Thermodynamics of tubelike flexible polymers

Semiflexible macromolecules in quasi-one-dimensional confinement: Discrete versus continuous bond angles

The conformations of semiflexible polymers in two dimensions confined in a strip of width D are studied by computer simulations, investigating two different models for the mechanism by which chain stiffness is realized. One model (studied by molecular dynamics) is a bead-spring model in the continuum, where stiffness is controlled by a bond angle potential allowing for arbitrary bond angles. The other model (studied by Monte Carlo) is a self-avoiding walk chain on the square lattice, where only discrete bond angles (0° and ±90°) are possible, and the bond angle potential then controls the density of kinks along the chain contour. The first model is a crude description of DNA-like biopolymers, while the second model (roughly) describes synthetic polymers like alkane chains. It is first demonstrated that in the bulk the crossover from rods to self-avoiding walks for both models is very similar, when one studies average chain linear dimensions, transverse fluctuations, etc., despite their differences in local conformations. However, in quasi-one-dimensional confinement two significant differences between both models occur: (i) The persistence length (extracted from the average cosine of the bond angle) gets renormalized for the lattice model when D gets less than the bulk persistence length, while in the continuum model it stays unchanged. (ii) The monomer density near the repulsive walls for semiflexible polymers is compatible with a power law predicted for the Kratky-Porod model in the case of the bead-spring model, while for the lattice case it tends to a nonzero constant across the strip. However, for the density of chain ends, such a constant behavior seems to occur for both models, unlike the power law observed for flexible polymers. In the regime where the bulk persistence length ℓp is comparable to D, hairpin conformations are detected, and the chain linear dimensions are discussed in terms of a crossover from the Daoud/De Gennes "string of blobs"-picture to the flexible rod picture when D decreases and/or the chain stiffness increases. Introducing a suitable further coarse-graining of the chain contours of the continuum model, direct estimates for the deflection length and its distribution could be obtained.

Dilute Semiflexible Polymers with Attraction: Collapse, Folding and Aggregation

We review the current state on the thermodynamic behavior and structural phases of self- and mutually-attractive dilute semiflexible polymers that undergo temperature-driven transitions. In extreme dilution, polymers may be considered isolated, and this single polymer undergoes a collapse or folding transition depending on the internal structure. This may go as far as to stable knot phases. Adding polymers results in aggregation, where structural motifs again depend on the internal structure. We discuss in detail the effect of semiflexibility on the collapse and aggregation transition and provide perspectives for interesting future investigations.

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

Helical polymer bundles are an important fixture in biomolecular systems. The particular structural geometry of helix bundles is dependent on many factors including the length of the polymer chain. In this study, we performed Monte Carlo simulations of a coarse-grained model for helical polymers to determine the influence of polymer length on tertiary structure formation. Helical structures of semiflexible polymers are analyzed for several chain lengths under thermal conditions. Structural hyperphase diagrams, parametrized by torsion strength and temperature, are constructed and compared.

Significance of bending restraints for the stability of helical polymer conformations

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.

Mapping the Protein Fold Universe Using the CamTube Force Field in Molecular Dynamics Simulations

It has been recently shown that the coarse-graining of the structures of polypeptide chains as self-avoiding tubes can provide an effective representation of the conformational space of proteins. In order to fully exploit the opportunities offered by such a ‘tube model’ approach, we present here a strategy to combine it with molecular dynamics simulations. This strategy is based on the incorporation of the ‘CamTube’ force field into the Gromacs molecular dynamics package. By considering the case of a 60-residue polyvaline chain, we show that CamTube molecular dynamics simulations can comprehensively explore the conformational space of proteins. We obtain this result by a 20 μs metadynamics simulation of the polyvaline chain that recapitulates the currently known protein fold universe. We further show that, if residue-specific interaction potentials are added to the CamTube force field, it is possible to fold a protein into a topology close to that of its native state. These results illustrate how the CamTube force field can be used to explore efficiently the universe of protein folds with good accuracy and very limited computational cost.

Modelling protein behaviour using computer simulations has progressively emerged in the last 50 years as a powerful strategy in structural and molecular biology. Over this period there has been a continuing interest in pushing the boundaries of this approach in terms of the size of the systems and the timescale of the processes that can be studied. Coarse-grained models offer in principle great opportunities in this context, but it has been extremely challenging to obtain force fields of accuracy comparable to that typical of fully atomistic models. We show here that the representation of protein molecules as self-avoiding tubes within the CamTube model enables the comprehensive, accurate and very fast exploration of the conformational space of proteins in molecular dynamics simulations. We illustrate in particular how the comprehensive mapping of the protein fold universe obtained using the CamTube model offers the possibility of analysing the behaviour of proteins in a wide range of non-native states.

Stabilization of Helical Macromolecular Phases by Confined Bending

By means of extensive replica-exchange simulations of generic coarse-grained models for helical polymers, we systematically investigate the structural transitions into all possible helical phases for flexible and semiflexible elastic polymers with self-interaction under the influence of torsion barriers. The competing interactions lead to a variety of conformational phases including disordered helical arrangements, single helices, and ordered, tertiary helix bundles. Most remarkably, we find that a bending restraint entails a clear separation and stabilization of the helical phases. This aids in understanding why semiflexible polymers such as double-stranded DNA tend to form pronounced helical structures and proteins often exhibit an abundance of helical structures, such as helix bundles, within their tertiary structure.

Effects of the interaction range on structural phases of flexible polymers

We systematically investigate how the range of interaction between non-bonded monomers influences the formation of structural phases of elastic, flexible polymers. Massively parallel replica-exchange simulations of a generic, coarse-grained model, performed partly on graphics processing units and in multiple-gaussian modified ensembles, pave the way for the construction of the structural phase diagram, parametrized by interaction range and temperature. Conformational transitions between gas-like, liquid, and diverse solid (pseudo) phases are identified by microcanonical statistical inflection-point analysis. We find evidence for finite-size effects that cause the crossover of "collapse" and "freezing" transitions for very short interaction ranges.

Ground-state properties of tubelike flexible polymers

In this work we investigate the structural properties of native states of a simple model for short flexible homopolymers, where the steric influence of monomeric side chains is effectively introduced by a thickness constraint. This geometric constraint is implemented through the concept of the global radius of curvature and affects the conformational topology of ground-state structures. A systematic analysis allows for a thickness-dependent classification of the dominant ground-state topologies. It turns out that helical structures, strands, rings, and coils are natural, intrinsic geometries of such tubelike objects.