How to determine the binding of two proteins to each other, they may be those amino acid fragments? I had known that the two proteins can combine with each other, then I want to determine the motif.
Determining the domains/sequences that are involved in protein-protein interactions is not a straightforward thing..
Although quite complex, one strategy could be to use hydrogen-deuterium (H/D) exchange. In that case, you'd induce protein interaction of interest in an aqueous buffer containing D2O (instead of H2O). This would result in exposed protein backbone hydrogens to be exchanged for deuterium. This can be investigated by determining the mass increase (as a result of deuterium uptake, which is heavier than hydrogen) of the proteolytic peptides generated from your proteins by mass spectrometry (MS). The backbone hydrogens that are not exposed -due to the protein-protein interaction- will not exchange (and hence, their peptide mass will not increase).
There is a lot of literature on the matter out there, e.g. https://www.ncbi.nlm.nih.gov/pubmed/25436986
Another approach is chemical crosslinking, followed by trypsin digestion, peptide mapping, and mass spectrometry to identify the two crosslinked peptides.
Crosslinking can be misleading since any crosslinker will randomly attach all proteins to each other. J. Amster (U Ga) has done some work in this area. You have to go very light on the crosslinker and you really want an MS2 cleavable crosslinker (Amster's work) to get it right. H/D exchange has similar issues with ambiguity since any interior hydrophobic domains are also shielded from the exchange. NMR can also be a useful tool, particularly if the NMR structures for the individual proteins are already worked out. The best method is generally site-directed mutagenesis (Frances Arnold, CalTech has done a lot of related work here). In general, however, you need corroboration by multiple methods before you have any confidence in the result.
I can recommend an easy analytical tool of HPLC-Surfactant-SEC (see file; CA agg Dr. De Felice and SEC column 300A silica).
This method is similar to non-denaturing PAGE (or Davis method) without losing the quaternary structure; i.e., Avidin, Histone H3.1, and HbA are eluted as the tetramer molecules at 15 C. It seems intersting that at what column temperature can non-ionic detergent can destroy the quaternary structure, although it is not yet tested.
Similar method to denaturing SDS-PAGE may be possible in HPLC-SEC using 6M guanidine chloride or 8M urea in the eluent (containing non-ionic detergent).