The process that transmits information stored in DNA to protein synthesis is called gene expression. Here's how it works:

1. Transcription: The DNA sequence of a gene is copied into a messenger RNA (mRNA) molecule. This happens within the nucleus of the cell.

2. Translation: The mRNA molecule travels out of the nucleus and attaches to a ribosome. The ribosome reads the mRNA sequence, which is a series of codons (three-nucleotide units). Each codon specifies a particular amino acid.

3. Amino Acid Assembly: Transfer RNA (tRNA) molecules, each carrying a specific amino acid, bind to the mRNA codons. The ribosome links the amino acids together in the order specified by the mRNA, forming a polypeptide chain.

4. Folding and Modification: The polypeptide chain folds into a specific three-dimensional shape, often with the help of other proteins. It may also undergo further modifications, such as the addition of sugars or lipids.

In summary: DNA stores the genetic information, and mRNA acts as a messenger to carry this information to the ribosomes where protein synthesis takes place. The protein's final shape and function are determined by the DNA sequence and the process of translation.