A Ca²⁺-based computational model for NMDA receptordependent synaptic plasticity at individual post-synaptic spines in the hippocampus

Associative synaptic plasticity is synapse specific and requires coincident activity in pre-synaptic and post-synaptic neurons to activate NMDA receptors (NMDARs). The resultant Ca²⁺ influx is the critical trigger for the induction of synaptic plasticity. Given its centrality for the induction of synaptic plasticity, a model for NMDAR activation incorporating the timing of pre-synaptic glutamate release and post-synaptic depolarization by back-propagating action potentials could potentially predict the pre- and post-synaptic spike patterns required to induce synaptic plasticity. We have developed such a model by incorporating currently available data on the timecourse and amplitude of the post-synaptic membrane potential within individual spines. We couple this with data on the kinetics of synaptic NMDARs and then use the model to predict the continuous spine [Ca²+] in response to regular or irregular pre- and post-synaptic spike patterns. We then incorporate experimental data from synaptic plasticity induction protocols by regular activity patterns to couple the predicted local peak [Ca²⁺] to changes in synaptic strength. We find that our model accurately describes [Ca²⁺] in dendritic spines resulting from NMDAR activation during pre-synaptic and post-synaptic activity when compared to previous experimental observations. The model also replicates the experimentally determined plasticity outcome of regular and irregular spike patterns when applied to a single synapse. This model could therefore be used to predict the induction of synaptic plasticity under a variety of experimental conditions and spike patterns.