DNA sequences exhibit significant intra-genomic fluctuations with respect to a model of conditional uniformity under which (1) the expected frequency of each dinuceotide (base step) is proportional to the product of the marginal (base) frequencies and (2) the observed number follows a Poisson distribution with that conditional mean. The empirical relation between dinucleotide relative density (DRD) and Shannon mutual information in base steps is explained by broadening the model to include local modulation of the conditional mean. This modulation takes the form of a power law as local and global DRD components are log-linearly related.