Lactose-Free Milk: Choosing Reactor Conditions for Immobilised Lactase
Alina runs a small dairy in Xewkija that wants to sell lactose-free milk. Each batch is 8,000 L, and the lactose concentration is about 140 mM. She has data for a fungal lactase: free enzyme has Km = 12 mM and Vmax = 1,800 µmol min−1 mg−1 at its optimum (37 °C, pH 4.5), but it loses activity above 50 °C. The same enzyme immobilised on alginate beads has Km = 35 mM and Vmax = 1,100 µmol min−1 mg−1, is stable from 4 to 55 °C and from pH 3.5 to 6.5. Milk is pH 6.6 and is pasteurised at 72 °C for 15 s before treatment. In bench trials at pH 6.6, free enzyme retained only 30% of its stated Vmax, whereas the immobilised preparation retained 80%. Alina needs at least 99.5% lactose hydrolysis, no enzyme protein in the final milk, and a process she can run every day without buying fresh enzyme. She is considering either a stirred batch tank or a packed-bed column.
1. Using the kinetic data, explain why the immobilised enzyme has a lower Vmax and higher Km, and calculate the fractional saturation of the immobilised enzyme at 140 mM lactose.
Read the worked answer
For a Michaelis–Menten enzyme, v = Vmax[S]/(Km + [S]). The immobilised enzyme has a lower apparent Vmax because only active sites on or near the bead surface are accessible; substrate must diffuse through the alginate, and some enzyme molecules are denatured or sterically blocked during immobilisation. The higher Km (35 mM versus 12 mM) means lower apparent affinity, again consistent with diffusion limitation and a less favourable local environment.
At 140 mM lactose the fractional saturation is 140/(35 + 140) = 0.80, so the immobilised enzyme works at 80% of its own Vmax: 0.80 × 1,100 = 880 µmol min−1 mg−1.
The free enzyme at milk pH 6.6 gives only 0.30 × 1,800 = 540 µmol min−1 mg−1. Despite the worse Km, the immobilised preparation is therefore about 63% faster under actual milk conditions, before allowing for reuse. The comparison also shows that at 140 mM the immobilised enzyme is close to saturation, so modest lactose depletion near the end of hydrolysis will slow the reaction.
2. Recommend a reactor configuration and operating conditions, and justify why pasteurisation cannot be used to stop the reaction.
Read the worked answer
A packed-bed column is preferable. The beads are retained, so the product contains no enzyme protein and the same enzyme can be used for many batches; a stirred batch tank would need a separation step (filtration or heat) to remove enzyme and would damage beads by abrasion. Pasteurise the milk first, cool it to 40–45 °C, adjust pH to 6.6 if needed, then pump it through the column at a rate giving the required residence time.
Do not pasteurise milk containing the enzyme: 72 °C for 15 s exceeds the 55 °C stability limit and would inactivate the biocatalyst, and heating after hydrolysis would not reliably remove enzyme protein. Because the enzyme is physically retained, no inactivation step is needed at the end; the product can be cooled and packed. Monitor conversion and flow rate, and back-flush periodically.
3. Alina finds the column loses 20% activity after 30 days. Suggest two likely causes and one operational change for each.
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Two likely causes are microbial fouling (milk proteins and bacteria form a film on the beads, blocking pores) and gradual loss of alginate integrity or enzyme leakage. Operational changes: (1) include a sanitising rinse and back-flush cycle between batches, and pre-filter or pasteurise milk before the column to reduce protein load; (2) change the bead formulation or cross-link with more calcium and operate at a lower temperature to reduce swelling and abrasion. Re-assay activity monthly to decide when to replace beads, and keep a record of pressure drop because a rising pressure often signals fouling.