Coarse-grained computational models of two therapeutic monoclonal antibodies are constructed to understand the effect of domain-level charge-charge electrostatics on the self-association phenomena at high protein concentrations. The coarse-grained representations of the individual antibodies are constructed using an elastic network normal-mode analysis. Two different models are constructed for each antibody for a compact Y-shaped and an extended Y-shaped configuration. The resulting simulations of these coarse-grained antibodies that interact through screened electrostatics are done at six different concentrations. It is observed that a particular monoclonal antibody (hereafter referred to as MAb1) forms three-dimensional heterogeneous structures with dense regions or clusters compared to a different monoclonal antibody (hereafter referred to as MAb2) that forms more homogeneous structures (no clusters). These structures, together with the potential mean force (PMF) and radial distribution functions (RDF) between pairs of coarse-grained regions on the MAbs, are qualitatively consistent with the experimental observation that MAb1 has a significantly higher viscosity compared to MAb2, especially at concentrations >50 mg/mL, even though the only difference between the MAbs lies with a few amino acids at the antigen-binding loops (CDRs). It is also observed that the structures in MAb1 are formed due to stronger Fab-Fab interactions in corroboration with experimental observations. Evidence is also shown that Fab-Fc interactions can be equally important in addition to Fab-Fab interactions. The coarse-grained representations are effective in picking up differences based on local charge distributions of domains and make predictions on the self-association characteristics of these protein solutions. This is the first computational study of its kind to show that there are differences in structures formed by two different monoclonal antibodies at high concentrations.