Improving the Efficiency of the Genetic Code by Varying the Codon Length—The Perfect Genetic Code

Abstract

The function of DNA is to specify protein sequences. The four-base “alphabet” used in nucleic acids is translated to the 20 base alphabet of proteins (plus a stop signal) via the genetic code. The code is neither overlapping nor punctuated, but has mRNA sequences read in successive triplet codons until reaching a stop codon. The true genetic code uses three bases for every amino acid. The efficiency of the genetic code can be significantly increased if the requirement for a fixed codon length is dropped so that the more common amino acids have shorter codon lengths and rare amino acids have longer codon lengths. More efficient codes can be derived using the Shannon–Fano and Huffman coding algorithms. The compression achieved using a Huffman code cannot be improved upon. I have used these algorithms to derive efficient codes for representing protein sequences using both two and four bases. The length of DNA required to specify the complete set of protein sequences could be significantly shorter if transcription used a variable codon length. The restriction to a fixed codon length of three bases means that it takes 42% more DNA than the minimum necessary, and the genetic code is 70% efficient. One can think of many reasons why this maximally efficient code has not evolved: there is very little redundancy so almost any mutation causes an amino acid change. Many mutations will be potentially lethal frame-shift mutations, if the mutation leads to a change in codon length. It would be more difficult for the machinery of transcription to cope with a variable codon length. Nevertheless, in the strict and narrow sense of coding for protein sequences using the minimum length of DNA possible, the Huffman code derived here is perfect.