The codons in DNA specifying amino acids in proteins. 

Demonstration of the existence of “messenger” RNA. The following paper (pp. 581-85) by F. Gros et al. is also relevant.

Order of authorship in the original publication: Sarabhai, Stretton, Brenner, Bolle. Brenner (Nobel Prize 2002) and colleagues performed the first study to show co-linearity; i.e., that there is a simple congruence between the amino acid sequence of a protein and the nucleotide sequence of the gene determining that protein. Brenner and his team were working with "nonsense" mutants, called amber mutants, that terminated protein synthesis in E. coli genes.

            "The presence of random nonsense mutants would therefore yield multiple random protein fragments of different sizes. . . . [W]e now suddenly realized that since we had all these amber mutants in this gene we could give a topological proof of co-linearity. And we wouldn't have to do any protein sequencing! The only assumption we would have to make is that the protein is always read from the same end, which seemed a very reasonable one. So in 1964 we published a paper which proved that the gene and the protein were co-linear by an argument that was totally unexpected at that time. We showed that as the amber mutations moved further and further to the right in the position of the gene, we got progressively more and more of the protein made. (Brenner, My Life, p. 103). 

In 2002 Brenner shared the Nobel Prize in Physiology or Medicine in Physiology or Medicine with H. Robert Horvitz and John Sulston "for their discoveries concerning genetic regulation of organ development and programmed cell death." Digital facsimile from PubMedCentral at this link.

Digital facsimile from PubMedCentral at this link.