Yeast Continuous Culture — Are Other Products Synthesized?: 04-BS-13, December 2015, Q2

Question 2: Yeast Continuous Culture — Are Other Products Synthesized? (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.

Quantity	Value
Biomass yield, $Y_{XS}$ (dry wt., incl. ash)	0.37 g/g glucose
Measured O₂ consumption	0.88 g O₂/g cells formed
Ash content	5%
Biomass formula (ash-free)	CH_1.79O_0.56N_0.17, MW = 25.13 g/cmol
MW glucose	180 g/mol

Find. Whether the measured O₂ consumption is consistent with a "biomass + CO₂ + H₂O only" stoichiometry (i.e. $f=0$), or whether a metabolic by-product must also be forming.

Approach. First predict the O₂ demand that the atom and electron balances require if no by-product forms ($f=0$). Then compare that prediction against the O₂ consumption actually measured (0.88 g/g). Because both routes to the "no by-product" prediction are internally consistent (atom balance and degree-of-reduction balance must agree with each other regardless of whether the physical assumption is right), a mismatch against the measured value is real evidence of a missing product, not an arithmetic error.

Biomass coefficient $c$. Per mole glucose (180 g): dry biomass $=0.37(180)=66.6$ g; ash-free $=66.6(0.95)=63.27$ g; $$c=\frac{63.27}{25.13}=\boxed{2.518\ \text{cmol biomass/mol glucose}}.$$
Nitrogen balance → $b$. $b=0.17c=0.428$ mol NH₃/mol glucose.
Predict $a$ assuming NO by-product ($f=0$). C: $d=6-c=3.482$. H: $12+3b=1.79c+2e\Rightarrow e=4.389$. O: $6+2a=0.56c+2d+e\Rightarrow$ $$a_{\text{predicted}}=\frac{0.56(2.518)+2(3.482)+4.389-6}{2}=\boxed{3.382\ \text{mol O}_2\text{/mol glucose}}.$$ Cross-check via the degree-of-reduction balance ($\gamma_S=4.0$ for glucose, $\gamma_B=4\!\cdot\!1+1.79-2(0.56)-3(0.17)=4.16$ for the biomass formula): $$a_{\text{predicted}}=\frac{\gamma_S(6)-\gamma_B c}{4}=\frac{4.0(6)-4.16(2.518)}{4}=3.382\ \text{mol O}_2\text{/mol glucose}$$ — identical, confirming the "no by-product" prediction is internally consistent.
Convert the prediction to the same mass units as the given data. $$\left(\frac{\text{g O}_2}{\text{g cells}}\right)_{\text{predicted}}=\frac{a_{\text{predicted}}(32)}{66.6}=\boxed{1.625\ \text{g O}_2/\text{g cells}}$$ — nearly double the measured value of 0.88 g O₂/g cells.
Quantify the shortfall via the electron balance using the measured $a$. Back-calculate $a_{\text{actual}}$ from the measured ratio: $a_{\text{actual}}=0.88(66.6)/32=1.832$ mol O₂/mol glucose. The available electrons this actually accounts for are $$\gamma_B c+4a_{\text{actual}}=4.16(2.518)+4(1.832)=10.47+7.33=17.80\ \text{e}^-\text{eq/mol glucose},$$ against a total supply of $\gamma_S(6)=24.0$ e⁻eq/mol glucose — a deficit of $\boxed{6.2\ \text{available-electron equivalents per mole glucose}}$ that is not accounted for by either biomass or the measured O₂ uptake.
Conclusion. Since the culture consumes far less O₂ than complete "biomass + CO₂" stoichiometry would require, the missing 6.2 available-electron equivalents per mole glucose must be exported in a reduced metabolic product (the classic case for yeast under these conditions is a fermentative by-product such as ethanol, glycerol, or an organic acid) — yes, other product(s) are being synthesized. The exam data do not specify the product's identity, so its exact formula $\text{C}_j\text{H}_k\text{O}_l\text{N}_m$ and coefficient $f$ cannot be solved uniquely (7 unknowns $d,e,f,j,k,l,m$ remain against 4 atom balances once $f\ne0$), but the electron-deficiency argument proves its existence and quantifies the available electrons it must carry.

Quantity	Result
Biomass coefficient, $c$	2.518 cmol/mol glucose
Predicted O₂ demand (no by-product)	3.382 mol/mol glucose = 1.625 g/g cells
Measured O₂ demand	1.832 mol/mol glucose = 0.88 g/g cells
Unaccounted available electrons	6.2 eq/mol glucose
Conclusion	Yes — a reduced by-product is being formed

Topic: Using the degree-of-reduction (available-electron) balance to detect an unspecified metabolic by-product.

Key relations: $\gamma_S n_S=\gamma_B c+\sum \gamma_{P_i}f_i+4a$; when a by-product formula is unknown, compare the measured $a$ against the $a$ required for zero by-product.

Why this works: available electrons (relative to the CO₂/H₂O/NH₃ reference states) can only leave a fermentation in three ways — fixed into biomass, exported in a product, or transferred to O₂. If the measured O₂ uptake is too small to close the balance against biomass alone, the remainder is conserved in an as-yet-unspecified product; no assumption about that product's identity is needed to prove it exists.

Common pitfall: concluding "yes/no" from the O₂ number alone without a reference-case comparison — the raw 0.88 g/g figure means nothing on its own; it must be checked against what stoichiometry demands if there really were no product.

Source: Shuler & Kargi, Bioprocess Engineering: Basic Concepts, Ch. 5 (degree of reduction, product formation).

Question 2 of 10: Yeast Continuous Culture — Are Other Products Synthesized?

Question 2: Yeast Continuous Culture — Are Other Products Synthesized? (20 marks)