The estimation of diversity based on the number of E.coli colonies is not a perfect estimation at all. But its an acceptable measure in practical terms, useful to compare libraries, for instance... It is based on two main assumptions. None of them is 100% true. 1. There is no more tan one inserted gene in each E.coli colony. Depending on the ratio between electrocompetent cells and plasmid DNA during transformation in library construction, and on the ratio between E.coli cells and phages during infection after selection rounds, this can be approximately true or not. when using large amounts of DNA/phages and not so many cells this assumption may be completely false.

 2. Every colony contains a different DNA. In normal situations, its true that most colonies contain different DNAs, at least in the original library and probably after the first round of selection. Anyway, some colonies can be replicates of the same clone. After selection, diversity diverges from the number of colonies beacause enrichment means that the same clone is repeated multiple times.

Ill continue later qithe other questions.

The estimation of diversity based on the number of E.coli colonies is not a perfect estimation at all. But its an acceptable measure in practical terms, useful to compare libraries, for instance... It is based on two main assumptions. None of them is 100% true. 1. There is no more tan one inserted gene in each E.coli colony. Depending on the ratio between electrocompetent cells and plasmid DNA during transformation in library construction, and on the ratio between E.coli cells and phages during infection after selection rounds, this can be approximately true or not. when using large amounts of DNA/phages and not so many cells this assumption may be completely false.

 2. Every colony contains a different DNA. In normal situations, its true that most colonies contain different DNAs, at least in the original library and probably after the first round of selection. Anyway, some colonies can be replicates of the same clone. After selection, diversity diverges from the number of colonies beacause enrichment means that the same clone is repeated multiple times.

Ill continue later qithe other questions.

I come with more detailed answers. Just tell me if the following helps or not.

1. When you start the first round, how do you choose the starting library with the right diversity? In the experiment, I did according to my predecessor's lab manual chose 1 mL total E Coli library. And he said this is of high enough diversity. This confused me a lot.

Perhaps its easier with an example. If after electroporation to construct the library you have 10 ^ 9 colonies, then the diversity of your library (with all the concerns explained above) is 10  ^ 9 different molecules. That means that in every subsequent procedure you should use a suffcient number of clones to have all this diversity represented in selection. If you select a phage pool of 10  ^ 8 phages from the library against a given target, you would loose most of your diversity. Even if you use 10  ^ 9 phages to start selection, you can loose some molecules, because some clones can be over-represented during phage production. You need to use even more.

Thats why if you are going to produce phages from the same  library (glicerol stocks of electroporated bacteria) you would need to start phage production with at least 10 ^ 10 or even better 10 ^ 11 bacteria, then you would have each original colony in the library represented 10 or 100 times during phage production on average. Even if this estimation is not perfect because of phage production biases, you would have a high likelihood of having each original clone represented at least once during phage production.

In a similar way, if you have a phage stock having 10  ^13 phages/ml after phage production, you should take at least one microliter (or even better ten microliters) to start selection, in order to have a high probability of putting in contact with the target at least one phage displaying each molecule from the library.

In both cases, if you calculate the minimal required amounts of bacteria/phages to keep diversity and measure the concentration of your stocks, you can calculate the required volumen in each step. The above mentioned numbers are just examples for a given library.

2. The diversity determination using plated e coli is much more confusing and to me, is a little ridiculous. First, you count the numbers of colonies in the agar plate passaged with diluted transfected e coli. and then you time it with the dilution factor and the volume of the original stock to get the diversity. (Sometimes, a factor of '20' will be multiplied, why?)

I don't understand this part. I mean how do you know that in a single colony that you won't have different sequences. Why can't a single colony have more than one diversity(more than one sequence)?

You have to trace back the way you did the titration and make the calculations to know the total number of colonies in the library. You cannot count all of them, of course. I dont know your protocols. In my case I do the following.

I prepare serial dilutions of the library (bacteria) in 100 microliters of media, then I plate 5 microliters of each dilution. Thats why I have to multiply the number of colonies not only by the dilution factor, but also by the ratio between the stock volumen and the final plated volume (equivalent to plating the whole library without any dilution). If I have 5 ml stock, my factor in this case is 1000 x the dilution factor Im working with and the result is given as total cfu.

For infections with selected  phages I have I prepare phage dilutions in 500 microliters of media, I mix the dilutions with 500 microliters of grown bacteria and I plate 100 microliters of the mixture.   

Thats why I have to multiply the number of colonies by 20 (equivalent to using 1ml of phages to infect bacteria and plating all the infected bacteria), multiply also by the dilution factor and the results are given as titers (cfu/ml).

Depending on your protocol details and the final number you want to obtain (cfu or cfu/ml) you can have diffferent calculations. The important thing is that you are able to reconstruct the whole dilution process.

That looks very detail. I need some time to digest your answer. I will give you feedback soon.

Thanks to you Rojas in advance

Thanks Rojas. I understand your logics now.

So basically, based on those two imperfect assumptions, I just think that one colony has one sequence and imagine it as pure strain. Then, the number of colonies is directly related to the total number of strains of  E Coli in the diluted solution. I get it now.

It is weird to think about in this way, since I was a chemistry Ph. D and pretty new to biologists' logics. 

Thank you very much.  

Yes. Actually each colony is a pure strain because all the cells come from a single one. But this single cell can contain more than one phagemid (if an excess of DNA was used for electroporation, for instance) so cells in the progeny (same colony) can keep one of them, or even the whole mixture. It introduces some heterogeneity in the theoretically pure strain.

During all the discussion we have apparently missed the clonal integrity and diversity analyses by PCR and BstNI fingerprinting. This is applied as quality assurance step following library constructin and after each panning cycle. 

many use the 454 sequencing in batch now as a measure of diversity - not perfect either..

Diversity estimation in terms of number of colonies is just a first indication of library quality- the bigger the better. In normal situations (without gross artifacts during library construction) a larger size indicates a higher probability of having a good library. 

Fingerprinting pattern restriction analysis with BstnI is useful to assess the presence of different inserts in a sample of clones, but its only useful for some libraries, for instance naive antibody libraries (useless for very short inserts like small peptides-coding genes and synthetic libraries of mutated genes).

A more reliable estimation of diversity would require sequencing a sample of clones (useful at least to exclude gross problems during library construction) but using standard sequencing the number of clones is always too small to allow a real sampling. Sequencing a vast number of clones (using next generation sequencing) is an ideal way to study library diversity, although an expensive one.