Gamow's Diamond Code
How it worked and gave 20 amino-acids
Gamow’s Diamond Code: Gamow’s proposed the so-called overlapping “diamond genetic code” (Gamow, G. Possible relation between deoxyribonucleic acid and protein structures. Nature, 1954. 173, 318). In his code, each amino acid corresponds to a configuration of 4 bases. Two of the bases are paired on complementary strands (so only one of them is free to vary, the other is the complement of the first A=T, G=C) and the other two are adjacent bases on both sides of the central paired base so they could be different. The amino acids fit into the groove formed by the diamond and are then stitched together into a linear chain to create a protein. Gamow assumed that that the diamond formed by the four bases could be flipped end-for-end or flopped side-to-side without changing its meaning (i.e. it would code for the same amino-acid). For example, the triplet CAG becomes GAC when it is flipped end-for-end, hence both of these codons must specify the same amino acid. Flopping CAG side-to-side changes the middle A into a complementary T, so that CTG and GTC are also members of the same family of equivalent codons. Show that if one accounts for these degeneracies, the number of possible configurations is exactly 20.
Hint: The diamond code is really a 3 nucleotide code because one of the nucleotides is always paired with its complement. Suppose we place the paired nucleotide in the middle. Then, the codon is represented by XYZ where Y is paired with its complement. If Y is the complement of Y, then when X≠Z, the equivalency operations (which do not change the amino acid) are represented by the transformations:
X Y Z = X Y Z = Z Y X=Z Y X.
On the other hand, when X=Z, the equivalency operation is
X Y X = X Y X
Solution: The above symmetry operations give the following 20 equivalence classes for the 4 possible values of X,Y,Z:
AAA=ATA
CCC=CGC
GGG=GCG
TTT=TAT
CAC=CTC
GAG=GTG
ACA=AGA
TCT=TGT
AAC=ATC=CAA=CTA
AAG=ATG=GAA=GTA
AAT=ATT=TAA=TTA
GGA=GCA=AGG=ACG
ACT=AGT=TCA=TGA
CAG=CTG=GAC=GTC
CAT=CTT=TAC=TTC
CCG=CGG=GCC=GGC
CCT=CGT=TCC=TGC
GAT=GTT=TAG=TTG
GCT=GGT=TCG=TGG
ACC=AGC=CCA=CGA
It is easy to check that each one of the 64 possible ways to combine the nucleotides three at a time is represented exactly once in the above set of equivalence classes. Gamow’s diamond coding would choose one member of each equivalence class to assign to a unique amino acid.