What is the role of cis-acting and trans-acting factors in transcription? Explain how these factors ...

If a factor is trans-acting, genes that are not physically adjacent can be regulated together and are mediated by genes that encode regulatory proteins. The lac repressor is an example of a trans-acting element because mutations can be complemented by a second gene with normal function.
If a factor is cis-acting, the DNA sequence must be adjacent to the genes it regulates. The lac operator is an example of a cis-acting element because mutations cannot be complemented by a second normal element.
Trans-acting factors (and complementation) indicate mutations in structural genes, whereas
cis-acting factors indicate regulatory sequences have been mutated.
IS is a trans-acting mutation because the mutation disrupts ligand binding of the repressor to the operator on both copies of the DNA. OC is a cis-acting mutation because only one molecule of DNA is unable to be repressed due to the mutation. The operon is constitutively active on the molecule of DNA that contains the OC allele, but the other copy of the gene is intact and functions properly when the repressor is present.