## 2 Methods
### Fourier Transform Methods  
If a length of DNA contains a repetitive structural property motif this will be observed as a peak in the power spectrum obtained by taking the Fourier transform of that length of structural property values. The procedure we have followed is therefore:  
1. Take a long DNA sequence S, such as an entire chromosome, of length N bases and also a structural parameter, p, (for example roll 3). 2. First pre-process the DNA sequence. For simplicity, any bases represented by N's are deleted. (There are relatively very few of these with 140 N's in the euchromatic portion of chromosome 21 and 333 in the euchromatic portion of chromosome 22. ) All lower case entries are replaced by their upper case equivalent. 3. Consider S as a set of N-7 overlapping octamers. Divide the sequence of octamers into blocks of size M. (M is 1024 in all the work described here. N.B. 1024 octamer comprise 1031 nucleotides. In preliminary work values of M = 512 and M = 2048 gave very similar results.) 4. For each block, 1. Replace the sequence of letters by a numeric vector, consisting of the value of p determined by the minimum energy structure of each octamer. 2. Take the M-step Fourier transform of the structural property vector. 3. Obtain the power spectrum. (NB Although the power spectra are of length 1024, they are symmetric about the centre and so only the first 512 elements need be considered). 5. Sum the power spectra. 6. Optionally, normalise by dividing each element of the total spectrum by the number of blocks, to obtain a mean structural power spectrum representing the entire DNA length. When dealing with lengths of DNA comprising fewer than 1024 octamers, the process is similar, except that the structural parameter vector is padded with zeroes to give 1024 values, prior to taking its Fourier transform. Since the persistence length (the distance over which the direction of a polymer segment persists, owing to limited flexibility of the polymer) of DNA is about 150 bp, the structural parameters within each block are independent of those in the remaining blocks. We therefore sum the power spectra (Step 5), which has the effect of amplifying peaks which are found in multiple blocks. Using this method it is possible to miss patterns which overlap two blocks. However, if such a pattern occurs only once or twice within a very long sequence it will certainly be lost amongst the noise since, for example, there are 33,369 such blocks in human chromosome 21, the smallest chromosome, whilst if it occurs multiple times, most occurrences will miss an overlap. We implemented an overlapping scheme (data not shown) and found no noticeable difference in the patterns of peaks obtained to those shown here. We thus proceeded without overlap since this method facilitates the matching of a peak to the subsequences which caused it. It is common to estimate the noise in such spectra by randomising the DNA sequence and obtaining the power spectrum of the shuffled sequence [10]. We have followed this procedure, with an important modification. Rather than randomise a single sequence, we have preserved the proportion of nucleotides at a local level by randomising each block of M octamers separately. This ensures that local peaks are not solely due to the local base composition of the sequence, since such peaks will also be present in the spectrum of the randomised DNA. We then obtain a difference spectrum for the set of blocks by subtracting the summed shuffled spectra from the summed genomic spectra. Bistable octamers have two low energy structures. Our previous studies have shown that bistability is an important structural feature. In order to calculate a power spectrum representing bistability we generate a numeric sequence by replacing each octamer by 1.0 if it is bistable and 0.0 otherwise in step 4a above. In order to compare the structural parameter spectra with sequence we have followed the methods adopted by several previous workers [10,14,28] to obtain the power spectrum of a DNA sequence.