Download White, Maximum Symmetry in the Genetic Code

White, Maximum
Symmetry in the
Genetic Code
www.codefun.com/Genetic_max.htm
Title
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Title, “Maximum Symmetry…”
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Symmetry refers to a type of pattern that
organizes something’s shape
General “shape” is “invariant”
Introduction
(at beginning of paper)
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First figure
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(the standard transcription
codon table)
Leftmost column
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Topmost row
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shows the second
Rightmost column
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shows the first nucleotide
shows the third
Arguably unpleasant, what with its
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Repetetiveness,
inability to group amino acids together,
etc.
Introduction II
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Subjective and objective
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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
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…in contrast to…
“..the genetic code…must be based on a
purely objective structure in nature”
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Means nature provides a reality that does not
depend on our minds
Introduction III
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Par. 4, beginning “Any…”
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“Any spreadsheet standing for the genetic
code must employ a reading algorithm that
permutes single nucleotides into triplets”
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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
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Par. 5, “Regardless…”
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Key concept of the work is characterized
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“Symmetry…can be defined [as]
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You can rotate a wheel but it still looks similar
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Not true for rotating a person
You can change the 3rd codon
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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
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Par. 6, “The goal…”
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“The goal of this paper is to describe a
configuration of nucleotides that is
maximally symmetric.”
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What do you think of this goal?
Introduction VI
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Par. 6, “The goal…” (cont.)
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The central visualization tool is…
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The dodecahedron
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(“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)
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Par. 1: begin with a tetrahedron
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How many corners are hidden from view?
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How about sides? Faces?
How many non-fold
angles for a given
color?
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Fold angles
are not angles
if you unfold!
“Constructing the Rafiki Map”
III
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Labeling the 120 thingies
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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…”)
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“The major poles create four primary triplets that
have homogenous nucleotides; UUU for instance.”
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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
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What vertex numbers are the poles?
“Constructing the Rafiki Map”
VI
Par. 5 (“From here…”)
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“There are twelve semi-homogenous secondary
triplets, such as UUG, and four completely
heterogeneous tertiary triplets, such as ACG.”
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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
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Use a paper dodecahedron (see next figure!)
Make Your Own Dodecahedron!
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Needed: scissors, tape, printout of good figure
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Cut along the dotted lines to make tabs
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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
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Fold it all up into a dodecahedron
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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
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Secondary triplets
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Triangle is a rounded
version of the 6subtriangles
How does region 2
generate type 2
examples?
Region 1? 3?
Tertiary triplets
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Region 1? 2?
“Constructing the Rafiki Map” VIII
From list of bullets:
 “Sixty doublet permutations”
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12 “singlets” (faces) x 5 adjacent faces
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Are there repeats? Prove it and/or find one
“Sixteen multiplets”
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Multiplet:
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set of 4 codons with same 1st & 2nd nucleotide
Why 16?
“Constructing the Rafiki Map” IX
From list of bullets:
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“Twenty…triplets with six…permutations each”
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Triplet – unordered triple
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4 primary, 12 secondary, 4 tertiary
Each triplet has a corresponding vertex
Does each triplet code an amino acid?
“Sixty-four…triplet permutations”
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What is meant is 64 ways to generate a codon
64 = 4x4x4
“Constructing the Rafiki Map” XI
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4 poles define a tetrahedron
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Put a finger on each pole, A at top
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How to order the poles?
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If you changed their labeling, then
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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!
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L (“levo-,” or left) and D (“dextro-,” or right)
Call the Rafikihedron option “L”
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(like standard amino acids)
“Constructing the Rafiki Map” XII
Last par.:
 Let’s look at the map and amino acids
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Consider water affinity
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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)
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Advantages of Rafiki map include that it is
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Maximally symmetric
Compressed (in nucleotide arrangement)
Maximally objective
3-D
For thought/discussion
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Why are each of these desirable? Useful?
Closing Quote
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“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.” –
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