Step 1: Understanding the Question
The goal is to identify the specific gene product of the {z} structural gene within the {lac} operon. The {lac} operon is a polycistronic system found in {E. coli} that regulates the metabolism of lactose. It is one of the most studied models of gene regulation in prokaryotes.
Step 2: Key Formula or Approach
The {lac} operon consists of a regulatory gene ({i} gene) and three structural genes ({z}, {y}, and {a}). Each gene encodes a specific protein involved in the transport or breakdown of lactose. To solve this, one must memorize the sequence and function of the structural genes: {z} $\rightarrow$ {y} $\rightarrow$ {a}.
Step 3: Detailed Explanation
The z gene: This gene encodes the primary metabolic enzyme beta-galactosidase ($\beta$-gal). This enzyme is responsible for hydrolyzing the disaccharide lactose into its two constituent monosaccharides: glucose and galactose. It also converts some lactose to allolactose, which acts as the inducer for the operon.
The y gene: This gene codes for the enzyme permease. Permease is a membrane-bound protein that increases the cell's permeability to $\beta$-galactosides, allowing lactose to enter the bacterial cell more efficiently.
The a gene: This gene codes for transacetylase. While its exact role in lactose metabolism is less critical, it is involved in transferring an acetyl group from acetyl-CoA to certain galactosides.
The i gene: This is the regulatory gene that codes for the repressor protein, which keeps the operon turned off in the absence of lactose.
Step 4: Final Answer
The {z} gene in the {lac} operon is specifically responsible for coding the enzyme beta-galactosidase. Thus, (C) is the correct option.