Final answer:
High levels of tryptophan in the medium inhibit transcription of the trp operon due to the trp repressor binding to the trp operator; this is a classic example of a repressible operon in prokaryotic gene regulation.
Step-by-step explanation:
Under the system of genetic control of the tryptophan operon, when there are high levels of tryptophan in the medium, transcription of the trp operon does not occur at high levels. Instead, transcription is inhibited. This is because the trp operon is a repressible system. When tryptophan is abundant in the cell, it binds to the trp repressor, which in turn binds to the trp operator, preventing RNA polymerase from transcribing the genes needed for tryptophan synthesis. This is a negative feedback mechanism ensuring that the cell does not waste energy producing tryptophan when it is already plentiful. When tryptophan is not present, the repressor cannot bind to the operator, and the operon is active, leading to the synthesis of tryptophan.