  We modify the classical Shimada-Yamakawa theory of DNA looping by
generalizing the form of boundary constraints. This generalization is important
in the context of DNA cyclization experiments since it mimics the reduced local
rigidity of the "nicked" DNA loop. Our results indicate that the non-trivial
boundary constraints may be responsible for the existing dramatic discrepancy
between various DNA cyclization experiments. The developed effective
Hamiltonian method may be further extended to a broad class of DNA looping
problems.
