What mutation rate do I want for my experiment?

I need to decide on a desirable mutation rate for my murE mutagenesis experiment (described here).  To do this I need to think about (at least) how big the gene is, how large a region of the gene I want to investigate, what fraction of mutations will interfere with or eliminate gene function, and what fraction of mutations might cause hypercompetence.

How big is the gene?  1467 bp (489 aa).

Are hypercompetence mutations  equally likely to occur anywhere in the gene?  The mutations we have are in domain 3, at amino acids 361 and 435, so maybe other mutations would be nearby.  But maybe not.  Let's first consider the whole gene, and then decide * if focusing on the last third of it would make any difference.

What are the expected frequencies of mutations with different effects?  About 50% of random base changes change an amino acid (surely someone has done this calculation...).  Since all three of our known mutations change an amino acid, let's assume that silent mutations don't affect competence. About 34% of random amino acid changes interfere seriously with protein function (Guo et al. 2004).  Our known mutants appear to have normal MurE catalytic function, and defective mutants will not show up in our screen because murE is an essential gene.  So that leaves about 1/3 of all the mutations as causing well-tolerated amino acid substitutions.

What fraction of well tolerated amino acid substitutions cause hypercompetence?  We know of three that do.  How many different amino acids can each codon mutate to?  Probably about 9 or10 on average.  So let's say we have 500 codons of interest, that's about 5000 different possible amino acid substitutions.  About 2/3 of these will be well-tolerated.  So we know that 3 out of 3,300 amino acid changes cause hypercompetence.  Other mutations may cause hypercompetence too, but since half the mutations will be silent, this lower-bound means that at least 1/2000 colonies with a single murE mutation can be expected to be hypercompetent.  That's pretty good odds, given that our transformation-selection step can enrich 1000-fold for hypercompetence mutations.

So an average of 1-2 mutations per kb should give us easy-to-find hypercompetence mutations. Will higher mutagenesis give us more? Issues to consider:

1. More mutations means more non-tolerated mutations, which means that some hypercompetence mutations won't be seen because their cells died.  I don't think this is a big deal, unless we made the mutation rate very high.
2. More  mutations means more irrelevant mutations in each gene we sequence.  This is important.  Inference will be greatly simplified if genes from hypercompetent cells have only one mutation.  So it's probably best to  use the lowest level of mutagenesis that will give us easily-detected mutants.

The Lai et al paper had 5-6 mutations per kb. This is probably too high for us.

Another concern is mutations in the genes between the CAT cassette and murE.  Some of these are essential, and mutations in them will reduce the frequency of recovering viable transformants that contain both the CAT cassette and murE.  This is another reason to go for a low mutation rate.

* Back to a previous point.  Does it matter whether we want to screen only the last third of the gene?  No, because we don't have any way to isolate this from the rest.