(300e) A Tri-Frame Code Controls Entropy and Expression Levels of Proteins

The tri-frame coding theory shows that the genetic code uses all three reading frames to encode for the following information: what must be synthesized, how much of it must be synthesized and how accurately it must be synthesized. The zero reading frame (0RF) encodes for the amino acid sequence. The combination of rare codons in the 0RF and stop codons in the +/-1RF controls the ribosome transit time of the mRNA and hence the expression level. Rare codons in 0RF causes the ribosome to frame-shift and the incomplete polypeptide chain is tagged and terminated in the -1RF and +1RF with high probability. If the out-of-frame stop frequency is low, termination is delayed and ribosome processing time is extended and vice versa. Entropy is the antithesis of accuracy. Codon definition in the DNA is presumably exact and thus the (information) entropy is zero. Mistranscription causes an increase in the codon's entropy. A further entropy increase follows the translation step. The system's entropy is the weighted sum of codon entropies and the probability distribution of the ribosome's occupancy of the reading frames. The tri-frame coding theory provides exact expressions for: (1) the yield of error-free protein, (2) the fraction of prematurely terminated polypeptides, (3) the percentage mistranscription in proteins, (4) the percentage mistranslation in proteins, (5) the percentage mutations due to frameshifting and (5) the energy and entropy cost to synthesize a protein. The theory is demonstrated for the three genes rpsU, dnaG and rpoD of E. coli. The dnaG gene, which has an exceptional high usage of rare codons, has much lower levels of expression compared to the other two genes, consistent with experimental findings. The entropies of all three genes are calculated and it is shown that the entropy decreases and energy cost increases as the use of rare codons increases.