Figure 3.

A schematic illustration of the thermodynamic cycle used to calculate the difference in free energy between the open and closed microstates. For both microstates, the calculations start from the same reference state: a fixed template (gray partial circle) soaked in water (parallel lines) which appears in the bottom. In step 1, a set of 40 loop conformations selected (for each microstate) from a 2 ns MD trajectory are reconstructed in water by HSMD leading to the loop contribution to the free energy, F_loop = E_loop − TS_loop, where E_loop [Eq. 1] consists of the loop-loop and loop-template energy and S_loop is the converged results of the entropy defined in Eqs. 13, 14; the parallel lines indicate that the loop is soaked in water, which affects its behavior, while the free energy of water is not considered directly. In step 2, the contribution of water to the free energy, $F_{\mathrm{water}}^{\mathrm{TI}}$ [Eq. 17], is calculated for each of the 40 configurations by a thermodynamic integration procedure where the loop-water interactions are increased gradually from zero (the reference state) to their full value (in practice these interactions were decreased to zero). The squared background means that the free energy of water is calculated. The total free-energy difference is $\Delta F_{\mathrm{total}}=\Delta E_{\mathrm{loop}}-T\Delta S_{\mathrm{loop}}^{}+\Delta F_{\mathrm{water}}$ [Eq. 19].