13. A merodiploid strain of E. coli with the genotype F⁺O^CZ^–Y⁺/ O⁺Z⁺Y⁺was constructed. The activity of β-galactosidase enzyme was measured in this strain upon following treatments.
(A) no induction
(B) induction with n moles of IPTG
(C) induction with n moles of lactose
(D) induction with n moles of lactose in the presence of n moles of glucose
Which one of the following graphs depicts the expected trends in ß-galactosidase activity under the four different conditions?

A merodiploid E. coli strain with the genotype F+OCZ–Y+/O+Z+Y+ contains two copies of the lac operon: one with an operator-constitutive mutation (OC) and one wild-type. Understanding how β-galactosidase activity responds to different inducers and the presence of glucose reveals the logic of operon regulation and catabolite repression.

Genotype Breakdown

• F+OCZ–Y+: F’ plasmid with operator-constitutive (OC, non-repressible) mutation, lacZ– (no functional β-galactosidase), lacY+ (functional permease).

• O+Z+Y+: Chromosomal wild-type operator, functional lacZ+ (β-galactosidase), lacY+ (permease).

Expected β-Galactosidase Activity in Each Condition

(A) No Induction

• The OC mutation on the F’ plasmid means the operon is always ON, even without inducer.

• The chromosomal wild-type operon is OFF without inducer.

• Result: Basal β-galactosidase activity from the OC operon, but since F’ carries Z–, only the chromosomal Z+ produces enzyme. Thus, activity is low but above zero.

(B) Induction with IPTG

• IPTG induces the wild-type operon fully.

• OC operon remains ON (but Z–, so no additional enzyme from F’).

• Result: High β-galactosidase activity due to full induction of chromosomal Z+.

(C) Induction with Lactose

• Lactose induces the wild-type operon, but induction may be slightly less than with IPTG due to lactose transport limitations.

• OC operon remains ON (but Z–).

• Result: High β-galactosidase activity, slightly less than with IPTG if transport is limiting.

(D) Induction with Lactose + Glucose

• Glucose causes catabolite repression, lowering cAMP and reducing CAP activation.

• Wild-type operon induction is suppressed.

• OC operon remains ON (but Z–).

• Result: Activity drops compared to (B) and (C), but is still above (A) due to constitutive OC expression.

Graphical Trend (Relative Activity)

• (A) No induction: Moderate (constitutive from OC, but only chromosomal Z+ produces enzyme)

• (B) IPTG: Highest (full induction of wild-type Z+)

• (C) Lactose: High (induction of wild-type Z+, but possibly less than IPTG)

• (D) Lactose + Glucose: Lower than (B) and (C), but above (A) due to OC constitutive expression

Order: (B) > (C) > (D) > (A)

Visual Representation

Conclusion

The correct graph will show the highest β-galactosidase activity with IPTG, slightly lower with lactose, a further drop with lactose plus glucose, and the lowest (but nonzero) activity with no induction. This pattern reflects constitutive expression from the OC operator and inducible, glucose-repressible expression from the wild-type operon.

Keywords: β-galactosidase activity, merodiploid E. coli, lac operon, OC mutation, IPTG induction, lactose induction, glucose repression, catabolite repression, gene regulation, F’ plasmid, operon model, molecular biology.