Long range correlations in DNA sequences

Abstract

The so called long range correlation properties of DNA sequences are studied using the variance analyses of the density distribution of a single or a group of nucleotides in a model independent way. This new method which was suggested earlier has been applied to extract slope parameters that characterize the correlation properties for several intron containing and intron less DNA sequences. An important aspect of all the DNA sequences is the properties of complimentarity by virtue of which any two complimentary distributions (like GA is complimentary to TC or G is complimentary to ATC) have identical fluctuations at all scales although their distribution functions need not be identical. Due to this complimentarity, the famous DNA walk representation whose statistical interpretation is still unresolved is shown to be a special case of the present formalism with a density distribution corresponding to a purine or a pyrimidine group. Another interesting aspect of most of the DNA sequences is that the factorial moments as a function of length exceed unity around a region where the variance versus length in a log-log plot shows a bending. This is a pure phenomenological observation which is found for several DNA sequences with a few exception. Therefore, this length scale has been used as an approximate measure to exclude the bending regions from the slope analyses. The asymmetries in the nucleotide contents or the patchy structure as a possible origin of the long range correlations has also been investigated.