Theory for the Liquid–Liquid Phase Separation in Aqueous Antibody Solutions

Abstract

This study presents the theory for liquid-liquid phase separation for systems of molecules modeling monoclonal antibodies. Individual molecule is depicted as an assembly of seven hard spheres, organized to mimic the Y-shaped antibody. We consider the antibody-antibody interactions either through Fab, Fab' (two Fab fragments may be different), or Fc domain. Interaction between these three domains of the molecule (hereafter denoted as A, B, and C, respectively) is modeled by a short-range square-well attraction. To obtain numerical results for the model under study, we adapt Wertheim's thermodynamic perturbation theory. We use this model to calculate the liquid-liquid phase separation curve and the second virial coefficient B. Various interaction scenarios are examined to see how the strength of the site-site interactions and their range shape the coexistence curve. In the asymmetric case, where an attraction between two sites is favored and the interaction energies for the other sites kept constant, critical temperature first increases and than strongly decreases. Some more microscopic information, for example, the probability for the particular two sites to be connected, has been calculated. Analysis of the experimental liquid-liquid phase diagrams, obtained from literature, is presented. In addition, we calculate the second virial coefficient under conditions leading to the liquid-liquid phase separation and present this quantity on the graph B versus protein concentration.

Evaluating the Effects of Hinge Flexibility on the Solution Structure of Antibodies at Concentrated Conditions

“…12,14 In this regard, there is an increasing interest in developing computational mAb models to narrow this search space, if not, to predict the behavior of mAb solutions from low to high concentrations. [15][16][17][18][19][20] Notably, these models are limited to physically relevant, but computationally efficient coarse-grained representations, since fully atomistic simulations of concentrated mAb solutions remain out of reach due to the time-and length-scales of most of the protein instability phenomena.…”

“…In the specific case of antibodies, many coarse-grained models have been developed during the last decade to study different instability phenomena of mAb solutions; [15][16][17][18][19][20] however, most of these models assume mAbs as rigid-bodies, focusing on capturing short-and longrange interactions but neglecting any conformational fluctuation that may affect the overall mAb structure. Such models contrast with recent experimental studies employing highresolution structural techniques such as electron tomography 33 and small-angle scattering, 34,35 which have highlighted the highly flexible nature of mAbs.…”

Potential and limits of a colloid approach to protein solutions

“…There are indeed a number of quite successful attempts to use patchy particle theory to model protein interactions and the resulting self-assembly and phase behavior. 129,130,135 This is demonstrated in Fig. 7 (bottom), which shows a comparison between calculated and measured binodals for two different mAbs.…”

“…124,125 However, successful mAb applications require stable and low viscosity high concentration formulations, which are often difficult to achieve as mAbs are prone to exhibit reversible self-association at high concentrations that result in enhanced viscosity, and are also known to exhibit high turbidity due to the presence of liquid-liquid phase separation. 45,[126][127][128][129][130] A number of studies have made attempts to characterize cluster formation in mAb solutions, and to interpret antibody solution properties through analogies with colloids. [129][130][131][132][133][134][135][136][137] This is by no means straightforward due to the nonspherical shape and internal flexibility of mAbs, since interactions between proteins are frequently treated based on spherical approximations, and in particular the enormous effect that specific, directional interactions can have are often not considered.…”

“…7 (bottom), which shows a comparison between calculated and measured binodals for two different mAbs. 129 However, there is still need for significant improvements in relating model parameters to the actual composition and structure of the mAb and the solution, and we also need more work on establishing the impact of the high flexibility of the mAb structure.…”