Final answer:
The continuity of the plasma membrane, inner nuclear membrane, and ER is due to their composition of phospholipid bilayers and interconnectedness via the endomembrane system, facilitating protein and lipid transport across the cell.
Step-by-step explanation:
The plasma membrane, inner nuclear membrane, and endoplasmic reticulum (ER) are interconnected components of what is known as the endomembrane system. This system is responsible for multiple cellular processes, including the modification, packaging, tagging, and transport of proteins and lipids. The key to their continuity is that they are all made up of phospholipid bilayers embedded with proteins.
The ER, especially the rough endoplasmic reticulum (RER), is connected to the nuclear envelope, enabling the sharing of the lumen or cisternal space. The outer membrane of the nuclear envelope is continuous with the RER, allowing for the movement of materials between the nucleus and the cytoplasm. In this way, the nuclear membrane is part of the endomembrane system, which extends and includes the plasma membrane as well.
Moreover, vesicles pinch off from the rough ER and can fuse with the plasma membrane or with the Golgi apparatus, further illustrating the interconnected nature of these cellular structures. Consequently, the transport of proteins and lipids throughout the cell takes place efficiently due to this continuity.