Question 9 of 10: Diauxic Growth of E. coli on a Glucose:Lactose Medium

Question 9: Diauxic Growth of E. coli on a Glucose:Lactose Medium (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. A diauxic optical-density curve (read from the printed figure): a brief initial lag at OD ≈ 0.2 (0 to ≈1.5 h), a first linear rise to OD ≈ 0.9 at ≈8 h, a short flat step from ≈8 h to ≈9 h, a second, shallower rise to OD ≈ 1.7 at ≈20 h, then a plateau at OD ≈ 1.7 to the end of the record (≈26 h).

Find. (a) The time at which lacZY (β-galactosidase + lactose permease) transcription begins; (b) the lactose-utilization window; (c) the glucose-utilization window.

This is the classical diauxic growth pattern first described by Jacob and Monod for E. coli on a glucose+lactose mixture, and it reads directly off the two-step curve:

(a) $lacZY$ transcription onset ≈ 8 h. Glucose is the preferred carbon source: while any glucose remains, the lac operon is kept off by two simultaneous mechanisms — the LacI repressor blocks transcription in the absence of allolactose (inducer exclusion also directly blocks lactose uptake), and even if some induction occurred, low cyclic-AMP levels during glucose metabolism (catabolite repression via CRP·cAMP) would keep RNA polymerase from binding efficiently at the lac promoter. Only once glucose is exhausted (the short flat step beginning at ≈8 h) do intracellular cAMP levels rise and any trace of lactose relieve LacI repression — so transcription of lacZ (β-galactosidase) and lacY (permease) begins essentially at the start of that flat step, ≈8 h, which is also the start of the diauxic lag itself (the flat OD region ≈8–9 h reflects the time needed to synthesize enough of these new enzymes before growth on lactose can resume).

(b) Lactose utilized as sole carbon/energy source: ≈9–20 h. This is the second, slower growth phase (OD ≈0.9 → 1.7) — slower than the glucose phase because lactose supports a lower growth rate — after the lacZY enzymes induced during the ≈8–9 h lag have accumulated enough to support growth on lactose as the only remaining carbon source (glucose is already exhausted by 8 h).

(c) Glucose utilized as carbon-energy source: 0–8 h. This is the first, steeper growth phase (OD ≈0.2 → 0.9, active growth from ≈1.5 h after the initial lag); glucose is consumed preferentially over lactose throughout this window because of catabolite repression, and its exhaustion at ≈8 h is exactly what triggers the diauxic lag and the events in part (a).