Repeated stimuli that are spaced apart in time promote the transition from short- to long-term memory, while massing repetitions together does not. Previously, we showed that a model of integrative synaptic plasticity, in which plasticity induction signals are integrated by a low-pass filter before plasticity is expressed, gives rise to a natural timescale at which to repeat stimuli, hinting at a partial account of this spacing effect. The account was only partial because the important role of neuromodulation was not considered. We now show that by extending the model to allow dynamic integrative synaptic plasticity, the model permits synapses to robustly discriminate between spaced and massed repetition protocols, suppressing the response to massed stimuli while maintaining that to spaced stimuli. This is achieved by dynamically coupling the filter decay rate to neuromodulatory signaling in a very simple model of the signaling cascades downstream from cAMP production. In particular, the model's parameters may be interpreted as corresponding to the duration and amplitude of the waves of activity in the MAPK pathway. We identify choices of parameters and repetition times for stimuli in this model that optimize the ability of synapses to discriminate between spaced and massed repetition protocols. The model is very robust to reasonable changes around these optimal parameters and times, but for large changes in parameters, the model predicts that massed and spaced stimuli cannot be distinguished or that the responses to both patterns are suppressed. A model of dynamic integrative synaptic plasticity therefore explains the spacing effect under normal conditions and also predicts its breakdown under abnormal conditions.

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