  In modeling DNA chains, the number of alternations between Adenine-Thymine
(AT) and Guanine-Cytosine (GC) base pairs can be considered as a measure of the
heterogeneity of the chain, which in turn could affect its dynamics. A
probability distribution function of the number of these alternations is
derived for circular or periodic DNA. Since there are several symmetries to
account for in the periodic chain, necklace counting methods are used. In
particular, Polya's Enumeration Theorem is extended for the case of a group
action that preserves partitioned necklaces. This, along with the treatment of
generating functions as formal power series, allows for the direct calculation
of the number of possible necklaces with a given number of AT base pairs, GC
base pairs and alternations. The theoretically obtained probability
distribution functions of the number of alternations are accurately reproduced
by Monte Carlo simulations and fitted by Gaussians. The effect of the number of
base pairs on the characteristics of these distributions is also discussed, as
well as the effect of the ratios of the numbers of AT and GC base pairs.
