Final answer:
Eukaryotes differ from archaea and bacteria in that they contain a membrane-bound nucleus and mitochondria but do not have peptidoglycan in their cell membranes, making option 4 'a and c are correct' the true statement.
Step-by-step explanation:
Eukaryotes differ from archaea and bacteria because they contain a nucleus and mitochondria. Unlike prokaryotes which include archaea and bacteria, eukaryotic cells have membrane-bound organelles, including a membrane-bound nucleus and mitochondria, which are organelles responsible for energy production. The cell membrane of bacteria contains peptidoglycan, whereas eukaryotes do not have peptidoglycan in their cell membranes. Therefore, Option 4 (a and c are correct) is the correct answer to the question.
The unique structure of eukaryotic cells allows them to perform complex functions. The presence of a nucleus in eukaryotic cells provides a distinct advantage by separating DNA from the cytoplasm, thereby regulating gene expression and DNA replication more intricately. Furthermore, mitochondria are important in energy production and have a role in other cellular processes like signaling, cellular differentiation, and the maintenance of the cell cycle and cell growth.
Prokaryotic cells, such as those of archaea and bacteria, lack these membrane-bound organelles and instead, have a simplified cell structure. Their DNA is found in the nucleoid region, and while they may have structures such as flagella and pili for movement and attachment, these are not membrane-bound. Additionally, archaea's cell membrane is composed of phytanyl groups, making them resistant to extreme environments, which is another distinct difference between bacterial and eukaryotic cells.
In summary, while archaea and bacteria share some similarities, eukaryotes have distinct characteristics that set them apart, primarily their cellular organization which includes the existence of a nucleus and mitochondria, but not peptidoglycan in their cell membranes. These differences have enormous implications for the complexity and functionality of eukaryotic cells compared to prokaryotic ones.