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The endomembrane system comprises functionally connected internal membranes such as the endoplasmic reticulum, Golgi apparatus, endosomes and lysosomes, together with their transport carriers. Connections through carrier traffic differ from direct continuity of the membrane sheets.

The robust starting point is a topological accounting problem. An archaeal host related to Asgard archaea and an Alphaproteobacteria-related partner must become a cell with an internal mitochondrion, a cell nucleus separated from the cytoplasm, and an interconnected endomembrane system. Their modern relatives are not unchanged ancestors. Several historical sequences can satisfy these endpoints, so the required transformations should be separated from one particular engulfment story.

The bacterial partner must become enclosed within the host's overall cellular boundary and maintained through host reproduction. Its descendants retain inner and outer mitochondrial membranes, requiring preservation or remodelling of ancestral bacterial envelope topology rather than fusion of every membrane into one. If entry used engulfment, host membrane extension, closure and a fission event would enclose the partner, and an additional host-derived surrounding membrane would have to be removed or incorporated into the evolving system. If protrusions grew around an external partner and fused, an alternative sequence could internalize it without a fully developed modern phagocytosis pathway. The modern mitochondrial envelope alone does not decide between these routes.

The host also needs a plasma membrane separating its final cytoplasm from the environment. Producing internal compartments requires membrane curvature, membrane growth and controlled membrane fusion or membrane fission. A purely continuous infolding of the surface has an extracellular-facing lumen; invagination changes geometry but does not allow a molecule to cross a lipid bilayer. Subsequent sealing and traffic can produce an internal lumen while preserving this orientation. This distinction is developed under topology of membrane compartments.

For the cell nucleus, two membranes surround the chromosome-containing compartment, with the outer nuclear envelope continuous with the endoplasmic reticulum. Openings through the envelope become selective nuclear pore complexes, while the chromosome compartment must communicate with the cytoplasm for transport without losing its identity. In an outside-in scenario, internal membranes expand around the chromosomes and fuse. In an inside-out scenario, protrusions from an ancestral chromosome-containing body expand and merge into a surrounding cytoplasm; the original boundary contributes to the nuclear boundary. The latter is an explicit alternative hypothesis, not an observed reconstruction of the event.^[ref]

Culturing an Asgard archaeon revealed extensive protrusions and close metabolic associations, motivating an entangle–engulf–endogenize proposal. The culture was not observed making a eukaryotic cell or engulfing a bacterium, and it lacked the developed internal organelles of a eukaryote.^[ref] The evidence establishes plausibility of some components, not the order of every ancestral membrane event.

The lipid divide adds a biochemical problem: typical archaeal membranes and typical bacterial/eukaryotic membranes differ in lipid linkage and glycerol stereochemistry. Replacement, coexistence or redistribution of lipid-synthesis pathways must be compatible with continuing membrane function; an abrupt wholesale replacement is not forced. Finally, membrane remodelling must be coupled to regulated protein targeting, metabolite exchange and division, so that the mitochondrion becomes an inherited endosymbiont and the new compartments persist. These requirements constrain any scenario even where the historical route remains uncertain.