A simple, batch fermentation of an aerobic bacterium growing...

A simple, batch fermentation of an aerobic bacterium growing on methanol gave the results shown in the table. Calculate: a. Maximum growth rate $\left(\mu_{\max }\right)$ b. Yield on substrate $\left(Y_{X / S}\right)$ c. Mass doubling time $\left(t_{d}\right)$ d. Saturation constant $\left(K_{s}\right)$ e. Specific growth rate $\left(\mu_{n e t}\right)$ at $t=10 \mathrm{~h}$ $$ \begin{array}{cll} \hline \text { Time (h) } & X(\mathrm{~g} / \mathrm{l}) & S(\mathrm{~g} / \mathrm{l}) \\ \hline 0 & 0.2 & 9.23 \\ 2 & 0.211 & 9.21 \\ 4 & 0.305 & 9.07 \\ 8 & 0.98 & 8.03 \\ 10 & 1.77 & 6.8 \\ 12 & 3.2 & 4.6 \\ 14 & 5.6 & 0.92 \\ 16 & 6.15 & 0.077 \\ 18 & 6.2 & 0 \\ \hline \end{array} $$

A simple, batch fermentation of an aerobic bacterium growing on methanol gave the results shown in the table. Calculate:
a. Maximum growth rate $\left(\mu_{\max }\right)$
b. Yield on substrate $\left(Y_{X / S}\right)$
c. Mass doubling time $\left(t_{d}\right)$
d. Saturation constant $\left(K_{s}\right)$
e. Specific growth rate $\left(\mu_{n e t}\right)$ at $t=10 \mathrm{~h}$
$$
\begin{array}{cll}
\hline \text { Time (h) } & X(\mathrm{~g} / \mathrm{l}) & S(\mathrm{~g} / \mathrm{l}) \\
\hline 0 & 0.2 & 9.23 \\
2 & 0.211 & 9.21 \\
4 & 0.305 & 9.07 \\
8 & 0.98 & 8.03 \\
10 & 1.77 & 6.8 \\
12 & 3.2 & 4.6 \\
14 & 5.6 & 0.92 \\
16 & 6.15 & 0.077 \\
18 & 6.2 & 0 \\
\hline
\end{array}
$$

Key Concepts

Specific Growth Rate (?net)

The specific growth rate at any given time, such as ?net at a specific time point, measures the instantaneous rate of biomass accumulation per unit biomass concentration. It can vary over the course of the fermentation due to substrate depletion or accumulation of inhibitory metabolites, and is important for monitoring the dynamic state of the culture during fermentation.

Saturation Constant (Ks)

The saturation constant is a parameter in the Monod equation that indicates the substrate concentration at which the microbial growth rate is at half its maximum. It reflects the affinity of the microorganism for the substrate; a lower Ks implies higher affinity. This concept is essential for understanding how substrate limitation affects growth.

Mass Doubling Time (td)

Mass doubling time is the period required for the microbial biomass to double in concentration. It is inversely related to the specific growth rate and is a practical metric to assess the speed of population growth. Understanding the doubling time helps in optimizing production processes and scaling up fermentations.

Maximum Growth Rate (?max)

The maximum growth rate represents the highest rate at which the microorganism is able to reproduce under optimal conditions, often observed during the exponential phase of growth. It is typically determined from the steepest slope of the log-transformed biomass versus time data and is crucial for characterizing the efficiency of microbial growth.

Batch Fermentation

Batch fermentation is a process where microorganisms are cultured in a closed system with a fixed volume of medium. No additional substrate is added during growth, and waste products accumulate, which often limits growth. This method is important because it provides a controlled environment to study microbial kinetics and calculate growth parameters from a single set of batch experiments.

Yield Coefficient (YX/S)

The yield coefficient quantifies the efficiency of substrate conversion into biomass. It is defined as the ratio of the increase in biomass concentration to the amount of substrate consumed. This parameter is key in evaluating how effectively the available substrate is being used for microbial synthesis in fermentation processes.

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