1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Picking an appropriate distribution

  1. Feb 28, 2012 #1
    I am studying a biological system comprised of roughly 10000 cells. My model studies the probability that a cell accumulates four independent mutations and thus transform into a vicious cancer cell.
    Starting from basic theory of the binomial distribution it is easy to write an expression for the probability that a particular cell acquires k mutations after n timesteps. Calling the probability that an arbitrary cell acquires a mutation for p we have for a single cell:
    pcell = p/N
    And thus:

    p(k mutations on n tries) = K(n,k) * (p/N)^k * (1-p)^(n-k)

    And summing all these up should give us the total probability that one cell has acquires k mutations. Now multiplying by N wouldn't actually work since p is actually specific to each cell (I assumed it to be the same for simplicity).

    Now my question is: This expression becomes quite nasty when we add the fact that p differs from cell to cell. Is it possibly to make some estimations to make the expression more easy to work with. As N is pretty big (we could make it a lot bigger) would it be possible to model the distribution as a poisson distribution? And would that then make cell dependence of p easier to work with, or could we at least then find a straightforward expression for the deviation from the mean amount of mutations?
  2. jcsd
  3. Feb 28, 2012 #2
    Could you explain your model a little more clearly? First what exactly is N and "a mutation for p"?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook