Fig. 2: Impact of dynamic protonation on the membrane insertion of the permeation enhancer SNAC.

A λ-Coordinate definition for the CpHMD model. B PMF profiles (310.15 K, 0.15 M NaCl, pH = 5.0) for SNAC insertion into a POPC model membrane (64 lipids per leaflet). Data are provided as mean values ± SEM. The PMF compares a standard, fixed-protonation-state model for protonated SNAC (red curve) to the CpHMD model of SNAC (blue curve). The free energy curve was obtained by umbrella sampling as detailed in Supplementary Figs. 17 and 18, followed by standard WHAM analysis⁷⁰. See Supplementary Video 1 for the trajectory of the corresponding pulling simulation, which generated the initial frames for the WHAM windows. Shaded bands represent error estimates obtained with bootstrapping (n = 200) analysis implemented in the GROMACS WHAM analysis software. The distribution of lambda states at different z coordinates is shown with a grey dotted line to highlight the environment-dependent nature of SNAC protonation. These z-distance-dependent protonation probabilities were obtained from the CpHMD simulations by binning structures from select WHAM windows based on their z-positions and dividing the number of deprotonated frames by the total number of frames in each bin. Additionally, representative structures at key positions, both inside and outside of the membrane, are numbered and shown in panel (C). To evaluate how effectively different conformations of SNAC are being sampled using CpHMD as compared to standard methods, the distances d between the aromatic ring (centroid of the aromatic carbons) and carboxylic acid (centroid of the COOH functional group) of SNAC were plotted as normalized histograms. D Superimposed histogram plots with CpHMD on (blue) and off (red) for SNAC outside (1) and inside (3) of the membrane show that both methods readily sample extended and contracted conformations of SNAC inside and outside the membrane. Representative coiled and linear structures of SNAC are included with arrows pointing to their distance on each graph. SNAC favors a more coiled structure inside the membrane as compared to outside the membrane with both methods. The trajectories of both umbrella sampling windows are shown in Supplementary Video 16 and Supplementary Video 17. Source data are provided as a Source Data file.