Figure 2.

(a) Free energy (PMF) of the Na⁺ ion from the systems with 0 (blue) and ~240 mM (green) bulk NaCl concentrations, as described in the text. The two vertical dashed lines indicate the narrower portion of the channel where the maximum lateral distance of the ion to the pore axis during the simulation is smaller than R₀ (7 Å). In this segment the ion is thus effectively not subject to the lateral restraint u(x, y) (see Eq. 16). (b) Committor (splitting probability) for the system with 0 bulk ion concentration. The solid curve is calculated according to Eq. 12 using position-dependent diffusion coefficients D(z) (Fig. 3a), and the dashed curve shows ${\int }_z^{z_2}dz\text{exp}[G\left(z\right)∕k_{B}T]∕{\int }_{z_1}^{z_2}dz\text{exp}[G\left(z\right)∕k_{B}T]$, assuming a uniform diffusion coefficient in Eq. 12.