[Godevil]

Finally, in my experience, in 3/4 of the cases where a biologist asked me a question in an abstract way I have to change my advice once I learn what it is really about because the questioner omitted important details due to the abstraction.

Thank you for your advice, I should really tell the real case but not the transferred math question.

[krobison]

I must confess, my usual route for solving these is to simulate them with a quick program (learning this skill can be valuable!); I'm always nervous I'll choose the wrong probability model. The obvious field for the right model would be hypergeometric, Poisson & binomial.

The sort of obvious guess is that since you have 3X coverage of your genome, there should be only about 3 positive wells in your entire collection. If that logic holds, then you can superpool quite a bit.

I would be tempted to initially generate pools for each plate, then combine those to form 96 superpools. You expect 3ish hits in the superpools. One more round of PCR lets you identify which plates have positive wells, and then you can just screen the plates.

[Dbarker06]

Why not just arrange the 1680 plates into a 40X42 array. Then make pools of all the samples in each row of 40 and each column of 42. PCR these 82 pools. The results give you the row and column position of each positive 96 well plate in your 40x42 array. Then test each clone in the positive plates. You won't miss any positives--if there happen to be two positives in the same plate you will find that. Assuming that there are three positives,you will do less than 400 PCR reactions to find the individual positive clones.

[ECO]

For what it's worth, I'm really glad this wasn't homework and actual experimental biology.

In the future (and anyone reading this contemplating doing the same bounty for help...)...please be honest. As Simon said, the fun is in the biology...you're much more likely to get help being honest (with or without a bounty).

[Godevil]

I would be tempted to initially generate pools for each plate, then combine those to form 96 superpools. You expect 3ish hits in the superpools. One more round of PCR lets you identify which plates have positive wells, and then you can just screen the plates.

Actually, my question is just the relationship between that probability and the superpool number.
In your advice, you've already give the "96" as the superpool number, but I need the reason.

[Godevil]

Why not just arrange the 1680 plates into a 40X42 array. Then make pools of all the samples in each row of 40 and each column of 42. PCR these 82 pools. The results give you the row and column position of each positive 96 well plate in your 40x42 array. Then test each clone in the positive plates. You won't miss any positives--if there happen to be two positives in the same plate you will find that. Assuming that there are three positives,you will do less than 400 PCR reactions to find the individual positive clones.

What you said is the 2 dimension-based design. But I prefer to use 3 or higher dimension, which can save me much more time and money for PCR. I've already considered lots of screening design. Higher dimention means more false possitive.

As in the 2-dimension method, the most false positive results is 3^2-3; in 3D is 3^3-3. The only way to reduce the false positive is to make sure only one positive clone locates in one superpool.

So, please help me on my probability question.

[Godevil]

For what it's worth, I'm really glad this wasn't homework and actual experimental biology.

In the future (and anyone reading this contemplating doing the same bounty for help...)...please be honest. As Simon said, the fun is in the biology...you're much more likely to get help being honest (with or without a bounty).

Hey, I just want to make my question simple to be understand for everyone. It has nothing to do with honest or not.

Whatever, if you are good at probability, please help me.

[HESmith]

The recommended two-dimension design, followed by screening individual candidate plates (using 8x12 matrix, if you want to minimize the number of PCRs) is the most efficient method. If you're committed to higher order screening with fewer false positives, you may be able to incorporate a Steiner triple system (see http://www.nature.com/nmeth/journal/...nmeth1063.html for a similar application).