MUTATE: IN SILICO PERFORMANCE OF THE FLUCTUATION TEST

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- After download Mutate requires the Java 5.0 (or higher) Runtime Environment freely available at http://www.java.com.
- Whatever the operating system, you should be able to run the program just by double clicking on the mutate.jar file
- WINDOWS USERS: If double-clicking the .jar file does not open the program, make sure that the jar extension is associated with javaw.exe (in your JRE folder).

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Mutate Model

The underlying model is similar to the Haldane formulation as described in Zheng (2007) but with differential fitness incorporated
for the mutant cells. When implementing the process of bacterial grow it is assumed that if a mutation occurred, the cell divide in one
normal and one mutant. This is Kendall's assumption B (Kendall 1960; Zheng 2007).
We note

```
m
```_{t+1} = m_{t} *(2*b)

if

```
Let the initial number of cells N
```_{0} = 1.

*Generation t*: we have N_{t} cells with m_{t} of them being "old" mutants.

*Generation t+1*:
m_{t} mutant cells are not allowed to remute and just divide to produce
2*b*m_{t}.
N_{t} - m_{t} are normal cells and n of them will experience mutation so
N_{t} - m_{t} -n divide normally i.e. 2*(N_{t} -m_{t} -n).

The n new mutants just give one mutant plus one normal (assumption B) per cell
so we have n normal + n new mutants.

If we sum up:
N_{t+1} = 2*b*m_{t} + 2*(N_{t} -m_{t} -n) + n + n, which finally gives
N_{t+1} = 2*[N_{t} - m_{t}*(1-b)] and
m_{t+1} = 2bm_{t} + n

Given the above algorithm, the population size follows

```
N
```_{t} = 2^{t}N_{0} - (1-b)f(M)

where t is the generation number,

```
N
```_{t} = 2^{t}N_{0}

which corresponds to the Haldane's formulation as described in Zheng (2007).

Plating efficiency refers to the fraction of mutants that finally form observable colonies. It is equivalent to sampling the culture (Gerrish 2008). If we express plating efficiency as a fraction p from the number of mutants before plating

```
m'
```_{t+1} = 2bm_{t} + n
then we sample each mutant for platting with probability p to get an expected final number of
m_{t+1} = pm'_{t+1}

A. Carvajal-Rodriguez - Departamento de Bioquímica Genética e Inmunología - Universidad de Vigo.
( * Last update: December 2011)*