  We report a theoretical study of DNA flexibility and quantitatively predict
the ring closure probability as a function of DNA contour length. Recent
experimental studies show that the flexibility of short DNA fragments (as
compared to the persistence length of DNA l_P~150 base pairs) cannot be
described by the traditional worm-like chain (WLC) model, e.g., the observed
ring closure probability is much higher than predicted. To explain these
observations, DNA flexibility is investigated with explicit considerations of a
new length scale l_D~10 base pairs, over which DNA local bend angles are
correlated. In this correlated worm-like chain (C-WLC) model, a finite length
correction term is analytically derived and the persistence length is found to
be contour length dependent. While our model reduces to the traditional
worm-like chain model when treating long DNA at length scales much larger than
l_P, it predicts that DNA becomes much more flexible at shorter sizes, which
helps explain recent cyclization measurements of short DNA fragments around 100
base pairs.
