In E.coli, tryptophan switches off the trp operon by

Synthesis of several amino acids is regulated by feedback inhibition where the end product will bind to the enzyme and stops the reaction. Final product(tryptophan) binds to the repressor protein and causes conformational changes in the repressor protein. As a result repressor protein is activated. Activated repressor protein binds to the operator region preventing the RNA polymerase from binding.