Freezing and thawing play an important role in the manufacturing, storage, and distribution of biologics. While these processes are employed to enhance the storage time of drug substances and facilitate their transportation, they can also generate aggregates raising relevant safety concerns. Therefore, understanding the mechanisms that underlie freeze–thaw induced aggregation and to anticipate protein sensitivity during early formulation development is essential.[1].

The concentrations of drug substances, buffer salts and excipients are meticulously optimized in the liquid formulation to maximize stability. However, during freezing, the liquid concentration increases significantly as water molecules are captured into growing ice crystals. This freeze-concentration is dictated by local temperature and pressure conditions until the concentrations in the liquid phase of glass-forming excipients (e.g., sugars) approach glass transition, thereby creating a kinetic barrier that hinders further freeze-concentration.[1,2] Overall, freezing generates a local concentration polarization, a microscale dualism where high concentrated liquid becomes entrapped, forming microchannels (pores) within the solid structure of frozen water.[[2], [3], [4]] This situation poses two major threats to protein stability. Firstly, the elevated concentration promotes protein self-association, particularly within a temperature range where cold denaturation is favored and cryopreservatives or buffer salts can precipitate.[[5], [6], [7], [8], [9], [10]] Secondly, interfacial, and mechanical stress arises from the dispersion of the drug substance through the extensive ice microstructure.[[11], [12], [13], [14], [15], [16], [17]] The displacement of the concentrated liquid phase during freezing also leads to anisotropy throughout the frozen domain, depending on the rate and direction of ice growth.[[17], [18], [19], [20]] This anisotropy, commonly referred to as macro-freeze-concentration or cryoconcentration, is observed, for example, in formulations frozen in bottles, where a higher predominance of the concentrated liquid phase is found at the center and bottom of the container.[11,[20], [21], [22], [23]] Such anisotropic stress combined with interfacial effects, particularly at solid–liquid boundaries, can amplify protein aggregation, as shear and interface stresses interact synergistically to promote the formation of protein particles, as demonstrated by Gerlt et al.[17] Essentially, two levels of heterogeneity are present in the frozen solution: concentration polarization occurs at the interface between the ice and liquid (microscale) and the displacement of the concentrated liquid towards the regions that freeze last, generating anisotropy.

Frozen stability is typically ensured when the drug substance is in a vitreous state.[6,21] Although, freezing a few liters of formulation typically imposes a few hours of freezing stress before the total drug substance can reach the glass transition temperature of the freeze concentrate (Tg’). This stress-time is also relevant during thawing, as the drug substance is brought back from the vitreous state, being warmed up while entrapped within the ice structure under high concentration. Geraldes et al.[24] introduced the concept of 'stress-time', defined as the time during which a drug substance remains within ice, highly concentrated, and above its Tg’. This measure of freezing and thawing stress can be complicated to determine as it varies across the container. Areas that freeze first can induce a longer stress-time on the enclosed drug substance than regions that freeze last. The distribution of stress-time has been calculated for different containers using computational fluid dynamics (CFD) modelling. This modelling technique has also been employed to design downscale models that replicate the stress-time distribution of manufacturing equipment within a smaller volume.[22,24,25] Bluemel et al.[25] used an insulating device to match the stress-time between 2 L and 125 mL bottles, which resulted in comparable impact on quality attributes of a therapeutic IgG during a series of freeze–thaw cycles. However, when the stress-time of the 2 L bottle was replicated in a 5 mL vial, the fraction of aggregates was limited to 50 % of what was measured in the 2 L bottle. This suggests that even though the stress-time is similar, the intensity of the stress may be somewhat reduced when there is a significant decrease in the size of the container. CFD modelling is also a relevant tool for the direct and indirect estimation of shear stress, which also enables a qualitative prediction, generating full-field maps that would be extremely difficult to achieve experimentally.[26].

In this study we aim to elucidate the mechanisms contributing to protein aggregation during the freeze–thaw stress-time, which is critical to improve processes and develop more accurate downscale models. We will focus on two main aspects related to protein aggregation during the stress-time: cold denaturation and shear stress imposed by the ice structure. Cold denaturation has been observed in situ for a therapeutic IgG at −10 °C using neutron scattering and correlated to aggregation below freezing temperature.[7,10] However, these experiments were carried out at approximately 2 kbar to prevent freezing and therefore its correlation to freeze–thaw cycles cannot be directly established. Nevertheless, pressure can also increase significantly during freezing because the water crystals expand in volume as water crystallizes. The expansion increases local pressure at the vicinity of the ice crystals, which contributes to the displacement of the liquid phase through the ice porous structure. When freezing is promoted from multiple directions, there is a likelihood of restricting liquid portions within the ice microstructure, which can permeate through the ice microchannels under pressure, undergoing relevant shear stress.[1] The enclosure of the liquid during freezing and the resulting pressurization can be significantly mitigated by promoting bottom-up freezing, or alternatively by hindering the solution at the top from freezing too early enclosing the liquid core.[11,19] Duarte et al.[11], have demonstrated that the pressure increase in 2 L and 5 L bottles could be mitigated by installing a cover with a phase-change material. This method also led to a less pronounced aggregation of bovine serum albumin. Several studies suggest a synergistic effect of shear stress and interfaces as a triggering combination for aggregation, which in the case of freeze–thaw is further potentiated by low temperature and pressure.[17,27,28].

Freezing and thawing can be divided in two stages: one that is near-isothermal at approximately 0 °C, due to water’s phase-change, and a stage that consists in the temperature variation of the frozen matrix. Therefore, different stress variables can be probed by adjusting the stress-time incidence on each stage. For example, while total time within the partly frozen matrix should correlate with molecule ‘sensitivity’ to the ice interface, cold denaturation stress is only expected to become relevant closer to cold denaturation temperature (TCD), which is typically below −10 °C.[8,29,30] CFD simulations will be used in this study to generate the stress-time distribution during freezing and thawing in a 0.5 L bottle and to design freeze–thaw recipes for 10 mL vials that can be used as downscale models for the 0.5 L bottle. Moreover, by using heat transfer geometries that favor or hinder pressure buildup during freezing, we also expect to clarify the relevance of shear stress imposed by the ice structure on the aggregation of a monoclonal antibody.