Which of the following methodologies can be used for separating proteins by charge and mass?

The methodology that is used for separating proteins by both charge and mass is polyacrylamide gel electrophoresis (PAGE). In PAGE, proteins are subjected to an electric field within a polyacrylamide gel matrix. The movement of the proteins through the gel is influenced by their charge and size: proteins with a negative charge migrate toward the positive electrode, and smaller proteins typically move faster than larger ones. Therefore, this technique effectively separates proteins based on their molecular weight and their net charge at a given pH.

In contrast, while other methodologies listed also serve to separate components, they do not do so through a combination of charge and mass in the same manner as PAGE. Ion exchange chromatography, for example, separates proteins based on charge alone, and it does not distinctly separate them based on mass. Filtration separates based on size but does not take charge into account. Gas chromatography is typically used for volatile compounds rather than for proteins, and its operation is largely based on differences in boiling points rather than charge or mass.