  Intracellular transmission of information via chemical and transcriptional
networks is thwarted by a physical limitation: the finite copy number of the
constituent chemical species introduces unavoidable intrinsic noise. Here we
provide a method for solving for the complete probabilistic description of
intrinsically noisy oscillatory driving. We derive and numerically verify a
number of simple scaling laws. Unlike in the case of measuring a static
quantity, response to an oscillatory driving can exhibit a resonant frequency
which maximizes information transmission. Further, we show that the optimal
regulatory design is dependent on the biophysical constraints (i.e., the
allowed copy number and response time). The resulting phase diagram illustrates
under what conditions threshold regulation outperforms linear regulation.
