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A eukaryotic cell is easiest to diagnose the way a pathologist reads a tissue section. Identify structures first, then predict function from structure, then predict failure when that structure is disrupted. On an electron micrograph, start with the biggest landmarks and work inward.
Use the labeled micrograph to practice the same scan every time, boundary, nucleus, internal membranes, energy organelles, degradative compartments.
Membranes do more than separate spaces. They define which side of a protein faces the cytosol, and that orientation is preserved through vesicle traffic. This is why topology diagnoses pathway problems better than just where an organelle sits in the cell.
In the secretory pathway, the lumen is the interior aqueous space enclosed by a membrane, and the cytosol is the aqueous space outside those membranes. The ER lumen, Golgi lumen, transport vesicle lumen, and lysosome lumen are topologically equivalent compartments. They are all separated from cytosol by a membrane and they keep the same sidedness as cargo moves.
The nuclear envelope is a double membrane. Its nuclear pore complex is the gate that allows selected proteins and RNAs to cross while keeping chromatin and many enzymes compartmentalized. The outer nuclear membrane is continuous with rough ER, which is why ribosomes can decorate both.
Work through the cross sections and label which face is cytosolic and which is luminal before you assign function to any membrane protein.
Golden rule
If a protein domain is luminal in the ER, it will remain luminal in the Golgi and inside secretory vesicles. It will not spontaneously become cytosolic without a membrane crossing mechanism.
When an organelle fails, the phenotype often reflects a bottleneck in matter flow or information flow.
Match the vignette patterns to the organelle that best explains them mechanistically, not just by association.