  The native state structures of globular proteins are stable and well-packed
indicating that self-interactions are favored over protein-solvent interactions
under folding conditions. We use this as a guiding principle to derive the
geometry of the building blocks of protein structures, alpha-helices and
strands assembled into beta-sheets, with no adjustable parameters, no amino
acid sequence information, and no chemistry. There is an almost perfect fit
between the dictates of mathematics and physics and the rules of quantum
chemistry. Our theory establishes an energy landscape that channels protein
evolution by providing sequence-independent platforms for elaborating
sequence-dependent functional diversity. Our work highlights the vital role of
discreteness in life and has implications for the creation of artificial life
and on the nature of life elsewhere in the cosmos.

Biomolecules;Soft Condensed Matter;Statistical Mechanics;Biological Physics