Happy New Year

It may or may not be possible to re-constitute Zn into purified protein. Some binding sites are very hard to fill back up once Zn is gone (for example sites with more than one -SH ligand can and often do undergo oxidative crosslinking in the absence of a stabilizing ion - we ran into this plenty of times when working with Zn-finger proteins). Other sites (e.g. Zn proteases) can easily re-gain Zn that has been stripped away (a good method for avoiding autoproteolysis when purifying certain metalloenzymes, but it can also backfire horribly). Note that common reducing agent DTT is know to strip Zn and other transition elements out of protein (BME is much less likely to do this and TCEP is virtually safe from this perspective). Ditto common buffers - citrate, high phosphate (especially with Iron ions), malonate, imidazole and so on.

Please note that Zn complex chemistry in water is "...fundamental, rather complex, and has important consequences for the role of zinc in biology..." to quote Krezel & Maret (reference below) - so if reconstitution does not work in some conditions it very well might work in others.

So if your protein lost its Zn, there is no really good way to predict the outcome of an attempted re-fill -- but since you have frozen protein in spades your best bet is to try a few things, such as dialyzing a small sample of protein (ideally diluted to ~1mg/ml or so) against low concentration of Zn in a suitable buffer. A good place to start is ~10uM (that's micromolar) Zn - which is plenty to saturate the protein with reasonable binding constant but is (hopefully) not enough to precipitate the protein out. After dialysis, remove Zn from solution - by briefly re-dialyzing against Zn-free bufffer - then concentrate the protein and try it out. You can also attempt to stabilize Zn in solution with an equimolar (or slightly less than equimolar) amount of a mild chelator like malonate (not EDTA, its complex with Zn is far too stable) and then add it directly to your protein - note that adding Zn to protein directly tends to cause precipitation (but chelating the Zn with a moderate-strength agent tends to prevent this).

Good luck,

Artem