In 1611 Kepler proposed that the densest packing of spheres could be achieved by stacking close-packed planes of spheres. In such a packing, the spheres occupy π/ √ 18 ≈74.05% of space. The Kepler conjecture was (almost certainly) proved in 1998 by Thomas Hales. When we pour a large number of equal-sized spheres in a container and shake them down, we do not obtain the Kepler packing. Rather a d...

Voids exist in proteins as packing defects and are often associated with protein functions. We study the statistical geometry of voids in two-dimensional lattice chain polymers. We define voids as topological features and develop a simple algorithm for their detection. For short chains, void geometry is examined by enumerating all conformations. For long chains, the space of void geometry is ex...

Single domain proteins are thought to be tightly packed. The introduction of voids by mutations is often regarded as destabilizing. In this study we show that packing density for single domain proteins decreases with chain length. We find that the radius of gyration provides poor description of protein packing but the alpha contact number we introduce here characterize proteins well. We further...

Rod outer segment disk membranes are densely packed with rhodopsin. The recent notion of raft or microdomain structures in disk membranes suggests that the local density of rhodopsin in disk membranes could be much higher than the average density corresponding to the lipid/protein ratio. Little is known about the effect of high packing density of rhodopsin on the structure and function of rhodo...

Cereal Chem. 86(2):239–246 Test weight and groat proportion are two very important quality characteristics of oat grain. In this study, we pose the hypothesis that these two characteristics are related through characteristics of grain density. Test weight is defined as the product of kernel density and packing proportion. Groat proportion, in theory, is the ratio of the groat mass to the kernel...