Cell wall Updated +Created
Eukaryotes can do phatocytosis due to their cytoskeleton Updated +Created
Power, Sex, Suicide by Nick Lane (2006) page 53 suggests that one tremendous advantage of eukaryotes over bacteria is their ability to change shape due to the presence of the cytoskeleton, and the lack of a rigid bacterial cell wall.
Imagine in a world where there are only bacteria, and you can eat entire bacteria in one go, what a huge advantage that is!
Lysozyme Updated +Created
Breaks up peptidoglycan present in the bacterial cell wall, which is thicker in Gram-positive bacteria, which is what this enzyme seems to target.
Part of the inate immune system.
It is present on basically everything that mammals and birds excrete, and it kills bacteria, both of which are reasons why it was discovered relatively early on.
Peptidoglycan Updated +Created
From the Wikipedia image we can see clearly the polymer structure formed: it is a mesh with:
Figure 1.
Peptidoglycan polymer structure
. Source.