The stabilities of protein crystals

Prediction of Antibody Viscosity from Dilute Solution Measurements

The high antibody doses required to achieve a therapeutic effect often necessitate high-concentration products that can lead to challenging viscosity issues in production and delivery. Predicting antibody viscosity in early development can play a pivotal role in reducing late-stage development costs. In recent years, numerous efforts have been made to predict antibody viscosity through dilute solution measurements. A key finding is that the entanglement of long, flexible complexes contributes to the sharp rise in antibody viscosity at the required dosing. This entanglement model establishes a connection between the two-body binding affinity and the many-body viscosity. Exploiting this insight, this study connects dilute solution measurements of self-association to high-concentration viscosity profiles to quantify the relationship between these regimes. The resulting model has exhibited success in predicting viscosity at high concentrations (around 150 mg/mL) from dilute solution measurements, with only a few outliers remaining. Our physics-based approach provides an understanding of fundamental physics, interpretable connections to experimental data, the potential to extrapolate beyond training conditions, and the capacity to effectively explain the physical mechanics behind these outliers. Conducting hypothesis-driven experiments that specifically target the viscosity and relaxation mechanisms of outlier molecules may allow us to unravel the intricacies of their behavior and, in turn, enhance the performance of our model.

The crystallization enthalpy and entropy of protein solutions: microcalorimetry, van't Hoff determination and linearized Poisson–Boltzmann model of tetragonal lysozyme crystals

Microcalorimetric and van't Hoff determinations as well as a theoretical description provide a consistent picture of the crystallization enthalpy and entropy of protein solutions and their dependence on physicochemical solution parameters.

Comparative roles of charge, π, and hydrophobic interactions in sequence-dependent phase separation of intrinsically disordered proteins

Endeavoring toward a transferable, predictive coarse-grained explicit-chain model for biomolecular condensates underlain by liquid-liquid phase separation (LLPS) of proteins, we conducted multiple-chain simulations of the N-terminal intrinsically disordered region (IDR) of DEAD-box helicase Ddx4, as a test case, to assess roles of electrostatic, hydrophobic, cation-π, and aromatic interactions in amino acid sequence-dependent LLPS. We evaluated three different residue-residue interaction schemes with a shared electrostatic potential. Neither a common hydrophobicity scheme nor one augmented with arginine/lysine-aromatic cation-π interactions consistently accounted for available experimental LLPS data on the wild-type, a charge-scrambled, a phenylalanine-to-alanine (FtoA), and an arginine-to-lysine (RtoK) mutant of Ddx4 IDR. In contrast, interactions based on contact statistics among folded globular protein structures reproduce the overall experimental trend, including that the RtoK mutant has a much diminished LLPS propensity. Consistency between simulation and experiment was also found for RtoK mutants of P-granule protein LAF-1, underscoring that, to a degree, important LLPS-driving π-related interactions are embodied in classical statistical potentials. Further elucidation is necessary, however, especially of phenylalanine's role in condensate assembly because experiments on FtoA and tyrosine-to-phenylalanine mutants suggest that LLPS-driving phenylalanine interactions are significantly weaker than posited by common statistical potentials. Protein-protein electrostatic interactions are modulated by relative permittivity, which in general depends on aqueous protein concentration. Analytical theory suggests that this dependence entails enhanced interprotein interactions in the condensed phase but more favorable protein-solvent interactions in the dilute phase. The opposing trends lead to only a modest overall impact on LLPS.

Effects of non-pairwise repulsion on nanoparticle assembly

Electrostatic interactions provide a convenient way to modulate interactions between nanoparticles, colloids, and biomolecules because they can be adjusted by the solution pH or salt concentration. While the presence of salt provides an easy method to control the net interparticle interaction, the nonlinearities arising from electrostatic screening make it difficult to quantify the strength of the interaction. In particular, when charged particles assemble into clusters or aggregates, nonlinear effects render the interactions strongly non-pairwise. Here, we report Brownian dynamics simulations to investigate the effect that the non-pairwise nature of electrostatic interactions has on nanoparticle assembly. We compare these simulations to a system in which the electrostatics are modeled by a strictly pairwise Yukawa potential. We find that both systems show a narrow range in parameter space where the particles form well-ordered crystals. Bordering this range are regions where the net interactions are too weak to stabilize aggregated structures or strong enough that the system becomes kinetically trapped in a gel. The non-pairwise potential differs from the pairwise system in the appearance of an amorphous state for strongly charged particles. This state appears because the many-body electrostatic interactions limit the maximum density achievable in an assembly.

Ion Specificity and Nonmonotonic Protein Solubility from Salt Entropy

The addition of salt to protein solutions can either increase or decrease the protein solubility, and the magnitude of this effect depends on the salt used. We show that these effects can be captured using a theory that includes attractive and repulsive electrostatic interactions, nonelectrostatic protein-ion interactions, and ion-solvent interactions via an effective solvated ion radius. We find that the ion radius has significant effects on the translational entropy of the salt, which leads to salt specificity in the protein solubility. At low salt, the dominant effect comes from the entropic cost of confining ions within the aggregate, whereas at high concentrations, the salt drives a depletion attraction that favors aggregation. Our theory explains the reversal in the Hofmeister series observed in lysozyme cloud point measurements and semi-quantitatively describes the solubility of lysozyme and chymosin crystals. We present a comparison of the contributions to the free energy and give guidelines for when salting in or salting out should be expected.

Synthesis of luminescent lanthanide complexes within crosslinked protein crystal matrices

Eu(TTA)₃phen was synthesized inside of crosslinked protein crystals. And we characterized the volumetric changes quantitatively induced by DMSO.

Stable, metastable, and kinetically trapped amyloid aggregate phases

Self-assembly of proteins into amyloid fibrils plays a key role in a multitude of human disorders that range from Alzheimer's disease to type II diabetes. Compact oligomeric species, observed early during amyloid formation, are reported as the molecular entities responsible for the toxic effects of amyloid self-assembly. However, the relation between early-stage oligomeric aggregates and late-stage rigid fibrils, which are the hallmark structure of amyloid plaques, has remained unclear. We show that these different structures occupy well-defined regions in a peculiar phase diagram. Lysozyme amyloid oligomers and their curvilinear fibrils only form after they cross a salt and protein concentration-dependent threshold. We also determine a boundary for the onset of amyloid oligomer precipitation. The oligomeric aggregates are structurally distinct from rigid fibrils and are metastable against nucleation and growth of rigid fibrils. These experimentally determined boundaries match well with colloidal model predictions that account for salt-modulated charge repulsion. The model also incorporates the metastable and kinetic character of oligomer phases. Similarities and differences of amyloid oligomer assembly to metastable liquid-liquid phase separation of proteins and to surfactant aggregation are discussed.

Packing interface energetics in different crystal forms of the λ Cro dimer

Variation among crystal structures of the λ Cro dimer highlights conformational flexibility. The structures range from a wild type closed to a mutant fully open conformation, but it is unclear if each represents a stable solution state or if one may be the result of crystal packing. Here we use molecular dynamics (MD) simulation to investigate the energetics of crystal packing interfaces and the influence of site-directed mutagenesis on them in order to examine the effect of crystal packing on wild type and mutant Cro dimer conformation. Replica exchange MD of mutant Cro in solution shows that the observed conformational differences between the wild type and mutant protein are not the direct consequence of mutation. Instead, simulation of Cro in different crystal environments reveals that mutation affects the stability of crystal forms. Molecular Mechanics Poisson-Boltzmann Surface Area binding energy calculations reveal the detailed energetics of packing interfaces. Packing interfaces can have diverse properties in strength, energetic components, and some are stronger than the biological dimer interface. Further analysis shows that mutation can strengthen packing interfaces by as much as ∼5 kcal/mol in either crystal environment. Thus, in the case of Cro, mutation provides an additional energetic contribution during crystal formation that may stabilize a fully open higher energy state. Moreover, the effect of mutation in the lattice can extend to packing interfaces not involving mutation sites. Our results provide insight into possible models for the effect of crystallization on Cro conformational dynamics and emphasize careful consideration of protein crystal structures.

Growth rates of protein crystals

Protein crystallization is important for structural biology. The rate at which a protein crystallizes is often the bottleneck in determining the protein's structure. Here, we give a physical model for the growth rates of protein crystals. Most materials crystallize faster under stronger growth conditions; however, protein crystallization slows down under the strongest conditions. Proteins require a crystallization slot of 'just right' conditions. Our model provides an explanation. Unlike simpler materials, proteins are orientationally asymmetrical. Under strong conditions, protein molecules attempt to crystallize too quickly, in wrong orientations, blocking surface sites for more productive crystal growth. The model explains the observation that increasing the net charge on a protein increases the crystal growth rate. The model predictions are in good agreement with experiments on the growth rates of tetragonal lysozyme crystals as a function of pH, salt concentration, temperature, and protein concentration.

Generic pathways to stability in concentrated protein mixtures

We present a series of experimental results that disclose the crucial role of ionic strength and partial volume fractions in the control of the phase behaviour of binary protein mixtures. Our findings can be understood as that the ionic strength determines the relative contribution of the entropy of the protein counter-ions to the overall thermodynamics of the system. Associative phase separation and crystallization observed at, respectively, low and high ionic strength are suppressed at intermediate salt concentrations, where the entropy gain upon releasing the counter-ions from the double layer of the proteins is negligible and the entropy loss upon confining the counter-ions within the protein crystal phase significant. Moreover, we find that the partial volume fraction of the protein prone to crystallize determines the crystallization boundary and that the presence of other proteins strongly delays crystallization, leading to temporarily stable mixtures. These findings suggest that stability in more complex protein mixtures, such as the cytosol, relates to the ionic strength and protein composition rather than to protein specific properties.

Electrostatics and aggregation: how charge can turn a crystal into a gel

The crystallization of proteins or colloids is often hindered by the appearance of aggregates of low fractal dimension called gels. Here we study the effect of electrostatics upon crystal and gel formation using an analytic model of hard spheres bearing point charges and short range attractive interactions. We find that the chief electrostatic free energy cost of forming assemblies comes from the entropic loss of counterions that render assemblies charge-neutral. Because there exists more accessible volume for these counterions around an open gel than a dense crystal, there exists an electrostatic entropic driving force favoring the gel over the crystal. This driving force increases with increasing sphere charge, but can be counteracted by increasing counterion concentration. We show that these effects cannot be fully captured by pairwise-additive macroion interactions of the kind often used in simulations, and we show where on the phase diagram to go in order to suppress gel formation.