Final answer:
The separation of proteins with non-mixable liquids and a ligand is achieved through liquid-liquid extraction, with chromatography being a technique that incorporates this principle using immobilized ligands.
Step-by-step explanation:
The separation of proteins using two non-mixable liquids and a ligand is best achieved through the technique of liquid-liquid extraction. This method involves the differential partitioning of the proteins based on their solubility in the two immiscible phases. A ligand can be used to specifically bind a protein, allowing this complex to preferentially dissolve in one of the liquid phases. Among the options provided, chromatography is the technique that can also be modified to use liquid-liquid extraction principles, such as in the form of affinity chromatography where a ligand is immobilized on a solid support to capture the protein of interest from a mixture. In contrast, centrifugation can separate substances based on density or molecular size, electrophoresis separates based on charge and size, while filtration separates based on particle size and is used to separate solids from liquids.