What is a defining characteristic of eukaryotic organisms?

The defining characteristic of eukaryotic organisms is the presence of a membrane-bound nucleus. This significant feature differentiates eukaryotes from prokaryotes, which do not possess a nucleus enclosed within a membrane. In eukaryotic cells, the nucleus houses the cell's genetic material, organized into chromosomes, and regulates gene expression and cell behavior. The compartmentalization provided by the nucleus allows for more complex processing and regulation of genetic information, which is pivotal in the development and functioning of multicellular organisms.

The other options presented do not characterize eukaryotic organisms. For instance, a lack of any cell organization misrepresents both eukaryotes and prokaryotes, as neither can exist without some form of cellular organization. Regarding survival in extreme conditions, while some eukaryotes can inhabit harsh environments, this trait is not exclusive to them; many prokaryotes, especially archaea, are well-known for thriving in extreme conditions. Finally, reproduction solely through binary fission is a characteristic associated more with prokaryotes; eukaryotes can reproduce through various complex processes including mitosis and meiosis, allowing for genetic diversity and multicellular development. Thus, the presence of a membrane-bound nucleus is