Ion-Channel events! HELP!!!!!

[kto13]

A biological membrane contains N ion-channel proteins. The fraction of time that any one protein is open to allow ions to flow through is q. Express the probability P(m, N) that m of the channels will be open at any given time.

 

[tkhunny]

Are you familiar with the Binomial Distribution? If not, you will be...

 

[kto13]

yeah! I understand I need to use those... I just don't understand how to incorporate the function of time. I just need a little help starting this out please!

 

[tkhunny]

What has time to do with it? The chanel is open or it is not?

p = 1-q

If there were one chanel, the probability it is open is q.

If there were two chanels, the probability that something is open is: q^2 (both), 2*q*p (one or the other), p^2 (neither)

If there were three chanels, the probability that something is open is: q^3 (all three), 3*(q^2)*p (two), 3*q*(p^2) (one), p^3 (none)

The coefficients should start to look familiar.

What if there were 'n' chanels?