First observation of the coil–globule transition in a single polymer chain

Energy of the interacting self-avoiding walk at the θ point

We perform a numerical study of a new microcanonical polymer model on a three-dimensional cubic lattice, consisting of ideal chains whose range and number of nearest-neighbor contacts are fixed to given values. Our simulations suggest an interesting exact relation concerning the internal energy per monomer of the interacting self-avoiding walk at the θ point.

Diffusion dynamics of a single collapsed homopolymer globule at the solid-liquid interface

Contradictive to the conventional wisdom that a collapsed polymer globule in poor solvents adsorb on surfaces in a way analogous to the spreading of a liquid droplet, here we have shown via single molecule measurements that a single poly(N-isoporpylacrylamide) (PNIPAM) globule can jump from one spot to another as an elastic nonadhesive ball even on a hydrophobic polystyrene surface. The molecular weight dependence of the effective surface diffusion coefficient measured for the adsorbed globule suggested that it exhibited mostly a similar globular conformation to that in the bulk solution. Both the displacement and waiting time distributions of the adsorbed globules were found to follow a power-law decay rather than an exponential process, suggesting a broad distribution of binding energies due to the difference in degree of globule deformation. These effects together reflect a character of the viscoelasticity even in a single-chain globule in dilute solutions. Our findings also demonstrate that it is not the single-chain globule but the inter-globule aggregates at high concentration that lead to irreversible adsorption on the surface, which provides novel dynamics and mechanisms of how a thermosensitive polymer adsorbs on the hydrophobic surface above its lower critical solution temperature.

Conformational behavior of a semiflexible dipolar chain with a variable relative size of charged groups via molecular dynamics simulations

The conformational behavior of an isolated semiflexible dipolar chain has been studied by molecular dynamics simulations. The dipolar chain was modeled as a backbone chain of charged beads, each containing an oppositely charged unit connected to it by a rigid spring. The main focus was on the effect of the backbone chain rigidity and the size of the charged groups on the morphology of the collapsed states of the chain formed in low-polar media where the electrostatic interactions are essential. It has been found that the stable globular conformations of the long chain of N = 256 backbone beads are a toroid and an elliptical globule. The macroscopic parameters (such as the radius of gyration and shape factors) as well as the local characteristics of these conformations (radial density distributions of ions, orientational correlations of chain segments, dipoles etc.) are studied depending on the chain stiffness. The regions of stability of a torus and an elliptical globule are found for the dipolar chains with variable dipole length and stiffness, which depend on the strength of electrostatic interactions. It has been shown that a size asymmetry of oppositely charged beads destabilizes globular states favoring elongated chain conformations. A coexistence of various metastable states was demonstrated for shorter chains of N = 128, 64, and 32.

Pearl-Necklace-Like Local Ordering Drives Polypeptide Collapse

The collapse of the polypeptide backbone is an integral part of protein folding. Using polyglycine as a probe, we explore the nonequilibrium pathways of protein collapse in water. We find that the collapse depends on the competition between hydration effects and intrapeptide interactions. Once intrapeptide van der Waal interactions dominate, the chain collapses along a nonequilibrium pathway characterized by formation of pearl-necklace-like local clusters as intermediates that eventually coagulate into a single globule. By describing this coarsening through the contact probability as a function of distance along the chain, we extract a time-dependent length scale that grows in a linear fashion. The collapse dynamics is characterized by a dynamical critical exponent z ≈ 0.5 that is much smaller than the values of z = 1–2 reported for nonbiological polymers. This difference in the exponents is explained by the instantaneous formation of intrachain hydrogen bonds and local ordering that may be correlated with the observed fast folding times of proteins.

Polymer coil-globule phase transition is a universal folding principle of Drosophila epigenetic domains

Background

Localized functional domains within chromosomes, known as topologically associating domains (TADs), have been recently highlighted. In Drosophila, TADs are biochemically defined by epigenetic marks, this suggesting that the 3D arrangement may be the “missing link” between epigenetics and gene activity. Recent observations (Boettiger et al. in Nature 529(7586):418–422, 2016) provide access to structural features of these domains with unprecedented resolution thanks to super-resolution experiments. In particular, they give access to the distribution of the radii of gyration for domains of different linear length and associated with different transcriptional activity states: active, inactive or repressed. Intriguingly, the observed scaling laws lack consistent interpretation in polymer physics.

Results

We develop a new methodology conceived to extract the best information from such super-resolution data by exploiting the whole distribution of gyration radii, and to place these experimental results on a theoretical framework. We show that the experimental data are compatible with the finite-size behavior of a self-attracting polymer. The same generic polymer model leads to quantitative differences between active, inactive and repressed domains. Active domains behave as pure polymer coils, while inactive and repressed domains both lie at the coil–globule crossover. For the first time, the “color-specificity” of both the persistence length and the mean interaction energy are estimated, leading to important differences between epigenetic states.

Conclusion

These results point toward a crucial role of criticality to enhance the system responsivity, resulting in both energy transitions and structural rearrangements. We get strong indications that epigenetically induced changes in nucleosome–nucleosome interaction can cause chromatin to shift between different activity states.

Electronic supplementary material

The online version of this article (10.1186/s13072-019-0269-6) contains supplementary material, which is available to authorized users.

Quantitative determination of the spring entropy effect and its indication of the conformational change of polymer coils with varying concentration in aqueous poly(N-isopropylamide) solutions

The lower critical solution temperature (LCST) phase separation behaviors of thermosensitive poly(N-isopropylacrylamide) (PNIPAM) aqueous solutions were investigated by power-compensation differential scanning calorimetry (DSC). The entropic effect and hence the change of swelling state of PNIPAM polymer coils in homogeneous concentrated aqueous solutions with varied solution composition was elucidated by the isothermal enthalpy demixing recovery behaviors in distinct concentration regions.

Formation of Chromatin Subcompartments by Phase Separation

Chromatin is partitioned on multiple length scales into subcompartments that differ from each other with respect to their molecular composition and biological function. It is a key question how these compartments can form even though diffusion constantly mixes the nuclear interior and rapidly balances concentration gradients of soluble nuclear components. Different biophysical concepts are currently used to explain the formation of "chromatin bodies" in a self-organizing manner and without consuming energy. They rationalize how soluble protein factors that are dissolved in the liquid nuclear phase, the nucleoplasm, bind and organize transcriptionally active or silenced chromatin domains. In addition to cooperative binding of proteins to a preformed chromatin structure, two different mechanisms for the formation of phase-separated chromatin subcompartments have been proposed. One is based on bridging proteins that cross-link polymer segments with particular properties. Bridging can induce a collapse of the nucleosome chain and associated factors into an ordered globular phase. The other mechanism is based on multivalent interactions among soluble molecules that bind to chromatin. These interactions can induce liquid-liquid phase separation, which drives the assembly of liquid-like nuclear bodies around the respective binding sites on chromatin. Both phase separation mechanisms can explain that chromatin bodies are dynamic spherical structures, which can coalesce and are in constant and rapid exchange with the surrounding nucleoplasm. However, they make distinct predictions about how the size, density, and stability of chromatin bodies depends on the concentration and interaction behavior of the molecules involved. Here, we compare the different biophysical mechanisms for the assembly of chromatin bodies and discuss experimental strategies to distinguish them from each other. Furthermore, we outline the implications for the establishment and memory of functional chromatin state patterns.

Confinement Effects on Polymer Dynamics: Thermo-Responsive Behaviours of Hydroxypropyl Cellulose Polymers in Phospholipid-Coated Droplets (Water-in-Oil Emulsion)

In order to construct the artificial cells and to understand the physicochemical properties of living cells, it is important to clarify the cell-sized confinement effect on the behaviours of bio-inspired polymers. We report the dynamic behaviours of aqueous hydroxypropyl cellulose (HPC) solution coated with phospholipids in oil (water-in-oil droplets, W/O droplets), accompanied by an increase in the temperature. We directly observed the beginning of phase separation of HPC solution using a fluorescence microscope and confirmed the dependence of such phenomena on droplet size. The results indicate that the start time of phase separation is decreased with an increase in droplet size. The experimental results suggest that the confinement situation accelerates the phase separation of aqueous HPC solutions.

Controlled self-organization of polymer nanopatterns over large areas

Self-assembly methods allow to obtain ordered patterns on surfaces with exquisite precision, but often lack in effectiveness over large areas. Here we report on the realization of hierarchically ordered polymethylmethacrylate (PMMA) nanofibres and nanodots over large areas from solution via a fast, easy and low-cost method named ASB-SANS, based on a ternary solution that is cast on the substrate. Simple changes to the ternary solution composition allow to control the transition from nanofibres to nanodots, via a wide range of intermediate topologies. The ternary solution includes the material to be patterned, a liquid solvent and a solid substance able to sublimate. The analysis of the fibres/dots width and inter-pattern distance variations with respect to the ratio between the solution components suggests that the macromolecular chains mobility in the solidified sublimating substance follows Zimm-like models (mobility of macromolecules in diluted liquid solutions). A qualitative explanation of the self-assembly phenomena originating the observed nanopatterns is given. Finally, ASB-SANS-generated PMMA nanodots arrays have been used as lithographic masks for a silicon substrate and submitted to Inductively Coupled Plasma-Reactive Ion Etching (ICP-RIE). As a result, nanopillars with remarkably high aspect ratios have been achieved over areas as large as several millimeters square, highlighting an interesting potential of ASB-SANS in practical applications like photon trapping in photovoltaic cells, surface-enhanced sensors, plasmonics.

The importance of solvent quality on the modification of conjugated polymer conformation and thermodynamics with illumination

Device efficiency in key organic electronic devices such as organic photovoltaics, field transistors, and light emitting diodes has long been known to be closely tied to the conformation of the conjugated polymer chains which make up the active layers. Our previous results show that light exposure can have a profound effect on the structure and assembly of these optoelectronic materials in solution. In order to advance our understanding of the role which solvent quality plays in this phenomenon, we have further studied the modulation of these illumination dependent structural changes on the key benchmark conjugated polymers P3HT and MEH-PPV as a function of solvent quality over a wide range of polymer solubilities. Analysis of this data indicates that use of poorer conjugated polymer solvents ultimately results in larger absolute alterations to polymer conformation, denoting the crucial role which solution thermodynamics plays in this generic effect. This discovery opens the door to controlling final device morphology through careful manipulation of solvent composition during solution based device casting techniques, moving our efforts closer to the development of a powerful, non-destructive, and tunable method for light-driven control of polymer conformation in novel light-responsive organic materials.

Kinetics of polymer collapse: effect of temperature on cluster growth and aging

Using state of the art Monte Carlo simulations of a bead-spring model we investigate both the equilibrium and the nonequilibrium behavior of the homopolymer collapse. The equilibrium properties obtained via multicanonical sampling recover the well-known finite-size scaling behavior of collapse for our model polymer. For the nonequilibrium dynamics we study the collapse by quenching the homopolymer from an expanded coiled state into the globular phase. The sequence of events observed during the collapse is independent of the quench depth. In particular, we focus on finding out universal scaling behaviors related to the growth or coarsening of clusters of monomers, by drawing phenomenological analogies with ordering kinetics. We distinguish the cluster coarsening stage from the initial stage of primary cluster formation. By successful application of a nonequilibrium finite-size scaling analysis we show that at all quench temperatures, during the coarsening stage, the cluster growth is roughly linear and can be characterised by a universal finite-size scaling function. In addition, we provide evidence of aging by constructing a suitable autocorrelation function and its corresponding dynamical power-law scaling with respect to the growing cluster sizes. The predicted theoretical bound for the exponent governing such scaling is strictly obeyed by the numerical data irrespective of the quench temperature. The results and methods presented here in general should find application in similar phenomena such as the collapse of a protein molecule preceding its folding.

Going beyond the classical amphiphilicity paradigm: the self-assembly of completely hydrophobic polymers into free-standing sheets and hollow nanostructures in solvents of variable quality

Self-assembly is well-known to occur in amphiphiles, and the totally hydrophobic ones are never reported to self-assemble. In this work we report for the first time that the latter can self-assemble into free-standing sheets and hollow spheres in toluene/methanol mixed solvents by modulating the solvent quality. The homopolymers studied in this work are polystyrene (PS), polyphenylacetylene (PPA), and poly(3-hexyl thiophene) (P3HT), representing polymers with different rigidity. All the three form a homogenous solution in toluene, but self-assembly occurs in the toluene/methanol mixed solvents. Micrometer sized free-standing sheets were formed for PS, PPA, and P3HT at methanol volume fractions being 43%, 50%, and 67%, respectively, and hollow spheres were observed for PPA at higher methanol fractions of 75 and 90%. Under the latter solvent conditions, PS forms solid spheres, yet ill-defined aggregates and free-standing sheets coexist in the case of P3HT. This non-solvent induced self-assembly was explained by a delicate balance of two "opposing forces": van der Waals attractive and entropic repulsive forces generated between the segments of these homopolymers within a single chain, between two chains, and among more chains in the solvents of worsened quality.

Visualization of polymer relaxation in viscoelastic turbulent micro-channel flow

In micro-channels, the flow of viscous liquids e.g. water, is laminar due to the low Reynolds number in miniaturized dimensions. An aqueous solution becomes viscoelastic with a minute amount of polymer additives; its flow behavior can become drastically different and turbulent. However, the molecules are typically invisible. Here we have developed a novel visualization technique to examine the extension and relaxation of polymer molecules at high flow velocities in a viscoelastic turbulent flow. Using high speed videography to observe the fluorescein labeled molecules, we show that viscoelastic turbulence is caused by the sporadic, non-uniform release of energy by the polymer molecules. This developed technique allows the examination of a viscoelastic liquid at the molecular level, and demonstrates the inhomogeneity of viscoelastic liquids as a result of molecular aggregation. It paves the way for a deeper understanding of viscoelastic turbulence, and could provide some insights on the high Weissenberg number problem. In addition, the technique may serve as a useful tool for the investigations of polymer drag reduction.

Design rationale of thermally responsive microgel particle films that reversibly absorb large amounts of CO2: fine tuning the pKa of ammonium ions in the particles

Fine-tuning of pK_a value of ammonium ions at both CO₂ capture and release temperature is found to be crucial for the design of the thermally responsive gel particle films that reversibly capture large amounts of CO₂.

Herein we revealed the design rationale of thermally responsive gel particle (GP) films that reversibly capture and release large amounts of CO₂ over a narrow temperature range (30–75 °C). The pK_a value of ammonium ions in the GPs at both the CO₂ capture temperature (30 °C) and release temperature (75 °C) is found to be the primary factor responsible for the stoichiometry of reversible CO₂ capture by the amines in the GP films. The pK_a values can be tuned by the properties of GPs such as volume phase transition temperature (VPTT), size, swelling ratio, and the imprinted microenvironment surrounding the amines. The optimal GP obtained according to the design rationale showed high capture capacity (68 mL CO₂ per g dry GPs, 3.0 mmol CO₂ per g dry GPs), although the regeneration temperature was as low as 75 °C. We anticipate that GP films that reversibly capture other acidic and basic gases in large amounts can also be achieved by the pK_a tuning procedures.

Smart Nanoscale Drug Delivery Platforms from Stimuli-Responsive Polymers and Liposomes

Since the 1960's, stimuli-responsive polymers have been utilized as functional soft materials for biological applications such as the triggered-release delivery of biologically active cargos. Over the same period, liposomes have been explored as an alternative drug delivery system with potentials to decrease the toxic side effects often associated with conventional small-molecule drugs. However, the lack of drug-release triggers and the instability of bare liposomes often limit their practical applications, causing short circulation time and low therapeutic efficacy. This perspective article highlights recent work in integrating these two materials together to achieve a targetable, triggerable nanoscale platform that fulfills all the characteristics of a near-ideal drug delivery system. Through a drop-in, post-synthesis modification strategy, a network of stimuli-responsive polymers can be integrated onto the surface of liposomes to form polymer-caged nanobins, a multifunctional nanoscale delivery platform that allows for multi-drug loading, targeted delivery, triggered drug-release, and theranostic capabilities.

Theory of volume transition in polyelectrolyte gels with charge regularization

We present a theory for polyelectrolyte gels that allow the effective charge of the polymer backbone to self-regulate. Using a variational approach, we obtain an expression for the free energy of gels that accounts for the gel elasticity, free energy of mixing, counterion adsorption, local dielectric constant, electrostatic interaction among polymer segments, electrolyte ion correlations, and self-consistent charge regularization on the polymer strands. This free energy is then minimized to predict the behavior of the system as characterized by the gel volume fraction as a function of external variables such as temperature and salt concentration. We present results for the volume transition of polyelectrolyte gels in salt-free solvents, solvents with monovalent salts, and solvents with divalent salts. The results of our theoretical analysis capture the essential features of existing experimental results and also provide predictions for further experimentation. Our analysis highlights the importance of the self-regularization of the effective charge for the volume transition of gels in particular, and for charged polymer systems in general. Our analysis also enables us to identify the dominant free energy contributions for charged polymer networks and provides a framework for further investigation of specific experimental systems.

Collapse of a two-state sticky hard sphere chain

The collapse of a homopolymer gaussian chain into a globule is represented as a transition between two states, viz., extended and collapsed. Appropriately, this model has been labeled as the all-or-none view of chain collapse. In the collapsed state, the single polymer partition function is expressed by a single Mayer diagram with the maximum number of f-bonds arising from nonbonded square well interactions. Our target is the dependence of the transition temperature on chain length and the interaction range of the square well, as indicated through the behavior of the radius of gyration and the constant volume heat capacity. Properties of the collapse transition are calculated exactly for chains with three to six backbone atoms and heuristically for long chains using arguments derived from the small chains and from conditions of integrability. Comparison with simulation studies is made.

Phase transitions of a single polymer chain: A Wang-Landau simulation study

A single flexible homopolymer chain can assume a variety of conformations which can be broadly classified as expanded coil, collapsed globule, and compact crystallite. Here we study transitions between these conformational states for an interaction-site polymer chain comprised of N=128 square-well-sphere monomers with hard-sphere diameter sigma and square-well diameter lambdasigma. Wang-Landau sampling with bond-rebridging Monte Carlo moves is used to compute the density of states for this chain and both canonical and microcanonical analyses are used to identify and characterize phase transitions in this finite size system. The temperature-interaction range (i.e., T-lambda) phase diagram is constructed for lambda<or=1.30. Chains assume an expanded coil conformation at high temperatures and a crystallite structure at low temperatures. For lambda>1.06 these two states are separated by an intervening collapsed globule phase and thus, with decreasing temperature a chain undergoes a continuous coil-globule (collapse) transition followed by a discontinuous globule-crystal (freezing) transition. For well diameters lambda<1.06 the collapse transition is pre-empted by the freezing transition and thus there is a direct first-order coil-crystal phase transition. These results confirm the recent prediction, based on a lattice polymer model, that a collapsed globule state is unstable with respect to a solid phase for flexible polymers with sufficiently short-range monomer-monomer interactions.

Design of synthetic polymer nanoparticles that capture and neutralize a toxic peptide

Designed polymer nanoparticles (NPs) capable of binding and neutralizing a biomacromolecular toxin are prepared. A library of copolymer NPs is synthesized from combinations of functional monomers. The binding capacity and affinity of the NPs are individually analyzed. NPs with optimized composition are capable of neutralizing the toxin even in a complex biological milieu. It is anticipated that this strategy will be a starting point for the design of synthetic alternatives to antibodies.

Ionic and pH effects on the osmotic properties and structure of polyelectrolyte gels

We investigate the effects of salt concentration and pH on neutralized poly(acrylic acid) (PAA) gels in near physiological salt solutions. Either adding calcium ions or decreasing the pH are found to induce reversible volume transitions but the nature of these transitions seems to be different. For example, the osmotic pressure exhibits a simple power law dependence on the concentration as the transition is approached in both systems, but the power law exponent n is substantially different in the two cases. On decreasing the pH the value of n gradually increases from 2.1 (at pH = 7) to 3.2 (at pH = 1). By contrast, n decreases with increasing calcium ion concentration from 2.1 (in 100 mM NaCl solution) to 1.6 (0.8 mM CaCl(2) in 100 mM NaCl solution). In both systems, a strong increase of the small-angle neutron scattering intensity (SANS) is observed near the volume transition. The SANS results reveal that calcium ions favor the formation of linearly aligned regions in PAA gels.

Atomistic simulations of the effects of polyglutamine chain length and solvent quality on conformational equilibria and spontaneous homodimerization

Aggregation of expanded polyglutamine tracts is associated with nine different neurodegenerative diseases, including Huntington's disease. Experiments and computer simulations have demonstrated that monomeric forms of polyglutamine molecules sample heterogeneous sets of collapsed structures in water. The current work focuses on a mechanistic characterization of polyglutamine homodimerization as a function of chain length and temperature. These studies were carried out using molecular simulations based on a recently developed continuum solvation model that was designed for studying conformational and binding equilibria of intrinsically disordered molecules such as polyglutamine systems. The main results are as follows: Polyglutamine molecules form disordered, collapsed globules in aqueous solution. These molecules spontaneously associate at conditions approaching those of typical in vitro experiments for chains of length N>/=15. The spontaneity of these homotypic associations increases with increasing chain length and decreases with increasing temperature. Similar and generic driving forces govern both collapse and spontaneous homodimerization of polyglutamine in aqueous milieus. Collapse and dimerization maximize self-interactions and reduce the interface between polyglutamine molecules and the surrounding solvent. Other than these generic considerations, there do not appear to be any specific structural requirements for either chain collapse or chain dimerization; that is, both collapse and dimerization are nonspecific in that disordered globules form disordered dimers. In fact, it is shown that the driving force for intermolecular associations is governed by spontaneous conformational fluctuations within monomeric polyglutamine. These results suggest that polyglutamine aggregation is unlikely to follow a homogeneous nucleation mechanism with the monomer as the critical nucleus. Instead, the results support the formation of disordered, non-beta-sheet-like soluble molten oligomers as early intermediates--a proposal that is congruent with recent experimental data.