Closed-loop Phase Diagram Research Articles

Atomistic insights into the reentrant phase-transitions in polyuracil and polylysine mixtures.

The phase separation of protein and RNA mixtures underpins the assembly and regulation of numerous membraneless organelles in cells. The ubiquity of protein-RNA condensates in cellular regulatory processes is in part due to their sensitivity to RNA concentration, which affects their physical properties and stability. Recent experiments with poly-cationic peptide-RNA mixtures have revealed closed-loop phase diagrams featuring lower and upper critical solution temperatures. These diagrams indicate reentrant phase transitions shaped by biomolecular interactions and entropic forces such as solvent and ion reorganization. We employed atomistic simulations to study mixtures with various RNA-polylysine stoichiometries and temperatures to elucidate the microscopic driving forces behind reentrant phase transitions in protein-RNA mixtures. Our findings reveal an intricate interplay between hydration, ion condensation, and specific RNA-polylysine hydrogen bonding, resulting in distinct stoichiometry-dependent phase equilibria governing stabilities and structures of the condensate phase. Our simulations show that reentrant transitions are accompanied by desolvation around the phosphate groups of RNA, with increased contacts between phosphate and lysine side chains. In RNA-rich systems at lower temperatures, RNA molecules can form an extensive pi-stacking and hydrogen bond network, leading to percolation. In protein-rich systems, no such percolation-induced transitions are observed. Furthermore, we assessed the performance of three prominent water force fields-Optimal Point Charge (OPC), TIP4P-2005, and TIP4P-D-in capturing reentrant phase transitions. OPC provided a superior balance of interactions, enabling effective capture of reentrant transitions and accurate characterization of changes in solvent reorganization. This study offers atomistic insights into the nature of reentrant phase transitions using simple model peptide and nucleotide mixtures. We believe that our results are broadly applicable to larger classes of peptide-RNA mixtures exhibiting reentrant phase transitions.

Dual thermoresponsive polysaccharide derivative – water system. Partially substituted amylose butylcarbamate in water

Partially substituted amylose n-butylcarbamate (ABC) samples were synthesized with weight-average molar mass Mw ranging between 40 kg mol−1 and 220 kg mol−1 with different degree of substitution DS. When DS was between 0.17 and 0.33, the ABC samples were soluble in water. Furthermore, both LCST and UCST type phase separations were observed for the ABC samples in water when DS is >0.26. The closed-loop phase diagrams for the dual thermoresponsive ABC samples in water were constructed by turbidity measurement. The UCST ranged from 70 °C to 77 °C and the LCST ranged from 13 °C to 17 °C. SAXS measurements were performed for dilute aqueous ABC solutions to determine the chain conformation of ABC at various temperatures. The resulting form factor at the polymer mass concentration of 3 mg mL−1 indicated that the chain conformation is almost independent of temperature, except for the chain diameter, which is influenced by the temperature-dependent hydration behavior. This result suggests that the attractive interactions between ABC chains are not very significant even between UCST and LCST, where higher concentrated polymer solutions show macroscopic phase separation.

Charge Regulation of Polyelectrolyte Gels: Swelling Transition

We study the effects of charge-regulated acid/base equilibrium on the swelling of polyelectrolyte gels by considering a combination of the Poisson–Boltzmann theory and a two-site charge-regulation model based on the Langmuir adsorption isotherm. By exploring the volume change as a function of salt concentration for both nanogels and microgels, we identify conditions where the gel volume exhibits a discontinuous swelling transition. This transition is driven exclusively by the charge-regulation mechanism and is characterized by a closed-loop phase diagram. Our predictions can be tested experimentally for polypeptide gels.

Re-entrant transitions of locally stiff RNA chains in the presence of polycations leads to gelated architectures.

The liquid-liquid phase separation of protein and nucleic acid mixtures drives the formation of numerous membraneless compartments in cells. Temperature variation is commonly used for mapping condensate phase diagrams, which often display unique upper critical temperatures. Recent report on peptide-RNA mixtures has shown the existence of lower and upper critical solution temperatures, highlighting the importance of temperature-dependent solvent and ion-mediated forces. In the present work, we employ residue-level coarse-grained models of RNA and polycation peptide chains for simulating temperature-induced re-entrant transitions and shedding light on the role played by mobile ions, temperature-dependent dielectric permittivity, and local chain stiffness. We show that differences in bending rigidity can significantly modulate condensate topology leading to the formation of gelated or fibril like architectures. The study also finds that temperature dependence of water permittivity is generally sufficient for recapitulating experimentally observed closed loop and LCST phase diagrams of highly charged protein-RNA mixtures. However, we find that similar-looking closed-loop phase diagrams can correspond to vastly different condensate topologies.

Single Amino Acid Substitutions in Stickers, but Not Spacers, Substantially Alter UBQLN2 Phase Transitions and Dense Phase Material Properties.

UBQLN2 450-624 oligomerizes and undergoes temperature-responsive liquid-liquid phase transitions following a closed-loop temperature-concentration phase diagram. We recently showed that disease-linked mutations to UBQLN2 450-624 impart highly varying effects to its phase behavior, ranging from little change to significant decrease of saturation concentration and formation of gels and aggregates. However, how single mutations lead to these properties is unknown. Here, we use UBQLN2 450-624 as a model system to study the sequence determinants of phase separation. We hypothesized that UBQLN2 450-624 regions previously identified to promote its oligomerization are the "stickers" that drive interchain interactions and phase separation. We systematically investigated how phase behavior is affected by all 19 possible single amino acid substitutions at three sticker and two "spacer" (sequences separating stickers) positions. Overall, substitutions to stickers, but not spacers, substantially altered the shape of the phase diagram. Within the sticker regions, increasing hydrophobicity decreased saturation concentrations at low temperatures and enhanced oligomerization propensity and viscoelasticity of the dense phase. Conversely, substitutions to acidic residues at all positions greatly increased saturation concentrations. Our data demonstrate that single amino acid substitutions follow a molecular code to tune phase transition behavior of biopolymers.

Phase Separation Dynamics of a Binary Fluid with a Closed-Loop Phase Diagram

We perform molecular dynamics simulations of the phase separation processes of a binary quadrupolar fluid that shows a closed-loop phase diagram with two types of critical points. These simulations...

Heterogeneity Assisted Damping Enhancement of Low and High Frequency Mechanical Waves in a Soft Polymer Nanocomposite

Low-amplitude dynamic and morphological heterogeneities of a biphasic copolymeric matrix were amplified by soft nanoparticle loading and thermally induced phase separation (TIPS). The evolution of system concentration fluctuation size (ξ) was quantified as a function of quench depth in its closed-loop like phase diagram. The system characterization was then complemented by extracting its bimodal heterogeneity index as normalized interface length over area (L/A) from phase imaging analysis of atomic force microscopy (AFM). Both criteria were amplified by annealing temperature rise, resulting in damping enhancement under low and high frequency mechanical waves, shown by dynamic mechanical thermal analysis (DMTA) and ultrasound spectroscopy, respectively. At the highest annealing temperature, 160 °C, the morphogenesis led to simultaneous increase of effective damping temperature range (ΔTeff) and maximum tan δ to 190 °C and 2, respectively. Finally, damping efficacy (Deff, i.e., ΔTeff[tan δ]max) and the ultr...

Non-Monotonic Effect of Solutes on Miscibility Transition Temperatures; Simple Explanation of Closed-Loop Phase Diagrams

Non-Monotonic Effect of Solutes on Miscibility Transition Temperatures; Simple Explanation of Closed-Loop Phase Diagrams

Very low surface tension liquid–vapour interfaces of patchy colloids

The liquid–vapour interface of a model of one-component patchy colloids is re-visited. The model consists of hard spheres decorated with short-ranged attractive sites (‘patches’) of different types on their surfaces. In an earlier paper [A. Oleksy and P.I.C. Teixeira, Phys. Rev. E 91 (2015) 012301], the density-functional theory (DFT) form of Wertheim's first-order perturbation theory (TPT1) was used to study a realisation of this model with two patches of type A and nine patches of type B (2A9B colloids), which exhibit re-entrant liquid–vapour coexistence curves and very low-density liquid phases. Here, it is shown that the non-monotonic temperature dependence of the surface tension and interface thickness in this model can be qualitatively reproduced by a local DFT, where the spatial non-uniformity is introduced through the square gradient of the density multiplied by a density-dependent prefactor. This simpler theory is then applied to colloids decorated with two patches of type A and ten patches of type B (2A10B colloids), and interactions chosen so as to exhibit a closed-loop phase diagram when only AA and AB bonds are present [N.G. Almarza et al., J. Chem. Phys. 137 (2012) 244902]. In this case, the surface tension goes to zero at both upper and lower critical points, with a maximum at some intermediate temperature. As BB attractions are gradually switched on, the lower critical point disappears and the surface tension vs temperature curve acquires a very deep minimum at a temperature lower than that of the maximum. On further increasing the strength of the BB attractions, both the minimum and the maximum disappear and the surface tension becomes a monotonically decreasing function of the temperature, as in atomic fluids. The very low surface tension at the minimum for weak BB attractions, combined with the ability to form physical gels, suggests that 2AnB colloids might be exploited as temperature-controlled surfactants and foam stabilizers.

Solvation of polymers as mutual association. II. Basic thermodynamic properties

The theory of equilibrium solvation of polymers B by a relatively low molar mass solvent A, developed in the simplest form in Paper I, is used to explore some essential trends in basic thermodynamic properties of solvated polymer solutions, such as the equilibrium concentrations of solvated polymers AiB and free solvent molecules A, the mass distribution φ(AiB)(i) of solvated clusters, the extent of solvation of the polymer Φ(solv), the solvation transition lines T(solv)(φB(o)), the specific heat C(V), the osmotic second virial coefficient B2, phase stability boundaries, and the critical temperatures associated with closed loop phase diagrams. We discuss the differences between the basic thermodynamic properties of solvated polymers and those derived previously for hierarchical mutual association processes involving the association of two different species A and B into AB complexes and the subsequent polymerization of these AB complexes into linear polymeric structures. The properties of solvated polymer solutions are also compared to those for solutions of polymers in a self-associating solvent. Closed loop phase diagrams for solvated polymer solutions arise in the theory from the competition between the associative and van der Waals interactions, a behavior also typical for dispersed molecular and nanoparticle species that strongly associate with the host fluid. Our analysis of the temperature dependence of the second osmotic virial coefficient reveals that the theory must be generalized to describe the association of multiple solvent molecules with each chain monomer, and this complex extension of the present model will be developed in subsequent papers aimed at a quantitative rather than qualitative treatment of solvated polymer solutions.

Large-Scale Structures in Tetrahydrofuran–Water Mixture with a Trace Amount of Antioxidant Butylhydroxytoluene (BHT)

Author: Because of the closed-loop phase diagram of tetrahydrofuran (THF)-water mixture, THF aqueous solution naturally exhibits concentration fluctuations near the phase boundary. Besides the fast mode induced by concentration fluctuations, the 4.5% mole fraction THF aqueous solution is also characterized by a slow mode. The existence of a trace amount of butylhydroxytoluene (BHT) antioxidant in commercial THF strongly influences the slow mode in 4.5% mole fraction THF aqueous solution. A core-shell structure with a BHT core and a shell made from THF-rich THF-D(2)O mixture was identified by the combination of dynamic laser light scattering (DLS) and small-angle neutron scattering (SANS). BHT is hydrophobic, stabilized by a THF-rich domain in THF aqueous solution and acts as a tracer to make the large-scale structure (slow mode) "visible" through SANS because of its larger contrast with the solvent. In contrast, this large-scale structure was almost not detectable by SANS when BHT was removed from the THF-D(2)O mixture. Combined UV-vis, DLS, and static light scattering (SLS) indicated that slow-moving objects do exist and that their sizes almost do not change, but their concentration decreases to a small but nonzero value at the infinite dilution limit. The origin of the elusive large-scale structure at zero BHT concentration is still not clear, but it might be associated with some hydrophobic impurities or nanobubbles. However, a polydisperse sphere model of ∼8.5% mole fraction THF-D(2)O mixture can fit the structure with a radius of ∼100 nm, which gives the temperature-dependent low-q SANS profiles of 4.5% mole fraction THF aqueous solution at zero BHT concentration.

Understanding Liquid Mixture Phase Miscibility via Pair Energy Parameter Behaviors with Respect to Temperatures Determined from Molecular Simulations

The miscibility behaviors of binary liquid mixtures were studied by a combination of molecular simulations and thermodynamic theories. Pairwise interaction parameters were obtained from molecular simulations that accounted for the effect of temperature. From a thermodynamic perspective, different types of liquid-liquid equilibrium (LLE) and different degrees of miscibility can be expressed in terms of energy behaviors with respect to temperature. Our simulation results proved this viewpoint by showing a correspondence between the simulation results and experimental observations. To describe phase diagrams, thermodynamic modeling is presented using the energy parameters obtained from the simulations. Correlations are needed to correct size mismatches between the simulations and the thermodynamic model. Using this method, not only the upper critical solution temperature (UCST) but also the closed-loop miscibility phase diagrams could be calculated without requiring additional parameters for specific interactions. The utility of this method is demonstrated for mixtures containing water, hydrocarbon, alcohols, aldehydes, ketones, chlorides, amines, nitriles, sulfides, and other organic liquids in various temperature ranges. The method presented in this paper can facilitate the understanding of the miscibilities in binary liquid mixtures from the viewpoint of thermal energy behaviors.

Phenomenological Interpretation of the Systems Exhibiting a Closed-Loop Liquid-Liquid Phase Diagram by Using a Simple g E-Model

A simple phenomenological gE-model based on the Flory-Huggins lattice theory was used to interpret critical behavior, excess properties and liquid-liquid equilibria of three aqueous systems that exhibit a closed-loop phase diagram: (2-butoxyethanol + water), (2,6-dimethylpyridine + water) and (tetrahydrofuran (THF) + water). The model showed flexibility in application and good performance in all the aforementioned properties. Since it describes with a very good accuracy both binodal (coexistence) curves and excess enthalpies, it was used to calculate the molar excess enthalpies of the phases in equilibrium which may be a useful task in practice.

Reentrant swelling behavior of thermosensitive N-isopropylacrylamide nano-sized gel particles

The closed-loop phase diagram of poly N-isopropylacrylamide (PNIPA) in a water–N,N-dimethylformamide (DMF) system was measured by thermooptical analysis (TOA). The reentrant swelling behavior of N-isopropylacrylamide (NIPA) nano-sized gel particles in the water–DMF system was measured by using photon correlation spectroscopy (PCS) technique. Theoretically, a modified double lattice model (MDL) can be used to describe the closed-loop phase behavior of linear PNIPA in water–DMF systems. For crosslinked NIPA nano-sized gel particles in a water–DMF system, we combined MDL theory for the mixing contribution and Flory–Erman theory for the elastic contribution. Molecular interaction parameters obtained from the PNIPA solution were used to directly predict the swelling-ratio curves for the NIPA gel. Using our model, the calculated results were in good agreement with the experimental data using only one adjustable parameter.

Influence of Carbon Dioxide Swelling on the Closed-Loop Phase Behavior of Block Copolymers

The influence of carbon dioxide sorption on the closed-loop phase diagram of polystyrene-block-poly(n-pentyl methacrylate) copolymers, PS-b-PnPMA, was investigated. Differential dilation of the constituent blocks was used to induce microphase separation of the PS-b-PnPMA. With increasing carbon dioxide loading an appreciable expansion in the size of the closed loop was found. At a carbon dioxide activity of 0.1 the upper order-to-disorder transition temperature (UODT) was elevated by more than 20 °C, whereas the lower disorder-to-order transition temperature (LDOT) was depressed by the same magnitude. This arises from the entropic nature of the closed-loop miscibility gap in this weakly interacting system, where microphase separation is driven by disparity in free volumes between dissimilar segments of the chain.

Simple model of membrane proteins including solvent

We report a numerical simulation for the phase diagram of a simple two-dimensional model, similar to the one proposed by Noro and Frenkel [J. Chem. Phys. 114, 2477 (2001)] for membrane proteins, but one that includes the role of the solvent. We first use Gibbs ensemble Monte Carlo simulations to determine the phase behavior of particles interacting via a square-well potential in two dimensions for various values of the interaction range. A phenomenological model for the solute-solvent interactions is then studied to understand how the fluid-fluid coexistence curve is modified by solute-solvent interactions. It is shown that such a model can yield systems with liquid-liquid phase separation curves that have both upper and lower critical points, as well as closed loop phase diagrams, as is the case with the corresponding three-dimensional model.

Analyzing of segregation in mixtures of 3-methylpyridine and heavy water by dynamic neutron radiography (II)

In 3-methylpyridine-heavy water mixture, the segregation in the closed-loop phase diagram in relation to the temperature and heavy water concentration was studied by dynamic neutron radiography (DNR) at the 10 MW VVR-SM Research Reactor in Budapest, Hungary. On the pixel properties of the DNR images, taken from the phase separation process by Iman 2/spl beta/ v. image analyzing program, polynomial fitting, 3-D intensity histograms were applied. For modeling the segregation process, a two-variable segregation model: S=f(T,D) was set up. From the partial differentiation of the function f with respect to the temperature it was established that the highest rate changes in the segregation take place in the region of 50-55/spl deg/C and are modified by 3-methylpyridine concentration. The increase in the segregation process progresses up to 93-96/spl deg/C, then declines.

Analyzing of segregation in mixtures of 3-methylpyridine and heavy water by dynamic neutron radiography

The closed-loop phase diagram of 3-methylpyridine—heavy water mixture was studied, to our best knowledge, for the first time with dynamic neutron radiography (DNR) at the 10 MW VVR-SM Research Reactor in Budapest (Hungary). Visualized were the (i) lower temperature non-segregated states (below 38°C), (ii) transition (40–43°C), (iii) segregated states (46–128°C), (iv) higher temperature transition (110–128°C) and (v) higher temperature non-segregated states. The non-segregated state belonging to 141°C, was found to be definitely dissimilar from the lower temperature state. Existence of a solid-like structure at the liquid–liquid interface was indicated.

Effects of slit-like pore confinement on the closed loop immiscibility in symmetric binary model mixtures: fundamental measure density functional approach

We investigate the adsorption of model symmetric binary mixtures, exhibiting closed loop immiscibility in the bulk phase, in slit-like pores by using a density functional approach. Our focus is on changes in the closed loop phase diagram owing to Confinement. We have found that, in general, confinement narrows immiscibility loops in the temperature-selectivity plane.

Density functional approach on wetting behavior of binary associating mixtures

A density functional theory is applied to study wetting behaviors of binary associating mixtures, which are described by the statistical associating fluid theory of Wertheim. When the associating interaction is strong, the phase behavior of the binary associating mixture falls into the type-VI mixtures of the classification scheme of van Konynenburg and Scott. There are two types of closed-loop phase behaviors for the type-VI mixture. That is, a closed-loop phase diagram for vapor–liquid–liquid coexistence (along its triple line) at low pressures and the other one for liquid–liquid coexistence at a relatively high pressure. In this study, the wetting behavior of the lower liquid phase at the surface of the upper liquid phase is carefully examined for both vapor–liquid–liquid coexistence and liquid–liquid coexistence regimes. In the latter regime, a third inert air phase is introduced since wetting behavior always involves three phases. For both regimes the binary associating mixture exhibits a sequence of wetting transitions, complete wetting→partial wetting→complete wetting, along with increasing temperature. The order of wetting transitions is carefully examined. It is found that the order of wetting transitions is the consequence of the competition between the attractive interaction range and the associating strength of unlike pair molecules. The most intriguing behavior is that it is possible to observe the sequence of wetting transitions along with increasing temperature at two different orders for air–liquid–liquid coexistence at a high pressure. That is, the upper wetting transition is first order and the lower wetting transition is second order. The pressure effect on the order of wetting transitions for liquid–liquid coexistence is also discussed.