  We introduce an analytical method to generate the pathway of a closed
protein-bound DNA minicircle. This is a general method which can be used to
connect any two open curves with well defined mathematical definitions as well
as pairs of discrete systems found experimentally. We used this method to
describe the configurations of torsionally relaxed, 360-base pair DNA rings
with two evenly-spaced, ideal nucleosomes. We considered superhelical
nucleosomal pathways with different levels of DNA wrapping and allowed for
different inter-nucleosome orientations. We completed the DNA circles with the
smooth connectors and studied the associated bending and electrostatic energies
for different configurations in the absence and presence of salt. The predicted
stable states bear close resemblance to reconstituted minicircles observed
under low and high salt conditions.
