Final answer:
A mutation in the trp operon's operator sequence that enhances the repressor binding or a mutation that increases the levels or stability of the repressor would lead to increased negative control of the trp operon.
Step-by-step explanation:
A certain type of mutation that would cause negative control of the trp operon to be increased in a mutant would be a mutation in the trp operon's operator sequence that enhances the binding affinity of the repressor protein to the operator, or a mutation that increases the expression or stability of the repressor protein itself. Normally, when tryptophan levels are sufficient, the tryptophan-activated repressor binds to the operator sequence of the trp operon, preventing RNA polymerase from transcribing the genes required for tryptophan synthesis.
If a mutation occurs that either enhances the binding of the repressor to the operator or increases repressor levels, this would lead to a scenario where the operon is more frequently repressed, even possibly at lower concentrations of tryptophan, thus constituting increased negative control over the operon.