Patchy particle insights into self-assembly of transparent, graded index squid lenses.

Squids have spherical, gradient index lenses that maximize optical sensitivity while minimizing light scattering and geometric aberration. Previous studies have shown that the constituent lens proteins behave like patchy particles, and that a density gradient of packing fraction ∼0.01 to 1 assembles from a gradient of average particle valence, 〈M〉 ≈ 2.1 to 〈M〉 > 6. A priori, transparency requires that all regions within the larger gradient must minimize density fluctuations at length scales close to the wavelength of visible light. It is not known how a material can achieve this at all possible packing fractions via attractive interactions. We also observe that the set of proteins making the lens is remarkably polydisperse (there are around 40 isoforms expressed). Why does nature employ so many geometrically similar isoforms when theory suggests a few would suffice, and what, if any, is the physical role of the polydispersity? This study focuses on answering these questions for the sparsest regions of the lens, where the patchy nature of the system will have the largest influence on the final structure. We first simulated mixtures of bi- and trivalent patchy particles and found a strong influence of patch angle on the percolation and gel structure of the system. We then investigated the influence of the interaction polydispersity on the structure of the M = 2.1 system. We find that increasing the variance in patch energies and single-patch angle appears to decrease the length scale of density fluctuations while also moving the percolation line to lower temperature. S-Crystallin geometry and polydispersity appear to promote regular percolation of a gel structure while also limiting density fluctuations to small length scales, thereby promoting transparency in the annealed structure.

Using Schematic Models to Understand the Microscopic Basis for Inverted Solubility in γD-Crystallin.

Inverted solubility-melting a crystal by cooling-is observed in a handful of proteins, such as carbomonoxy hemoglobin C and γD-crystallin. In human γD-crystallin, the phenomenon is associated with the mutation of the 23rd residue, a proline, to a threonine, serine, or valine. One proposed microscopic mechanism entails an increase in surface hydrophobicity upon mutagenesis. Recent crystal structures of a double mutant that includes the P23T mutation allow for a more careful investigation of this proposal. Here, we first measure the surface hydrophobicity of various mutant structures of γD-crystallin and discern no notable increase in hydrophobicity upon mutating the 23rd residue. We then investigate the solubility inversion regime with a schematic patchy particle model that includes one of three variants of temperature-dependent patch energies: two of the hydrophobic effect, and one of a more generic nature. We conclude that, while solubility inversion due to the hydrophobic effect may be possible, microscopic evidence to support it in γD-crystallin is weak. More generally, we find that solubility inversion requires a fine balance between patch strengths and their temperature-dependent component, which may explain why inverted solubility is not commonly observed in proteins. We also find that the temperature-dependent interaction has only a negligible impact on liquid-liquid phase boundaries of γD-crystallin, in line with previous experimental observations.

Temperature-Dependent Interactions Explain Normal and Inverted Solubility in a γD-Crystallin Mutant.

Protein crystal production is a major bottleneck in the structural characterization of proteins. To advance beyond large-scale screening, rational strategies for protein crystallization are crucial. Understanding how chemical anisotropy (or patchiness) of the protein surface, due to the variety of amino-acid side chains in contact with solvent, contributes to protein-protein contact formation in the crystal lattice is a major obstacle to predicting and optimizing crystallization. The relative scarcity of sophisticated theoretical models that include sufficient detail to link collective behavior, captured in protein phase diagrams, and molecular-level details, determined from high-resolution structural information, is a further barrier. Here, we present two crystal structures for the P23T + R36S mutant of γD-crystallin, each with opposite solubility behavior: one melts when heated, the other when cooled. When combined with the protein phase diagram and a tailored patchy particle model, we show that a single temperature-dependent interaction is sufficient to stabilize the inverted solubility crystal. This contact, at the P23T substitution site, relates to a genetic cataract and reveals at a molecular level the origin of the lowered and retrograde solubility of the protein. Our results show that the approach employed here may present a productive strategy for the rationalization of protein crystallization.

Obtaining Soft Matter Models of Proteins and their Phase Behavior.

Globular proteins are roughly spherical biomolecules with attractive and highly directional interactions. This microscopic observation motivates describing these proteins as patchy particles: hard spheres with attractive surface patches. Mapping a biomolecule to a patchy model requires simplifying effective protein-protein interactions, which in turn provides a microscopic understanding of the protein solution behavior. The patchy model can indeed be fully analyzed, including its phase diagram. In this chapter, we detail the methodology of mapping a given protein to a patchy model and of determining the phase diagram of the latter. We also briefly describe the theory upon which the methodology is based, provide practical information, and discuss potential pitfalls. Data and scripts relevant to this work have been archived and can be accessed at https://doi.org/10.7924/r4ww7bs1p .

Correction to: Obtaining Soft Matter Models of Proteins and their Phase Behavior.

The acknowledgement section text has been updated in the chapter.

Learning about Biomolecular Solvation from Water in Protein Crystals.

Water occupies typically 50% of a protein crystal and thus significantly contributes to the diffraction signal in crystallography experiments. Separating its contribution from that of the protein is, however, challenging because most water molecules are not localized and are thus difficult to assign to specific density peaks. The intricateness of the protein-water interface compounds this difficulty. This information has, therefore, not often been used to study biomolecular solvation. Here, we develop a methodology to surmount in part this difficulty. More specifically, we compare the solvent structure obtained from diffraction data for which experimental phasing is available to that obtained from constrained molecular dynamics (MD) simulations. The resulting spatial density maps show that commonly used MD water models are only partially successful at reproducing the structural features of biomolecular solvation. The radial distribution of water is captured with only slightly higher accuracy than its angular distribution, and only a fraction of the water molecules assigned with high reliability to the crystal structure is recovered. These differences are likely due to shortcomings of both the water models and the protein force fields. Despite these limitations, we manage to infer protonation states of some of the side chains utilizing MD-derived densities.

Computational crystallization.

Crystallization is a key step in macromolecular structure determination by crystallography. While a robust theoretical treatment of the process is available, due to the complexity of the system, the experimental process is still largely one of trial and error. In this article, efforts in the field are discussed together with a theoretical underpinning using a solubility phase diagram. Prior knowledge has been used to develop tools that computationally predict the crystallization outcome and define mutational approaches that enhance the likelihood of crystallization. For the most part these tools are based on binary outcomes (crystal or no crystal), and the full information contained in an assembly of crystallization screening experiments is lost. The potential of this additional information is illustrated by examples where new biological knowledge can be obtained and where a target can be sub-categorized to predict which class of reagents provides the crystallization driving force. Computational analysis of crystallization requires complete and correctly formatted data. While massive crystallization screening efforts are under way, the data available from many of these studies are sparse. The potential for this data and the steps needed to realize this potential are discussed.