Noise characteristics of feed forward loops

A prominent feature of gene transcription regulatory networks is the presence in large numbers of motifs, i.e., patterns of interconnection, in the networks. One such motif is the feed forward loop (FFL) consisting of three genes X, Y and Z. The protein product x of X controls the synthesis of protein product y of Y. Proteins x and y jointly regulate the synthesis of z proteins from the gene Z. The FFLs, depending on the nature of the regulating interactions, can be of eight different types which can again be classified into two categories: coherent and incoherent. In this paper, we study the noise characteristics of FFLs using the Langevin formalism and the Monte Carlo simulation technique based on the Gillespie algorithm. We calculate the variances around the mean protein levels in the steady states of the FFLs and find that, in the case of coherent FFLs, the most abundant FFL, namely, the type-1 coherent FFL, is the least noisy. This is shown to be true for all parameter values when the FFLs operate above their thresholds of activation/repression. In the case of incoherent FFLs, no such general conclusion can be shown. The results suggest possible relationships between noise, functionality and abundance.