Behaviour of the model antibody fluid constrained by rigid spherical obstacles: Effects of the obstacle–antibody attraction

Abstract

This study investigates the behaviour of a fluid of monoclonal antibodies (mAbs) when trapped in a confinement represented by rigid spherical obstacles that attract antibodies. The antibody molecule is depicted as an assembly of seven hard spheres (7-bead model), organized to resemble a Y-shaped object. The model antibody has two Fab and one Fc domains located in the corners of letter Y. In this calculation, only the Fab–Fab and Fab–Fc attractive pairs of interactions are effective. The confinement is formed by the randomly distributed hard-spheres fixed in space. The spherical obstacles, besides the size exclusion, interact with beads of the antibody molecules via the Yukawa attractive potential. We applied the combination of the scaled particle theory, replica Ornstein–Zernike equations, Wertheim's thermodynamic perturbation approach and the Flory–Stockmayer theory to calculate: (i) the phase diagram of the liquid–liquid phase separation and the percolation threshold, (ii) the cluster size distributions, and (iii) the second virial coefficient of the protein fluid distributed among the obstacles. All these quantities were calculated as functions of the strength of the attraction between the monoclonal antibodies, and the monoclonal antibodies and obstacles. The conclusion is that while the hard-sphere obstacles decrease the critical density and the critical temperature of the mAbs fluid, the effect of the protein–obstacle attraction is more complex. Adding an attractive potential to the obstacle–mAbs interaction first increases the wideness of the T*–ρ envelope. However, with the further increase of the obstacle–mAbs attraction intensity, we observe reversal of the effect, the T*–ρ curves become narrower. At some point, depending on the obstacle–mAbs interaction, the situation is observed where two different temperatures have the same fluid density (re-entry point). In all the cases shown here the critical point decreases below the value for the neat fluid, but the behaviour with respect to an increase of the strength of the obstacle–mAbs attraction is not monotonic. Yet another interesting phenomenon, known in the literature as an approach toward the “empty liquid” state, is observed. The stability of the “protein droplets”, formed by the liquid–liquid phase separation, depends on their local environment and temperature.