Detection of persistent signals and its relation to coherent feed-forward loops

Many studies have shown that cells use the temporal dynamics of signalling molecules to encode information. One particular class of temporal dynamics is persistent and transient signals, i.e. signals of long and short duration, respectively. It has been shown that the coherent type-1 feed-forward loop with an AND logic at the output (or C1-FFL for short) can be used to discriminate a persistent input signal from a transient one. This has been done by modelling the C1-FFL, and then using the model to show that persistent and transient input signals give, respectively, a non-zero and zero output. The aim of this paper is to make a connection between the statistical detection of persistent signals and the C1-FFL. We begin by first formulating a statistical detection problem of distinguishing persistent signals from transient ones. The solution of the detection problem is to compute the log-likelihood ratio of observing a persistent signal to a transient signal. We show that, if this log-likelihood ratio is positive, which happens when the signal is likely to be persistent, then it can be approximately computed by a C1-FFL. Although the capability of C1-FFL to discriminate persistent signals is known, this paper adds an information processing interpretation on how a C1-FFL works as a detector of persistent signals.