From:    L.A. Moran                             
To:      All                                    Msg #69, Nov-29-92 06:39AM
Subject: Probability of good, neutral and bad mutations.

Organization: UTCS Public Access
From: lamoran@gpu.utcs.utoronto.ca (L.A. Moran)
Message-ID: ByHFDD.99G@gpu.utcs.utoronto.ca
Newsgroups: talk.origins


The original question (from David Rice?) was,

     "What is the probability of a "random" mutation being benificial
      to an organism?"

Mark Isaak asks,

     "Let's now extend the question a little. What is the ratio of good 
      and bad mutations to neutral mutations? I think this is a more 
      interesting question because neutral mutations won't necessarily 
      stay neutral as the environment changes. For a population with a 
      large variety of neutral mutations, when the environment changes, 
      some individuals may very well already have acquired a "good" 
      mutation needed to deal with the change. (Of course, many more won't
      be able to deal with the change, but they'll die off and leave the 
      picture eventually.)"

Let's consider a gene that has a coding region of 1800 base pairs. The 
protein that it encodes contains 600 amino acids (recall that a codon 
consists of three nucleotides). This is an average sized protein.

If we examine homologous proteins from many organisms we would typically 
find that about one third of the amino acid sequence is highly conserved
(ie. invariant); about one third is moderately conserved; and the remaining
third is poorly conserved. Let's use these estimates to calculate allowable
mutations.

Consider the conserved region. It appears that any mutation in this sequence
that results in an altered amino acid is harmful. That is why we don't see 
such changes preserved in modern living organisms. However, some nucleotide
substitutions ("mutations") are possible because they do not alter the sense
of a codon. For example, several different nucleotides can occupy the third
position of a codon without altering the amino acid encoded. For a rough
estimate of the probabilities of good, bad and neutral mutations let's
assume that the first two nucleotides of each codon in the conserved region
are invariant and that the third position can vary.

There are 600 nucleotides in the conserved region and each one can be mutated
to three other possibilities. Thus there are 1800 possible "mutants" if one
counts single nucleotide substitutions. Of these 1200 are "bad" because they
will alter the encoded amino acid. But many of the remaining 600 possible
mutations are also "bad" because they result in a new codon or because
they result in an unusual codon that is not used efficiently. As a rough
estimate let's assume that half of them are neutral and half are bad. In
summary, for the conserved region we have 1500 bad possibilities and 300
neutral possibilities.

Comparing with the  moderately and poorly conserved regions;

                             nucleotides    mutations    bad    neutral
                             -----------    ---------    ---    -------
      invariant (conserved)     400          1200       1200      0
      variable (conserved)      200           600        300     300  
      invariant (moderate)      300           900        900      0
      variable (moderate)       300           900        450     450
      invariant (poorly)        200           600        600      0
      variable (poorly)         400          1200        600     600
                                                        -----   -----
                                                totals  4050    1350       

For the entire gene we have 4050 bad mutations and 1350 neutral mutations.
Some of the neutral mutations will be slightly benificial and some will be
slightly harmful but the effect on fitness is too small to make much of a 
different. Some of the mutations will be "good" because they result in
changes that correct the accumulation of slightly harmful mutations (by 
genetic drift). It is difficult to guess the number of potentially "good"
mutations in a gene found in a living organism. I think that there may be
about 50 possibilities for a gene of average size that is moderately 
conserved. This gives 1% good mutations, 24% neutral mutations, and
75% bad mutations for the codong region of a typical gene.
   
Laurence A. Moran (Larry)