Question 5
Imagine an episode of Tom and Jerry, where Jerry uses the cat ('Butch') and the dog ('Spike') and switches their personalities in the lab. Tom was shocked and could not believe that Butch is behaving like a dog. Imagine you are a friend of Tom, and you have to explain him that it is possible to switch personalities by mutating their genes. You find the synteny blocks in the chromosomes of Butch, Tom and Spike as given below.
\begin{aligned} \mathit{Butch} &= {+5}\ {+3}\ {-1}\ {+4}\ {+2} \\ \mathit{Tom} &= {-3}\ {-2}\ {-1}\ {+5}\ {+4} \\ \mathit{Spike} &= {+1}\ {+2}\ {+3}\ {+4}\ {+5} \end{aligned} \tag{1}
Suppose Jerry's machine first runs an algorithm to determine the breakpoint graph and the sequence of transformations and then applies it on the species. Assume the algorithm only uses the minimum number of transformations needed to convert a species into another. Use the breakpoint graph to determine the total number of transformations Jerry needs to mutate Butch into Spike. Enter the answer as a single integer.