6.2.1 Free energy landscape

Once the intermediate states are identified, we can explore the localization of these states in the free energy landscape. The free energy landscape is calculated according to the tools exposed in Sec. 3.4.2. The force applied to the DNA molecule induces a tilt in the free energy landscape that tends to progressively decrease the energies of the states with a large number of open base pairs. The result is that the system is more stable for larger values of $ n$ as the force is increased.

Figure 6.5a shows the free energy landscape computed at a fixed force, together with the metastable states detected during unzipping according to the analysis of the previous section (see also Fig. 6.4). These states are localized at the beginning of the molecule and the separation between them increases as the molecule is unzipped. What is the characteristic property of these states that we observe during the unzipping? Why do we observe these states and not the other ones? The answer is not straightforward because there is no general theory to study the kinetics of systems that exhibit rough landscapes.

Nevertheless, we can suggest a heuristic explanation. These metastable states are separated by energy barriers that decrease their height as the force increases. At the beginning of the pulling (i.e., low forces), the tilt of the landscape induced by the force strongly affects the energy of the states with a few open base-pairs. This induces transitions between the initial states, characterized by the opening of a few base-pairs. As the force increases, the tilt reduces the energy of the states with a larger number of open base-pairs. The transitions then become less frequent and the number of open base-pairs in each transition increases significantly.

This very same effect is observed during the rezipping but in the opposite sense (see Fig. 6.5b). Initially we observe fast and small transitions between the states with a large number of open base-pairs. As the force decreases, the transitions become larger and less frequent until the molecule is completely folded.

This mechanism prevents the system to explore all the free energy landscape at the theoretical equilibrium force. This is the reason why we always observe hysteresis in CF experiments performed at the lab time scale.

Figure 6.5: Location of intermediate states in the free energy landscape for the 2.2 kbp sequence. (a) Free energy landscape (green curve) and localization of intermediate states observed during unzipping (red marks) at CF. The landscape has been calculated at the coexistence force, $ f=16.5$ pN. Note that more metastable states are detected at the beginning of the molecule. The arrow indicates the succession of observed states. (b) Same graphic for rezipping. The observed intermediate states are depicted in blue.

JM Huguet 2014-02-12