  Late long-term potentiation (L-LTP) appears essential for the formation of
long-term memory, with memories at least partly encoded by patterns of
strengthened synapses. How memories are preserved for months or years, despite
molecular turnover, is not well understood. Ongoing recurrent neuronal
activity, during memory recall or during sleep, has been hypothesized to
preferentially potentiate strong synapses, preserving memories. This hypothesis
has not been evaluated in the context of a mathematical model representing
biochemical pathways important for L-LTP. I incorporated ongoing activity into
two such models: a reduced model that represents some of the essential
biochemical processes, and a more detailed published model. The reduced model
represents synaptic tagging and gene induction intuitively, and the detailed
model adds activation of essential kinases by Ca. Ongoing activity was modeled
as continual brief elevations of [Ca]. In each model, two stable states of
synaptic weight resulted. Positive feedback between synaptic weight and the
amplitude of ongoing Ca transients underlies this bistability. A tetanic or
theta-burst stimulus switches a model synapse from a low weight to a high
weight stabilized by ongoing activity. Bistability was robust to parameter
variations. Simulations illustrated that prolonged decreased activity reset
synapses to low weights, suggesting a plausible forgetting mechanism. However,
episodic activity with shorter inactive intervals maintained strong synapses.
Both models support experimental predictions. Tests of these predictions are
expected to further understanding of how neuronal activity is coupled to
maintenance of synaptic strength.
