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Importantly, however, these rhythms have alternating peak heights. An illustration of this phenomenon is given in Figure?2A. This is a general feature of 12?hr rhythm generation by circadian AND funnels, as explained and proven in mathematical detail in the Extended Results. In the same way, we were able to show that unequal relative amplitudes of the two TFs in a circadian AND funnel lead to 12?hr rhythms where the troughs have alternating depths (see Extended Results for proofs). Also noteworthy is that if one TF in an?AND funnel has a circadian rhythm and the other TF has a 12?hr rhythm, the resulting waveform has an 8?hr [http://en.wikipedia.org/wiki/Terminal_deoxynucleotidyl_transferase Terminal deoxynucleotidyl transferase] component in addition to circadian and 12?hr components (see Extended Results for the derivation of this result). Interestingly, 8?hr rhythms were indeed observed by Hughes et?al. (2009), [http://www.selleckchem.com/products/birinapant-tl32711.html Birinapant] although in quite few genes. The synthetic proof of principle shows that the circadian AND funnel can produce 12?hr rhythms, in accordance with?theory. However, an analysis of genome-wide data is necessary to assess whether this mechanism could be common. Specifically, if our theory that many 12?hr rhythms arise through circadian AND funnels were correct, then a pattern of alternating peak heights should be detectable and common in experimental data. Furthermore, the promoters of genes with 12?hr rhythms should be enriched for binding sites for at least two circadian, antiphase activators (or repressors), and/or combinations of one activator and one repressor with the same phase. Both these predictions were investigated next. Because of biological variability, circadian TFs that form circadian AND funnels cannot be expected to be exactly 12?hr out of phase (for two activators or two repressors) or exactly in phase (for activator-repressor combinations). Therefore, our theory leads us to expect that observed 12?hr rhythms should exhibit alternating peak heights. To examine if this is indeed the case, we analyzed data from Hughes et?al. (2009), a gold standard genome-wide CT series microarray [http://www.selleckchem.com/products/dinaciclib-sch727965.html Dinaciclib] data set, based on mouse liver samples, spanning 48?hr with a sampling rate of one per hour. From these data, we collected 197 time courses corresponding to genes with transcripts for which 12?hr rhythms were robustly detected in the original study (Experimental Procedures). At the troughs, the signal-to-noise ratio deteriorates, but patterns in the peak heights should be readily detectable. Thus, we screened for alternating peak heights in the time courses, as predicted by our theory. Assuming statistically independent peak heights, the probability for such a pattern to arise by chance is 25%, corresponding to 49 of the 197 time courses. However, we found that out of the 197 time courses, 110 (56%) exhibited alternating peak heights. This number vastly exceeds that expected by pure chance (p?