Designability, thermodynamic stability, and dynamics in protein folding: a lattice model study

TL;DR

This study uses a lattice model to identify key criteria for protein-like behavior, linking structural designability and energy landscape features to folding stability and speed.

Contribution

It introduces two criteria based on structure designability and energy ratios that predict protein-like stability and folding speed, validated through computational analysis.

Findings

Highly designable structures correlate with large energy separation ratios.

Sequences with high $ ext{Δ/Γ}$ ratios tend to be fast folders.

Slow folding is associated with many nearly compact low-energy conformations.

Abstract

In the framework of a lattice-model study of protein folding, we investigate the interplay between designability, thermodynamic stability, and kinetics. To be ``protein-like'', heteropolymers must be thermodynamically stable, stable against mutating the amino-acid sequence, and must be fast folders. We find two criteria which, together, guarantee that a sequence will be ``protein like'': i) the ground state is a highly designable stucture, i. e. the native structure is the ground state of a large number of sequences, and ii) the sequence has a large $\Delta/\Gamma$ ratio, $\Delta$ being the average energy separation between the ground state and the excited compact conformations, and $\Gamma$ the dispersion in energy of excited compact conformations. These two criteria are not incompatible since, on average, sequences whose ground states are highly designable structures have large $\Delta/\Gamma$ values. These two criteria require knowledge only of the compact-state spectrum. These claims are substantiated by the study of 45 sequences, with various values of $\Delta/\Gamma$ and various degrees of designability, by means of a Borst-Kalos-Lebowitz algorithm, and the Ferrenberg-Swendsen histogram optimization method. Finally, we report on the reasons for slow folding. A comparison between a very slow folding sequence, an average folding one and a fast folding one suggests that slow folding originates from a proliferation of nearly compact low-energy conformations, not present for fast folders.