Fig. 2. The hydrophobic mismatch between protein and phospholipid bilayer impacts membrane protein interactions and diffusion.

a–d HS-AFM movie frames (Supplementary Movies 3–6) of single-molecule association-dissociation dynamics at the edges of AqpZ arrays in a C18 membrane (image parameters: (a) 1.0 nm/pixel, (b) 0.5 nm/pixel, (c) 0.33 nm/pixel, and (d) 0.17 nm/pixel). Dashed outlines: association-dissociation events. Asterisk 1: one-bond event. Asterisk 2: two-bond event. These image series have been acquired 40 min (a), 2 h (b), 40 min (c), and 15 min (d) after lipid vesicle addition and continuous bilayer formation. e, f Number of molecules vs time of Supplementary movies 3 and 4, respectively (panels (a) and (b)). g Dwell-time distributions of association-dissociation events in a C18-membrane. One-bond (left, (n = 246) and two-bond (center, n = 549) events were fitted separately based on imaging knowledge using one exponential, or collectively using two exponentials (right, n = 1096). h Normalized fittings of all events in C14 (n = 308, 3 replicas), C16 (n = 761, 3 replicas), C18 (n = 1096, 3 replicas) and C20 (n = 288, 3 replicas) membranes (as indicated). Insets: Detail views of the fast exponential decay. Thick lines: averages. Thin lines: ±s.e. i HS-AFM height spectroscopy (HS-AFM-HS). Left: Schematic of HS-AFM-HS principle: The tip is at a fixed location monitoring molecular diffusion events. Middle: HS-AFM-HS height-time trace. Light gray: raw data. Dark gray: diffusion events, threshold height H_T = 5std above mean of the height distribution next to the trace. The 0 nm height level was set to the membrane surface. Right: Distribution of event dwell times τ_D. j Model of the membrane-mediated protein interactions where a diffusing molecule U can engage a 1B (one-bond) or 2B (two-bond) interaction with the array. k Association energy (ΔG⁰_asso), defined as the energy difference between states U and B, (l) energy difference between states 1B and 2B (ΔG⁰_diff), and (m) diffusion coefficient (D_U), as functions of the acyl-chain length (top) and hydrophobic mismatch (u₀), or its squared value (u₀²) (bottom). l_bilayer: Hydrophobic thickness of the membrane. The hydrophobic mismatch is calculated as u₀ = 0.5|l_bilayer – l_AqpZ|, where l_AqpZ is the hydrophobic thickness of AqpZ (~28.6 Å, Supplementary Fig. 5, dashed red lines in the top panels). Solid curves are quadratic and linear fits to the data points. Statistics (mean±s.e.) in (k) and (m) are determined from three biological replica, in each condition. Statistics (mean±s.e.) in (i) is relevant to the statistics in (h), according to Eq. (4).