Interactions between calmodulin and neurogranin govern the dynamics of CaMKII as a leaky integrator

Calmodulin-dependent kinase II (CaMKII) has long been known to play an important role in learning and memory as well as long term potentiation (LTP). More recently it has been suggested that it might be involved in the time averaging of synaptic signals, which can then lead to the high precision of the information stored at a single synapse. However, the role of the scaffolding molecule, neurogranin (Ng), in governing the dynamics of CaMKII are not yet fully understood. In this work, we adopt a rule-based modeling approach through theMonte Carlo method to study the effect of calcium signals on the dynamics of CaMKII phosphorylation in the postsynaptic densities (PSD). Calcium surges are observed in the synaptic spines during an EPSP and back-propagating action potential due to the opening of NMDA receptors and voltage dependent calcium channels. We study the differences between the dynamics of phosphorylation of CaMKII monomers and dodecameric holoenzymes. The scaffolding molecule Ng, when present in significant concentration, limits the availability of free calmodulin (CaM), the protein which activates CaMKII in the presence of calcium. We show that it plays an important modulatory role in CaMKII phosphorylation following a surge of high calcium concentration. We find a non-intuitive dependence of this effect on CaM concentration that results from the different affinities of CaM for CaMKII depending on the number of calcium ions bound to the former. It has been shown previously that in the absence of phosphatase CaMKII monomers integrate over calcium signals of certain frequencies through autophosphorylation (Pepke et al, Plos Comp. Bio., 2010). We also study the effect of multiple calcium spikes on CaMKII holoenzyme autophosphorylation, and show that in the presence of phosphatase CaMKII behaves as a leaky integrator of calcium signals, a result that has been recently observed in vivo. Our models predict that the parameters of this leaky integrator are finely tuned through the interactions of Ng, CaM, CaMKII, and PP1. This is a possible mechanism to precisely control the sensitivity of synapses to calcium signals.