https://doi.org/10.1140/epje/s10189-024-00456-1
Regular Article - Living Systems
Multibody interactions between protein inclusions in the pointlike curvature model for tense and tensionless membranes
Université Paris Cité, CNRS, Laboratoire Matière et Systèmes Complexes (MSC), 75013, Paris, France
a
jean-baptiste.fournier@u-paris.fr
Received:
11
July
2024
Accepted:
18
September
2024
Published online:
16
October
2024
The pointlike curvature constraint (PCC) model and the disk detachment angle (DDA) model for the deformation-mediated interaction of conical integral protein inclusions in biomembranes are compared in the small deformation regime. Given the radius of membrane proteins, which is comparable to the membrane thickness, it is not obvious which of the two models should be considered the most adequate. For two proteins in a tensionless membranes, the PCC and DDA models coincide at the leading-order in their separation but differ at the next order. Yet, for distances larger than twice the proteins diameter, the difference is less than . Like the DDA model, the PCC model includes all multibody interactions in a non-approximate way. The asymptotic many-body energy of triangular and square protein clusters is exactly the same in both models. Pentagonal clusters, however, behave differently; they have a vanishing energy in the PCC model, while they have a non-vanishing weaker asymptotic power law in the DDA model. We quantify the importance of multibody interactions in small polygonal clusters of three, four and five inclusions with identical or opposite curvatures in tensionless or tense membranes. We find that the pairwise approximation is almost always very poor. At short separation, the three-body interaction is not sufficient to account for the full many-body interaction. This is confirmed by equilibrium Monte Carlo simulations of up to ten inclusions.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.