  We propose a model for synaptic plasticity based on a calcium signaling
cascade. The model simplifies the full signaling pathways from a calcium influx
to the phosphorylation (potentiation) and dephosphorylation (depression) of
glutamate receptors that are gated by fictive C1 and C2 catalysts,
respectively. This model is based on tangible chemical reactions, including
fictive catalysts, for long-term plasticity rather than the conceptual theories
commonplace in various models, such as preset thresholds of calcium
concentration. Our simplified model successfully reproduced the experimental
synaptic plasticity induced by different protocols such as (i) a synchronous
pairing protocol and (ii) correlated presynaptic and postsynaptic action
potentials (APs). Further, the ocular dominance plasticity (or the experimental
verification of the celebrated Bienenstock--Cooper--Munro theory) was
reproduced by two model synapses that compete by means of back-propagating APs
(bAPs). The key to this competition is synapse-specific bAPs with reference to
bAP-boosting on the physiological grounds.
