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White, Maximum Symmetry in the Genetic Code www.codefun.com/Genetic_max.htm Title Title, “Maximum Symmetry…” Symmetry refers to a type of pattern that organizes something’s shape General “shape” is “invariant” Introduction (at beginning of paper) First figure (the standard transcription codon table) Leftmost column Topmost row shows the second Rightmost column shows the first nucleotide shows the third Arguably unpleasant, what with its Repetetiveness, inability to group amino acids together, etc. Introduction II Subjective and objective Par. 3: “…data structures must adopt conventions … predicated on some form of subjectivity” Means the way the data is organized requires rules of interpretation to mean anything …in contrast to… “..the genetic code…must be based on a purely objective structure in nature” Means nature provides a reality that does not depend on our minds Introduction III Par. 4, beginning “Any…” “Any spreadsheet standing for the genetic code must employ a reading algorithm that permutes single nucleotides into triplets” The table must have rules for how to read it in order to mean anything The rules must say how to construct a permutation (ordered sequence) of 3 nucleotides Introduction IV Par. 5, “Regardless…” Key concept of the work is characterized “Symmetry…can be defined [as] You can rotate a wheel but it still looks similar Not true for rotating a person You can change the 3rd codon a transformation of that data that leaves fundamental properties unchanged” …but the AA is often still the same …so the codons have a kind of “symmetry” So, what is the point of this work?... Introduction V Par. 6, “The goal…” “The goal of this paper is to describe a configuration of nucleotides that is maximally symmetric.” What do you think of this goal? Introduction VI Par. 6, “The goal…” (cont.) The central visualization tool is… The dodecahedron (“dodec…” refers to what number?) I think it would make ideas more accessible if people just called such solids using numbers in English Instead of icosahedron, twentyhedron Instead of dodecahedron, __________ Why not? One less distraction! “Constructing the Rafiki Map” (section of paper) Par. 1: begin with a tetrahedron How many corners are hidden from view? How about sides? Faces? How many non-fold angles for a given color? Fold angles are not angles if you unfold! “Constructing the Rafiki Map” III Labeling the 120 thingies 12 pentagonal faces Divide each into 10 triangles Label each triangle with a triple or amino acid See Figure: “Constructing the Rafiki Map” IV Understanding the figure: Now let’s label the other 4! “Constructing the Rafiki Map” V Par. 5 (“From here…”) “The major poles create four primary triplets that have homogenous nucleotides; UUU for instance.” major pole – a vertex with faces AAA, CCC, GGG, or UUU homogenous – homogeneous primary triplet – AAA, CCC, GGG, or UUU “Constructing the Rafiki Map” V What vertex numbers are the poles? “Constructing the Rafiki Map” VI Par. 5 (“From here…”) “There are twelve semi-homogenous secondary triplets, such as UUG, and four completely heterogeneous tertiary triplets, such as ACG.” Triplet: an unordered triple of nucleotides Why twelve secondary triplets? (hint: 4*3=12) Why four tertiary triplets? (hint: 4 nucleotides, use only 3) Find the vertexes corresponding to some of these Use a paper dodecahedron (see next figure!) Make Your Own Dodecahedron! Needed: scissors, tape, printout of good figure Cut along the dotted lines to make tabs Card stock best, paper ok Where an outside side has no tab, cut along it Or don’t use tabs – many feel this works better Crease tabs (if present) and interior folds well by folding/unfolding Fold it all up into a dodecahedron Put tabs (if present) on the inside Tape as needed with clear tape on the outside Rafikihedron Template Tabs added to figure from paper by J. & S. Berleant (many people feel no tabs works better – try it both ways and decide for yourself!) “Constructing the Rafiki Map” VII Secondary triplets Triangle is a rounded version of the 6subtriangles How does region 2 generate type 2 examples? Region 1? 3? Tertiary triplets Region 1? 2? “Constructing the Rafiki Map” VIII From list of bullets: “Sixty doublet permutations” 12 “singlets” (faces) x 5 adjacent faces Are there repeats? Prove it and/or find one “Sixteen multiplets” Multiplet: set of 4 codons with same 1st & 2nd nucleotide Why 16? “Constructing the Rafiki Map” IX From list of bullets: “Twenty…triplets with six…permutations each” Triplet – unordered triple 4 primary, 12 secondary, 4 tertiary Each triplet has a corresponding vertex Does each triplet code an amino acid? “Sixty-four…triplet permutations” What is meant is 64 ways to generate a codon 64 = 4x4x4 “Constructing the Rafiki Map” XI 4 poles define a tetrahedron Put a finger on each pole, A at top How to order the poles? If you changed their labeling, then Imagine a tetrahedron with top a and base CGU in some cases rotating the object would “change” them back other times rotation + mirror-reflection would be necessary Only 2 genuine options exist! L (“levo-,” or left) and D (“dextro-,” or right) Call the Rafikihedron option “L” (like standard amino acids) “Constructing the Rafiki Map” XII Last par.: Let’s look at the map and amino acids Consider water affinity Let red mean hydrophobic (dislikes water) Let blue mean hydrophilic (likes water) Let yellow and green cover the middle ground Reddish-purple is most hydrophobic Blueish-purple is most hydrophilic See figure, next slide Hydrophilic/-phobic Coloration Summary Summary (last section) Advantages of Rafiki map include that it is Maximally symmetric Compressed (in nucleotide arrangement) Maximally objective 3-D For thought/discussion Why are each of these desirable? Useful? Closing Quote “The genetic code has an overall symmetry such that common transformations of existing exons will yield more "protein-like" polypeptides than will a random nucleotide sequence. Frameshifts, complementary strands, even inversions of existing protein coding sequences have a much higher chance of also becoming viable proteins than do random nucleotide sequences. This is due to the remarkably complex overall symmetry of codon assignments, and it is a benefit to living systems in that it greatly speeds up the search for new protein morphologies. A primary function of the genetic code is to facilitate the rapid and efficient search for new protein morphologies.” – http://www.codefun.com/