An analytical short- and long-term memory model of presynaptic plasticity.

A mathematical model, called the Learning Gate Model (LGM), that describes phenomena responsible for biological synaptic plasticity, is presented. The functionality of the model are mainly based on the work of Kandel and colleagues on the most elementary forms of learning observed in the Aplysia Californica marine mollusc. In particular, emphasis is placed on the double temporal dynamics of synaptic plasticity and the temporal specificity of classical conditioning. By properly modeling the effect of the binding of Ca++ ions to the serotonin-sensitive adenylate cyclase enzyme, it is shown how a positively accelerated learning curve can be obtained for sensitization and classical conditioning. Phenomena of spontaneous recovery and second-order conditioning are reproduced through simulations. Mathematical analyses of the temporal trace of conditioned stimulus and of the Short-Term Memory steady state are also given.