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 should be linear in curvature, and explores its applications in protein modeling and connections to physical theories.

Contribution

It establishes that the free energy functional for helical proteins must be linear in curvature, based on geometrical invariance and protein conformational facts.

Findings

The free energy density is linear in curvature.

The model can be used in Monte Carlo simulations for protein folding.

Connections to relativistic particles and strings are discussed.

Abstract

The effective 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. We briefly discuss the possibility of using the model proposed in Monte Carlo simulations of exhaustive searching the native stable state of the protein chain. The relation of this model to the rigid relativistic particles and strings is also considered.