Lac genes are most effectively expressed in presence of Lactose and its analogs when glucose is absent.
A unit of prokaryotic gene expression and regulation,which includes structural genes and regulatory sequences recognized by regulatory gene product is called operon.
Lac structural genes are a part of Lac operon. The Lac operon consists of three, structural genes,an operator and a promoter.The product of Lac operon is involved in the conversion of disaccharide lactose into glucose and Galactose.
Lactose and its analogs are inducers of Lac operon. So, the structural genes are best expressed in presence of Lactose. Glucose and galactose are repressors of lac gene so the genes are repressed in presence of glucose.
No glucose, high lactose
The lac operon is regulated by both negative and positive control.
The negative control involves a repressor protein which, when no lactose is present, is bound to the operator sequence of the operon and blocking transcription of the structural genes.
When lactose is present, it binds the inhibitor causing its release from the operator and thus allowing the transcription of the genes.
The positive control involves regulation by glucose. Glucose is more easily metabolized than lactose, so when it's present the bacteria will preferrably use glucose as fuel instead of lactose, so the expression of the lac operon genes is low.
When glucose levels are high, cAMP levels are low. cAMP is needed to activate a protein called CAP (Catabolite Activator Protein) which binds to a regulatory sequence of the operon lac and increases its transcription.