On the optimal contact potential of proteins

TL;DR

This paper analytically derives the lower bound of protein conformational energy based on contact potentials, linking the native structure to the Go potential and spectral properties, with implications for structure prediction.

Contribution

It provides a theoretical derivation of the optimal contact potential and its relation to the native contact matrix, advancing understanding of energy landscapes in proteins.

Findings

Lower bound of conformational energy derived analytically

Contact energy matrix is proportional to native contact matrix (Go potential)

Spectral relations between contact and energy matrices established

Abstract

We analytically derive the lower bound of the total conformational energy of a protein structure by assuming that the total conformational energy is well approximated by the sum of sequence-dependent pairwise contact energies. The condition for the native structure achieving the lower bound leads to the contact energy matrix that is a scalar multiple of the native contact matrix, i.e., the so-called Go potential. We also derive spectral relations between contact matrix and energy matrix, and approximations related to one-dimensional protein structures. Implications for protein structure prediction are discussed.