Phenotype is much more stable against point mutations of genotype as one might expect: Why?

Paul Kirsch sent an interesting link (see this) to a genetics related article discussing the question how stably genotype determines the phenotype. The article proposed a number theoretic formula for the probability that a point mutation does not affect the phenotype. This probability is called robustness of the phenotype. The number theory involved is very different from that in the TGD framework and I do not understand the technical details.

One considers the correspondence between genotype and phenotype and point mutations in which code letter changes. The point mutations that do not affect the phenotype, are called neutral.

1. It is empirically found that robustness defined as the probability that a point mutation does not change a phenotype is orders of magnitudes higher than expected by assuming that this property is given by the probability that a random letter sequence gives rise to the phenotype. This is very natural since it makes possible steady evolution: quite few point mutations change the phenotype.This requires that there are strong correlations between genes which can give rise to a given phenotype. The pool of allowed letter sequences is much smaller than the pool of all possible letter sequences.
2. It is argued that a certain number theoretical function gives a good estimate for this probability. I have no idea how they end up with this proposal. What this also suggests to me is that quite generally, the allowed genes are not random sequences of letters. There are correlations between them.

Could one understand these correlations by using the number theoretic view of biology proposed in the TGD framework? Consider first how general quantum states are constructed in number theoretical vision.

1. In the TGD framework, all quantum states are regarded as Galois singlets formed from dark particles. This universal mechanism for the formation of bound states is a number theoretic generalization of the notion of color confinement (see this).
2. One obtains a hierarchy of Galois confined states. If one has Galois singlets at a given level one can deform them to non-singlets. One can also consider a larger extension in which the Galois group is larger and singlets cease to be singlets. One can however form Galois singlets of them at the next level. This is the general picture and applies to any physical state in number theoretical vision. In biology dark codons, dark genes, parts of the genome, perhaps even the genome, can belong to this hierarchy.
3. What does Galois singletness mean? The momentum components assignable to the Galois singlet as a bound state are Galois singlets and therefore ordinary integers when the momentum unit defined by causal diamond is used. The momenta of the particles forming the Galois singlet state are not Galois singlets: they have momentum components which are algebraic integers which can be complex. They are analogous to virtual particles. Galois singletness gives a large number of constraints: their number is 4 times (d-1), where d is the dimension of the extension.

This mechanism for the formation of bound states is universal and should apply also to codons and genes.

1. Free dark codons would be Galois singlets formed from 3 dark protons, which are not Galois singles. In gene, dark codons need not be Galois singlets anymore but the gene itself must be a Galois singlet and therefore defines a quantum coherent state analogous to hadron and behaving like a single unit in its interactions.
2. Galois singletness poses a constraint on the gene as a quantum state. Not any combination of dark codons is possible as a dark gene. In the momentum representation, the total momentum of genes as a many-codon state must have components, which are ordinary integers in the unit defined by the causal diamond. The momentum components assignable to codons are algebraic integers: they are analogous to virtual particles.

For a summary of earlier postings see Latest progress in TGD.

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.