We study statistical properties of the Jensen-Shannon divergence D, which quantifies the difference between probability distributions, and which has been widely applied to analyses of symbolic sequences. We present three interpretations of D in the framework of statistical physics, information theory, and mathematical statistics, and obtain approximations of the mean, the variance, and the probability distribution of D in random, uncorrelated sequences. We present a segmentation method based on D that is able to segment a nonstationary symbolic sequence into stationary subsequences, and apply this method to DNA sequences, which are known to be nonstationary on a wide range of different length scales.

A segmentation algorithm based on the Jensen-Shannon entropic divergence is used to decompose longrange correlated DNA sequences into statistically significant, compositionally homogeneous patches. By adequately setting the significance level for segmenting the sequence, the underlying power-law distribution of patch lengths can be revealed. Some of the identified DNA domains were uncorrelated, but most of them continued to display long-range correlations even after several steps of recursive segmentation, thus indicating a complex multi-length-scaled structure for the sequence. On the other hand, by separately shuffling each segment, or by randomly rearranging the order in which the different segments occur in the sequence, shuffled sequences preserving the original statistical distribution of patch lengths were generated. Both types of random sequences displayed the same correlation scaling exponents as the original DNA sequence, thus demonstrating that neither the internal structure of patches nor the order in which these are arranged in the sequence is critical; therefore, long-range correlations in nucleotide sequences seem to rely only on the power-law distribution of patch lengths.

We present a new computational approach to finding borders between coding and noncoding DNA. This approach has two features: (i) DNA sequences are described by a 12-letter alphabet that captures the differential base composition at each codon position, and (ii) the search for the borders is carried out by means of an entropic segmentation method which uses only the general statistical properties of coding DNA. We find that this method is highly accurate in finding borders between coding and noncoding regions and requires no "prior training" on known data sets. Our results appear to be more accurate than those obtained with moving windows in the discrimination of coding from noncoding DNA.

A new complexity measure, based on the entropic segmentation of DNA sequences into compositionally homogeneous domains, is proposed. Sequence compositional complexity (SCC) deals directly with the complex heterogeneity in nonstationary DNA sequences. The plot of SCC as a function of significance level provides a profile of sequence structure at different length scales. SCC is found to be higher in sequences with long-range correlation than those without, and higher in noncoding sequences than coding sequences. Furthermore, a general agreement is found between the SCC of the DNA sequence, on one hand, and the biological complexity of the organism, on the other, attributable to an increasingly complex organization of noncoding DNA over the course of evolution.[S0031-9007(97)05210-1]

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