The viscosity of protein and nucleic acid solutions and their folded structures explored using the free-volume concept and Eyring's rate process theory

Abstract

This article aims to unify the understanding of protein and nucleic acid solution viscosity by integrating the free-volume concept and Eyring's rate process theory. The importance of controlling protein and nucleic acid solution viscosity in therapeutic formulations and manufacturing cannot be overstated, as numerous empirical and semi-empirical equations/models have been proposed to fit experimental data in the literature. These models are intended to extrapolate viscosity predictions at higher concentrations based on low-concentration data or provide guidance on how to reduce viscosity by adjusting pH and adding salt. However, none of these models can be universally applied to all systems, providing reasonable interpretations of experimental results. We borrow the reptation-tube concept from polymer science to treat the molecules of proteins and nucleic acids, and introduce the aspect ratio parameter to describe the fibrousness of the molecular shapes of the proteins and nucleic acids. The obtained equations can adequately correlate the viscosity with protein and nucleic acid volume fraction, salt concentration, zeta potential, pH, and temperature, and fit many experimental data very well. They show that the viscosity increases almost linearly with the volume fraction in low-volume-fraction regions, but increases dramatically with the volume fraction in high-volume-fraction regions; increases gradually with both zeta potential and the aspect ratio of the molecular chains; decreases with the square root of the ionic strength; reaches a minimum point with pH; and generally decreases with temperature, except in DNA solutions due to the transition from double-stranded to single-stranded molecules, etc. The viscosity of several protein and DNA solutions are regressed with our equations and very good agreements are obtained. Our work deepens the physical understanding of critical parameters, and provides clues for lowering viscosity in pharmaceutical formulations.