Runs of Amino Acids Are Longer Than Expected in Proteins Based on a Graph Theory Representation of the Genetic Code

Abstract

An in silico study of mRNA secondary structure has found a bias within the coding sequences of genes that favors "in-frame" pairing of nucleotides. This pairing of codons, each with its reverse-complement, partitions the 20 amino acids into three subsets. The genetic code can therefore be represented by a three-component graph. The composition of proteins in terms of amino acid membership in the three subgroups has been measured, and sequence runs of members within the same subgroup have been analyzed using a runs statistic based on Z-scores. In a GENBANK database of over 416,000 protein sequences, the distribution of this runs-test statistic is negatively skewed. To assess whether this statistical bias was due to a chance grouping of the amino acids in the real genetic code, several alternate partitions of the genetic code were examined by permuting the assignment of amino acids to groups. A metric was constructed to define the difference, or "distance", between any two such partitions, and an exhaustive search was conducted among alternate partitions maximally distant from the natural partition of the genetic code, to select sets of partitions that were also maximally distant from one another. The statistical skewness of the runs statistic distribution for native protein sequences were significantly more negative under the natural partition than they were under all of the maximally different partition of codons, although for all partitions, including the natural one, the randomized sequences had quite similar skewness. Hence under the natural graph theory partition of the genetic code there is a preference for more protein sequences to contain fewer runs of amino acids, than they do under the other partitions, meaning that the average run must be longer under the natural partition. This suggests that a corresponding bias may exist in the coding sequences of the actual genes that code for these proteins.