Re: Evolution of proteins in sequence space (correction)

Date: Wed Aug 08 2001 - 10:15:24 EDT

  • Next message: Keith B Miller: "Re: Evolution of proteins in sequence space"

    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

    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

    By Grace we proceed,


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