A noisy clock, explained at least sort of

If your clock has a lot of noise — which may not be at all the same thing as if your clock makes a lot of noise — telling time can be a bit involved. A fairly new study describes the situation:

“Telling time with an intrinsically noisy clock,” Andrew Mugler, Aleksandra M. Walczak, Chris H. Wiggins, arXiv:1002.2474v1, (Submitted on 12 Feb 2010)

Abstract: 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.