Significance of bending restraints for the stability of helical polymer conformations

Abstract

We performed parallel-tempering Monte Carlo simulations to investigate the formation and stability of helical tertiary structures for flexible and semiflexible polymers, employing a generic coarse-grained model. Structural conformations exhibit helical order with tertiary ordering into single helices, multiple helical segments organized into bundles, and disorganized helical arrangements. For both bending-restrained semiflexible and bending-unrestrained flexible helical polymers, the stability of the structural phases is discussed systematically by means of hyperphase diagrams parametrized by suitable order parameters, temperature, and torsion strength. This exploration lends insight into the restricted flexibility of biological polymers such as double-stranded DNA and proteins.

System-Size Dependence of Helix-Bundle Formation for Generic Semiflexible Polymers

“…We investigate how the stability of helix segments and the type of bundles in semiflexible helical polymers with bending restraint [5,32] depends on the system size. For this purpose, Monte Carlo computer simulations of a simplified coarse-grained polymer model were performed.…”

“…A bending potential is included, based on the angle formed by two successive bonds (see Figure 1), vbend(θ)=1−prefixcos()θ−θ0; where θ is the bending angle and the reference angle is chosen to be θ0=1.4. It has turned out that bending restraints are essential to stabilize helical structures [5,32] and by this, biomacromolecular matter in general.…”

“…The energy of a polymer conformation X is calculated as E(X)=SFENE∑ivFENE(rii+1)+SLJ∑i>j+1vLJ(rij)+Sθ∑kvbend(θk)+Sτ∑lvtor(τl). The overall energy scale is associated with the non-bonded interaction, SLJ, and is set to unity. In these units, we chose SFENE=98/5 and Sθ=200 [5,32]. The torsion strength Sτ is considered a “material” parameter in our study and varied over a range of values to explore its influence on helical structure formation.…”

“…Helical polymers have been successfully explored using such models [19,20,21,22]. In addition to the properties of helical secondary-structure formation, there has also been a growing interest in understanding tertiary helix-bundle geometries and transitions [23,24,25,26,27,28,29,30,31,32,33]. Macromolecular structure and function depend on the length of the polymer and differences in system size can also lead to a qualitative change in essential features of structural organization [34,35].…”

“…By analyzing an entire class of helical polymers at several lengths, we specifically investigate the influence of the system size on helical structural phases of semiflexible polymers. For this purpose, extensive replica-exchange (parallel tempering) Monte Carlo [39,40,41,42,43] simulations of a coarse-grained model for helical polymers [5,32] were performed.…”