Embedding a Native State into a Random Heteropolymer Model: The Dynamic Approach

TL;DR

This paper models a heteropolymer with a native state using Langevin dynamics, revealing phases where the system folds rapidly or gets trapped, depending on temperature and native affinity, with implications for understanding protein folding.

Contribution

It introduces a dynamic heteropolymer model with a native state controlled by a selection temperature, analyzing phase behavior and folding dynamics using a Gaussian variational approach.

Findings

At high selection temperature, the system exhibits a spin glass phase.

At low selection temperature, an ordered native-like phase emerges.

Folding is rapid between the glass transition and native state formation temperature.

Abstract

We study a random heteropolymer model with Langevin dynamics, in the supersymmetric formulation. Employing a procedure similar to one that has been used in static calculations, we construct an ensemble in which the affinity of the system for a native state is controlled by a "selection temperature" T0. In the limit of high T0, the model reduces to a random heteropolymer, while for T0-->0 the system is forced into the native state. Within the Gaussian variational approach that we employed previously for the random heteropolymer, we explore the phases of the system for large and small T0. For large T0, the system exhibits a (dynamical) spin glass phase, like that found for the random heteropolymer, below a temperature Tg. For small T0, we find an ordered phase, characterized by a nonzero overlap with the native state, below a temperature Tn \propto 1/T0 > Tg. However, the random-globule phase remains locally stable below Tn, down to the dynamical glass transition at Tg. Thus, in this model, folding is rapid for temperatures between Tg and Tn, but below Tg the system can get trapped in conformations uncorrelated with the native state. At a lower temperature, the ordered phase can also undergo a dynamical glass transition, splitting into substates separated by large barriers.