  Multiple interlinked positive feedback loops shape the stimulus responses of
various biochemical systems, such as the cell cycle or intracellular calcium
release. Recent studies with simplified models have identified two advantages
of coupling fast and slow feedback loops. Namely, this dual-time structure
enables a fast response while enhancing resistances of responses and
bistability to stimulus noise. We now find that in addition: 1) the dual-time
structure confers resistance to internal noise due to molecule number
fluctuations, and 2) model variants with altered coupling, which better
represent some specific systems, share all the above advantages. We develop a
similar bistable model with a fast autoactivation loop coupled to a slow loop,
which minimally represents positive feedback that may be essential for
long-term synaptic potentiation (LTP). The advantages of fast response and
noise resistance carry over to this model. Empirically, LTP develops resistance
to reversal over ~1 h. The model suggests this resistance may result from
increased amounts of synaptic kinases involved in positive feedback.
