Final answer:
Transcription of the lac operon would occur in the presence of lactose, but not glucose. Gene regulation is important in bacteria to ensure efficient utilization of resources and adaptation to changing environments. The lac operon and trp operon have different regulatory strategies to control gene expression based on the availability of specific nutrients.
Step-by-step explanation:
The genotypes provided represent partial diploids with different combinations of alleles in the lac operon. To determine if the cell would overall be Lac+ or Lac-, we need to look at the presence or absence of functional lacZ, lacY, and lacA genes. In the first genotype (I+P-O+Z+Y-/I+P+OCZ-Y+), all the structural genes (lacZ, lacY, lacA) are present, so the cell would be Lac+. However, transcription of the lac operon would not occur in the presence of only glucose and not lactose, as the lac operon is regulated by the presence of lactose in addition to low or absent glucose.
The importance of gene regulation in bacteria is to ensure efficient utilization of available resources and adaptation to changing environments. By controlling when and how genes are expressed, bacteria can conserve energy, avoid unnecessary protein production, and respond to different environmental conditions. The regulatory strategies of the lac operon and the trp operon support this by allowing bacteria to switch on or off the expression of specific genes depending on the availability of nutrients. The lac operon is induced in the presence of lactose when glucose is limited, while the trp operon is repressed in the presence of tryptophan.