Extracting signatures of spatial organization for biomolecular nanostructures

Considering that a variety of biomolecular structures are in size scales much smaller than 100 nm, analytical tools for extracting geometrical signatures from data obtained by indirect measurements are essential for obtaining accurate structural information. Insights into the underlying geometrical origins of constituents of diverse systems in 3-Dimensional (3-D) space have formed the foundations for tools leading to elucidation of chemical and biomolecular structures. In this work, we develop a geometrical tool that transforms arrangement of apparently randomly positioned points in 3-D space into 2-D maps. This allows extraction of signatures of spatial organization and geometrical origins of the points in 3-D space. To test the geometrical tool, we analyze 13550 crystal structures of naturally occurring folded proteins. We report extraction of signatures of a universal spatial organization of backbones of folded proteins. We also report the remarkable finding that the "globular" shape of soluble proteins is ellipsoidal rather than spherical.