Functionals linear in curvature and statistics of helical proteins

TL;DR

This paper derives a unique, geometrically invariant free energy functional for globular protein chains, showing it must be linear in curvature, which aids in simulating protein conformations.

Contribution

It establishes that the free energy functional for helical proteins is uniquely linear in curvature based on geometric invariance and protein structure facts.

Findings

The free energy density is linear in curvature.

The model can be used for Monte Carlo simulations.

Provides a basis for understanding protein stability.

Abstract

The free energy of globular protein chain is considered to be a functional defined on smooth curves in three dimensional Euclidean space. From the requirement of geometrical invariance, together with basic facts on conformation of helical proteins and dynamical characteristics of the protein chains, we are able to determine, in a unique way, the exact form of the free energy functional. Namely, the free energy density should be a linear function of the curvature of curves on which the free energy functional is defined. This model can be used, for example, in Monte Carlo simulations of exhaustive searching the native stable state of the protein chain.