Coil-globule Transition Research Articles

Why Sequence Blockiness Sharpens Coil–Globule Transition in Heteropolymers

Why Sequence Blockiness Sharpens Coil–Globule Transition in Heteropolymers

Entropy-favorable adsorption of polymer-grafted nanoparticles at fluid-fluid interfaces.

The adsorption of polymer-grafted nanoparticles at interfaces is a problem of fundamental interest in physics and soft materials. This adsorption behavior is governed by the interplay between interaction potentials and entropic effects. Here, we use molecular dynamics simulations and umbrella sampling methods to study the adsorption behavior of a Janus-like homopolymer-grafted nanoparticle at fluid-fluid interfaces. By calculating the potential of the mean force as the particle moves from fluid A to the interface, the adsorption energy Ea can be obtained. When two homopolymer chains with types A and B are grafted to the opposite poles of the particle, Ea shows a scaling behavior with respect to chain length N: Ea ∝ N0.598. This is determined by the interactions between polymers and fluids. The enthalpy dominates, and the entropy effects mainly come from the rotational entropy loss of the polymer-grafted nanoparticle at interfaces, which disfavors the stabilization of particles at interfaces. When the grafted polymer number m is large, the adsorption energy exhibits a linear dependence on m. While the enthalpy dominates the behavior, the entropy becomes significant at a larger chain length of N = 15, where the configurational entropy of the polymer chains dominates the entropy of the system. The globule-coil transition occurs when polymers move from poor solvents to good solvents, increasing the configurational entropy and favoring the stabilization of particles at interfaces. Our study provides novel insights into the stabilization mechanism of polymer-grafted nanoparticles at interfaces and reveals the stabilization mechanism favored by the configurational entropy of grafted polymer chains.

Marangoni Droplets of Dextran in PEG Solution and Its Motile Change Due to Coil-Globule Transition of Coexisting DNA.

Motile droplets using Marangoni convection are attracting attention for their potential as cell-mimicking small robots. However, the motion of droplets relative to the internal and external environments that generate Marangoni convection has not been quantitatively described. In this study, we used an aqueous two-phase system [poly(ethylene glycol) (PEG) and dextran] in an elongated chamber to generate motile dextran droplets in a constant PEG concentration gradient. We demonstrated that dextran droplets move by Marangoni convection, resulting from the PEG concentration gradient and the active transport of PEG and dextran into and out of the motile dextran droplet. Furthermore, by spontaneously incorporating long DNA into the dextran droplets, we achieved cell-like motility changes controlled by coexisting environment-sensing molecules. The DNA changes its position within the droplet and motile speed in response to external conditions. In the presence of Mg2+, the coil-globule transition of DNA inside the droplet accelerates the motile speed due to the decrease in the droplet's dynamic viscosity. Globule DNA condenses at the rear part of the droplet along the convection, while coil DNA moves away from the droplet's central axis, separating the dipole convections. These results provide a blueprint for designing autonomous small robots using phase-separated droplets, which change the mobility and molecular distribution within the droplet in reaction with the environment. It will also open unexplored areas of self-assembly mechanisms through phase separation under convections, such as intracellular phase separation.

Asymmetry in Polymer-Solvent Interactions Yields Complex Thermoresponsive Behavior.

We introduce a lattice framework that incorporates elements of Flory-Huggins solution theory and the q-state Potts model to study the phase behavior of polymer solutions and single-chain conformational characteristics. Without empirically introducing temperature-dependent interaction parameters, standard Flory-Huggins theory describes systems that are either homogeneous across temperatures or exhibit upper critical solution temperatures. The proposed Flory-Huggins-Potts framework extends these capabilities by predicting lower critical solution temperatures, miscibility loops, and hourglass-shaped spinodal curves. We particularly show that including orientation-dependent interactions, specifically between monomer segments and solvent particles, is alone sufficient to observe such phase behavior. Signatures of emergent phase behavior are found in single-chain Monte Carlo simulations, which display heating- and cooling-induced coil-globule transitions linked to energy fluctuations. The framework also capably describes a range of experimental systems. Importantly, and by contrast to many prior theoretical approaches, the framework does not employ any temperature- or composition-dependent parameters. This work provides new insights regarding the microscopic physics that underpin complex thermoresponsive behavior in polymers.

Dipole Theory of Polyzwitterion Microgels and Gels.

The behavior of polyzwitterions, constituted by dipole-like zwitterionic monomers, is significantly different from that of uniformly charged polyelectrolytes. The origin of this difference lies in the intrinsic capacity of polyzwitterions to self-associate intramolecularly and associate with interpenetrating chains driven by dominant dipolar interactions. Earlier attempts to treat polyzwitterions implicitly assume that the dipoles of zwitterion monomers are randomly oriented. At ambient temperatures, the dipolar zwitterion monomers can readily align with each other generating quadrupoles and other multipoles and thus generating heterogeneous structures even in homogeneous solutions. Towards an attempt to understand the role of such dipolar associations, we present a mean field theory of solutions of polyzwitterions. Generally, we delineate a high-temperature regime where the zwitterion dipoles are randomly oriented from a low-temperature regime where quadrupole formation is significantly prevalent. We present closed-form formulas for: (1) Coil-globule transition in the low-temperature regime, the anti-polyelectrolyte effect of chain expansion upon addition of low molar mass salt, and chain relaxation times in dilute solutions. (2) Spontaneous formation of a mesomorphic state at the borderline between the high-temperature and low-temperature regimes and its characteristics. A universal law is presented for the radius of gyration of the microgel, as a proportionality to one-sixth power of the polymer concentration. (3) Swelling equilibrium of chemically cross-linked polyzwitterion gels in both the high temperature and low-temperature regimes. Addressing the hierarchical internal dynamics of polyzwitterion gels, we present a general stretched exponential law for the time-correlation function of gel displacement vector, that can be measured in dynamic light scattering experiments. The present theory is of direct experimental relevance and additional theoretical developments to all polyzwitterion systems, and generally to biological macromolecular systems such as intrinsically disordered proteins.

Effect of counterion size on polyelectrolyte conformations and thermodynamics.

We present a theoretical model to study the effect of counterion size on the effective charge, size, and thermodynamic behavior of a single, isolated, and flexible polyelectrolyte (PE) chain. We analyze how altering counterion size modifies the energy and entropy contributions to the system, including the ion-pair free energy, excluded volume interactions, entropy of free and condensed ions, and dipolar attraction among monomer-counterion pairs, which result in competing effects challenging intuitive predictions. The PE self-energy is calculated using the Edwards-Muthukumar Hamiltonian, considering a Gaussian monomer distribution for the PE. The condensed ions are assumed to be confined within a cylindrical volume around the PE backbone. The dipolar and excluded volume interactions are described by the second and third virial coefficients. The assumption of freely rotating dipoles results in a first-order coil-globule transition of the PE chain. A more realistic, weaker dipolar attraction, parameterized in our theory, shifts it to a second-order continuous transition. We calculate the size scaling-exponent of the PE and find exponents according to the relative dominance of the electrostatic, excluded volume, or dipolar effects. We further identify the entropy- and energy-driven regimes of the effective charge and conformation of the PE, highlighting the interplay of free ion entropy and ion-pair energy with varying electrostatic strengths. The crossover strength, dependent on the counterion size, indicates that diminishing sizes favor counterion condensation at the expense of free ion entropy. The predictions of the model are consistent with trends in simulations and generalize the findings of the point-like counterion theories.

Interactions between Water and a Hydrophobic Polymer.

To investigate the mechanisms of interactions between a hydrophobic polymer and water, molecular dynamics calculations and Raman spectroscopic measurements of cis-1,4-polyisoprene (PI)-water systems were performed. The results show that PI in water undergoes a coil-globule transition at around 248 K. The transition is attributed to changes in the density and diffusivity of water. The volume expansion of the supercooled liquid water induces the coil structure of PI. The phase separation of PI from water with an increase in the self-diffusion coefficient of water molecules results in the globule structure of PI. The self-diffusion coefficient of free water with PI is larger than that of pure water because PI has an effect to decrease the hydrogen-bonding strength of water. The result suggests that the effects of the coexisting water are important factors governing the physical and chemical properties of hydrophobic polymers.

Bioinspired hydrogels: polymeric designs towards artificial photosynthesis.

Aquatic environments host various living organisms with active molecular systems, such as the enzymes in the thylakoid membrane that realise photosynthesis. Various challenges in achieving artificial photosynthesis, such as water splitting, have been studied using both inorganic and organic molecules. However, several problems persist, including diffusion-limited reactions and multiple redox reactions in the liquid phase. In this Feature Article, we discuss the significant challenges in using polymer networks as active mediators for photoinduced water splitting. In the creation of artificial chloroplasts, polymer networks offer various advantages, such as stable dispersions of multiple types of functional molecules and close molecular arrangements. To incorporate these features, stepwise synthesis and integration can be utilized during the hierarchical construction of polymer networks. The constituent molecules such as ruthenium complex and platinum nanoparticles in the photoinduced electron transfer circuits are closely arranged to smoothly operate forward reactions by polymer networks. The quantum efficiency of photoinduced H2 generation in gel systems is considerably higher than that of conventional solution systems. Additionally, a thermoresponsive poly(N-isopropylacrylamide) (PNIPAAm) network of microgels can be used to integrate catalytic nanoparticles into the inside by using the electrostatic interaction and the mesh size changes. By focusing on the redox changes of copolymerised molecules that induce swelling/shrinking at a constant temperature, active electron transfer can be precisely achieved using the coil-globule transition of the PNIPAAm having viologen. This article highlights the potential of polymer networks to develop strategies for active electron transfer and energy conversion systems similar to those found in living organisms.

Shift of the “coil–globule” transition in porous polymer films

Using the model of Gaussian subchains “beads on a thread”, the reduced parameters of the state equation for porous polypropylene films in various solvents are found. It is shown that to satisfy to experimental data, the coil-globule transition is shifted towards higher values of the Flory–Huggins interaction parameter.

Direct Conversion of Phase-Transition Entropy into Electrochemical Thermopower and Peltier Effect.

Thermocell generates thermopower from a temperature difference (ΔT) between two electrodes. The converse process of thermocells is an electrochemical Peltier effect, which creates a ΔT on the electrodes by applying an external current. The Seebeck coefficient (Se ) of the electrochemical system is proportional to the entropy change of the redox reaction; therefore, a redox system having a significant entropy change is expected to increase the Se . In this study, a thermo-responsive polymer having a redox-active moiety, poly(N-isopropyl acrylamide-co-N-(2-acrylamide ethyl)-N'-n-propylviologen) (PNV), is used as the redox species of a thermocell. PNV2+ dication undergoes the coil-globule phase transition upon the reduction to PNV+ cation radical, and a large entropy change is introduced because water molecules are freed from the polymer chains. The Se of PNV thermocell drastically increased to +2.1mV K-1 at the lower critical solution temperature (LCST) of PNV. The entropy change calculated from the increment of Se agreed with the value evaluated by differential scanning calorimetry. Moreover, the electrochemical Peltier effect was observed when the device temperature was increased above the LCST. This study shows that the large entropy change associated with the coil-globule phase transition can be used in electrochemical thermal management and refrigeration technologies. This article is protected by copyright. All rights reserved.

Hydrophobic Homopolymer's Coil-Globule Transition and Adsorption onto a Hydrophobic Surface under Different Conditions.

Unstructured proteins can modulate cellular responses to environmental conditions by undergoing coil-globule transitions and phase separation. However, the molecular mechanisms of these phenomena still need to be fully understood. Here, we use Monte Carlo calculations of a coarse-grained model incorporating water's effects on the system's free energy. Following previous studies, we modeled an unstructured protein as a polymer chain. Because we are interested in investigating how it responds to thermodynamic changes near a hydrophobic surface under different conditions, we chose an entirely hydrophobic sequence to maximize the interaction with the interface. We show that a slit pore confinement without top-down symmetry enhances the unfolding and adsorption of the chain in both random coil and globular states. Moreover, we demonstrate that the hydration water modulates this behavior depending on the thermodynamic parameters. Our findings provide insights into how homopolymers and possibly unstructured proteins can sense and adjust to external stimuli such as nanointerfaces or stresses.

All-Atom Molecular Dynamics Simulations of the Temperature Response of Poly(glycidyl ether)s with Oligooxyethylene Side Chains Terminated with Alkyl Groups.

Recently, experimental investigations of a class of temperature-responsive polymers tethered to oligooxyethylene side chains terminated with alkyl groups have been conducted. In this study, aqueous solutions of poly(glycidyl ether)s (PGE) with varying numbers of oxyethylene units, poly(methyl(oligooxyethylene)n glycidyl ether) (poly(Me(EO)nGE)), and poly(ethyl(oligooxyethylene)n glycidyl ether) (poly(Et(EO)nGE) (n = 0, 1, and 2) were investigated by all-atom molecular dynamics simulations, focusing on the thermal responses of their chain extensions, the recombination of intrapolymer and polymer-water hydrogen bonds, and water-solvation shells around the alkyl groups. No clear relationship was established between the phase-transition temperature and the polymer-chain extensions unlike the case for the coil-globule transition of poly(N-isopropylacrylamide). However, the temperature response of the first water-solvation shell around the alkyl group exhibited a notable correlation with the phase-transition temperature. In addition, the temperature at which the hydrophobic hydration shell strength around the terminal alkyl group equals the bulk water density (TCRP) was slightly lower than the cloud point temperature (TCLP) for the methyl-terminated poly(Me(EO)nGE) and slightly higher for the ethyl-terminated poly(Et(EO)nGE). It was concluded that the polymer-chain fluctuation affects the relationship between TCRP and TCLP.

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.

Machine learning of an implicit solvent for dynamic Monte Carlo simulations.

The Bond Fluctuation Model (BFM) is a highly efficient and versatile method for simulating polymers, membranes, and soft matter. Due to its coarse-grained nature, the BFM is employed to understand the universal properties of polymers. Solvent effects are often mediated by explicit solvent particles, while implicit solvent models have had limited use as they may lead to frozen states and, thus, ergodicity-related problems. In simulation setups, such as coagulated multiple homopolymers chains, explicit solvent models are computationally expensive because the region of interest can be localized in a small space compared to the dimension of the periodic box. We introduce an implicit solvent model based on an artificial neural network (NN) that was trained with BFM simulation data for single homopolymers in an explicit solvent. We demonstrate that NN-based simulations that take into account only the information of the local environment of monomers reproduce the expected universal macroscopic properties of the polymer under varying solvent conditions. The homopolymer chains simulated using the NN reproduce the coil-globule transition, the static and dynamic bond autocorrelation, and the mean square displacement of chain monomers. We show that the learned parameters from a single chain system can be transferred to a system containing multiple homopolymers, indicating that the learned parameters are transferable to considerably different systems.

The effect of configurational complexity in hetero-polymers on the coil-globule phase transition

The coil-globule transition of hetero-polymer chains is studied here. By means of extensive Molecular Dynamics simulations, we show that the transition is directly linked to the complexity of the chain, which depends on the number of chemical species defined in the environment and the location of the binding sites along the polymer. In addition, when the number of species increases, we find that the distribution of binding sites plays an important role in triggering the transition, beyond the standard control parameters of the polymer model, i.e. binders concentration and binding affinity. Overall, our results show that by increasing the system complexity new organizational layers emerge, thus allowing a more structured control on the polymer thermodynamic state. This can be potentially applied to the study of chromatin architecture, as such polymer models have been broadly used to understand the molecular mechanisms of genome folding.

Chain length and amino acid composition dependence of coil-globule transition in intrinsically disordered proteins.

A fundamental question related to intrinsically disordered proteins (IDPs) is whether they undergo a coil-to-globule transition with changes in cosolvent conditions. IDPs are hetero-polymers and finite in size. The chain length and amino acid composition could lead to the varying extent of compaction in IDPs and the coil-to-globule transition (theta condition). To probe the theta condition in polypeptides, we studied the behavior of polyleucine and polyglutamine with six different chain lengths (N = 16 to 512) in various concentrations (0 to 8 M) of Urea (denaturant) and TMAO (osmolyte) using coarse-grained models and computer simulations. The Flory scaling exponent of polyleucine (polyglutamine) undergoes a transition from approximately 0.6 (0.6) to 0.3 (0.5) with increasing N in water. We observed that the theta condition for both the IDPs strongly depends on N and varies as N−0.5. Depending on N, polyglutamine (polyleucine) chains reach the theta condition at different [TMAO] ([TMAO] or [Urea]), confirming that in addition to chain length, the amino acid composition also influences the theta solvent condition for the IDPs. Moreover, the theta point for smaller chain lengths (N = 16 to 64) calculated using the structure factor mimicking the small-angle X-ray scattering (SAXS) experiments and using pair distances mimicking fluorescence resonance energy transfer (FRET) experiments are in disagreement. The theta condition computed using the structure factor and pair distances converge to the same point only at large N. As the theta condition is correlated with the critical condition of liquid-liquid phase separation (LLPS) for IDPs, we predict that LLPS propensity of IDPs will increase with N.

Water model determines thermosensitive and physicochemical properties of poly(N-isopropylacrylamide) in molecular simulations

Poly (N-isopropylacrylamide) (PNIPAM) is a famous representative of thermosensitive polymers. Thermosensitive polymers undergo a phase transition with lower critical solution temperature. Commonly, their phase behavior is linked to a conformational collapse above a certain temperature. This thermosensitive conformational transition is called Coil-Globule transition. In contrast, most other polymers usually show inverse temperature behavior, i.e., an upper critical solution temperature, corresponding to a Globule-Coil transition. Besides their numerous possible applications, thermosensitive polymers are of interest for fundamental research, because of similarities to macromolecular conformational transitions, e.g., protein folding. The counter-intuitive behavior of thermosensitive polymers is commonly associated with solvation effects. Thus, an accurate description of the solvent is crucial for the investigation of thermosensitive polymers in molecular simulations. Here, we investigate the influence of the in silico water model on the thermosensitive Coil-Globule transition in molecular dynamics simulations. To this end, we performed extensive atomistic simulations of the syndiotactic PNIPAM 20-mer at multiple temperatures with eight different water models–four of which are 3-point water models (TIP3P-type) and four are 4-point water models (TIP4P-type). We found that the thermosensitive Coil-Globule transition is strongly influenced by the water model in the simulations. Depending on the water model, the conformational ensemble of the polymer is shifted significantly, which leads to dramatically different results: The estimated transition temperature may span between 255 and 350 K. Consequently, depending on the description of the solvent, the physicochemical and mechanical properties of these polymers, e.g., the polymer-solvent affinity and persistence length, vary. These divergent results originate from the strength of interactions between polymer and solvent, but also on the bulk state of the solvent. Both these quantities vary between water models. We found that the Lennard-Jones interaction parameter ϵ of the water model correlates with the transition temperature of the polymer. Indeed, the quadrupole moment of the water model shows an even higher correlation with this quantity. Our results suggest a connection between the phase diagram of the solvent and the thermosensitive transition of the polymer.

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.

Universality and Identity Ordering in Heteropolymer Coil–Globule Transition

Universality and Identity Ordering in Heteropolymer Coil–Globule Transition

Extension and dynamical phases in random walkers depositing and following chemical trails

Active walker models have proved to be extremely effective in understanding the evolution of a large class of systems in biology like ant trail formation and pedestrian trails. We propose a simple model of a random walker which modifies its local environment that in turn influences the motion of the walker at a later time. We perform direct numerical simulations of the walker in a discrete lattice with the walker actively depositing a chemical which attracts the walker trajectory and also evaporates in time. We propose a method to look at the structural transitions of the trajectory using radius of gyration for finite time walks. The extension over a definite time window shows a non-monotonic change with the deposition rate characteristic of a coil-globule transition. At certain regions of the parameter space of the chemical deposition and evaporation rates, the extensions of the walker shows a re-entrant behavior. The dynamics, characterised by the mean-squared displacement, shows deviation from diffusive scaling at intermediate time scales, returning to diffusive behavior asymptotically. A mean-field theory captures the variation of the asymptotic diffusivity.