Blue-white screening is a technique used in molecular biology to identify bacterial colonies that contain recombinant plasmids after transformation.
This method relies on the disruption of the lacZ gene, which encodes the enzyme $\beta$-galactosidase.
Therefore, the blue-white screening process is fundamentally based on the enzymatic activity of $\beta$-galactosidase.
In the provided options, the activity of $\beta$-galactosidase is the basis for this screening method.