Question 8 of 14: Thermal Process Lethality and the Bacterial Growth Curve

Question 8: Thermal Process Lethality and the Bacterial Growth Curve (12.5 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.

(a)(i) The $F_0$ value is the equivalent time, in minutes at a reference temperature of 121.1°C ($z=10\ {}^{\circ}\text{C}$), that a thermal process delivers to a product — it converts a real, possibly varying, come-up/hold/cool-down time–temperature history into a single lethality number on a common scale, so that two different heating profiles can be compared or a process can be verified against a microbiological safety target. For Clostridium botulinum, the reference "botulinum cook" is an $F_0$ of about 3 minutes, representing a 12-log (12D) reduction in spore population — the regulatory minimum needed to reduce the probability of a surviving, toxin-producing spore in a can to a negligible level.

(a)(ii) Low-acid foods (pH > 4.6) processed and sealed in an anaerobic container at ambient storage temperature provide exactly the conditions C. botulinum spores need to germinate, grow, and produce lethal neurotoxin, so the process must guarantee that 12D spore-lethality target, giving the minimum $F_0\approx3$ min. High-acid foods (pH $\le$ 4.6) do not need this: C. botulinum spores cannot germinate and grow below about pH 4.6, so the target organism shifts from a heat-resistant spore-former to far more heat-sensitive vegetative spoilage yeasts, moulds and bacteria (and pathogens like non-proteolytic strains are similarly acid-inhibited); a much milder pasteurising heat treatment is therefore sufficient, and the required $F_0$ for a high-acid product is correspondingly lower.

(b)

Given. Colony-forming-unit counts recorded every 30 min from $t=0$ to $t=480$ min (table above).

Find. The duration of the lag phase and the bacterium's growth rate.

Approach. Identify the three classical batch-growth regions from the data itself — a flat lag region, a log-linear exponential region, and a plateaued stationary region — then fit the specific growth rate $\mu$ from the exponential region by linear regression of $\ln(N)$ against time.

1. Identify the lag phase. From $t=0$ to $t=120$ min the count stays within 47–50 CFU/mL — essentially unchanged, no net growth. The lag phase therefore lasts $\boxed{120\ \text{min (2 h)}}$.
2. Identify the exponential phase. From $t=120$ min ($N=50$) to $t=360$ min ($N=12{,}800$) the count doubles on every 30 min interval ($50\to100\to200\to400\to800\to1600\to3200\to6400\to12{,}800$), the hallmark of exponential (log-phase) growth.
3. Fit the specific growth rate. Linear regression of $\ln N$ against $t$ over the exponential-phase points gives $$\mu = \frac{\Delta\ln N}{\Delta t} = \frac{\ln(12{,}800/50)}{360-120} = \boxed{0.0231\ \text{min}^{-1}}\ (=1.386\ \text{h}^{-1}).$$
4. Convert to a doubling time (cross-check). $$t_d = \frac{\ln 2}{\mu} = \frac{0.693}{0.0231} \approx 30\ \text{min},$$ exactly matching the observed 30 min doubling seen directly in the data, confirming the fit.
5. Note the stationary phase. From $t=360$ min onward the count plateaus at about 12,750–12,760 CFU/mL, indicating the culture has entered stationary phase (nutrient depletion/waste accumulation halting net growth).