If the inducer [allolactose] is present in the negative control then it will bind to the repressor decreasing its ability to bind to the operator due to which the transcription begins again and the operon is turned on.
Lac Operon is a set of three genes z, y & a which are regulated under the same promoter which regulates the amount of lactose production in the cell.
An inducer is a molecule that has the ability to induce or activate the operon. ex- in the case of the lac operon, allolactose acts as an inducer.
A repressor is a molecule that will repress or restricts the transcription of the genes of the operon, as a result, the operon will be switched off.
When the lac operon is under negative control, with no CAP [catabolite repressor protein] binding activity, the repressor remains active and thus binds to the operator region of the operon, as a result, no transcription takes place and the operon will be switched off.
But if the inducer will be present even in the negative control then the transcription takes place and the operon will be on.
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