Register to reply

Picking an appropriate distribution

by aaaa202
Tags: distribution, picking
Share this thread:
aaaa202
#1
Feb28-12, 01:49 PM
P: 1,005
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?
Phys.Org News Partner Physics news on Phys.org
Symphony of nanoplasmonic and optical resonators produces laser-like light emission
Do we live in a 2-D hologram? New Fermilab experiment will test the nature of the universe
Duality principle is 'safe and sound': Researchers clear up apparent violation of wave-particle duality
bp_psy
#2
Feb28-12, 10:04 PM
P: 452
Could you explain your model a little more clearly? First what exactly is N and "a mutation for p"?


Register to reply

Related Discussions
Bayes formula and picking variance from distribution General Math 3
Picking AS/A2... Academic Guidance 2
Picking a university Academic Guidance 2
Picking yourself up General Physics 2
Lock picking General Discussion 41