I don't know anything about electrodialysis, but in aqueous solution, the ionization of peptide amino and carboxyl termini is determined by the pH. At low pH, the groups are NH3+ and COOH, whereas at high pH they are NH2 and COO-. Of course, at intermediate pHs there would be a mixture. In addition to the amino and carboxyl termini, some amino acid side chains are ionizable, including aspartate, glutamate, histidine, lysine, arginine, tyrosine and cysteine, each with a characteristic pKa.

The pH determines the charges on the amino acids, not the electric field. Or, more accurately the sum of the positive and negative charges in the mixture must equal zero, and water ionizes to make this so, generating protons (pH) in the process. The problem is as ions separate during the electrodialysis, the local pH will change. See my attached lecture notes on ionization. I really wish they would start to teach this correctly in Chemistry and Biochemistry courses, but it appears to have become a lost art form.

In any electrolysis, you want the total number of ions to be small to control the current, so you generally don't want a lot of buffer salts around to control the pH. You can use polyionic polymers (e.g., acrylamide/N-substituted acrylamide copolymers) to control the pH. These will move slower in the applied electric field than the amino acids and may be blocked from moving through the dialysis membrane based on size. The problem is you can't buy these and have to synthesize them.

Adam B Shapiro thank you for valuable answer. it is really helpful to me. In electrodialysis, we have cation-selective membrane and Anion selective membrane, in which we which driving force is the electric force.

So my question is that we get only cationic or anionic amino acids at one time? (because it depend on the pH of the solution)

An individual amino acid has 2 to 3 pKas .(I'm talking about the 20 canonical amino acids. There are others that are not incorporated into proteins by translation.) The N-terminus has a pKa of about 9-10, the C-terminus has a pKa of about 2. Some of the amino acids have a 3rd pKa for the side chain. In peptides, of course, there is one N-terminus and one C-terminus for the whole peptide, and some of the side chains have their own pKas. Sometimes, the N-terminus is blocked by a non-ionizable group. The charge on the peptide depends on the pH and the amino acid sequence. It is possible to have a peptide sequence that is only cationic or anionic if the pH and sequence are chosen properly.

For example, the sequence NH2-Ala-Glu-Val-COO- will be anionic (-2) at a basic pH. The sequence NH3+-Ala-Lys-Val-COO- will be net cationic (+2) at a neutral or mildly acidic pH and (+3) at strongly acidic pH (e.g. pH 0) as NH3+-Ala-Lys-Val-COOH.

Some peptides may have net zero charge, such as NH3+-Ala-Gly-Val-COO- at neutral pH.

Adam B Shapiro thank you very much for your reply.