A constant extension ensembles model of double-stranded chain molecules

TL;DR

This paper develops a model for double-stranded chain molecules under fixed extension constraints, revealing differences from force ensembles and analyzing structural and force-related properties with sequence dependence.

Contribution

It introduces a novel constant extension ensemble model for double-stranded molecules, explicitly incorporating sequence dependence and excluded-volume interactions.

Findings

Force-extension curves align with conjugate force ensembles for homogeneous chains.

Sequence heterogeneity causes significant differences between extension and force ensemble curves.

Contact distributions indicate double-stranded regions tend to localize at chain ends.

Abstract

Because the constant extension ensemble of single chain molecule is not always equivalent with constant force ensemble, a model of double-stranded conformations, as in RNA molecules and $\beta$-sheets in proteins, with fixed extension constraint is built in this paper. Based on polymer-graph theory and the self-avoiding walks, sequence dependence and excluded-volume interactions are explicitly taken into account. Using the model, we investigate force-extension curves, contact distributions and force-temperature curves at given extensions. We find that, for the same homogeneous chains, the force-extension curves are almost consistent with the extension-force curves in the conjugated force ensembles. Especially, the consistence depends on chain lengths. But the curves of the two ensembles are completely different from each other if sequences are considered. In addition, contact distributions of homogeneous sequence show that the double-stranded regions in hairpin conformations tend to locate at two sides of the chain. We contribute the unexpected phenomena to the nonuniformity of excluded-volume interactions of the region and two tails with different lengths. This tendency will disappear if the interactions are canceled. Finally, in constant extension ensemble, the force-flipping transitions conjugated with re-entering phenomena in constant force ensemble are observed in hairpin conformations, while they do not present in secondary structure conformations.