(598h) Modeling Concentrated Protein Solutions – from Flory-Huggins Solution Theory to Modern Equation-of-State Based Approaches

Water is essential for the structure and function of proteins and their formulations. The residual moisture content has a significant impact on the physical and chemical solid-state stability of formulations of all kinds. Whilst the tendency for low molecular weight pharmaceutical solids to absorb significant amounts of water vapor over a wide range of relative humidities and temperatures is well documented (Callahan, J.; Cleary, G.; Elefant, M.; Kaplan, G.; Kensler, T. Drug. Dev. Indust. Pharm., 1982, 8, 355-369) and as is the ability of this water to affect many critical physical and chemical properties of these solids (Ahlneck, C.; Zografi, G. Int. J. Pharm., 1990, 62, 87-95), these phenomena have not been equally well studied for solid-state protein-based formulations. Interpreting the mechanisms of water absorption/desorption and ultimately the nature of protein-water interactions from a simple sorption isotherm is critical. Here, the authors present a comprehensive study of moisture sorption phenomena over a range of formulation-relevant temperatures in high-purity lyophilized protein formulations together with a canon of thermo-physical characterization techniques to produce experimental data that allows us to model the protein-water system from a statistical mechanical perspective. In this context, the protein’s behaviour is analyzed in terms of ‘glassy’ state dynamics. The ability to treat protein-water system with some of the most seminal theories in polymer solution science (e.g. Flory Huggins, Gibbs-DiMarzio, Sanchez-Lacombe) is demonstrated here. Both water sorption isotherms as well as the concentration dependence of the glass transition temperature were modeled for a number of model protein-solution systems. The strong concentrational variation of the glass transition temperature for a number of lyophilised proteins is reported here. It was found that relatively low (< 5  g water / g dry protein) concentrations of water can depress the glass transition temperature by up 100 K compared to the dry state. It was found that the Gibbs-DiMarzio theory (Dimarzio, E. A; Gibbs, J. H. J. Polym. Chem. A, 1963, 1, 1417-1428), and its extensions by Chow (Chow, T. S. Macromolecules, 1980, 13, 362-364) and Panayiotou (Panayiotou, C. G. Polym. J. , 1986, 18, 895-902) provided suitable theoretical frameworks to model the experimentally observed depression of the glass transition temperature and allow molecular insight other empirical or semi-empirical expression for the same phenomenon do not allow. Another striking example of the amorphous protein formulations studied here was the significant uptake of moisture at even low relative humidity and the onset of deliquescence for relative humidity levels > 80 %. For all protein systems studied here, it is observed that the standard Flory-Huggins lattice theory predicts an isotherm shape that does not correlate to the experimentally determined one. While the shape of our isotherms collected between 278 K and 333 K resembles that of a BET type ii isotherm, this study stretches the common view, that sorption in protein formulation can be explained from surface-based approaches such as the Brunnauer-Emmett-Teller theory and its extensions, and focuses on the solution character of the systems studied. Only a concentration-dependent chi interaction parameter allows for a good fit of the standard Flory-Huggins model. In fact, it was found that the sign of the chi interaction parameter would change from an exothermic to an endothermic mode of sorption at a equilibrium moisture content of 4 - 8 g water / g dry protein depending on the protein. This finding was later confirmed experimentally by a heat of mixing study. Volume-corrections of the Flory-Huggins theory such as Vrentas-Vrentas’ treatment (Vrentas, J. S.; Vrentas, C. M. Macromolecules, 1991, 24, 2404-2412) were found to allow for reasonably good fits of our sorption isotherms too. To test the hypothesis, we directly measured the volume of mixing as well as the heat of mixing for our systems. The data suggests that water affects the physico-chemical state of a protein formulation with complex dynamics well beyond the simplistic ones associated with solvent-induced plasticization. This points towards the need of employing lattice models that allow for volume changes (i.e. compressibility) upon mixing such as the Sanchez-Lacombe equation of state (Eos) model.  The pure component EoS parameters for the protein were obtained by fitting the Sanchez-Lacombe EoS to isothermal compressibility data. Two independent mixing properties, i.e. concentration dependence of glass transition temperature and specific volume of mixing, were collected and modeled with the Sanchez-Lacombe EoS. This then allowed us to truly predict the water-sorption isotherm of two model protein systems. Our predictions agree well with the collected isotherms. Overall, the work carried out explores the applicability of polymer-derived solution thermodynamics to the realm of protein science and engineering and the importance of furthering the understanding of a protein’s phase behaviour in binary and higher-order solutions.