Download Bacterial Mutation Analysis

Bacterial Mutation Analysis
The Bio Part
What we want to do…
• Determine the rate of mutations in
plasmids pBR325 CCTG 36 and
pBR325 CCTG 58 in strains of E. coli
MC4100 and Hfq-.
• The mutations are the shrinking in
length of a CCTG tract of 36 or 58
repeats.
How we are doing it…
• Transformations!
• Add the DNA containing the plasmids to
the strains.
Let the cultures grow.
Purify DNA from those cultures.
Put the new DNA in another type of E. coli
that we can selectively pick out to check if
it has the plasmid.
The CAT gene in plasmid pBR325 is used for genetic selection .
EcoRI
5’CTCATCCGGAATTCCGTATGGCAATG3’
3’GAGTAGGCCTTAAGGCATACCGTTAC5’
Plasmid gel from transformants!
Some Reversion Frequencies!
Sample #
# viable cells
Cells/per ml
10-8
10-8
Revertant #
of cells for
0.2 ml
Revertant
cells/ml
CAP
1
338
3.38E10
> 30000
1.5E7
4.44E-4
4
130
1.3E10
N/A
N/A
N/A
253
2.53E10
3068
1.53E6
6.05E-5
148
1.48E10
N/A
N/A
N/A
7
10
Sample Legend:
1 - MC4100 + pBR325 CCTG 36
4 - Hfq- + pBR325 CCTG 36
7 - MC4100 + pBR325 CCTG 58
10 - Hfq- + pBR325 CCTG 58
Chloramphenicol
Reversion Freq.
Why we want to do it…
• To learn more about the diseasecausing CCTG repeat.
The Math Part
The Foster paper…
• Offers us a comparison of the current
methods being used to analyze the
mutation rates in bacterial populations.
• The paper starts with the first model
developed, the Luria and Delbrück
(1943) model.
Where we are…
• Reading the Luria and Delbrück paper!
• Proposes that there is a finite probability
for any bacteria to mutate during its lifetime
from “sensitive” to “resistant” (mutation
hypothesis).
• If this is the case, the population of
bacteria should increase with time, as this
new resistant bacteria multiply.
Where we are…
• We have an exponential growth model!
dN t
 Nt
dt
where t is units of division cycles of bacteria.
• Derives that the number of mutations
occurring
 on a finite interval is given by
m  a(Nt  N0 )
where a is the mutation rate.
Where we are…
• Assumes that the number of mutations
is small, hence the distribution is given
through Poisson’s law…
• If we can determine the fraction of
bacteria in which no mutation occurred,
this fraction should be
p0  e
m
Where we are…
• From that we can determine ‘m’, and
hence find the mutation rate ‘a’.
What’s next…
• Finish working out the Luria and
Delbrück paper.
• Work out Lea and Coulson who build on
Luria and Delbrück by giving us ways to
calculate the actual distribution of
mutants.
• Go from there…
The truth according to XKCD
(June 11, 2008)