Modelling the dynamics of CaMKII-NMDAR complex related to memory formation in synapses: The possible roles of threonine 286 autophosphorylation of CaMKII in long term potentiation

A synaptic protein, Ca2+/Calmodulin dependent protein kinase II (CaMKII), has complex state transitions and facilitates the emergence of long term potentiation (LTP), which is highly correlated to memory formation. Two of the state transitions are critical for LTP: (1) threonine 286 autophosphorylation of CaMKII; and (2) binding to N-methyl-d-aspartate receptor (NMDAR) in the postsynaptic density (PSD) to form CaMKII-NMDAR complex. Both of these state transitions retain the activity of CaMKII when the induction signal disappears which is very important for the long-lasting characteristics of LTP. However, the possible relationships between the state transitions in the emergence of LTP are not well understood. We develop a mathematical model of the formation of CaMKII-NMDAR complex with the full state transitions of CaMKII, including the autophosphorylation, based on ordinary differential equations. In addition, we formulate a probabilistic framework for the binding between CaMKII and NMDAR. The model gives accurate predictions of the behaviours of CaMKII in comparisons to the experimental observations. Using the model, we show that: (1) the formation of CaMKII-NMDAR complex is dependent not only on the binding affinity between CaMKII and NMDAR, but also on the translocation of CaMKII into PSD; and (2) the autophosphorylation is not a requirement for the formation of CaMKII-NMDAR complex, but is important for the rapid formation of CaMKII-NMDAR complex during LTP.