The statement 'viruses and self-proteins are examples of proteins produced inside of the cell' is TRUE. Viruses use the molecular machinery of the host to produce their structural proteins.
Viruses are often pathogenic entities that use the molecular machinery of the host cell to reproduce.
Viruses may have a genome made of DNA or RNA, which is replicated by using polymerase (either DNA or RNA polymerase) enzymes found in the host cell.
Viral proteins such as, for example, viral envelope and viral capsid, are proteins synthesized by a virus by hijacking the host's cellular machinery.
Moreover, self-proteins are also always synthesized within the cell.
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