Explain why (a) inactivation of the O2 or O3 sequence of the lac operon causes only a twofold loss in repression, and (b) inactivation of both O2 and O3 reduces repression 70-fold. The following passage wasn't included with the question, but it might be helpful: "The lac operon actually contains three operator sequences to which lac repressor binds with high affinity, known as O1, O2, and O3. O1, the primary repressor-binding site, was identified through its protection by lac repressor from nuclease digestion. The 26-bp protected sequence lies within a nearly twofold symmetrical sequence of 35 bp. O1 overlaps the transcription start site of the lacZ gene. The operator sequence O2 is centered 401 bp downstream, fully within the lacZ gene, and O3 is centered 93 bp upstream.

The lac operon has been found to contain three operator sequences, O1 being the main and O2 and O3 the secondary sequences. The lac repressor has been found to bind to the operator region and inhibit transcription. The researchers have found the arrangement of operators roughly as: O3, followed by the promoter region, O1, and O2.

Researchers have found that the tetrameric lac repressor binds to two operators simultaneously (O1 and O2/O3) forming a stable DNA loop that shows strong repression. Such a loop has been found to form in presence of either O2 or O3 but not when both O2 and O3 are absent. The absence of such a DNA loop has been suggested to lead to weak suppression.

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