Methods of inactivating contaminants of a biological matrix are disclosed. The methods include the steps of: (a) contacting a biological matrix with an inactivating agent including an aziridino moiety, where a portion of the agent reacts with and inactivates the contaminant, and a portion of the agent remains unreacted; (b) contacting the product of step (a) with a solid support including at least 1 quenching moiety attached to the solid support through covalent bonds, under conditions and for a time sufficient to allow the unreacted agent to bond covalently to the quenching moiety; and (c) separating the solid support and the unreacted agent from the biological matrix, where the unreacted agent is attached to the solid support through covalent bonds.