that the PKMζ inhibitor zeta inhibitory peptide (ZIP) has experimentally demonstrated. The model is consistent with available experimental results regarding the phosphorylation levels of PKMζ and the temporal aspects of blocking experiments and produces a new prediction.