Protein synthesis occurs primarily in the ribosomes of a cell. These ribosomes can either be found floating freely in the cytoplasm or attached to the endoplasmic reticulum, which is then referred to as rough ER due to its studded appearance from the ribosomes.
The process of protein synthesis involves two main steps: transcription and translation. During transcription, the DNA in the nucleus is transcribed to produce messenger RNA (mRNA), which then exits the nucleus. This mRNA travels to the ribosome in the cytoplasm where translation occurs.
During translation, the ribosome reads the sequence of the mRNA and assembles amino acids in the correct order to form a polypeptide chain, which will fold into a functional protein. Therefore, while the entire process of protein synthesis begins in the nucleus, the actual synthesis of the protein takes place in the ribosomes.