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A generic but simple model is presented to evaluate the effect of the heterogeneous surface charge distribution of proteins and zwitterionic nanoparticles on their thermodynamic phase behavior. By considering surface charges as continuous "patches," the rich set of surface patterns that is embedded in proteins and charged patchy particles can readily be described. This model is used to study the fluid phase separation of charged particles where the screening length is of the same order of magnitude as the particle size. In particular, two types of charged particles are studied: dipolar fluids and protein-like fluids. The former represents the simplest case of zwitterionic particles, whose charge distribution can be described by their dipole moment. The latter system corresponds to molecules/particles with complex surface charge arrangements such as those found in biomolecules. The results for both systems suggest a relation between the critical region, the strength of the interparticle interactions, and the arrangement of charged patches, where the critical temperature is strongly correlated to the magnitude of the dipole moment. Additionally, competition between attractive and repulsive charge-charge interactions seems to be related to the formation of fluctuating clusters in the dilute phase of dipolar fluids, as well as to the broadening of the binodal curve in protein-like fluids. Finally, a variety of self-assembled architectures are detected for dipolar fluids upon small changes to the charge distribution, providing the groundwork for studying the self-assembly of charged patchy particles.

Protein-protein interactions in solution may be quantified by the osmotic second virial coefficient (OSVC), which can be measured by various experimental techniques including light scattering. Analysis of Rayleigh light scattering measurements from such experiments requires identification of a scattering volume and the thermodynamic constraints imposed on that volume, i.e., the statistical mechanical ensemble in which light scattering occurs. Depending on the set of constraints imposed on the scattering volume, one can obtain either an apparent OSVC, A(2,app), or the true thermodynamic OSVC, B(22)(osm), that is rigorously defined in solution theory [M. A. Blanco, E. Sahin, Y. Li, and C. J. Roberts, J. Chem. Phys. 134, 225103 (2011)]. However, it is unclear to what extent A(2,app) and B(22)(osm) differ, which may have implications on the physical interpretation of OSVC measurements from light scattering experiments. In this paper, we use the multicomponent hard-sphere model and a well-known equation of state to directly compare A(2,app) and B(22)(osm). Our results from the hard-sphere equation of state indicate that A(2,app) underestimates B(22)(osm), but in a systematic manner that may be explained using fundamental thermodynamic expressions for the two OSVCs. The difference between A(2,app) and B(22)(osm) may be quantitatively significant, but may also be obscured in experimental application by statistical uncertainty or non-steric interactions. Consequently, the two OSVCs that arise in the analysis of light scattering measurements do formally differ, but in a manner that may not be detectable in actual application.

Proteins aggregate and precipitate from high concentration solutions in a wide variety of problems of natural and technological interest. Consequently, there is a broad interest in developing new ways to model the thermodynamic and kinetic aspects of protein stability in these crowded cellular or solution environments. We use a coarse-grained modeling approach to study the effects of different crowding agents on the conformational equilibria of proteins and the thermodynamic phase behavior of their solutions. At low to moderate protein concentrations, we find that crowding species can either stabilize or destabilize the native state, depending on the strength of their attractive interaction with the proteins. At high protein concentrations, crowders tend to stabilize the native state due to excluded volume effects, irrespective of the strength of the crowder-protein attraction. Crowding agents reduce the tendency of protein solutions to undergo a liquid-liquid phase separation driven by strong protein-protein attractions. The aforementioned equilibrium trends represent, to our knowledge, the first simulation predictions for how the properties of crowding species impact the global thermodynamic stability of proteins and their solutions.

We extend our coarse-grained modeling strategy described in parts I and II of this investigation to account for nonuniform spatial distributions of hydrophobic residues on the solvent-exposed surfaces of native proteins. Within this framework, we explore how patchy surfaces can influence the solvent-mediated protein-protein interactions, and the unfolding and self-assembly behaviors of proteins in solution. In particular, we compare the equilibrium unfolding and self-assembly trends for three model proteins that share the same overall sequence hydrophobicity, but exhibit folded configurations with different solvent-exposed native-state surface morphologies. Our model provides new insights into how directional interactions can affect native-state protein stability in solution. We find that strongly-directional attractions between native molecules with patchy surfaces can help stabilize the folded conformation through the formation of self-assembled clusters. In contrast, native proteins with more uniform surfaces are destabilized by protein-protein attractions involving the denatured state. Finally, we discuss how the simulation results provide insights into the experimental solution behaviors of several proteins that display directional interactions in their native states.

We use highly efficient transition-matrix Monte Carlo simulations to determine equilibrium unfolding curves and fluid phase boundaries for solutions of coarse-grained globular proteins. The model we analyze derives the intrinsic stability of the native state and protein-protein interactions from basic information about protein sequence using heteropolymer collapse theory. It predicts that solutions of low hydrophobicity proteins generally exhibit a single liquid phase near their midpoint temperatures for unfolding, while solutions of proteins with high sequence hydrophobicity display the type of temperature-inverted, liquid-liquid transition associated with aggregation processes of proteins and other amphiphilic molecules. The phase transition occurring in solutions of the most hydrophobic protein we study extends below the unfolding curve, creating an immiscibility gap between a dilute, mostly native phase and a concentrated, mostly denatured phase. The results are qualitatively consistent with the solution behavior of hemoglobin (HbA) and its sickle variant (HbS), and they suggest that a liquid-liquid transition resulting in significant protein denaturation should generally be expected on the phase diagram of high-hydrophobicity protein solutions. The concentration fluctuations associated with this transition could be a driving force for the nonnative aggregation that can occur below the midpoint temperature.