Enzymes: Question 5

Worked solution

Part (a)(i): Defining Km

Km, the Michaelis constant, is the substrate concentration at which an enzyme’s rate of reaction is exactly half of its maximum rate, Vmax.

Part (a)(ii): Comparing the affinity of enzyme R and enzyme S

Km can be used as a measure of how strongly, or how readily, an enzyme binds its substrate:

• A low Km means the enzyme only needs a small substrate concentration to reach half of its maximum rate. It is binding and processing substrate effectively even when substrate is scarce, so it has a high affinity for the substrate.
• A high Km means a much larger substrate concentration is needed before the enzyme reaches half of its maximum rate. It is binding substrate less readily at any given concentration, so it has a lower affinity.

Enzyme R has a Km of 0.15 mmol dm-3, forty times lower than enzyme S’s Km of 6.0 mmol dm-3. Enzyme R therefore reaches half of its maximum rate at a much lower substrate concentration than enzyme S does, showing that enzyme R has the higher affinity for the substrate.

Part (b): Immobilising enzyme R in alginate beads

Method: enzyme R is mixed thoroughly with a solution of sodium alginate. This mixture is then added drop by drop (for example, from a syringe) into a solution of calcium chloride. Calcium ions cause each drop of the alginate mixture to gel almost instantly into a small bead, trapping the enzyme molecules within a porous, insoluble network of calcium alginate. The enzyme is now immobilised, held within the bead rather than dissolved freely in solution, while the beads themselves are large enough to be easily collected, retained in a container, or packed into a reaction column.

Advantage 1. The enzyme can be recovered and reused. Because the beads are solid and insoluble, they can be simply filtered out of the reaction mixture (or held in place within a flow-through column) once the reaction is complete, and used again for further batches of substrate. This is much more cost-effective than using free enzyme in solution, where it would be difficult or impossible to recover and would typically need to be added fresh for every batch.

Advantage 2 (the product is not contaminated with enzyme, and the process can run continuously. Since the enzyme stays trapped within the beads rather than mixing with the product, the product solution can be collected without needing a further purification step to remove the enzyme) important in food processing, where the enzyme should not remain in the final product. Immobilisation also makes it practical to run the process continuously: a stream of substrate solution can be passed constantly through a column packed with the beads, with product continuously collected at the other end, rather than having to run and reset a fresh batch reaction each time.

Final answers

• (a)(i) Km is the substrate concentration at which the rate of reaction is half of Vmax.
• (a)(ii) Enzyme R has the higher affinity, since its much lower Km (0.15 mmol dm-3 vs 6.0 mmol dm-3) means it reaches half of its maximum rate at a much lower substrate concentration.
• (b) Enzyme R is trapped in calcium alginate beads (mixed with sodium alginate, then dripped into calcium chloride solution). Advantages include: the enzyme can be recovered and reused (lowering cost), and the product is not contaminated with enzyme while the process can run continuously.