Calcium messenger heterogeneity: a possible signal for spike timing-dependent plasticity

Calcium concentrations as well as time courses have been used to model the signaling cascades leading to changes in the strength of synaptic connections. Previous models consider the dendritic spines as uniform compartments regarding calcium signaling. However, calcium concentrations can vary drastically on distances much smaller than typical spine sizes, and downstream targets of calcium signals are often found exactly in these calcium nanodomains. Even though most downstream targets are activated by calcium via calmodulin, which is a diffusive molecule, the capacity of calmodulin to bind to its targets even when it is not fully loaded with calcium allows its downstream cascade to be highly local. In this study, a model is proposed which uses the heterogeneity of calcium concentrations as a signal for spike-timing-dependent plasticity (STDP). The model is minimalistic and includes three sources of calcium in spines: NMDA receptors (NMDARs), voltage gated calcium channels (VGCCs) and IP3 receptors (IP3Rs). It is based on the biochemical cascades and assumption of spatial locations of four calcium-dependent enzymes: calcium/calmodulin-dependent protein kinase II located near NMDARs, calcineurin located near VGCCs, cyclic nucleotide phosphodiesterase (PDE) located near IP3Rs or NMDARs and adenylyl cyclase, located between VDCCs and NMDARs. To quantify the changes in synaptic weights the model also includes a simple description of AMPA receptor insertion in the membrane and docking to the postsynaptic density. Two parameters of the model are tuned such that weight changes produced by either pre or postsynaptic firing alone are minimal. The model reproduces the typical shape of STDP for spike doublets. If PDE is located near IP3Rs, the behavior for spike triplets is consistent with that observed in hippocampal cell culture; if near NMDAR, the behavior is similar to that observed in cortical L2/3 slices.