Figure 1.

Calculation scheme of free energy profile of a protein. The distance between alpha carbon atoms at the C-terminus and N-terminus (shown as yellow spheres) is introduced as the coordinate R specifying the dimensions of the protein. (a) Thermodynamic cycle depicting the relationship in Eq. 1 among the free energy profile of the protein in water, F(R), the free energy profile in vacuum, F_vac(R), and the excess chemical potential profile, μ_ex(R), at a distance R. (b) Two different thermodynamic cycles, which allow for the calculation of F(R) and F_vac(R), if the following are obtained: free energy profile determined by the generalized Born (GB) model umbrella sampling MD simulations with a dielectric constant ε_r = 80, F_GB(R), excess chemical potential profile of the protein in the GB model with ε_r = 80 (Eq. 4), ${\mu }_{ex}^{\mathrm{GB}}(R)$, and free energy difference between the protein in water described by the GB model and that described by the RMDFT model (Eq. 7), $\mathrm{\Delta }{\mu }_{\mathrm{DFT}}^{\mathrm{GB}}(R)$.