Mathematical modeling and bistability analysis for synaptic tagging and synapse-specific long-term facilitation in Aplysia

Long-term facilitation (LTF) of sensory to motor neuron synapses of the gill-withdrawal reflex in Aplysia is synapse-specific that requires local protein synthesis at activated synapses. At molecular and cellular levels, a multi-scale model is proposed to characterize synapse specificity of LTF which integrates transcription and local translation controlled by cytoplasmic polyadenylation element binding protein (CPEB) in presynaptic sensory neuron, and presynaptic membrane action potential with the excitatory postsynaptic potential (EPSP) of a sensory neuron connected with three different motor neurons. Motif of a positive feedback loop involving local protein synthesis exhibits reversible and irreversible bistable switches, and the bistability crucial for LTF induction is robust to variations of parameters in the subsystem of the positive feedback loop. Moreover, the EPSP amplitude increases with level of active protein kinase A (PKA) due to spike broadening of the presynaptic action potential produced by PKA. Simulations through four stimulus protocols in the model verify synapse-specific LTF is established only at activated synapses, based on the bistable switch in the subsystem of the positive feedback loop. The model brings insights into underlying mechanisms of the synapse specificity of LTF in Aplysia, and further understanding of fundamental processes involved in synaptic plasticity and memory formation.