Spatial inhomogeneities are essential for biological membrane function. They could trigger structural transformations in membranes as well as changes in their global behaviours, and influence intercell communications. This study investigates how curvature-enforcing inclusions and in-plane orientational order generate such patterns. We focus on membranes exhibiting spherical topology, consisting of primary (lipids) and secondary (inclusions) constituents. Using Monte Carlo simulations, we show that, for a high enough concentration of inclusions, a budding instability appears below a critical temperature. The complexity of patterns is further increased if membranes exhibit in-plane order. According to the Gauss–Bonnet and Poincare–Hopf theorems in membranes of non-toroidal topology, topological defects are inevitably formed which introduce centres exhibiting strongly local elastic distortions. Regions exhibiting a large enough local curvature could trigger additional pairs of defects. Furthermore, condensed in-plane order could generate a Flory–Huggins-type contribution, promoting the assembly of membrane inclusions. Finally, memory effects are expected to play an important role.
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