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22-Agric-A7 Chemistry and Microbiology of Foods · May 2017

Question 9 of 12: Growth-Reaction Order and Salmonellosis

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

Paper format. 04-Agric-A7 Chemistry and Microbiology of Foods, National Exams May 2017 — a three-hour closed-book exam (one aid sheet, both sides; approved calculator permitted). The paper is in two sections: Section I (Food Chemistry, Questions 1–6) and Section II (Food Microbiology, Questions 7–12); candidates answer any three questions from each section for a 100-mark paper (each question worth 16.7 marks). All twelve questions are worked here so the set is a complete study resource.

Reference texts. S. Damodaran, K.L. Parkin and O.R. Fennema (eds.), Fennema's Food Chemistry, 5th ed. (enzyme kinetics, water activity and sorption isotherms, lipid crystallization/polymorphism, protein gelation, popcorn starch/glass transition); R.P. Singh and D.R. Heldman, Introduction to Food Engineering, 5th ed. (reaction-order kinetics, quality-loss modelling); J.M. Steffe, Rheological Methods in Food Process Engineering, 2nd ed. (creep-recovery of viscoelastic doughs); J. Jay, M. Loessner and D. Golden, Modern Food Microbiology, 7th ed. (bacterial growth curve, intrinsic/ extrinsic factors, Salmonella, quorum sensing, viral/prion foodborne agents, rapid methods, sampling plans); C. Mortimore and C. Wallace, HACCP: A Practical Approach, 3rd ed. (the seven HACCP principles).

Section I — Food Chemistry

Question 9: Growth-Reaction Order and Salmonellosis (16.7 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) Order of a constant-doubling-time growth reaction

Given. Bacterial count doubles every $t_d=10$ min, indefinitely (constant doubling time, not slowing as the population grows).

Find. The kinetic order of the growth reaction.

Approach. Write the population balance $dN/dt = kN$ and check that it is the unique order whose solution has a doubling time independent of the current population $N$.

  1. Set up the balance. Binary fission means the growth rate is proportional to how many cells are currently present: $dN/dt = kN$, i.e. growth is first order in cell number.
  2. Confirm via the doubling-time signature. Integrating gives $N=N_0e^{kt}$, so the time to double, $t_d=\ln2/k$, is a constant that does not depend on $N_0$ — exactly the behaviour observed (the same 10 min doubling time holds however large the population has grown), which only a first-order (exponential) law produces; a zero-order law would double in ever-shorter intervals as $N$ grows, and any order $>1$ would take ever-longer intervals.
  3. Compute the rate constant. $$k = \frac{\ln 2}{t_d} = \frac{\ln 2}{10\ \text{min}} = \boxed{0.0693\ \text{min}^{-1}}.$$
Final results — Question 9(a)
QuantityValue
Order of the growth reactionFirst order ($dN/dt=kN$)
Rate constant $k$$0.0693\ \text{min}^{-1}$

(b) Mode, sources and dissemination of Salmonella

Salmonella causes illness predominantly as an infection, not a preformed-toxin intoxication: ingested viable cells must survive the stomach's gastric acid barrier, then invade the epithelial lining of the ileum and colon via a Type III secretion system that injects effector proteins, triggering the host cell to engulf the bacterium by a process resembling phagocytosis. Inside the intestinal mucosa the bacteria multiply and provoke a strong local inflammatory response (fluid secretion, neutrophil influx), which produces the classic diarrhoeal illness; in invasive cases the organism can breach the mucosa into the bloodstream to cause systemic infection.

Ingested viable cells Survive gastric acid barrier T3SS invasion of ileal/colonic epithelium Diarrhoea Bloodstream
Mode of illness: ingested cells survive gastric acid, invade intestinal epithelium via a Type III secretion system, and provoke local inflammation (diarrhoea) or, in invasive cases, systemic bloodstream spread.

Salmonella's principal reservoir is the intestinal tract of a very wide range of warm- and cold-blooded animals — poultry, cattle, pigs, and also reptiles/amphibians — so its sources include raw poultry and meat, eggs (including transovarian contamination before the calcified outer covering forms), unpasteurized dairy, and produce or water contaminated by animal or human faecal material. Dissemination through the food chain is largely faecal– oral: contaminated animal faeces reach carcasses during slaughter, contaminate feed and irrigation/wash water, cross-contaminate other foods via shared equipment or unwashed hands/surfaces in processing and food-service settings, and ultimately reach the consumer through undercooked or cross-contaminated food, or directly from an infected food handler.