* Protein synthesis occurs in the cytoplasm. Specifically, it takes place on ribosomes, which are either free-floating in the cytoplasm or attached to the endoplasmic reticulum (ER).

* The cell membrane's primary function is to regulate the movement of substances in and out of the cell. It acts as a barrier, controlling what enters and exits the cell.

Here's a breakdown of where protein synthesis takes place:

1. DNA in the nucleus contains the genetic code for proteins.

2. mRNA (messenger RNA) is transcribed from DNA in the nucleus.

3. mRNA travels to the cytoplasm and binds to ribosomes.

4. Ribosomes "read" the mRNA code and assemble amino acids into protein chains.

While the ER plays a role in protein folding and modification after synthesis, the actual process of protein synthesis itself happens in the cytoplasm on ribosomes, not on the cell membrane.