Tutorial Question 13

After the discussion with Dr Des, he has also agreed that another method would be a better way to find the shelf life of insulin.

The shelf life of insulin is the time taken for 10% of p.insulin to be formed. The time taken, on the other hand, would depend on the rate at which p.insulin is formed. Since the conversion of insulin to p.insulin is of the first order, the rate of p.insulin formation relies on the concentration of the reactant, ie. insulin.

If insulin is only degraded to p.insulin, we could easily find the shelf life by calculating t0.9 of insulin. However, this is not the case. Insulin is converted to d.insulin too. While one may argue that d.insulin is equally active as insulin, we must be aware that d.insulin is not insulin and does not contribute to the concentration of insulin nor convert to p.insulin. Therefore, the concentration of insulin is not 90% when p.insulin is 10%. Moreover, the concentration of insulin falls at a greater rate (since it is converted to d.insulin as well) than it would if p.insulin is the only product of degradation. Hence, we can conclude that it would take a longer time for 10% of p.insulin to form compared to if only one route of degradation, which is insulin to p.insulin, exist.

To find the shelf life, use the equation for parallel reactions found in the chemical stability notes. If you have the time, you might want to figure everything out from scratch, which is IMO rather interesting.

The answer would be somewhere around 2.78 months. Note that this is longer than the shelf life calculated by assuming that the degradation of insulin is a simple first order reaction, supporting the arguments put forth above.