Using biochemical circuits to approximately compute log-likelihood ratio for detecting persistent signals

Given that biochemical circuits can process information by using analog computation, a question is: What compute? This paper considers the problem of to distinguish persistent signals from transient ones. We define statistical detection over reaction pathway consisting three species: an inducer, transcription factor (TF) and gene promoter, where inducer activate TF active bind promoter. model chemical master equation so counts bound promoters time is stochastic signal. consider continuous-time signal infer whether or not. use theory derive solution this problem, which compute log-likelihood ratio observing one. then show, time-scale separation other assumptions, be approximately computed number molecules when input persistent. Finally, we show coherent feedforward used