Nucleic acid subsequences comprising the 1st and/or 3rd codon residues in mRNAs express significantly higher free folding energy (FFE) than the subsequence containing only the 2nd residues (P < 0.0001, n = 81). This periodic FFE difference is not present in introns. The FFE in the 1st and 3rd residues is additive, which suggests that these residues contain a significant number of complementary bases and contribute to selection for local mRNA secondary structures. This periodic, codon-related structure forming of mRNAs indicates a connection between the structure of exons and the corresponding (translated) proteins. The folding energy dot plots of RNAs and the residue contact maps of the coded proteins are indeed similar. Residue contact statistics using 81 different protein structures confirmed that amino acids that are coded by partially reverse and complementary codons (Watson-Crick base pairs at the 1st and 3rd codon positions and translated in reverse orientation) are preferentially co-located in protein structures.