Image:Genetic Code Bias 2.JPG

Simplified diagram showing codon bias in hydropathy - molar volume space. The strongest components (bias) for the encoding of anino acid residues are, in order:

C in 2nd position = NCN -> small size, medium hydropathy

U in 2nd position = NUN -> average size, hydrophobic

A in 2nd position = NAN -> average size, hydrophilic

U in 1st position = UNN -> not hydrophilic

where N is any of {A, C, G, U}

The y-axis is accurate (cubic Angstroms), but the x-axis could have some error from estimates of hydropathy.

Redrawn from Figure 4 in http://www.complexity.org.au/ci/vol01/fullen01/html/

which attributes the graph to Yang, M. M., W. J. Coleman and D. C. Youvan. 1990. In Reaction Centers of Photosynthetic Bacteria. M.-E. Michel-Beyerle. (Ed.) (Springer-Verlag, Germany) p209-218; abstract:

"A solution to the problem of relating the physicochemical properties of the amino acids to their codon sequences has been achieved by treating the genetic code as a system of linear equations and applying the numerical method, Singular Value Decomposition (SVD). For example, hydropathy and molar volume, which are important deteminants of protein structure and function, can be quantitatively related to the nucleotide sequence. The 20 hydropathy values of the amino acid residues were remapped to 12 nucleotide determined values which, in turn, were used to predict structural aspects the photosynthetic reaction center protein, without DNA to protein translation."

More recently, a faster method has been found to determine the SVD PseudoInverse, here in Mathematica format:

(* complete dictionary of words, one per row, number of rows is (alpha^word), using words of length "word" and an alphabet of "alpha" number of characters *) (* "PseudoInverse" is the canonical method of taking the pseudoinverse as per Mathematica function implemented*)

alpha=4;word=3;dict=.;

dict=Partition[Flatten[Tuples[Reverse[IdentityMatrix[alpha]],word]],(alpha*word)]

PseudoInverse[dict]==((Transpose[dict])*((alpha)^-(word -1)))-((word - 1)/(alpha^word)/word)

True

(* There is nothing special for alpha=4;word=3 - The method works for all cases where word < alpha, but that is a more verbose loop, and the Mathematica PseudoInverse function takes too long to calculate for values of alpha and word that are large, whereas the transpose side of the equation is fast. *)

More complex diagrams illustrating the codon bias can be found on Commons at:

http://commons.wikimedia.org/wiki/Image:Genetic_Code.JPG

http://commons.wikimedia.org/w/index.php?title=Image:Genetic_Code_Structure_FWY.JPG

I created this image entirely by myself.

6/3/2008

Doug youvan (talk)

See below.