Rheology of mRNA-loaded lipid nanodumbbells

In one important chemical engineering unit operation of messenger ribonucleic acid (mRNA) vaccine manufacture, the precious mRNA payload is encapsulated in lipid nanoparticles (LNPs). Recent elegant cryogenic-transmission electron microscopy [Brader et al., Biophys. J. 120, 2766 (2021)] reveals that these lipid nanoparticles take the form of dumbbell suspensions. When encapsulating their mRNA payloads, these dumbbells can be both lopsided and interpenetrating, with the smaller of the two beads carrying the payload. In this work, we arrive at analytical expressions for these suspensions of lopsided lipid nanoparticle dumbbells encapsulating mRNA payloads. For this, we first exploit rigid dumbbell theory [Abdel-Khalik and Bird, Appl. Sci. Res. 30, 268 (1975)], which relies on the orientation distributions of the lopsided dumbbells, to predict the suspension rheology, and specifically to predict how this departs from Newtonian behavior. We next exploit elastic dumbbell theory [Phan-Thien et al., Phys. Fluids 36, 071707 (2024)], which also relies on the orientation distributions of the lopsided dumbbells and to which we add dumbbell stretching. Our results include analytical expressions for the relaxation time, rotational diffusivity, zero-shear viscosity, shear stress relaxation function, steady-shear viscosity and both the viscous part and minus the elastic part of the complex viscosity. We determine the rotational diffusivity of the mRNA-loaded lipid nanoparticle nanodumbbells from small-amplitude oscillatory shear measurements.