Figure 2. Change of PPL protonation state during permeation.

(A) Free energy surface (FES) as a function of insertion depth (ΔZCOM) and the titration coordinate of PPL (λ^PPL) at pH 7. Contour lines are displayed every 1 k_BT. The dashed vertical white lines mark where PPL titrates (λ^PPL changes from 0, i.e., PPL⁺, to 1, i.e., PPL⁰). The average standard deviation from block analysis is 0.3 k_BT. (B) Volume probability distributions for the density profile model¹⁰⁰ of components of the POPC bilayer. Componentization follows Kucerka et al.:¹⁰¹ water (H₂O, brown), phosphate and CH₂CH₂N part of choline (PCN, red), 3xCH₃ part of choline (CholCH₃, green), carbonyl and glycerol groups (CG, black), methine group (CH, cyan), methylene groups (CH₂, blue), methyl groups (CH₃, magenta), and the total hydrocarbon tails (HC, orange). Data collected from the umbrella sampling run at pH 7 with PPL at ΔZCOM = 13.5 Å. The vertical purple and dark green dot-dashed lines mark the hydrophobic boundary (D_C) and bilayer surface (D_B/2),¹⁰⁰ respectively. The background gray box highlights the titration region (same below). A schematic POPC molecule is mapped along the bilayer normal in the center with components colored accordingly. (C) The ΔpK_a of PPL as a function of ΔZCOM. Black line was calculated from the PMFs in Figure 1B with error bars calculated from error propagation. Red circles represent the pK_a values calculated from CpHMD with error bars calculated from three independent runs. (D) The hydration number of PPL, counted as the number of water oxygen atoms within 3.5 Å of the PPL titrating nitrogen (Figure 1A) as a function of ΔZCOM. Error bars indicate the standard deviations from block analysis and are shown every 3 Å for clarity.