Optimal Stimulation Protocol in a Bistable Synaptic Consolidation Model

Synaptic changes induced by neural activity need to be consolidated to maintain memory over a timescale of hours. In experiments, synaptic consolidation can be induced by repeating a stimulation protocol several times and the effectiveness of consolidation depends crucially on the repetition frequency of the stimulations. We address the question: is there an understandable reason why induction protocols with repetitions at some frequency work better than sustained protocols-even though the accumulated stimulation strength might be exactly the same in both cases? In real synapses, plasticity occurs on multiple time scales from seconds (induction), to several minutes (early phase of long-term potentiation) to hours and days (late phase of synaptic consolidation). We use a simplified mathematical model of just two times scales to elucidate the above question in a purified setting. Our mathematical results show that, even in such a simple model, the repetition frequency of stimulation plays an important role for the successful induction, and stabilization, of potentiation.