Patchy Particle Models to Understand Protein Phase Behavior

Computational models for studying physical instabilities in high concentration biotherapeutic formulations

Computational prediction of the behavior of concentrated protein solutions is particularly advantageous in early development stages of biotherapeutics when material availability is limited and a large set of formulation conditions needs to be explored. This review provides an overview of the different computational paradigms that have been successfully used in modeling undesirable physical behaviors of protein solutions with a particular emphasis on high-concentration drug formulations. This includes models ranging from all-atom simulations, coarse-grained representations to macro-scale mathematical descriptions used to study physical instability phenomena of protein solutions such as aggregation, elevated viscosity, and phase separation. These models are compared and summarized in the context of the physical processes and their underlying assumptions and limitations. A detailed analysis is also given for identifying protein interaction processes that are explicitly or implicitly considered in the different modeling approaches and particularly their relations to various formulation parameters. Lastly, many of the shortcomings of existing computational models are discussed, providing perspectives and possible directions toward an efficient computational framework for designing effective protein formulations.

A Modeling-Based Design to Engineering Protein Hydrogels with Random Copolymers

Protein enzymes have shown great potential in numerous technological applications. However, the design of supporting materials is needed to preserve protein functionality outside their native environment. Direct enzyme-polymer self-assembly offers a promising alternative to immobilize proteins in an aqueous solution, achieving higher control of their stability and enzymatic activity in industrial applications. Herein, we propose a modeling-based design to engineering hydrogels of cytochrome P450 and of PETase with styrene/2-vinylpyridine (2VP) random copolymers. By tuning the copolymer fraction of polar groups and of charged groups via quaternization of 2VP for coassembly with cytochrome P450 and via sulfonation of styrene for coassembly with PETase, we provide quantitative guidelines to select either a protein-polymer hydrogel structure or a single-protein encapsulation. The results highlight that, regardless of the protein surface domains, the presence of polar interactions and hydration effects promote the formation of a more elongated enzyme-polymer complex, suggesting a membrane-like coassembly. On the other hand, the effectiveness of a single-protein encapsulation is reached by decreasing the fraction of polar groups and by increasing the charge fraction up to 15%. Our computational analysis demonstrates that the enzyme-polymer assemblies are first promoted by the hydrophobic interactions which lead the protein nonpolar residues to achieve the maximum coverage and to play the role of the most robust contact points. The mechanisms of coassembly are unveiled in the light of both protein and polymer physical-chemistry, providing bioconjugate phase diagrams for the optimal material design.

Protein-polymer mixtures in the colloid limit: Aggregation, sedimentation, and crystallization

While proteins have been treated as particles with a spherically symmetric interaction, of course in reality, the situation is rather more complex. A simple step toward higher complexity is to treat the proteins as non-spherical particles and that is the approach we pursue here. We investigate the phase behavior of the enhanced green fluorescent protein (eGFP) under the addition of a non-adsorbing polymer, polyethylene glycol. From small angle x-ray scattering, we infer that the eGFP undergoes dimerization and we treat the dimers as spherocylinders with aspect ratio L/D - 1 = 1.05. Despite the complex nature of the proteins, we find that the phase behavior is similar to that of hard spherocylinders with an ideal polymer depletant, exhibiting aggregation and, in a small region of the phase diagram, crystallization. By comparing our measurements of the onset of aggregation with predictions for hard colloids and ideal polymers [S. V. Savenko and M. Dijkstra, J. Chem. Phys. 124, 234902 (2006) and Lo Verso et al., Phys. Rev. E 73, 061407 (2006)], we find good agreement, which suggests that the behavior of the eGFP is consistent with that of hard spherocylinders and ideal polymers.

Effective potentials induced by mixtures of patchy and hard co-solutes

The addition of co-solutes to colloidal suspensions is often employed to induce tunable depletion interactions. In this work, we investigate effective colloidal interactions arising from binary co-solute mixtures of hard spheres and patchy particles. By changing the relative concentration of the two species, we show that the resulting effective potential V_eff continuously changes from the one obtained for a single-component hard sphere co-solute to that mediated by the single-component patchy particle co-solute. Interestingly, we find that, independent of the relative concentration of the two components, the resulting V_eff is additive, i.e., it is well-described by the linear combination of the effective interactions mediated by respective pure co-solutes. However, a breakdown of the additivity occurs when the co-solute mixture is close to the onset of a demixing transition. These results represent a step forward in understanding and predicting colloidal behavior in complex and crowded environments and for exploiting this knowledge to design targeted colloidal superstructures.