## 3 Results and Discussion
### Transcription Factor Binding Site Transforms  
We plotted the summed difference spectra of the Sp1, p53 and cMyc tfbs from chromosome 21 (Figures 3-5) and chromosome 22 (Figures 6-8) against the summed difference spectra of the randomised subsequences for each of the structural parameters of Table 1. Each summed difference spectrum is normalised by dividing by its range; the spectra are then offset. This means that the heights of the peaks are not directly comparable - the purpose of the plots is to see the relative positions of peaks for each transcription factor type. The plots are grouped as follows: flexibility force constants (Figures 3, 6), partition coefficients (Figures 4, 7) and the remaining non-flexibility properties (Figures 5, 8). The original Sp1 difference spectrum in chromosome 21 was dominated by the spectrum of a particular tfbs, number 76 (see the discussion below) and so, in the comparison plots of Figures 3-5 this tfbs is omitted from each of the Sp1 difference spectra. Similarly, the Sp1 spectrum in chromosome 22 was also dominated by a particular tfbs, number 209 (position 49476821 - 49477821), and the p53 spectrum in chromosome 22 was dominated by spectra 62 (position 49408559 - 49409559) and 63 (position 49410481 - 49411481) and so these tfbs were omitted from the Sp1 and p53 difference spectra respectively of chromosome 22 (Figures 6, 7, 8). **Figures 3-5. ** Comparison between Flexibility Force Constant Difference Spectra, Partition Coefficient Difference Spectra and Non-flexibility Property Difference Spectra of Tfbs in Chromosome 21. **Figure 6-8. ** Comparison between Flexibility Force Constant Difference Spectra, Partition Coefficient Difference Spectra and Non-flexibility Property Difference Spectra of Tfbs in Chromosome 22. These six figures provide an overview of the spectra of these set of tfbs. Peaks occur in several properties for the same set of tfbs, giving some confidence that they represent genuine features, rather than random fluctuations. In order to see common peaks more clearly we have added boxes colouredaccording to peak position for selected positions, as follows: - black - 3 bp; yellow - 5 bp; brown - 11.5 bp; blue - 16.5 bp; grey - 20 bp, purple - 30 bp and magenta - 40 bp. We notice that both chromosome 21 and 22 show peaks in the sequence spectra at 3 bp (black boxes) for all three TFs, indicating the presence of codons in at least some of the sequences [Figures 5(h) and 8(h)]. This is not surprising since the sequences are all 1001 bp, with the actual TFBS somewhere within the sequence- it is very likely that the coding sequence will overlap the 1001 bp for some of the tfbs. The coding peaks also show up in some of the structural properties, such as 3-step shift [Figures 5(d) and 8(d)]. In chromosome 21, Sp1 spectra have peaks at 16.5 bp (blue boxes) for most structural properties, although not for sequence. The same peaks are present for p53 spectra in most cases, but are absent from the cMyc spectra. Sp1 and p53 tfbs show some of the same peaks in chromosome 22. Sp1 spectra in chromosome 21 also have peaks at 20 bp (grey boxes) which are not present in the p53 or cMyc spectra, but which do occur for Sp1 in chromosome 22 for some spectra (Figures 7, 8). Several p53 spectra, including sequence and decreasing twist flexibility, have a particularly sharp peak at 5 bp (yellow boxes) which is not apparent in any of the other tfbs spectra in either chromosome. Interestingly, however, the whole chromosome 21 sequence spectra of Figure 2 has a similar very sharp peak. p53 spectra have several other clear common peaks--we have indicated those at 11.5 bp with a brown box. These 11.5 bp peaks often co-occur with other sharp peaks (not boxed), suggesting that they may be related [Figures 3(g) and 5(c), (e), (f)]. The cMyc spectra seem to have fewer common peaks. However, many properties have a peak at about 30 bp (purple box) which are shared with p53 properties, for example, most of the partition coefficients (Figure 4).