Geometrically Reduced Number of Protein Ground State Candidates

TL;DR

This study reveals that the set of potential protein ground states is surprisingly small and structured, with a limited number of candidates that are stable across different interaction parameters, using an algebraic approach on a lattice model.

Contribution

It introduces an algebraic method to analyze protein ground states, demonstrating their limited number and the parameter space segmentation into stable domains.

Findings

Number of ground state candidates grows as L^2 for L-mers.

Interaction parameter space divides into domains each with a unique ground state.

Some sequences have a single, absolutely stable native state.

Abstract

Geometrical properties of protein ground states are studied using an algebraic approach. It is shown that independent from inter-monomer 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, the space of the interaction parameters of the model breaks up into well-defined domains, each corresponding to one ground state candidate, which are separated by sharp boundaries. In addition, by exact enumeration, we show there are some sequences which have one absolute unique native state. These absolute ground states have perfect stability against change of inter-monomer interaction potential.