DNA error rates

Robert Bradbury bradbury at sftwks.UUCP
Thu May 14 09:44:14 EST 1992

In article <9205121706.AA07357 at rust.zso.dec.com> french at RUST.ZSO.DEC.COM writes:
>In article <9205071432.AA10616 at genbank.bio.net> 
>rbradbur at hardy.u.washington.edu (Robert Bradbury)
>> This means by the time you hit 80, your mutation frequency is 
>> 2.2 x 10^-5 in a single gene.  Multiply by 5000 active
>> genes per cell and you have 1 in 10 cells with a broken gene...
>> Hmmmm, so damaging .2% of a gene makes it non-functional.  Due to the
>> degenerate code from DNA to proteins and the large portions of proteins
>> which aren't critical to structure/function you can make a case that a
>> large fraction of the DNA for a protein can be damaged without harming the
>> protein.  ...
>> If we say that 10x the critical active area is important for 
>> general functioning then every cell in the body has a gene suffering a 
>> loss of function due to DNA damage!  
>If the DNA coding sequences really are redundant, wouldn't you divide 
>the mutation frequency by 10 instead of multiplying it by 10?  If so, 
>then by age 80 only 1 in 100 cells would be suffering loss of function
>due to DNA damage.  This defect rate appears to be too low to account 
>for the effects of aging.
I should probably try to be more complete but I worry about the bandwith
problem.  Proteins are complex in terms of what is important and what
isn't.  Proteins which are enzymes (as opposed to structural components)
have one or more active sites where they do their dirty work.  These sites
have a small number (2-10?) of amino acids which are critical to the
catalytic activity of the enzyme.  Change one of these and the enzyme
is broken!  There are a number of other sites which are involve in the
protein maintaining its shape and in aligning molecules properly for
catalysis to occur, these are perhaps a much larger fraction (10-30%?).
And there may be additional places which are normally unimportant to
the functioning of the protein but if you stick something wrong (large
amino acid replaces small amino acid, hydrophobic replaces hydrophilic,
etc) in that location things are impacted as well.

Now, we are lucky that we have repair processes that keep things from
changing very much.  And when they do the redundancy of the code keeps
things from becoming too messed up.  If I read my RNA codon->Protein
chart correctly, you can change the 1st, 2nd and 3rd bases of a codon
3.1%, 1.6% and 81% of the time respectively without changing the protein.
So if we were to assume base mutations all occur with equal frequency
(which is untrue) then about 29% of the time a base change does not
affect the protein.

So, to take a real (perhaps extreme) example this time.  In CuZn superoxide
dismutase, 38 out of 151 (25%) of the amino acids are conserved across 19
species (from bacteria to plants and mammals).  Such a high conservation
rate would argue that all of the a.a. are critical.  If we take the numbers
from my previous article for 4x10^-8 for the mutation rate of the amino
acid responsible for sickle cell anemia, estimate 1 order of magnitude
increase due to age (quibble here if you want) gives you 4x10^-7 times
38 / 2 copies per cell gives a mutation rate in critical amino acids of
SOD at approx. 10^-5 or one in 100,000 cells have broken SOD genes.

Well, you say that's not bad but realize that if you break the SOD genes
the mutation rate of every other gene in those cells goes up significantly.
(my crystal ball says I see cancer in your future.... :-)).  Now, given
5,000-10,000 active genes, a higher mutation rate among those that aren't
often turned on and allowing for defective alleles that you do not normally
see because they are masked by the "normal" allele but that you will see
if the "normal" allele is broken and you start to have a good case for
mutated genes in every cell.

Now, back to Larry's question.  The 10x in the original posting was the
factor going from .2% of the gene being critical to function (break this
and the gene doesn't work) to 2% of the gene being "useful" to function
(break this and the enzyme works more slowly).  Damaging any of the
amino acids involved in useful function impacts the function which is
why I multiply by 10.  If you correct (roughly) for the degenerate code
as I indicate above you need to divide by 3 and then by 2 to correct
for those genes for which you have 2 active copies.  But then if you use
the "critical" region of SOD as typical (25% vs. 2%) then you need to
multiply by 10 again so you end up roughly back where you started.

I emphasize the back-of-the-envelope nature of these calculations.
Someone needs to do some work on how critical various enzymes are
to the cell and what fraction of those amino acids are "critical"
and what the mutation rate is for those amino acids.  Then we
could have a complete picture.  But as my calculation above shows
you can damage a critical gene in a few cells and start them on
a very rapid downhill slide which leads to very unpleasant disease
Robert Bradbury			uunet!sftwks!bradbury

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