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Identifying non-monotonicity in time-series gene expression data: on the construction of feed-forward network motifs

A feed-forward loop (FFL), a three-gene pattern normally consisting of two input transcription factors and a target gene, is a genetic network motif that regulates the responses of living cells. FFLs are often detected by computing the monotonic correlation between the expression levels of genes in a multi-sample expression experiment. However, as FFLs are involved in the dynamic behavior of transcription networks, in many cases time-series gene expression data are required. In this abstract we propose a novel strategy for the identification of non-monotonicity in time-series gene expression data. The non-monotonic relationships are then used to construct the putative feed-forward network motifs.

The gene expression data came from an 11-point time-series mESC differentiation experiment (Affymetrix Mouse Expression 430A, three biological replicates, taken at 0 h, 6 h, 12 h, 18 h, 24 h, 36 h, 48 h, 4 d, 7 d, 9 d, and 14 d). As in the original Spearman’s coefficient, our method starts by ranking the 11 time-point data according to their respective expression levels. Then we are to detect the non-monotonicity in a time-series data in which the monotonic relationship, that is, the expression level of one gene increases, so does the level of the other gene, or the level of one gene increases, the other gene’s level decreases, is only valid up to a certain time point. We achieve the detection by adjusting the rank of the original data so that the inversion of the expression trend, such as from increasing to decreasing, or vice versa, can be better reflected by the new “pseudo-rank”. In summary we are thus able to determine whether two given genes hold a non-monotonic expression relationship, and if they did, the time point at which the non-monotonic relationship starts to be evident. Putative feed-forward network motifs can be subsequently constructed using the relationships.

An initial screening reveals that a transcription factor, ZIC3, shows a negative correlation with another transcription factor, FOXM1. The inversion of the expression trend occurs between the seventh and the eighth time points (48h and 4d, respectively). The two transcription factors simultaneously regulate a target gene, IGF2BP3, in which ZIC3 initially shows a positive correlation with IGF2BP3, and then switches to a negative correlation at a point between the sixth and the seventh time points (36h and 48h, respectively). Lastly, FOXM1 is initially positively correlated with IGF2BP3, and then changes to a negative correlation between the seventh and the eighth time points. The evidences suggest that ZIC3, FOXM1 and IGF2BP3 may form a feed-forward network motif and the seventh time point plays a significant role in the regulation.