Thermodynamics of volume-spanning self-assembly in the squid eye lens

Squids have developed spherical eye lenses with a graded refractive index (GRIN) for underwater vision. While the sphericity increases the lens sensitivity, GRIN corrects for spherical aberration. This system is an example of a complex, macroscopic optical device that reaches its optical properties through volume-spanning, error-minimizing self-assembly, a feat that is currently unreachable via engineered materials. The lens is built from the patchy-particle interactions of S-crystallin proteins, which have a globular body and protruding, disordered loops that form the low-valence patches. A remaining mystery about the lens system is that the squid expresses over 40 distinct versions of S-crystallin. To understand what nature is telling us about realizing volume-spanning self-assembly, we studied the details of the S-crystallin patch geometry and interaction polydispersity on the percolation behavior and material properties of the system. We found that the low-valence particle geometry influences whether the system percolates or not, as well as the structure of the resulting gel. Further, we found that a distribution of patch energies (as realized by the many different S-crystallin sequences in nature) may facilitate the transparency of the system, by suppressing the growth of the correlation length at low densities and temperatures.