Categorical spectral analysis of periodicity in nucleosomal DNA

DNA helical twist imposes geometric constraints on the location of histone-DNA interaction sites along nucleosomal DNA. Certain 10.5-bp periodic nucleotides in phase with these geometric constraints have been suggested to facilitate nucleosome positioning. However, the extent of nucleotide periodicity in nucleosomal DNA and its significance in directing nucleosome positioning still remain unclear. We clarify these issues by applying categorical spectral analysis to high-resolution nucleosome maps in two yeast species. We find that only a small fraction of nucleosomal sequences contain significant 10.5-bp periodicity. We further develop a spectral decomposition method to show that the previously observed periodicity in aligned nucleosomal sequences mainly results from proper phasing among nucleosomal sequences, and not from a preponderant occurrence of periodicity within individual sequences. Importantly, we show that this phasing may arise from the histones' proclivity for putting preferred nucleotides at some of the evenly spaced histone-DNA contact points with respect to the dyad axis. We demonstrate that 10.5-bp periodicity, when present, significantly facilitates rotational, but not translational, nucleosome positioning. Finally, although periodicity only moderately affects nucleosome occupancy genome wide, reduced periodicity is an evolutionarily conserved signature of nucleosome-depleted regions around transcription start/termination sites.