5.2.3 Free energy of the end loop

The end loop of the molecule is a group of 4 bases that forms a different structure from the Watson-Crick base-pairs. The loop is a motif in which the backbone of the ssDNA molecule bends and twists itself. This induces a change in the orientation of the backbone that permits the formation of the DNA duplex (see Fig. 5.6a). The loop is quite useful in unzipping/rezipping experiments because the two strands of DNA are not completely split apart after unzipping, which facilitates the rezipping. Moreover, the end loop allows us to measure the elastic response of a ssDNA above $ \sim15$ pN, which is an important piece of information to infer the NNBP energies from unzipping experiments (see Fig. 5.3c,d).

The free energy formation of the loop gets contributions from the bending energy, the stacking of the bases in the loop and the loss of entropy of the ssDNA. The energy formation of the loop is positive, meaning that the loop is an unstable structure at zero force. Upon decreasing the total extension, the formation of complementary base pairs along the sequence reduces the total energy of the molecule and the loop can be formed.

The effect of the loop is appreciated only in the last rip of the FDC. It introduces a correction to the free energy of the fully extended ssDNA molecule and modifies the force at which the last rip is observed (Fig. 5.6b).

Figure 5.6: End loop. (a) The formation of the end loop involves the bending and twisting of the sugar-phosphate backbone of the DNA (depicted in blue). The four bases of the tetraloop (depicted in green) cannot form Watson-Crick base-pairs and the free energy of formation is positive (the loop is unstable). (b) Effect of the loop contribution on the FDC. The free energy of the loop modifies the shape of the theoretical FDC only at the last rip just before the elastic response of the full ssDNA is observed. The black curve is the experimental FDC. All other curves show theoretical FDCs with different values of $ \epsilon _\mathrm {loop}$. Red curve, best fit with $ \epsilon _\mathrm {loop}=2.27$ kcal$ \cdot $mol$ ^{-1}$; magenta curve, $ \epsilon _\mathrm {loop}=0.0$ kcal$ \cdot $mol$ ^{-1}$; green curve, $ \epsilon _\mathrm {loop}=1.00$ kcal$ \cdot $mol$ ^{-1}$; blue curve, $ \epsilon _\mathrm {loop}=2.00$ kcal$ \cdot $mol$ ^{-1}$ and orange curve, $ \epsilon _\mathrm {loop}=3.00$ kcal$ \cdot $mol$ ^{-1}$.
\includegraphics[width=\textwidth]{figs/chapter5/loop.eps}

JM Huguet 2014-02-12