Information Theory for Equalizing the Residue-Wise Information Amounts of the Proteins and Protein-Coding DNA

Information content of a polymeric macromolecule can be calculated in bits, by multiplying the number of building blocks that encompasses the entire length of the macromolecule with the Shannon’s entropy of each building block, which could be determined through the degree of variation (in the number) of those building blocks. DNA and the proteins that are encoded by genes, which are certain protein-coding regions of the DNA, are also polymeric macromolecules that are comprised of such building blocks, named residues. However, there is seemingly lower residue-based information amount in the protein if the mentioned approach is applied to a protein of specific size and the DNA that would be encoding the same length of a protein. Accordingly, this work initially presents the attempt to eliminate the decrease in the information amount of the protein by implementation of a new parameter in the calculation with the assumption that the information is not lost (or gained) during the protein translation process. An important additional biological significance of the work is revealed during latter calculations for the equalization of the information amounts in the protein and DNA molecules, which is the resolution of the problem of the presence of immense variation in the sizes of the proteins by accounting for the presence of introns in the eukaryotic genome