  A ubiquitous building block of signaling pathways is a cycle of covalent
modification (e.g., phosphorylation and dephosphorylation in MAPK cascades).
Our paper explores the kind of information processing and filtering that can be
accomplished by this simple biochemical circuit.
  Signaling cycles are particularly known for exhibiting a highly sigmoidal
(ultrasensitive) input-output characteristic in a certain steady-state regime.
Here we systematically study the cycle's steady-state behavior and its response
to time-varying stimuli. We demonstrate that the cycle can actually operate in
four different regimes, each with its specific input-output characteristics.
These results are obtained using the total quasi-steady-state approximation,
which is more generally valid than the typically used Michaelis-Menten
approximation for enzymatic reactions. We invoke experimental data that
suggests the possibility of signaling cycles operating in one of the new
regimes.
  We then consider the cycle's dynamic behavior, which has so far been
relatively neglected. We demonstrate that the intrinsic architecture of the
cycles makes them act - in all four regimes - as tunable low-pass filters,
filtering out high-frequency fluctuations or noise in signals and environmental
cues. Moreover, the cutoff frequency can be adjusted by the cell. Numerical
simulations show that our analytical results hold well even for noise of large
amplitude. We suggest that noise filtering and tunability make signaling cycles
versatile components of more elaborate cell signaling pathways.
