A theory of ordering of elongated and curved proteins on membranes driven by density and curvature

Cell membranes interact with a myriad of curvature-active proteins that control membrane morphology and are responsible for mechanosensation and mechanotransduction. Some of these proteins, such as those containing BAR domains, are curved and elongated, and hence may adopt different states of orientational order, from isotropic to maximize entropy to nematic as a result of crowding or to adapt to the curvature of the underlying membrane. Here, extending the work of [Nascimento et. al, Phys. Rev. E, 2017, 96, 022704], we develop a mean-field density functional theory to predict the orientational order and evaluate the free-energy of ensembles of elongated and curved objects on curved membranes. This theory depends on the microscopic properties of the particles and explains how a density-dependent isotropic-to-nematic transition is modified by anisotropic curvature. We also examine the coexistence of isotropic and nematic phases. This theory lays the ground to understand the interplay between membrane reshaping by BAR proteins and molecular order, examined in [Le Roux et. al, Submitted, 2020].This work was supported by the Spanish Ministry of Economy and Competitiveness/FEDER (BES-2016-078220 to C.T.), the European Commission (H2020-FETPROACT-01-2016-669 731957), the European Research Council (CoG-681434 to M.A.), the Generalitat de Catalunya (2017-SGR-1602 to P.R-C., 2017-SGR-1278 to M.A.), the prize “ICREA Academia” for excellence in research to P.R-C. and to M.A., and Obra Social “La Caixa”. IBEC and CIMNE are recipients of a Severo Ochoa Award of Excellence from the MINECO.Peer ReviewedPreprin