Geometrically Reduced Number of Protein Ground State Candidates

Geometrical properties of protein ground states are studied using an algebraic approach. It is shown that independent from intermonomer interactions, the collection of ground state candidates for any folded protein is unexpectedly small: For the case of a two-parameter hydrophobic-polar lattice model for $L$-mers, the number of these candidates grows only as $L^2$. Moreover, by exact enumeration, we show there are some sequences which have one absolute unique native state. These absolute ground states have perfect stability against any change of intermonomer interaction potential.