  If a semiflexible polymer confined to a narrow channel bends around by 180
degrees, the polymer is said to exhibit a hairpin. The equilibrium extension
statistics of the confined polymer are well understood when hairpins are
vanishingly rare or when they are plentiful. Here we analyze the extension
statistics in the intermediate situation via experiments with DNA coated by the
protein RecA, which enhances the stiffness of the DNA molecule by approximately
one order of magnitude. We find that the extension distribution is highly
non-Gaussian, in good agreement with Monte Carlo simulations of confined
discrete wormlike chains. We develop a simple model that qualitatively explains
the form of the extension distribution. The model shows that the tail of the
distribution at short extensions is determined by conformations with one
hairpin.
