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Calculations in degenerate oligo mutagenesis

the End jgraham at bronze.ucs.indiana.edu
Wed Jul 13 12:14:33 EST 1994

One for the archives from Clyde A. Hutchison III's Carolina Workshop on 
Sequencing and Mutagenesis, May 20 - June 5, 1988. Brought to you by 
Jim Graham (jgraham at bio.indiana.edu) at the Institute for Free Exchange 
of Scientific Information.

First you can determine what is average number of mutations per oligo that 
will give you the right size of desried "class".
         y         -n
p(y) =( n /y!)  x e     where:

y    is number of mutations per oligo (eg 0, 1, 2 ...) in class that you are
     interested in.
p(y) is the fraction of the pool that will have that many mutations.
n    is the average number of changes introduced per molecule (Poisson


If the synthesis is done so that there are on average 1.5 changes per oligo
(see below), this gives 22% wt, 33% one change, 22% two changes, 12.5% three,
and 5% four mutations. If the mutagenesis is 100% efficient, including any 
subcloning, then 78% of the clones are mutant. 

Then you need to calculate the "doping level" of contaminating nucleotides.
This is best done by a manufacturer under non-aqueous conditions and by first 
making a mixture of equimolar all four NTP's and mixing that as a minor 
component of each primary base where mutations are desired. This reduces bias 
introduced by control on mixing, and raises the overall level of the minor 
component of the mixture.

C(%) = (m x 4 x 100)/ (T x 3)  where:

C  is the % by volume of the equimolar phosphoramidite mixture added to 
   each NTP.
m  is the desired average number of substitutions per oligo.
T  is the size of the mutagenic target in nucleotides.

Lastly, you may need to screen you libraries, and will find yourself asking 
how many need be examined in order to see all combinations of the class in 
question (eg. all triple mutants).
N = [ln (1 - p   ) / ln (1 - 1/s)] + s/2  where:

N  is the number that needs to be examined.
p  is the probablility that you have seen all in the class (eg. 90-95%).
s  is the total number of an possible combinations whithin that class (eg. 
   number of different single mutants, for 39 positions 3x39 or s=117).

In this case 950 clones would have a 95% chance of containing all single 
mutants. Since only 33% of the oligos in the pool of oligos synthesized 
(mixed for average 1.5 changes per oligo) are single mutants, then 
950 / .33 = ~3000 clones on a good day. Since real libraries are not 100% 
efficient and not all days are good (eg. subcloning, type of procedure for 
incorporating oligo), at 50% efficiency, 6000 clones would probably contain 
all single mutants.

I have had the best result with PCR procedures to incorporate such mutagenic 
oligos into cloneable products. If your regions lacks good restriction sites, 
you may want to try the "megaprimer" method to avoid synthesizing a huge 
mutagenic oligo, but watch those non-templated A's !

More information always welcome. Any improvements on these calculations ?

Good luck,

J. E. Graham
Biology and Chemistry Departments
Indiana University Bloomington
..............."Il n'y a pas des sciences appliquees, mais il y a
..................des applications de la science."  L. Pasteur.......


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