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.