What do you call the semi-permeable barrier that controls molecular movement into and out of the cell?

The semi-permeable barrier that controls molecular movement into and out of the cell is called the plasma membrane. This membrane is essential for maintaining the internal environment of the cell, allowing certain substances to pass while restricting others. The plasma membrane is composed mainly of a phospholipid bilayer with embedded proteins that facilitate transport processes, communication, and cell recognition. This selective permeability is vital for the cell's ability to maintain homeostasis, respond to external signals, and engage in various metabolic activities.

In contrast, the cell wall provides structural support and protection in plants, bacteria, fungi, and some algae, but it does not play a role in regulating the movement of molecules into and out of the cell like the plasma membrane. The nuclear membrane, which surrounds the nucleus, controls the movement of substances between the nucleus and the cytoplasm but is not involved in the overall barrier function of the cell itself. Finally, the cytoplasmic matrix refers to the fluid and organelles within the cell but does not serve as a barrier for molecular movement. Hence, the plasma membrane is the key structure responsible for the selective control of substance passage in and out of the cell.