Aggregation, liquid–liquid phase separation, and percolation behaviour of a model antibody fluid constrained by hard-sphere obstacles

Abstract

This study is concerned with the behaviour of proteins within confinement created by hard-sphere obstacles. An individual antibody molecule is depicted as an assembly of seven hard spheres, organized to resemble a Y-shaped (on average) antibody (7-bead model) protein. For comparison with other studies we, in one case, model the protein as a hard sphere decorated by three short-range attractive sites. The antibody has two Fab and one Fc domains located in the corners of the letter Y. In this calculation, only the Fab–Fab and Fab–Fc attractive pair interactions are possible. The confinement is formed by the randomly distributed hard-sphere obstacles fixed in space. Aside from size exclusion, the obstacles do not interact with antibodies, but they affect the protein–protein correlation. We used a combination of the scaled-particle theory, Wertheim's thermodynamic perturbation theory and the Flory–Stockmayer theory to calculate: (i) the second virial coefficient of the protein fluid, (ii) the percolation threshold, (iii) cluster size distributions, and (iv) the liquid–liquid phase separation as a function of the strength of the various pair interactions of the protein and the model parameters, such as protein concentration and the packing fraction of obstacles. The conclusion is that hard-sphere obstacles strongly decrease the critical density and also, but to a much lesser extent, the critical temperature. Also, the confinement enhances clustering, making the percolating region broader. The effect depends on the model parameters, such as the packing fraction of obstacles η₀, the inter-site interaction strength ε_IJ, and the ratio between the size of the obstacle σ₀ and the size of one bead of the model antibody σ_hs; the value of this ratio is varied here from 2 to 5. Interestingly, at low to moderate packing fractions of obstacles, the second virial coefficient first slightly decreases (destabilization), and the slope depends on the observation temperature, but then at higher values of η₀ it increases. The calculated values of the second virial coefficient also depend on the size of the obstacles.