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Cell membranes interact with a myriad of curvature-active proteins thatcontrol membrane morphology and are responsible for mechanosensation andmechanotransduction. Some of these proteins, such as those containing BARdomains, are curved and elongated, and hence may adopt different states oforientational order, from isotropic to maximize entropy to nematic as a resultof 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], wedevelop a mean-field density functional theory to predict the orientationalorder and evaluate the free-energy of ensembles of elongated and curved objectson curved membranes. This theory depends on the microscopic properties of theparticles and explains how a density-dependent isotropic-to-nematic transitionis modified by anisotropic curvature. We also examine the coexistence ofisotropic and nematic phases. This theory lays the ground to understand theinterplay between membrane reshaping by BAR proteins and molecular order,examined in [Le Roux et. al, Submitted, 2020].

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