# fluctuation test-check my calculations?

John BRATTY bratty at BCH.UMontreal.CA
Mon Nov 28 17:42:07 EST 1994

```Fellow yeasties,

I am a graduate student who actually needs to measure mutation rates
for the first time in his career.  As far as I know, this means doing
a fluctuation test.  As I have not been able to find anybody at my
university who has ever actually done a fluctuation test, I have only
the articles by Luria and Delbruck, and Lea and Coulson to go by.  It
seems quite simple, but nevertheless I would be grateful to anybody
out there who is at ease with the technique and would be willing to
check my methodology and the calculations from my first experiment
before I go out and make the many more measurements that I am
planning.

The experiment was carried out as follows:

I am measuring the rate of mutation of one strain (for now) in two
different culture media.

I began with a single colony 1-2mm in diametre that I presume
contained no mutants.  I suspended the colony in medium and determined
the density by counting the cells with a hemocytometre.  Using this
value, I inoculated ten 2.5ml cultures of each test medium with 1000
cells per culture and grew them until they were apparently dense.
With medium A this took two days, while medium B required three days
and reached a lower final density.

I then plated dilutions of the cultures on rich medium to determine
the culture densities, and plated 20 ul from my 2.5 ml cultures on
selective medium to count mutants.

The results were as follows:

medium A: mutants on each of the ten plates:
14,17,19,21,23,28,33,60,122,135.

medium B:
5,14,15,22,31,63,72,112,1900,3000
(the last two were counted from plates at a higher dilution).

Using the method of the mean (Lea and Coulson, J. Genetics 49, 264-285
(1949)), I find the mean to be 25 in medium A and 47 in B, to give
r=3125 for A and 5875 for B after scaling up to 2.5 ml.  I introduced
these values into table 3 of Lea and Coulson and find m=428 for A and
747 for B (I extended the table up to r=5894 with r/m=7.86 using
equation 37, and took this to be a close enough approximation).

My culture density plates worked out to 2.9exp7 per ml (7.2exp7 total
cells) for the culture in medium A but only 1.8exp6 /ml in B (4.5exp6
total).  I used the average of all 10 cultures here, as it makes no
sense to me to chose any one culture.  The cultures all had reasonably
similar densities, as would be expected.

Dividing my m's by my total cell numbers I get a mutation rate of
6.1exp-6 in medium A and 1.7exp-4 in medium B.

So, are there any errors here?  Is it normal that in medium B, which
gave a higher mutation rate I also have a much wider dispersion of the
data points?

Also, is it worthwhile in general to continue the calculation by the
method of S[x]=0?  If I do this, my m for culture A is essentially
unchanged, while that for culture B goes down to about 615, giving a
mutation rate of 1.4exp-4.  In this case, it hardly seems worth the
extra work -- are there types of data sets that can be easily
recognised as benefitting from the S[x]=0 treatment?

I anticipate that at some point I will also have data sets that show a
very low rate, and will give me a number of plates with zero mutants.
In this case is it _better_ to use the method of m from the proportion
of cultures without mutants, or just easier (since m=-ln(proportion of
zeros))?

Thank you very much for your time.  I doubt if other people would be
interested in re-hashing my data, so I suppose a response by email
would be the most appropriate -- but you decide.

Yours gratefully,

John Bratty
--
=========================================================
John Bratty			bratty at bch.umontreal.ca
Departement de biochimie
Universite de Montreal		(514) 343-6111, ext. 5165