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. 2022 Nov 30;13:7373. doi: 10.1038/s41467-022-35202-8

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© The Author(s) 2022

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 5 — The AqpZ-W14A oligomerization energetics was estimated based on observation statistics of non-tetrameric complexes. The protomer interaction ΔG⁰_olig is weakest (~−2 k_BT) in C20 lipids that match the hydrophobic thickness of the protomer interface. AqpZ diffusion D_U is slowed in lipids with larger hydrophobic mismatch (thicker and thinner). Membrane-mediated membrane protein interaction ΔG⁰_asso is most favorable (~−6.5 k_BT) in lipids with thickness close to the hydrophobic thickness of the protein. Bond formation with two array-bound proteins, filling gaps in the 2D-plane, provides a maximum energy gain ΔG⁰_diff in lipids with strong mismatch (~−3 k_BT). The latter driving the assembly towards the formation of membrane protein arrays. The direct (not membrane-mediated) protein–protein interaction ΔG⁰_P-P (~−2 k_BT) stabilizes these interactions at very short distances.