Depicting a mechanism of peptide bond formation with protonated and deprotonated amino group
In neutral aqueous solution, the amino group is protonated (3 bound hydrogen atoms ) and the carboxilic acid group deprotonated (no bound hydrogen atom). In other solvents, you might have both groups in the neutral form the name amino acid suggests.
The mechanism of peptide bond formation is complex and involves intermediates with tRNA in the cell and starting materials distinct from amino acids for synthesis in the lab.