3.4 Modeling of experimental setup

In order to understand the mechanism of the unzipping process it is useful to have a model that reproduces the physics behind the experiments. A description of the experiment can be done at several degrees of accuracy: from an atomistic description to mesoscopic models. In general, each model focuses on a particular aspect of the experiments: thermodynamics, kinetics, scaling properties, etc. The aim of this section is to develop a mesoscopic model to study the thermodynamics of the DNA [112]. The model describes separately the different constituents of the experimental setup by using other submodels such as the NN model (described in the previous section) and the models for the elasticity of polymers. The standard techniques of statistical mechanics can be applied to the model in order to compute the partition function, the free energy landscape and the equation of state of the system.

In most macroscopic thermodynamic systems (e.g., ideal gas) the computation of the equation of state can be performed in different statistical ensembles (microcanonical, canonical, grand canonical). In principle, the result should not depend on the ensemble selected to perform the calculation if we take the thermodynamic limit. In the case of the DNA, the calculation of the thermodynamic properties of the model can be done in two ensembles: controlled position (also known as mixed [122,112] or isometric [123]) ensemble and controlled force (also known as isotensional [123]) ensemble (see Fig. 3.14). In DNA unzipping, though, the resulting equation of state depends on the ensemble. The differences between them are due to the finite size effects. Following, there are two separate descriptions of the model, one for each ensemble.

Figure 3.14: Ensembles. (a) Controlled position ensemble. The total distance ( $ x_\mathrm {tot}$) between the anchor point and the center of the optical trap is held constant. The position of the bead ($ x_b$) in the optical trap fluctuates and so does the applied force $ f$ ($ k$ is the trap stiffness). (b) Controlled force ensemble. The force is controlled by keeping constant the position of the bead in the optical trap ($ x_b$). In order to do so, the total distance of the system ( $ x_\mathrm {tot}$) must be corrected by a feedback. Therefore, $ x_\mathrm {tot}$ fluctuates. This ensemble can also be implemented by applying a uniform field of force as in magnetic tweezers.

JM Huguet 2014-02-12