Information-optimal transcriptional response to oscillatory driving

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 solve for the complete probabilistic description of the intrinsically noisy response to an oscillatory driving signal. We derive and numerically verify a number of simple scaling laws. Unlike in the case of measuring a static quantity, response to an oscillatory signal can exhibit a resonant frequency which maximizes information transmission. Furthermore, we show that the optimal regulatory design is dependent on biophysical constraints (i.e., the allowed copy number and response time). The resulting phase diagram illustrates under what conditions threshold regulation outperforms linear regulation.