Concept:
Blue-white screening is a molecular biology technique used to identify recombinant bacterial colonies. It is based on the activity of the enzyme:
\[
\beta\text{-galactosidase}
\]
which is encoded by the lacZ gene.
The method uses a chromogenic substrate called X-gal:
• Functional \(\beta\)-galactosidase breaks X-gal and produces blue colonies.
• Disrupted lacZ gene cannot produce active enzyme, resulting in white colonies.
Step 1: Understanding the basis of blue-white screening.
In recombinant DNA technology:
• Foreign DNA is inserted into the lacZ gene of a plasmid.
• If insertion occurs, the lacZ gene becomes inactive.
Therefore:
\[
\text{No functional } \beta\text{-galactosidase} \Rightarrow \text{White colonies}
\]
If no insertion occurs:
\[
\text{Active } \beta\text{-galactosidase} \Rightarrow \text{Blue colonies}
\]
Hence, blue-white screening depends on the activity of:
\[
\boxed{\beta\text{-galactosidase}}
\]
Step 2: Eliminating the incorrect options.
• Option (A): Lac repressor regulates the lac operon but is not directly responsible for blue-white screening.
• Option (C): Alkaline phosphatase is an enzyme used in molecular biology but not in blue-white selection.
• Option (D): \(\beta\)-galactoamidase is not involved in this screening process.
Thus, the correct answer is \(\beta\)-galactosidase.