Thermodynamic equilibrium of biological macromolecules under mechanical constraints

TL;DR

This paper introduces a novel simulation method using steered molecular dynamics for constrained equilibration of biomacromolecules, exemplified by a stretched amyloid beta strand, to facilitate free energy profiling under mechanical constraints.

Contribution

The work presents a new simulation trick for constrained equilibration in molecular dynamics, enabling accurate free energy calculations with fixed-end biomolecular systems.

Findings

Validated the method with a stretched amyloid beta strand

Supported the approach through energy and force curve analysis

Demonstrated applicability to systems with mechanical constraints

Abstract

Equilibrating proteins and other biomacromolecules is cardinal for molecular dynamics simulation of such biological systems in which they perform free dynamics without any externally-applied mechanical constraint, until thermodynamic equilibrium with the surrounding is attained. However, in some important cases, we have to equilibrate the system of interest in the constant presence of certain constraints, being referred to as constrained equilibration in the present work. A clear illustration of this type is a single amyloid \b{eta}-strand or RNA, when the reaction coordinate is defined as the distance between the two ends of the strand and we are interested in carrying out replica-exchange umbrella sampling to map the associated free energy profile as the dependent quantity of interest. In such cases, each sample has to be equilibrated with the two ends fixed. Here, we introduced a simulation trick to perform this so-called constrained equilibration using steered molecular dynamics. We then applied this method to equilibrate a single, stretched \b{eta}-strand of an amyloid beta dodecamer fibril with fixed ends. Examining the associated curves of the total energy and the force exerted on the practically-fixed SMD atom over the total timespan broadly supported the validity of this kind of equilibration.