I thought over what I wrote here and I think
this needs to be corrected....
> Hence, I would be inclined to argue that the number of degrees
> of freedom have been greatly overestimated in L^20, and
> L^(20/3) is a more realistic estimate of the odds involved.
> That is admittedly still a big number for any long protein
> chain, and may still lead to astronomically huge odds, but
> certainly not _as_ huge.
I was reasoning that the distinguishability of the
different peptides is reduced by the extended
persistence length, but that should have been
worked out from the following.
(1) The persistence length affects the *base* of
the expression L' = L/3 (approximately).
(2) On the other hand, the exponent (n') of the
expression should be largely defined by the basic
chemistry of the interacting side chains:
hydrophobic, hydrophilic acid, base.
That allows a maximum of say 8 categories
hydrophobic: weakly -> moderately -> strongly
hydrophilic: weakly -> moderately -> strongly
acidic
basic
I think weakly hydrophobic/philic is
really the same thing (Gly for example),
but perhaps a special class involving steric
interactions (e.g., Trp or Pro) could also be
invoked, so perhaps a maximum of 8 classes
of truly *distinguishable* peptides is
reasonable in this case.
Of course there are some examples where
a single peptide change can be lethal, but
more often the changes are far less pernicious
tending only to accumulate noticeable problems
in old age. In any case, polymorphism in the
human genome makes such things as the CD4 receptor
more vulnerable to HIV infection in some groups,
and less so in others, so variation in proteins
is not something particularly profound.
Thus, I think 8 represents an estimate of the
chemically *distinguishable* set of peptides
in a sequence which means the exponent in the
expression is probably about 8. Smaller values
are probably too small, but I also don't see
a lot of reason to argue that there should be
more categories in such a rough estimation
procedure. Certainly 20 is pushing it.
This means that a reasonable estimate on the
upper bounds for the odds of getting a correct
sequence are probably around (L/3)^8. Again, this
can be a large number for L large.
Since there is as yet no evidence of intelligent life
elsewhere in the universe, the probability
of this process progressing to the point where
intelligent life can emerge is clearly small. Perhaps
"bacteria" levels of "life" may exist elsewhere but
even that remains questionable if the exponent really
implies "inevitable" as some people might wish to think.
In that sense, a chance in a trillion is not to far out
of reason to allow possibility in God's formation
economy, but not mere inevitability. Since I have
enough problems with my own ego and submitting to
Christ's call in my life, and I'm sure I am not alone
in that regard, that seems like God's divine wisdom in
action.
By Grace we proceed,
Wayne
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