On 8/6/2023 4:13 PM, Glenn wrote:
On Sunday, August 6, 2023 at 9:46:04 AM UTC-7, RonO wrote:
https://www.sciencedaily.com/releases/2023/08/230801131650.htm
Science daily has an article about some math that doesn't seem to be so
surprising. Why wouldn't integer mathematics apply to the possible
evolution of RNA secondary structure and protein folding when there are
no partial amino acids or nucleotides? You have a set integer number of
nucleotides for any RNA secondary structure. Even deletions and
insertions have to change by a specific integer number of units.
https://royalsocietypublishing.org/doi/10.1098/rsif.2023.0169
Maximum mutational robustness in genotype–phenotype maps follows a
self-similar blancmange-like curve
Vaibhav Mohanty, Sam F. Greenbury, Tasmin Sarkany, Shyam Narayanan,
Kamaludin Dingle, Sebastian E. Ahnert and Ard A. Louis
Published:26 July 2023https://doi.org/10.1098/rsif.2023.0169
Abstract
Phenotype robustness, defined as the average mutational robustness of
all the genotypes that map to a given phenotype, plays a key role in
facilitating neutral exploration of novel phenotypic variation by an
evolving population. By applying results from coding theory, we prove
that the maximum phenotype robustness occurs when
Seems odd that coding theory knows anything about phenotype robustness, but I suppose it can since they proved it.
They didn't prove anything. All they did was determine that a type of sum-of-digits function would produce the pattern we observe of the
accumulation of neutral mutations in the genomes of organisms as they
evolved. These are the neutral changes that Yockey was talking about
when he claimed that the pattern of substitutions in the protein that he
was looking at was much less likely to have occurred by chance all at
the same time than the probability of constructing his 100 amino acid
long protein in any specific sequence. The changes have to not be
selected against, and they have to occur in a pattern that reflects
descent with modification in order to produce the phylogenies that occur
in nature.
The cytochrome c protein didn't just have one sequence, but the various lineages had their own sequence. Denton pointed out that each
multicellular animal lineage had about the same number of substitutions
from some ancestral protein sequence (all lineages have been evolving
for the same length of time from a common ancestor), but he left out the
fact that substitutions created a pattern. Some species were closely
related like chimps and humans that had an identical sequence. Both
chimps and humans had the same number of amino acid substitutions from
the ancestral protein sequence, because they had an identical sequence
and there hadn't been enough time for substitutions to occur in the
lineages after they had separated, but both chimps and humans were 2 substitutions different from monkeys, and a few more different from
rats. The protein sequences showed a pattern of genetic relationships
that could be generated by descent with modification, but as Yockey
pointed out, were highly unlikely to have occurred in their current
pattern reflecting biological evolution than by chance.
Ron Okimoto
genotypes are
organized as bricklayer’s graphs, so-called because they resemble the
way in which a bricklayer would fill in a Hamming graph. The value of
the maximal robustness is given by a fractal continuous everywhere but
differentiable nowhere sums-of-digits function from number theory.
Interestingly, genotype–phenotype maps for RNA secondary structure and
the hydrophobic-polar (HP) model for protein folding can exhibit
phenotype robustness that exactly attains this upper bound. By
exploiting properties of the sums-of-digits function, we prove a lower
bound on the deviation of the maximum robustness of phenotypes with
multiple neutral components from the bricklayer’s graph bound, and show
that RNA secondary structure phenotypes obey this bound. Finally, we
show how robustness changes when phenotypes are coarse-grained and
derive a formula and associated bounds for the transition probabilities
between such phenotypes.
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