Figure 1. The dynamics of the protein output can result in a faithful representation of the current biological environment.

We consider a 2-stage model of gene expression [22]. The extracellular environment or input, , gives the current rate of transcription and the signal of interest . We model as either a 2-state Markov chain with equal switching rates between states (the states each have unconditional probability of ) (A&C); or as proportional to a Poissonian birth-death process for a transcriptional activator (B&D; proportionality constant of 0.025). The transformed signals (in red, lower panels) are a perfect representation of , although protein levels (in blue) are not. , the lifetime of equals 1 hr, and the translation rate . Degradation rates of mRNA and protein are chosen to maximize the fidelity, Eq. 7. The units for are chosen so that its variance equals one.