What structure facilitates the transport of materials in and out of the nucleus?

The structure responsible for facilitating the transport of materials in and out of the nucleus is the nuclear pore complex. This complex consists of multiple proteins that form channels in the nuclear envelope, which is the membrane surrounding the nucleus. These channels allow for the selective passage of molecules such as RNA and ribosomal proteins from the nucleus to the cytoplasm, and the import of proteins and other necessary materials into the nucleus from the cytoplasm. The nuclear pore complex ensures that only specific molecules can enter or exit, maintaining the nucleus's environment and function throughout the cell cycle.

The other options serve different roles within the cell. The plasma membrane encloses the cell as a whole, the endoplasmic reticulum contributes to protein and lipid synthesis and transport within the cytoplasm, and the Golgi apparatus is involved in modifying, sorting, and packaging proteins and lipids for secretion or delivery to other organelles. However, none of these directly mediate transport through the nuclear envelope like the nuclear pore complex does.