Quantifying Protein Shape to Elucidate Its Influence on Solution Viscosity in High-Concentration Electrolyte Solutions

Therapeutic proteins with a high concentration and low viscosity are highly desirable for subcutaneous and certain local injections. The shape of a protein is known to influence solution viscosity; however, the precise quantification of protein shape and its relative impact compared to other factors like charge-charge interactions remains unclear. In this study, we utilized seven model proteins of varying shapes and experimentally determined their shape factors (v) based on Einstein's viscosity theory, which correlate strongly with the ratios of the proteins' surface area to the 2/3 power of their respective volumes, based on protein crystal structures resolved experimentally or predicted by AlphaFold. This finding confirms the feasibility of computationally estimating protein shape factors from amino acid sequences alone. Furthermore, our results demonstrated that, in high-concentration electrolyte solutions, a more spherical protein shape increases the protein's critical concentration (C*), the transition concentration beyond which protein viscosity increases exponentially relative to concentration increases. In summary, our work elucidates protein shape as a key determinant of solution viscosity through quantitative analysis and comparison with other contributing factors. This provides insights into molecular engineering strategies to optimize the molecular design of therapeutic proteins, thus optimizing their viscosity.