Reversible self-association of therapeutic antibodies is a key factor in high protein solution viscosities. In the present work, a coarse-grained computational model accounting for electrostatic, dispersion, and long-ranged hydrodynamic interactions of two model monoclonal antibodies is applied to understand the nature of self-association, predicting the solution microstructure and resulting transport properties of the solution. For the proteins investigated, the structure factor across a range of solution conditions shows quantitative agreement with neutron-scattering experiments. We observe a homogeneous, dynamical association of the antibodies with no evidence of phase separation. Calculations of self-diffusivity and viscosity from coarse-grained dynamic simulations show the appropriate trends with concentration but, respectively, over- and under-predict the experimentally measured values. By adding constraints to the self-associated clusters that rigidify them under flow, prediction of the transport properties is significantly improved with respect to experimental measurements. We hypothesize that these rigidity constraints are associated with missing degrees of freedom in the coarse-grained model resulting from patchy and heterogeneous interactions among coarse-grained domains. These results demonstrate how structural anisotropy and anisotropy of interactions generated by features at the 2-5 nm length scale in antibodies are sufficient to recover the dynamics and rheological properties of these important macromolecular solutions.

Colloidal gels are formed during arrested phase separation. Sub-micron, mutually attractive particles aggregate to form a system spanning network with high interfacial area, far from equilibrium. Models for microstructural evolution during colloidal gelation have often struggled to match experimental results with long standing questions regarding the role of hydrodynamic interactions. In nearly all models, these interactions are neglected entirely. In the present work, we report simulations of gelation with and without hydrodynamic interactions between the suspended particles executed in HOOMD-blue. The disparities between these simulations are striking and mirror the experimental-theoretical mismatch in the literature. The hydrodynamic simulations agree with experimental observations, however. We explore a simple model of the competing transport processes in gelation that anticipates these disparities, and conclude that hydrodynamic forces are essential. Near the gel boundary, there exists a competition between compaction of individual aggregates which suppresses gelation and coagulation of aggregates which enhances it. The time scale for compaction is mildly slowed by hydrodynamic interactions, while the time scale for coagulation is greatly accelerated. This enhancement to coagulation leads to a shift in the gel boundary to lower strengths of attraction and lower particle concentrations when compared to models that neglect hydrodynamic interactions. Away from the gel boundary, differences in the nearest neighbor distribution and fractal dimension persist within gels produced by both simulation methods. This result necessitates a fundamental rethinking of how dynamic, discrete element models for gelation kinetics are developed as well as how collective hydrodynamic interactions influence the arrest of attractive colloidal dispersions.

Charge anisotropy or the presence of charge patches at protein surfaces has long been thought to shift the coacervation curves of proteins and has been used to explain the ability of some proteins to coacervate on the “wrong side” of their isoelectric point. This work makes use of a panel of engineered superfolder green fluorescent protein mutants with varying surface charge distributions but equivalent net charge and a suite of strong and weak polyelectrolytes to explore this concept. A patchiness parameter, which assessed the charge correlation between points on the surface of the protein, was used to quantify the patchiness of the designed mutants. Complexation between the polyelectrolytes and proteins showed that the mutant with the largest patchiness parameter was the most likely to form complexes, while the smallest was the least likely to do so. The patchiness parameter was found to correlate well with the phase behavior of the protein–polymer mixtures, where both macrophase separation and the formation of soluble aggregates were promoted by increasing the patchiness depending on the polyelectrolyte with which the protein was mixed. Increasing total charge and increasing strength of the polyelectrolyte promote interactions for oppositely charged polyelectrolytes, while charge regulation is also key to interactions for similarly charged polyelectrolytes, which must interact selectively with oppositely charged patches.

A new method for calculating the resistance tensors of arbitrarily shaped particles and the translational and rotational self-diffusivity in suspensions of such particles is developed. This approach can be harnessed to efficiently and accurately predict the hydrodynamic and transport properties of large macromolecules such as antibodies in solution. Particles are modeled as a rigid composite of spherical beads, and the continuum equations for low Reynolds number fluid mechanics are used to calculate the drag on the composite or its diffusivity in a solution of other composites. The hydrodynamic calculations are driven by a graphics processing unit (GPU) implementation of the particle-mesh-Ewald technique which offers log-linear scaling with respect to the complexity of the composite-bead particles modeled as well as high speed execution leveraging the hyper-parallelization of the GPU. Matrix-free expressions for the hydrodynamic resistance and translational and rotational diffusivity of composite bead particles are developed, which exhibit substantial improvements in computational complexity over existing approaches. The effectiveness of these methods is demonstrated through a series of calculations for composite-bead particles having a spherical geometry, and the results are compared to exact solutions for spheres. Included in the supplementary material is an implementation of the proposed algorithm which functions as a plug-in for the GPU molecular dynamics suite HOOMD-blue (http://codeblue.umich.edu/hoomd-blue) [J. A. Anderson, C. D. Lorenz, and A. Travesset, “General purpose molecular dynamics simulations fully implemented on graphics processing units,” J. Comput. Phys. 227(10), 5342–5359 (2008) and Glaser et al., “Strong scaling of general-purpose molecular dynamics simulations on GPUs,” Comput. Phys. Commun. 192, 97–107 (2015)].

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