Expansion of tandem repeats and oligomer clustering in coding and noncoding DNA sequences

We review recent studies of distribution of dimeric tandem repeats and short oligomer clustering in DNA sequences. We find that distribution of dimeric tandem repeats in coding DNA is exponential, while in noncoding DNA it often has long power-law tails. We explain this phenomenon using mutation models based on random multiplicative processes. We also develop a clustering measure based on percolation theory that quantifies the degree of clustering of short oligomers. We find that mono-, di-, and tetramers cluster more in noncoding DNA than in coding DNA. However trimers have some degree of clustering in coding DNA and noncoding DNA. We relate this phenomena to modes of tandem repeat expansion.