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If the gene encoding the trp repressor is mutated such that it can no longer bind to tryptophan, will transcription of the trp operon occur?
A. Yes, because the trp repressor can only bin the trp operon and block transcriptional initiation when it is bound to tryptophan.
B. No, because this mutation does not affect the part of the repressor that can bind the operator.
C. No, because the trp operon is repressed only when tryptophan levels are high.
D. Yes, because the trp operon can allosterically regulate the enzymes needed to synthesize the amino acid tryptophan.

Answer
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Hint: A set of interconnected genes that, during transcription, combine to form a single messenger RNA molecule and include both structural and regulatory genes (such as an operator and promoter).

Complete step by step solution:
A set of genes known as the trp operon is discovered in the bacteria E. coli and codes for the tryptophan biosynthesis enzymes. When tryptophan levels are low, the trp operon is expressed (or "turned on"), and when levels are high, it is repressed (or "shut off"). The trp repressor controls the trp operon.
The transcription factor tryptophan repressor, also known as trp repressor, regulates the metabolism of amino acids. In Escherichia coli, a dimeric protein that controls the transcription of the five genes in the tryptophan operon, it has been investigated the most extensively. The operon is controlled such that tryptophan production genes are not activated when tryptophan is present in the environment. It served as a crucial experimental framework for studying gene regulation and is frequently employed in the instruction of gene regulation.
Yes, because only when the trp repressor is coupled to tryptophan can it bind the trp operon and prevent transcriptional start. It cannot bind the operator if the repressor can no longer bind tryptophan, hence transcription of the trp operon will constantly depend on whether tryptophan levels are high or low in the cell.
So, option (A) is correct.

Note:
The inducer that separates the repressor from the operator and derepresses the operon causes the lac operon to react. A repressor protein that binds to two tryptophan molecules activates the trp operon.