Is it important that the lac I gene be located next to the operator?
No.
When Lac I is mutated in an operon, the repressor will not be produced and it does not bind to the operator. But, repressor produced from lac I in a second lac operon copy was sufficient for the proper functioning of the operator and shutting off of the lac operon. This implies the presence of repressor protein is more important rather than the position of lac I.
Note that, position od ZYA is important with respect to the operation because the operator is a cis-regulatory sequence and it acts only on same DNA.
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