Entropic Barriers, Frustration and Order: Basic Ingredients in Protein Folding

TL;DR

This paper presents a model of protein folding that incorporates entropic barriers and frustration, explaining the size limitations and stability range of foldable proteins, aligning with observed biological properties.

Contribution

It introduces a solvable model that accounts for entropic barriers and frustration, revealing how these factors influence folding times and stability in protein-like molecules.

Findings

Folding time scales as M^3 without frustration.

Frustration limits foldable proteins to about 300 monomers.

Proteins are stable within a specific temperature range regardless of size.

Abstract

We solve a model that takes into account entropic barriers, frustration, and the organization of a protein-like molecule. For a chain of size $M$, there is an effective folding transition to an ordered structure. Without frustration, this state is reached in a time that scales as $M^{\lambda}$, with $\lambda\simeq 3$. This scaling is limited by the amount of frustration which leads to the dynamical selectivity of proteins: foldable proteins are limited to $\sim 300$ monomers; and they are stable in {\it one} range of temperatures, independent of size and structure. These predictions explain generic properties of {\it in vivo} proteins.