Distribution Functions, Loop Formation Probabilities and Force-Extension Relations in a Model for Short Double-Stranded DNA Molecules

We obtain, using transfer matrix methods, the distribution function $P(R)$ of the end-to-end distance, the loop formation probability and force-extension relations in a model for short double-stranded DNA molecules. Accounting for the appearance of ``bubbles'', localized regions of enhanced flexibility associated with the opening of a few base pairs of double-stranded DNA in thermal equilibrium, leads to dramatic changes in $P(R)$ and unusual force-extension curves. An analytic formula for the loop formation probability in the presence of bubbles is proposed. For short {\em heterogeneous} chains, we demonstrate a strong dependence of loop formation probabilities on sequence, as seen in recent experiments.