The folding pathways and thermodynamics of semiflexible polymers

Secondary-structure phase formation for semiflexible polymers by bifurcation in hyperphase space

Canonical analysis has long been the primary analysis method for studies of phase transitions. However, this approach is not sensitive enough if transition signals are too close in temperature space. The recently introduced generalized microcanonical inflection-point analysis method not only enables the systematic identification and classification of transitions in systems of any size, but it can also distinguish transitions that standard canonical analysis cannot resolve. By applying this method to a generic coarse-grained model for semiflexible polymers, we identify a mixed structural phase dominated by secondary structures such as hairpins and loops that originates from a bifurcation in the hyperspace spanned by inverse temperature and bending stiffness. This intermediate phase, which is embraced by the well-known random-coil and toroidal phases, is testimony to the necessity of balancing entropic variability and energetic stability in functional macromolecules under physiological conditions.

Stable intermediate phase of secondary structures for semiflexible polymers

Systematic microcanonical inflection-point analysis of precise numerical results obtained in extensive generalized-ensemble Monte Carlo simulations reveals a bifurcation of the coil-globule transition line for polymers with a bending stiffness exceeding a threshold value. The region, enclosed by the toroidal and random-coil phases, is dominated by structures crossing over from hairpins to loops upon lowering the energy. Conventional canonical statistical analysis is not sufficiently sensitive to allow for the identification of these separate phases.

Competing single-chain folding and multi-chain aggregation pathways control solution-phase aggregate morphology of organic semiconducting polymers

Understanding the solution-phase behaviour of organic semiconducting polymers is important for systematically improving the performance of devices based on solution-processed thin films of these molecules. Conventional polymer theory predicts that polymer conformations become more compact as solvent quality decreases, but recent experiments have shown the high-performance organic-semiconducting polymer P(NDI2OD-T2) to form extended rod-like aggregates much larger than a single chain in poor solvents, with the formation of these extended aggregates correlated with enhanced electron mobility in films deposited from these solutions. We explain the unexpected formation of extended aggregates using a novel coarse-grained simulation model of P(NDI2OD-T2) that we have developed to study the effect of solvent quality on its solution-phase behaviour. In poor solvents, we find that aggregation through only a few monomers gives effectively inseparable chains, leading to the formation of extended structures of partially overlapping chains via non-equilibrium assembly. This behaviour requires that multi-chain aggregation occurs faster than chain folding, which we show is the case for the chain lengths and concentrations shown experimentally to form rod-like aggregates. This kinetically controlled process introduces a dependence of aggregate structure on concentration, chain length, and chain flexibility, which we show is able to reconcile experimental findings and is generalisable to the solution-phase assembly of other semiflexible polymers.

Forming a Double-Helix Phase of Single Polymer Chains by the Cooperation between Local Structure and Nonlocal Attraction

Double-helix structures, such as DNA, are formed in nature to realize many unique functions. Inspired by this, researchers are pursuing strategies to design such structures from polymers. A key question is whether the double helix can be formed from the self-folding of a single polymer chain without specific interactions. Here, using Langevin dynamics simulation and theoretical analysis, we find that a stable double-helix phase can be achieved by the self-folding of single semiflexible polymers as a result of the cooperation between local structure and nonlocal attraction. The critical temperature of double-helix formation approximately follows T^{cri}∼ln(k_{θ}) and T^{cri}∼ln(k_{τ}), where k_{θ} and k_{τ} are the polymer bending and torsion stiffness, respectively. Furthermore, the double helix can exhibit major and minor grooves due to symmetric break for better packing. Our results provide a novel guide to the experimental design of the double helix.

Dynamical properties of different models of elastic polymer rings: Confirming the link between deformation and fragility

We report extensive numerical simulations of different models of 2D polymer rings with internal elasticity. We monitor the dynamical behavior of the rings as a function of the packing fraction to address the effects of particle deformation on the collective response of the system. In particular, we compare three different models: (i) a recently investigated model [N. Gnan and E. Zaccarelli, Nat. Phys. 15, 683 (2019)] where an inner Hertzian field providing the internal elasticity acts on the monomers of the ring, (ii) the same model where the effect of such a field on the center of mass is balanced by opposite forces, and (iii) a semi-flexible model where an angular potential between adjacent monomers induces strong particle deformations. By analyzing the dynamics of the three models, we find that in all cases, there exists a direct link between the system fragility and particle asphericity. Among the three, only the first model displays anomalous dynamics in the form of a super-diffusive behavior of the mean-squared displacement and of a compressed exponential relaxation of the density auto-correlation function. We show that this is due to the combination of internal elasticity and the out-of-equilibrium force self-generated by each ring, both of which are necessary ingredients to induce such a peculiar behavior often observed in experiments of colloidal gels. These findings reinforce the role of particle deformation, connected to internal elasticity, in driving the dynamical response of dense soft particles.

Cation folding and the thermal stability limit of the ionic liquid [BMIM+][BF4 -] under total vacuum

Molecular dynamics simulations reveal the behavior of the bimodal distribution of cation conformations (folded/unfolded) in ionic liquids based on alkylated imidazoles, such as [BMIM+][BF4 -]. The alkyl chains of the cations can fold and block interactions between the cations and anions, thereby reducing the cohesivity of the liquid. At room temperature, the folded conformations represent less than one-third of the total conformations. In contrast to the behavior observed during the thermal denaturation of proteins, in ionic liquids, the concentration of folded cations grows when the temperature increases. At the equimolar concentration, the system reaches the reported experimental temperature of thermal stability (similar to the thermal denaturation behavior). There is an outermost layer of cations at the interface that can tilt toward the interface and cover a layer of anions adsorbed at the interface. This interfacial conformation makes the system stable in transverse directions and unstable in the normal direction at temperatures in the region of thermal instability, limiting the rate of vaporization of neutral ion pairs, which are observed as rare events at temperatures as low as 773.15 K.

Organization of associating or crosslinked actin filaments in confinement

A key factor of actin cytoskeleton organization in cells is the interplay between the dynamical properties of actin filaments and cell geometry, which restricts, confines and directs their orientation. Crosslinking interactions among actin filaments, together with geometrical cues and regulatory proteins can give rise to contractile rings in dividing cells and actin rings in neurons. Motivated by recent in vitro experiments, in this work we performed computer simulations to study basic aspects of the interplay between confinement and attractive interactions between actin filaments. We used a spring-bead model and Brownian dynamics to simulate semiflexible actin filaments that polymerize in a confining sphere with a rate proportional to the monomer concentration. We model crosslinking, or attraction through the depletion interaction, implicitly as an attractive short-range potential between filament beads. In confining geometries smaller than the persistence length of actin filaments, we show rings can form by curving of filaments of length comparable to, or longer than the confinement diameter. Rings form for optimal ranges of attractive interactions that exist in between open bundles, irregular loops, aggregated, and unbundled morphologies. The probability of ring formation is promoted by attraction to the confining sphere boundary and decreases for large radii and initial monomer concentrations, in agreement with prior experimental data. The model reproduces ring formation along the flat plane of oblate ellipsoids.

The role of solvent quality and chain stiffness on the end-to-end contact kinetics of semiflexible polymers

Motivated by loop closure during protein folding and DNA packing, we systemically studied the effects of the solvent quality and chain stiffness on the thermodynamics and kinetics of the end-to-end contact formation for semiflexible polymer chains with reactive ends by Langevin dynamics simulations. In thermodynamics, a rich variety of products of the end-to-end contact have been discovered, such as loop, hairpin, toroid, and rodlike bundle, the populations of which are dependent on the solvent quality and chain stiffness. In kinetics, the overall pathways to form the end-to-end contact have been identified. The change of solvent quality and chain stiffness can tune the roughness of energy landscape and modulate the kinetic partitioning of the end-to-end contact formation pathways, leading to differing kinetic behaviors. In good or poor solvents, the first end-to-end contact rate k _c decreases with increasing the strength of bending stiffness k _θ monotonically. In very poor solvents, however, the dependence of the logarithm of the first end-to-end contact rate ln k _c on k _θ exhibits erratic behavior, which stems from more rugged energy landscape due to the polymer chain getting trapped into the intermediate state composed of the rodlike bundles with two ends in separation. For semiflexible chains, with increasing chain length N, the rate k _c increases initially and then decreases: in good solvents, the rate k _c exhibits a power-law relationship to chain length N with an exponent of ∼-1.50 in the region of long chains, which is in good agreement with the value derived from the experiment in the asymptotic limit of large N; and in poor solvents, the rate k _c exhibits a significantly stronger chain length dependence than those observed in good solvents in the region of long chains due to frustration to form the end-to-end contact along a specific path, especially the scaling exponent between the rate k _c and chain length N is ∼-3.62 for the case of polymer chains with k _θ = 4 at the solvent quality ε _ij = 1, in accord with the value obtained from the experiments.