Proteins are unstable molecules that may be severely injured by stresses encountered during freeze-thawing. Despite this, the selection of freeze-thaw conditions is currently empirical, and this results in reduced process control. Here we propose a mathematical model that takes into account the leading causes of protein instability during freeze-thawing, i.e. cold denaturation and surface-induced unfolding, and may guide the selection of optimal operating conditions. It is observed that a high cooling rate is beneficial for molecules that are extremely sensitive to cold denaturation, while the opposite is true when ice-induced unfolding is dominant. In all cases, a fast thawing rate is observed to be beneficial. The simulation outputs are confirmed by experimental data for myoglobin and lactate dehydrogenase, suggesting that the proposed modeling approach can reproduce the main features of protein behavior during freeze-thawing. This approach can therefore guide the selection of optimal conditions for protein-based formulations that are stored in a frozen or freeze-dried state.

蛋白质是不稳定的分子，在冻融过程中可能会受到应力的严重伤害。尽管如此，目前对冻融条件的选择仍然是经验性的，这导致了过程控制的减少。在这里，我们提出了一个数学模型，该模型考虑了冻融过程中蛋白质不稳定的主要原因，即冷变性和表面诱导的展开，并可以指导最佳操作条件的选择。观察到高冷却速率对于对冷变性极其敏感的分子是有利的，而当冰诱导的展开占主导时则相反。在所有情况下，观察到快速解冻率都是有益的。模拟输出由肌红蛋白和乳酸脱氢酶的实验数据证实，这表明所提出的建模方法可以重现冻融过程中蛋白质行为的主要特征。因此，该方法可以指导选择以冷冻或冻干状态存储的基于蛋白质的制剂的最佳条件。