Rigorous results on the local equilibrium kinetics of a protein folding model

TL;DR

This paper provides rigorous proofs for a local equilibrium approach to protein folding kinetics, demonstrating its properties such as free energy decrease, convergence to equilibrium, and computational efficiency, in a simplified model.

Contribution

It offers detailed rigorous proofs for the properties of a local equilibrium kinetic approach in a simplified protein folding model, confirming its theoretical validity.

Findings

Free energy decreases over time.

Exact equilibrium is recovered at infinite time.

The approach's equilibration rate bounds the true rate.

Abstract

A local equilibrium approach for the kinetics of a simplified protein folding model, whose equilibrium thermodynamics is exactly solvable, was developed in [M. Zamparo and A. Pelizzola, Phys. Rev. Lett. 97, 068106 (2006)]. Important properties of this approach are (i) the free energy decreases with time, (ii) the exact equilibrium is recovered in the infinite time limit, (iii) the equilibration rate is an upper bound of the exact one and (iv) computational complexity is polynomial in the number of variables. Moreover, (v) this method is equivalent to another approximate approach to the kinetics: the path probability method. In this paper we give detailed rigorous proofs for the above results.