The following gives a list of possible symmetries of DNA inspired by the identification of braid color.
1. Color confinement in strong form
The states of quarks and anti-quarks associated with DNA both wormhole wormhole throats of braided (living) DNA strand can be color singlets and have thus integer valued anomalous em charge. The resulting prediction depends on the assignment of quarks and antiquarks to A,T,C,G which in principle should be determined by the minimization of em interaction energy between quark and nucleotide. For instance 2(A-T)-(G-C) mod 3=0 for a piece of living DNA which could make possible color singletness. As a matter fact, color singletness conditions are equivalent for all possible for braid color assignments. This hypothesis might be weakened. For instance, it could hold true only for braided parts of DNA and this braiding are dynamical. It could also hold for entire braid with both ends included only: in this case it does not pose any conditions on DNA. Questions: Do all living DNA strands satisfy this rule? Are only the double stranded parts of DNA braided and satisfy the rule. What about loops of hairpins?
2. Matter antimatter asymmetry at quark level
A←→ T and G←→ C corresponds to charge conjugation at the level of quarks (quark ←→ antiquark). Chargaff's rules states A≈ T and C≈ G for long DNA strands and mean matter-antimatter symmetry in the scale of DNA strand. Double strand as a whole is matter anti-matter symmetric. Matter-antimatter asymmetry is realized functionally at the level of DNA double strand in the sense that only DNA strand is transcribed. The study of some examples shows that genes defined as transcribed parts of DNA do not satisfy Chargaff's rule. This inspires the hypothesis about the breaking of matter antimatter symmetry. Genes have non-vanishing net A-T and C-G and therefore also net Qa with sign opposite to that in control regions. Just as the Universe is matter-antimatter asymmetric, also genes would be matter-antimatter asymmetric.
3. Isospin symmetry at quark level
A←→ G and T←→ A correspond change of anomalous em charge by 1 unit and these operations respect color confinement condition. Local modifications of DNA inducing these changes should be preferred. The identification for the symmetries A←→ G and T←→ A for the third nucleotide of code is as isospin symmetries. For the vertebrate mitochondrial code the symmetry exact and for nuclear code slightly broken.
4. Matter antimatter asymmetry and isospin symmetries for the first two nucleotides
The first two nucleotides of the codon dictate to a high degree which amino-acid is coded. This inspires the idea that 3-code has emerged as fusion of 1- and 2-codes in some sense. There are two kinds of 2-codons. The codons of type A have fractional em charge and net quark number (consisting of either matter or antimatter at quark level) and are not able to form color singlets. The codons of type B have integer em charge and vanishing quark number (consisting of matter and antimatter) and are able to form color singlets. The 2-codons of type A (resp. B) are related by isospin rotations and there should be some property distinguishing between types A and B. There indeed is: if 2-codon is matter-antimatter asymmetric, 1-codon is not and vice versa.
5. Em stability
Anomalous em charge Qa vanishes for DNA and perhaps also mRNA strand containing also the G cap and poly-A tail which could compensate for the Qa of the transcribed region so that
or some variant of it holds true. Chargaff's rules for long DNA strands imply the smallness of Qa.
6. Summary of testable working hypothesis
Following gives a summary of testable working hypothesis related to the isospin symmetry and color singletness. The property of having integer valued/vanishing Qa is referred to as property P.
For a more detailed exposition and background see the chapter DNA as Topological Quantum Computer.