Question 9 of 9: Growth Yields, Microbial Classification, Monod Kinetics, and Thermal Death

Question 8: Growth Yields, Microbial Classification, Monod Kinetics, and Thermal Death (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.

(a) Conditions leading to low growth yield of yeast cells. Growth yield $Y_{X/S}$ falls when a smaller fraction of the substrate's available electrons/carbon is routed into biomass and more is diverted elsewhere: (1) anaerobic/fermentative conditions — without O₂ as the terminal electron acceptor, yeast ferments glucose to ethanol + CO₂, a far less efficient route to biomass than aerobic respiration (much of the substrate's available electrons leave in ethanol rather than being used for biosynthesis); (2) substrate/energy uncoupling under stress (osmotic, high substrate concentration — the Crabtree effect switches even aerobic yeast toward fermentative metabolism at high glucose), where extra maintenance energy is spent without a proportional biomass gain; (3) nutrient limitation other than the carbon source (N, P, trace metals, vitamins) forcing cells to spend substrate on maintenance rather than growth; (4) high maintenance-energy demand (e.g. extreme temperature, pH stress, toxic by-product accumulation) that consumes an increasing share of the catabolized substrate for cell maintenance rather than new biomass synthesis.

(b) Bacteria, yeasts, molds, algae, and protozoa — comparison.

All five groups share basic cellular machinery (ribosomes, membrane, genetic material), but differ fundamentally on the prokaryote/eukaryote axis (bacteria alone are prokaryotic, lacking a membrane-bound nucleus and organelles) and on nutritional mode (algae are the only obligate photoautotrophs of the group; bacteria span both autotrophy and heterotrophy; yeasts, molds, and protozoa are heterotrophic). Morphologically, molds are distinguished by their filamentous, multicellular hyphal growth form (a mycelium) versus the unicellular habit of bacteria, yeasts, and most protozoa; algae range from unicellular (e.g. Chlorella) to complex multicellular (seaweeds).

(c) Monod growth kinetics and other forms. The Monod equation relates the specific growth rate $\mu$ to the concentration of a single limiting substrate $S$: $$\mu=\mu_{max}\frac{S}{K_S+S}$$ where $\mu_{max}$ is the maximum specific growth rate (at substrate saturation) and $K_S$ is the half-saturation constant (the substrate concentration at which $\mu=\mu_{max}/2$) — a measure of the organism's affinity for that substrate (low $K_S$ = high affinity). At $S\gg K_S$, $\mu\to\mu_{max}$ (zero-order in $S$, substrate-saturated); at $S\ll K_S$, $\mu\approx(\mu_{max}/K_S)S$ (first-order, substrate-limited). It is mathematically the same form as Michaelis–Menten enzyme kinetics, reflecting that growth rate is ultimately paced by a rate-limiting uptake/enzymatic step. Two other forms of growth kinetics: (1) Monod kinetics with substrate inhibition (e.g. the Andrews/Haldane equation, $\mu=\mu_{max}S/(K_S+S+S^2/K_I)$) — growth rate rises with $S$ at low concentration but is inhibited at high $S$, giving a maximum at an intermediate substrate concentration rather than a monotonic saturation curve; (2) logistic growth kinetics, $dX/dt=\mu_{max}X(1-X/X_{max})$ — growth rate is limited directly by approach to a maximum population/carrying capacity $X_{max}$ rather than by a single dissolved substrate concentration, commonly used to describe growth curves with an explicit, empirically observed plateau.

(d) Thermal death kinetics. Microbial death under lethal heat follows first-order kinetics in the number of viable cells $N$: $$\frac{dN}{dt}=-k_dN \;\Rightarrow\; N=N_0e^{-k_dt}$$ where $k_d$ is the specific death-rate constant (temperature-dependent, typically following an Arrhenius relationship $k_d=Ae^{-E_a/RT}$ with a very high activation energy $E_a$, which is why lethality is extremely sensitive to small temperature increases). In sterilization practice this is usually expressed via the decimal reduction time $D=\ln10/k_d=2.303/k_d$, the time at a given temperature required to reduce the viable population by a factor of 10 (one log cycle); a plot of $\log_{10}N$ vs. time is a straight line of slope $-1/D$. The temperature-dependence of $D$ itself is characterized by the z-value, the temperature increase needed to reduce $D$ by a factor of 10 — together $D$ and $z$ let a process designer compute an equivalent sterilization time (e.g. the $F_0$ value in thermal processing) at any reference temperature.