Final answer:
Polypeptide synthesis or translation occurs in the cytoplasm, not the nucleus, and is carried out by ribosomes. After synthesis, polypeptides might undergo folding, post-translational modification, and targeting.
Step-by-step explanation:
The statement, "Polypeptide synthesis occurs in the nucleus of a cell" is False. Polypeptide synthesis, or translation, involves the decoding of an mRNA message into a polypeptide product and this process takes place in the cytoplasm of the cell, not the nucleus. Specifically, translation is carried out at the ribosomes, which may be located in the cytoplasm or attached to the endoplasmic reticulum. Transcription, which is the process of creating mRNA from DNA, does occur in the nucleus of eukaryotic cells. The mRNA then travels out of the nucleus into the cytoplasm where it undergoes translation to produce polypeptides.
After a polypeptide chain is synthesized, it may undergo several additional processes including folding into its functional three-dimensional shape, post-translational modification (such as the addition of phosphate groups or carbohydrates), and targeting to its correct location within the cell or secretion outside the cell. To address part of your question, the mRNA molecule carries the codons that correspond to the genetic sequence that will be translated into a polypeptide, while tRNA molecules carry anticodons that pair with the mRNA codons and rRNA along with proteins, makes up the ribosome. The process of translation, and consequentially polypeptide synthesis, is essential for cellular function as proteins are crucial for virtually every cellular operation and structural component of the cell.