Coil-to-globule transition by dissipative particle dynamics simulation

Collapse and expansion kinetics of a single polyelectrolyte chain with hydrodynamic interactions

We investigate the collapse and expansion dynamics of a linear polyelectrolyte (PE) with hydrodynamic interactions. Using dissipative particle dynamics with a bead-spring PE model, long-range electrostatics, and explicit ions, we examine how the timescales of collapse tcol and expansion texp depend on the chain length N and obtain scaling relationships tcol ∼ Nα and texp ∼ Nβ. For neutral polymers, we derive values of α = 0.94 ± 0.01 and β = 1.97 ± 0.10. Interestingly, the introduction of electrostatic interaction markedly shifts α to α ≈ 1.4 ± 0.1 for salt concentrations within c = 10-4 to 10-2 M. A reduction in the ion-to-monomer size ratio noticeably reduces α. On the other hand, the expansion scaling remains approximately constant, β ≈ 2, regardless of the salt concentration or ion size considered. We find β > α for all conditions considered, implying that expansion is always slower than collapse in the limit of long polymers. This asymmetry is explained by distinct kinetic pathways of collapse and expansion processes.

Coil-globule transition in two-dimensional polymer chains in an explicit solvent

The structure of two-dimensional polymer chains in a solvent at different temperatures is still far from being fully understood. Computer simulations of high-density macromolecular systems require the use of appropriate algorithms, and therefore the simulations were carried out using the Cooperative Motion Algorithm. The polymer model studied was exactly two-dimensional, coarse-grained and based on a triangular lattice. The theta temperature and temperature of coil-to-globule transition, and critical exponents were determined. The differences between the structure of such a disk and that of a chain in a dense polymer liquid were shown.

Structure of Strongly Adsorbed Polymer Systems: A Computer Simulation Study

The structure of very thin polymer films formed by strongly adsorbed macromolecules was studied by computer simulation. A coarse-grained model of strictly two-dimensional polymer systems was built, and its properties determined by an efficient Monte Carlo simulation algorithm. Properties of the model system were determined by means of Monte Carlo simulations with a sampling algorithm that combines Verdier-Stockmayer, pivot and reputation moves. The effects of temperature, chain length and polymer concentration on the macromolecular structure were investigated. It was shown that at low temperatures, the chain size increases with the concentration, that is, inversely with high temperatures. This behavior should be explained by the influence of inter-chain interactions.

Dynamics and Equilibration Mechanisms in Block Copolymer Particles

Self-assembly of block copolymers into interesting and useful nanostructures, in both solution and bulk, is a vibrant research arena. While much attention has been paid to characterization and prediction of equilibrium phases, the associated dynamic processes are far from fully understood. Here, we explore what is known and not known about the equilibration of particle phases in the bulk, and spherical micelles in solution. The presumed primary equilibration mechanisms are chain exchange, fusion, and fragmentation. These processes have been extensively studied in surfactants and lipids, where they occur on subsecond time scales. In contrast, increased chain lengths in block copolymers create much larger barriers, and time scales can become prohibitively slow. In practice, equilibration of block copolymers is achievable only in proximity to the critical micelle temperature (in solution) or the order-disorder transition (in the bulk). Detailed theories for these processes in block copolymers are few. In the bulk, the rate of chain exchange can be quantified by tracer diffusion measurements. Often the rate of equilibration, in terms of number density and aggregation number of particles, is much slower than chain exchange, and consequently observed particle phases are often metastable. This is particularly true in regions of the phase diagram where Frank-Kasper phases occur. Chain exchange in solution has been explored quantitatively by time-resolved SANS, but the results are not well captured by theory. Computer simulations, particularly via dissipative particle dynamics, are beginning to shed light on the chain escape mechanism at the molecular level. The rate of fragmentation has been quantified in a few experimental systems, and TEM images support a mechanism akin to the anaphase stage of mitosis in cells, via a thin neck that pinches off to produce two smaller micelles. Direct measurements of micelle fusion are quite rare. Suggestions for future theoretical, computational, and experimental efforts are offered.

Activity mediated globule to coil transition of a flexible polymer in a poor solvent

Understanding the role of self-propulsion on the conformational properties of active filamentous objects has relevance in biology. In this work, we consider a flexible bead-spring model for active polymers with both attractive and repulsive interactions among the non-bonded monomers. The activity for each monomer works along its intrinsic direction of self-propulsion which changes diffusively with time. We study its kinetics in the overdamped limit, following quenching from good to poor solvent conditions. We observe that with low activities, though the kinetic pathways remain similar, the scaling exponent for the relaxation time of globule formation becomes smaller than that for the case with no activity. Interestingly, for higher activities when self-propulsion dominates over interaction energy, the polymer conformation becomes extended coil-like. There, in the steady state, the variation of the spatial extension of the polymer, measured via its gyration radius, shows two completely different scaling regimes: the corresponding Flory exponent ν changes from 1/3 to 3/5 similar to a transition of the polymer from a globular state to a self-avoiding walk. This can be explained by an interplay among the three energy scales present in the system, viz., the "ballistic", thermal, and interaction energy.

Mesoscale Modeling of Agglomeration of Molecular Bottlebrushes: Focus on Conformations and Clustering Criteria

Using dissipative particle dynamics, we characterize dynamics of aggregation of molecular bottlebrushes in solvents of various qualities by tracking the number of clusters, the size of the largest cluster, and an average aggregation number. We focus on a low volume fraction of bottlebrushes in a range of solvents and probe three different cutoff criteria to identify bottlebrushes belonging to the same cluster. We demonstrate that the cutoff criteria which depend on both the coordination number and the length of the side chain allows one to correlate the agglomeration status with the structural characteristics of bottlebrushes in solvents of various qualities. We characterize conformational changes of the bottlebrush within the agglomerates with respect to those of an isolated bottlebrush in the same solvents. The characterization of bottlebrush conformations within the agglomerates is an important step in understanding the relationship between the bottlebrush architecture and material properties. An analysis of three distinct cutoff criteria to identify bottlebrushes belonging to the same cluster introduces a framework to identify both short-lived transient and long-lived agglomerates; the same approach could be further extended to characterize agglomerates of various macromolecules with complex architectures beyond the specific bottlebrush architecture considered herein.

Delayed collapse transitions in a pinned polymer system

Employing Langevin dynamics simulations, we investigated the kinetics of the collapse transition for a polymer of length N when a particular monomer at a position 1≤X≤N is pinned. The results are compared with the kinetics of a free polymer. The equilibrium θ-point separating the coil from the globule phase is located by a crossover in 〈R_{g}^{2}〉/N plots of different chain lengths. Our simulation supports a three-stage mechanism for free and pinned polymer collapse: the formation of pearls, the coarsening of pearls, and the formation of a compact globule. Pinning the central monomer has negligible effects on the kinetics as it does not break the symmetry. However, pinning a monomer elsewhere causes the process to be delayed by a constant factor ϕ_{X} depending linearly upon X. The total collapse time scales with N as τ_{c}∼ϕ_{X}N^{1.60±0.03}, which implies τ_{c} is maximum when an end monomer is pinned (X=1 or N), while when pinning the central monomer (X=N/2) it is minimum and identical to that of a free polymer. The average cluster size N_{c}(t) grows in time as t^{z}, where z=1.00±0.04 for a free particle, whereas we identify two time regimes separated by a plateau for pinned polymers. At longer times, z=1.00±0.04, while it deviates in early time regimes significantly, depending on the value of X.

Kick effect of enzymes causes filament compression

We investigate the influence of enzymes on the structure and dynamics of a filament by dissipative particle dynamics simulations. Enzyme exerts a kick force on the filament monomer. We pay particular attention to two factors: the magnitude of kick force and enzyme concentration. Large kick force as well as high enzyme concentration prefers a remarkable compression of the filament reminiscent of the effective depletion interaction owing to an effective increase in enzyme size and the reduction of solvent quality. Additionally, the kick effect gives rise to an increase of enzyme density from the center-of-mass of the filament to its periphery. Moreover, the increase of enzyme concentration and kick force also causes a decrease in relaxation time. Our finding is helpful to understand the role of catalytic force in chemo-mechano-biological function and the filament behavior under chemical reaction via kick-induced change of solvent quality.

Effects of alignment activity on the collapse kinetics of a flexible polymer

The dynamics of various biological filaments can be understood within the framework of active polymer models. Here we consider a bead-spring model for a flexible polymer chain in which the active interaction among the beads is introduced via an alignment rule adapted from the Vicsek model. Following quenching from the high-temperature coil phase to a low-temperature state point, we study the coarsening kinetics via molecular dynamics (MD) simulations using the Langevin thermostat. For the passive polymer case the low-temperature equilibrium state is a compact globule. The results from our MD simulations reveal that though the globular state is also the typical final state in the active case, the nonequilibrium pathways to arrive at such a state differ from the picture for the passive case due to the alignment interaction among the beads. We notice that deviations from the intermediate "pearl-necklace"-like arrangement, which is observed in the passive case, and the formation of more elongated dumbbell-like structures increase with increasing activity. Furthermore, it appears that while a small active force on the beads certainly makes the coarsening process much faster, there exists a nonmonotonic dependence of the collapse time on the strength of active interaction. We quantify these observations by comparing the scaling laws for the collapse time and growth of pearls with the passive case.

Free Energy Trajectory for Escape of a Single Chain from a Diblock Copolymer Micelle

We use umbrella sampling to compute the free energy trajectory of a single chain undergoing expulsion from an isolated diblock copolymer micelle. This approach elucidates the experimentally unobservable transition state, identifies the spatial position of the maximum free energy, and reveals the chain conformation of a single chain as it undergoes expulsion. Combining umbrella sampling with dissipative particle dynamics simulations of A₄B₈ micelles reveals that the core block (A) of the expelled chain remains partially stretched at the transition state, in contrast with the collapsed state assumed in some previous models. The free energy barrier increases linearly with the Flory-Huggins interaction parameter χ up to large interaction energies, where the structure of the otherwise spherical core apparently deforms near the transition state.

First events in the coil-to-globule transition of PVME in water: An ultrafast temperature jump - time-resolved elastic light scattering study

HYPOTHESIS

The coil-to-globule transition is an essential phenomenon in protein and polymer solutions. Late stages of such transitions, >1 µs, have been thoroughly studied. Yet, the initial ones are a matter of speculations. Here, we present the first observation of a sub-nanosecond stage of the coil-to-globule transition of poly (vinyl methyl ether), PVME, in water.

EXPERIMENTS

The detection of an early stage of the coil-to-globule transition has been possible thanks to a novel experimental approach - time-resolved elastic light scattering study, following an ultrafast temperature jump. We identified a molecular process active in the observed stage of the transition with use of broadband dielectric spectroscopy.

FINDINGS

In the experiment's time window, from a few ps to around 600 ps, we observed an increase in the light scattering intensity 300-400 ps after the temperature jump that heated the sample above its lower critical solution temperature (LCST). The observed time coincides with the time of segmental relaxation of PVME, determined by broadband dielectric spectroscopy in the temperature range of the LCST of the PVME/water mixture. This coincidence strongly suggests that the observed herein stage of coil-to-globule transition is the rapid formation of local nuclei along the polymer chain. Those nuclei may grow and aggregate in later stages of the process, which are out of our experimental time window.

Responsive polymers for medical diagnostics

Stimulus-responsive polymers have been used in improving the efficacy of medical diagnostics through different approaches including enhancing the contrast in imaging techniques and promoting the molecular recognition in diagnostic assays. This review overviews the mechanisms of stimulus-responsive polymers in response to external stimuli including temperature, pH, ion, light, etc. The applications of responsive polymers in magnetic resonance imaging, capture and purification of biomolecules through protein-ligand recognition and lab-on-a-chip technology are discussed.

Dissipative particle dynamics for systems with polar species: Interactions in dielectric media

In this work, we develop a method for simulating polar species in the dissipative particle dynamics (DPD) method. The main idea behind the method is to treat each bead as a dumb-bell, i.e., two sub-beads kept at a fixed distance, instead of a point-like particle. The relation between the bead dipole moment and the bulk dielectric permittivity was obtained. The interaction force of single charges in polar liquid showed that the effective dielectric permittivity is somewhat smaller than that obtained for the bulk case at large separation between the charges. In order to understand the reasons behind the observed drop in the dielectric permittivity, we calculate the electric field of an isolated charge in a polar liquid; no permittivity drop is observed for this case. We can assume that the behavior observed for the force is due to the fact that the probing point is always associated with the charged bead, which is a force center, which essentially leads to a non-homogeneous density distribution around it on average; this is not the case when the field is measured. The interaction of a single charge with an interface between two liquids with different permittivities was studied after that; the model is found to correctly reproduce the "mirror image" effects. Finally, we show why it is necessary to treat the polar species in DPD explicitly by investigating the behavior of a charged colloidal particle at a liquid-liquid interface.

Polymer Knot in Solution near the θ Point

We study knot effects on polymer dynamics in aqueous solution by dissipative particle dynamics. A methodology to identify the θ point is developed by combining simulation data and analytical methods. Polymer internal motions are investigated systematically by gradually changing solvent quality from a good to poor case. In a good solvent, the knot length grows with fluctuations (breathing stage) and then moves to chain ends (moving stage) to release. Nearby the θ point from the good solvent side, the breathing effect becomes stronger with a weak moving effect. As a result, it is easy for the knot to release because of strong fluctuations in chain conformation. In a poor solvent, both breathing and moving effects are weak. A knot is confined in the chain and suppresses polymer condensation because of the excluded volume effect. Our results are useful for the interpretation of relevant experiments and industrial applications of polymer knots.

Structure Evolution of Binary Ligands on Nanoparticles Triggered by Competition between Adsorption Reaction and Phase Separation

The ligand shell of a nanoparticle (NP) determines most of the interfacial properties through its composition and structure. Despite widespread study over the years, the factors impacting the ligand shell structures, especially the effects of ligand-adsorption kinetics in solution, are still not clear and even conflict with each other. We have developed an adsorption-migration reaction model to study the dynamic evolution processes of binary ligands on NP surfaces during adsorption reaction. Apparent dependence of the structure of ligand shells on ligand-adsorption and phase-separation rates has been found, which induces the formation of different shell patterns, including Janus, patchy, stripe, and island patterns. The formation process of these patterns accords with different reaction kinetic pathways, depending on the nature of ligands. Further screening the role of the NPs' curvature reveals that it can indirectly influence the ligand-adsorption and phase-separation kinetics. As the NPs' curvature increases, an accelerated ligand-adsorption and phase-separation process on NPs will happen, resulting in the preferential formation of more ordered Janus or stripe patterns. These results suggest that controlling the reaction kinetics is key to effectively regulating the composition and morphology of binary ligands on NPs. They also provide principles for guiding the experimental studies to fabricate novel NPs with a functional surface for use in broad nanoscience fields.

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.

The folding pathways and thermodynamics of semiflexible polymers

Inspired by the protein folding and DNA packing, we have systematically studied the thermodynamic and kinetic behaviors of single semiflexible homopolymers by Langevin dynamics simulations. In line with experiments, a rich variety of folding products, such as rod-like bundles, hairpins, toroids, and a mixture of them, are observed in the complete diagram of states. Moreover, knotted structures with a significant population are found in a certain range of bending stiffness in thermal equilibrium. As the solvent quality becomes poorer, the population of the intermediate occurring in the folding process increases, which leads to a severe chevron rollover for the folding arm. However, the population of the intermediates in the unfolding process is very low, insufficient to induce unfolding arm rollover. The total types of folding pathways from the coil state to the toroidal state for a semiflexible polymer chain remain unchanged by varying the solvent quality or temperature, whereas the kinetic partitioning into different folding events can be tuned significantly. In the process of knotting, three types of mechanisms, namely, plugging, slipknotting, and sliding, are discovered. Along the folding evolution, a semiflexible homopolymer chain can knot at any stage of folding upon leaving the extended coil state, and the probability to find a knot increases with chain compactness. In addition, we find rich types of knotted topologies during the folding of a semiflexible homopolymer chain. This study should be helpful in gaining insight into the general principles of biopolymer folding.

Time-resolved structural evolution during the collapse of responsive hydrogels: The microgel-to-particle transition

Adaptive hydrogels, often termed smart materials, are macromolecules whose structure adjusts to external stimuli. Responsive micro- and nanogels are particularly interesting because the small length scale enables very fast response times. Chemical cross-links provide topological constraints and define the three-dimensional structure of the microgels, whereas their porous structure permits fast mass transfer, enabling very rapid structural adaption of the microgel to the environment. The change of microgel structure involves a unique transition from a flexible, swollen finite-size macromolecular network, characterized by a fuzzy surface, to a colloidal particle with homogeneous density and a sharp surface. In this contribution, we determine, for the first time, the structural evolution during the microgel-to-particle transition. Time-resolved small-angle x-ray scattering experiments and computer simulations unambiguously reveal a two-stage process: In a first, very fast process, collapsed clusters form at the periphery, leading to an intermediate, hollowish core-shell structure that slowly transforms to a globule. This structural evolution is independent of the type of stimulus and thus applies to instantaneous transitions as in a temperature jump or to slower stimuli that rely on the uptake of active molecules from and/or exchange with the environment. The fast transitions of size and shape provide unique opportunities for various applications as, for example, in uptake and release, catalysis, or sensing.

Micellar polymerization: Computer simulations by dissipative particle dynamics

Nowadays, micellar polymerization is widely used in different fields of industry and research, including modern living polymerization technique. However, this process has many variables and there is no comprehensive model to describe all features. This research presents simulation methodology which describes key properties of such reactions to take a guide through a variety of their modifications. Dissipative particle dynamics is used in addition to Monte Carlo scheme to simulate initiation, propagation, and termination events. Influence of initiation probability and different termination processes on final conversion and molecular-weight distribution are presented. We demonstrate that prolonged initiation leads to increasing in polymer average molecular weight, and surface termination events play major role in conversion limitation, in comparison with recombination. © 2018 Wiley Periodicals, Inc.

Dynamic Feature of Incipient Polymer Collapse below the Theta Point

We study the dynamics of a polymer chain with gradually changing the solvent quality from good to poor by dissipative particle dynamics simulation. We find several spectral modes related to internal motions of intrachain interaction. Approaching the coil-to-globule transition point, all fast modes of spectrum ω > 1 (ns)^-1 disappear. There is only a slow mode at ω ≈ 0.66 (ns)^-1. Moreover, the spectral density at this slow mode reaches a maximum value at the transition point. We suggest that, at the transition point, the chain conformation relaxes to the most probable distribution only by the slow mode. There is a critical slowing down of internal motion with passing through the transition point.

Copolymerization on Selective Substrates: Experimental Test and Computer Simulations

We explore the influence of a selective substrate on the composition and sequence statistics during the free radical copolymerization. In particular, we study the radical copolymerization of styrene and acrylic acid in bulk and in silica pores of different sizes. We show that the substrate affects both polymer composition and sequence statistics. We use dissipative particle dynamics simulations to study the polymerization process in detail, trying to pinpoint the parameters responsible for the observed differences in the polymer chain composition and sequences. The magnitude of the observed effect depends on the fraction of adsorbed monomer units, which cannot be described in the framework of the copolymerization theories based on the terminal unit model.

Harnessing Cooperative Interactions between Thermoresponsive Aptamers and Gels To Trap and Release Nanoparticles

We use computational modeling to design a device that can controllably trap and release particles in solution in response to variations in temperature. The system exploits the thermoresponsive properties of end-grafted fibers and the underlying gel substrate. The fibers mimic the temperature-dependent behavior of biological aptamers, which form a hairpin structure at low temperatures (T) and unfold at higher T, consequently losing their binding affinity. The gel substrate exhibits a lower critical solution temperature and thus, expands at low temperatures and contracts at higher T. By developing a new dissipative particle dynamics simulation, we examine the behavior of this hybrid system in a flowing fluid that contains buoyant nanoparticles. At low T, the expansion of the gel causes the hairpin-shaped fibers to extend into the path of the fluid-driven particle. Exhibiting a high binding affinity for these particles at low temperature, the fibers effectively trap and extract the particles from the surrounding solution. When the temperature is increased, the unfolding of the fiber and collapse of the supporting gel layer cause the particles to be released and transported away from the layer by the applied shear flow. Since the temperature-induced conformational changes of the fiber and polymer gel are reversible, the system can be used repeatedly to "catch and release" particles in solution. Our findings provide guidelines for creating fluidic devices that are effective at purifying contaminated solutions or trapping cells for biological assays.

Transferability of a coarse-grained atactic polystyrene model: the non-bonded potential effect

In this paper, we construct an efficient and simple coarse grained (CG) model for atactic polystyrene (PS) by using a 1 : 1 mapping scheme at 463 K and 1 atm pressure and derive the corresponding bonded and non-bonded potentials in the CG force field (FF) via a direct Boltzmann inversion approach and a combined structure-based and thermodynamic quantities-based CG method, respectively.

Designing a gel-fiber composite to extract nanoparticles from solution

The extraction of nanoscopic particulates from flowing fluids is a vital step in filtration processes, as well as the fabrication of nanocomposites. Inspired by the ability of carnivorous plants to use hair-like filaments to entrap species, we use computational modeling to design a multi-component system that integrates compliant fibers and thermo-responsive gels to extract particles from the surrounding solution. In particular, hydrophobic fibers are embedded in a gel that exhibits a lower critical solution temperature (LCST). With an increase in temperature, the gel collapses to expose fibers that self-assemble into bundles, which act as nanoscale "grippers" that bind the particles and draw them into the underlying gel. By varying the relative stiffness of the fibers, the fiber-particle interaction strength and the shear rate in the solution, we identify optimal parameters where the particles are effectively drawn from the solution and remain firmly bound within the gel layer. Hence, the system can be harnessed in purifying fluids and creating novel hybrid materials that integrate nanoparticles with polymer gels.

Crumpled globule formation during collapse of a long flexible and semiflexible polymer in poor solvent

By introducing explicit solvent particles and hydrodynamic interactions we demonstrate that crumpled globules are formed after the collapse of long polymer chains (N = 10(4)) in a poor solvent. During the collapse crumples of all sizes form sequentially, but small crumples are not stable and convert to blobs with Gaussian statistics. The observed effective mean squared distance R(2)(n) ∼ n(0.38) at n > Ne and contact probability index p(n) ∼ n(-0.5) at n ≫ Ne, which is not following either the model of a fractal globule, or the predictions for an equilibrium globule. Polymer chain stiffness pushes the system to form globular crystallite, and this freezes crumpled structure with R(2)(n) ∼ n(0.33) at n > Ne as a stable state. We note that there is some similarity to crumple globule formation and crystallization of polymer melt.

Designing Composite Coatings That Provide a Dual Defense against Fouling

Inspired by marine organisms that utilize spines and shape changes to prevent the biofouling of their surfaces, we use computational modeling to design a gel-based composite coating that provides a two-pronged defense mechanism against the fouling of the underlying substrate. Using dissipative particle dynamics (DPD) simulations, we construct a coating that encompasses rigid posts embedded in a thermoresponsive gel, which exhibits a lower critical solution temperature (LCST). When the gel is heated above its LCST, it collapses to expose the buried posts, which act as spines or spikes that prevent a solid particle from penetrating the layer. Moreover, we show that an imposed shear flow readily dislodges these particles and washes them away from the coated substrate. As the system dissipates heat and cools, the LCST gel expands, and this dynamic morphological change can also be harnessed to dislodge the adsorbed particles. Thus, both the exposed posts and the swelling gels can provide barriers to the penetration of particulates through the coating. In this manner, the coating provides a dual mechanism against the fouling of the substrate. This physical approach can be particularly beneficial because it does not require the release of any chemical substances that could have detrimental consequences to the environment.