Which structure protects the cell and controls the movement of substances in and out of the cell?

The cell membrane is the correct choice because it serves as the protective barrier of the cell while also regulating the movement of substances in and out. This semi-permeable structure allows essential nutrients to enter the cell and waste products to exit, maintaining the internal environment critical for cellular function. The fluid mosaic model describes the structure of the cell membrane, highlighting its flexibility and the presence of various proteins that facilitate the transport of molecules.

In contrast, the cytoplasm is the gel-like substance within the cell where chemical processes occur but does not serve as a barrier. The cell wall, prevalent in plant cells and some bacteria, provides additional support and structure but is not involved in the selective transport of materials. The nucleus, on the other hand, houses the cell's genetic material and controls cellular activities but does not have a role in controlling the movement of substances across the cell's boundary.