Begin by understanding the basic unit of eukaryotic chromosome compaction, which is the nucleosome. A nucleosome consists of DNA wrapped around histone proteins, forming a 'bead-on-a-string' structure.
Next, recognize that nucleosomes further compact into a 30-nm fiber. This level of compaction involves the coiling of the nucleosome chain into a thicker fiber, often referred to as the solenoid model.
After the 30-nm fiber, the structure is organized into looped domains. These loops are attached to a scaffold within the nucleus, providing additional compaction and organization.
Finally, during cell division, these looped domains are further compacted into the metaphase chromosome. This is the most condensed form of the chromosome, visible under a microscope during metaphase of mitosis.
Understand that the correct sequence of eukaryotic chromosome compaction is: Nucleosome, 30-nm fiber, looped domains, metaphase chromosome. This sequence reflects the increasing levels of DNA compaction necessary for efficient packaging within the cell nucleus.