An integrated mathematical model of synaptic plasticity induction by postsynaptic Ca²⁺ influx through the interactions of AMPA and NMDA receptors

N-methyl-D-aspartate receptors (NMDAR) dependent Long-Term Potentiation and Depression (LTP and LTD) are widely studied forms of synaptic plasticity and are believed to be crucial mechanisms related to memory formation. In CA1 of the hippocampus, Ca2+ influx in the postsynaptic spine, triggered by glutamate stimulation of the synapse through a complex process involving NMDARs and α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptors (AMPARs), is a key component of both LTP and LTD inductions. Postsynaptic Ca2+ activates calmodulin (CaM), which triggers a signalling pathway leading to LTD or LTP if the synapse is stimulated by the low- or high-frequency signals, respectively. In this study, we develop an integrated mathematical model, using the frequency of the glutamate stimulation as the input, to explain the Ca2+ dynamics as a result of the interaction of AMPAR and NMDAR and the subsequent Ca2+-dependent activation of CaM. We discuss the development of the model and the linkage between a few model components, including receptor dynamics, Ca2+ dynamics, and CaM activation, through an electrophysical model of the postsynaptic membrane. Using this model, we investigate the receptor behaviours and Ca2+ patterns following low- and high- frequency stimulations. The levels of the CaM activation as the result of the distinct Ca2+ patterns may explain the frequency dependence of LTD/LTP inductions