Step 1: Understanding the Question:
The question asks to identify the structural gene of the lac operon that is located most immediately downstream of the promoter elements, specifically the -10 box (Pribnow box).
The lac operon is a classic model of gene regulation in prokaryotes (E. coli) used to control the metabolism of lactose.
Step 2: Detailed Explanation:
• Structure of the Lac Operon: The lac operon consists of a regulatory gene (lacI), a promoter (P), an operator (O), and three structural genes: lacZ, lacY, and lacA.
• Promoter Region: The promoter contains two essential conserved sequences recognized by the RNA polymerase sigma factor: the -35 box and the -10 box (Pribnow box). These are located upstream of the transcription start site (+1).
• Linear Arrangement: The transcription of the operon produces a single polycistronic mRNA. The order of genes from the promoter moving downstream is lacZ $\rightarrow$ lacY $\rightarrow$ lacA.
• Proximity: Because lacZ (encoding $\beta$-galactosidase) is the first structural gene in the sequence, it is the one nearest to the promoter's regulatory elements like the -10 box.
• Analysis of lacI: Although lacI is part of the overall lac system, it is a regulatory gene located far upstream and has its own independent promoter. It is not considered part of the polycistronic structural unit.
Step 3: Final Answer:
The lacZ gene is the first gene of the lac operon and is therefore the closest gene downstream of the -10 promoter sequence.