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.  Recent elegant cryogenic-transmission electron microscopy [Biophys J 120, 2766 (2021)] reveals 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 exploit rigid dumbbell theory [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.  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.