## 4 Conclusions  
In this work we have applied Fourier analysis to the structural properties of human chromosomes 21 and 22. By considering a chromosome as a set of units, each 1031 bp (1024 octamers) long, and summing the power spectra obtained from each unit, we obtain an overview of the power spectrum of an entire chromosome. We showed that, for a given structural parameter, the structural property spectra of chromosomes 21 and 22 are strikingly similar (Figure 2). A comparison of structural spectra with the occurrence spectra (obtained from the sequence) revealed many common peaks, in particular that at 3 bp, indicative of the presence of codons. This peak was expected in the occurrence spectra, and it is pleasing that it is also present in many structural property spectra demonstrating that such spectra can reveal known DNA characteristics. Prominent peaks found at 10.3 bp in all increasing twist flexibility spectra and also in minor groove width may indicate nucleosome wrapping propensities. Other peaks at, for example those found at 6.4 bp in all decreasing roll flexibility spectra, need further investigation in order to elucidate potential function(s).  
We have also examined the structural power spectra of three sets of transcription factor binding site regions in searches for common peaks, both for the same tfbs within different chromosomes and for different tfbs within the same chromosome (Figures 3 - 8). We found peaks at 16.5 bp for Sp1 and p53 tfbs in both chromosomes 21 and 22 for several structural properties, and also some (although fewer) common peaks at 20 bp for the same tfbs. However there are also clear differences, both between transcription factors and between chromosomes. For example p53 tfbs have a very sharp peak at 5 bp in chromosome 21 spectra for properties related to the ability to decrease roll and also in the p53 occurrence spectrum. Although this peak is not present at all in the p53 spectra of chromosome 22, it is prominent in the entire chromosome 21 occurrence spectrum (Figure 2).  
If tfbs have common peaks, which are not present in the majority of a chromosome, it should be possible to use them in a similarity search. We tested this premise using Sp1 tfbs spectra from chromosome 21. In a similarity search using the cosine distance, minor groove width retrieved on average three times as many tfbs as would be expected by chance. Fusing several properties, including minor groove width and occurrence, increased the retrieval rate to four times that of chance. Clearly this retrieval rate would not be acceptable as a means of finding tfbs. However there are already very many TFBS prediction methods, which have very high rates of false positive predictions. We anticipate that structural methods could be used as part of a consensus score, in an attempt to increase the hit rate for genuine TFBS.  
This approach provides a new strategy for searching the genome data for information. There is clear experimental evidence that DNA structure plays an important role in determining functional properties such as protein binding and that DNA structure contains information that is different from DNA sequence. Although it is difficult to understand the relationship between specific functional properties and the set of structural parameters in our database, our structural fingerprints nevertheless provide a useful tool for searching for function information in sequence data. The Fourier power spectrum fingerprints provide a simple, fast method for comparing a set of functional sequences, in this case transcription factor binding site regions, with the sequences of whole chromosomes. On its own, the power spectrum fingerprint does not find all tfbs in a chromosome, but the results presented here showthat in combination with other approaches, this technique will improve the chances of identifying functional sequences hidden in genomic data.