William Phil, there is a difference between population size and library complexity. I very much wonder whether you have generated a library that truly has a complexity of 10e10, that is very very hard to do. You can have a library of complexity N (where the number of initial transformants usually being the limiting factor) and then that gets amplified to some much larger number like 10e10. But the complexity of the library never exceeds the initial value of N and is often decreased to some degree as you amplify. Although I think 10e10 has been rarely achieved, most libraries are really on the order of 10e8 or 10e9.

@Michael J. Benedik. I know the difference between size and complexity. The library that I made has a size about 10e14. After the electroporation, I immediately performed a titration on 2YT-AG agar dish. I count the titration result as the complexity of the library. Thank you very much for your kind reply.

What you are doing is OK. However, if you do not reach the desired diversity in one shot, you might want to do the electroporation in multiple batches and combine the resulting phages.

The articles that I read about construction of phage library don't contain the exact quantity of DNA corresponding to the diversity of their libraries. So I am wondering if they have adopted some sophisticated technologies. There are two articles claiming that they have constructed a phage library with a 10e12 diversity. However, I haven't got any clues to that kind of library, which makes me frustrated. Thank you very much for your kind reply. @Annemarie Honegger

In generating naive libraries, to be used repeatedly to generate antibodies against multiple different antigens, a high initial diversity is essential. Even the best protocol is insufficient to cover the vast theoretical diversity of the antibody sequence space. With the libraries we generated in the Plückthun Lab, we first did our best to optimise the electroporation process, then repeated the process as often as deemed necessary to get to the desired library diversity. E.g in the very first generation of the HuCAL library, the 2.1 x 10e9 independent colonies were obtained as a result combining 24 separate libraries based on different combination of VH and VL frameworks (Knappik, A., Ge, L., Honegger, A., Pack, P., Fischer, M., Wellnhofer, G., Hoess, A., Wölle, J., Plückthun, A. and Virnekäs, B. (2000) Fully synthetic human combinatorial antibody libraries (HuCAL) based on modular consensus frameworks and CDRs randomized with trinucleotides. J. Mol. Biol. 296, 57-86. https://plueckthun.bioc.uzh.ch/wp-content/uploads/Publications/APpub0180.pdf .

In comparison, the human body at any time contains between 10e9 and 10e10 different B-cells, this is the library diversity our immune system has to work with - although somatic hypermutation will further diversify the initial hits in that system.

In a phage display setting, somatic hypermutation can be simulated by further diversifying the clones recovered after initial rounds of selection through mutagenesis, error prone PCR or gene shuffling, followed by additional rounds of selection.

Of course, ribosome display as an alternative selection method does circumvent the bottleneck of electroporation efficiency and can therefore sample larger library sizes. In addition, with this method it is easier to apply additional diversification steps, leading to an in-vitro evolution process.

It is very kind of you to give such an detailed and helpful answer. Thank you very much!@Annemarie Honegger