According to PubChem, the solubility of quercetin in water is low: 60 mg/L

This corresponds to, more or less, 200 μM.

Then, it is no surprise your 5 mM quercetin solution precipitated.

You should reduce the concentration of quercetin in the syringe for the ITC experiment, or place quercetin in the cell and inject the metal ion solution.

Dear Chuanqi Huan ,

In addition to what is already said by Adrian Velazquez-Campoy I advise you to have look at the following paper and poster:

Srinivas, K., King, J. W., Howard, L. R., & Monrad, J. K. (2010). Solubility and solution thermodynamic properties of quercetin and quercetin dihydrate in subcritical water. Journal of Food Engineering, 100(2), 208-218. (in Google Scholar you find a downloadable version)

https://www.researchgate.net/publication/320297605_Increasing_water_solubility_of_Quercetin_by_increasing_the_temperature

and the answers given in the following question here on RG:

https://www.researchgate.net/post/which_solvent_is_suitable_for_quercetin_solubility

Best regards.

My advice, which may be unpopular, is to forget about quercetin. It is a promiscuous inhibitor, meaning that it lacks specificity. Its mechanism of inhibition is probably not stoichiometric. It may act as an aggregator or as a denaturant. Exceptions would be the enzymes that are directly involved in its biosynthetic pathway and possibly multidrug transporters.