Binodal Research Articles

Experimental and Theoretical Methods for Mapping Coexistence Curves of Phase-Separating Biological Macromolecules

Phase separation of multivalent proteins and RNA molecules is recognized as an important phenomenon in a variety of biological processes, including the regulation of cellular signaling, transcriptional control, and stress response. Aberrant phase behavior appears to underlie the etiology of various complex diseases such as neurodegeneration and cancers. Thermodynamic description of the phase behavior of multivalent molecules requires the construction of coexistence curves known as binodals. The development of sequence-to-binodal relationships provides an information-rich route to comparing sequence-specific phase behaviors of various systems. However, the measurement of full binodals can be exceptionally challenging. This is especially true of the high concentration arm of the binodal. Several methods have been implemented albeit with varying degrees of success. However, to date, no gold standard has emerged for the determination of complete binodals. We propose, develop, and deploy a new approach that leverages tie line theory to enable calculation of data points on the high concentration arm using measurements of the low concentration arm and the relative volumes of phases, both of which can be readily measured using routine optical and microfluidic methods. We show how this approach can be applied to a model phase separating system, namely an IDP with a lower critical saturation temperature (LCST). We also demonstrate how a similar approach can be applied to more complex multicomponent systems. We anticipate that this approach will facilitate more accurate measurements of complete phase diagrams while minimizing the burden on the required sample volumes and masses. When coupled to high-throughput methods, we anticipate that our method will enable the rapid prototyping of sequence-to-phase behavior relationships thus enabling the design of sequences with bespoke phase behavior that lead to de novo biomolecular condensates.

Integration of aqueous (micellar) two-phase systems on the proteins separation

A two-step approach combining an aqueous two-phase system (ATPS) and an aqueous micellar two-phase system (AMTPS), both based on the thermo-responsive copolymer Pluronic L-35, is here proposed for the purification of proteins and tested on the sequential separation of three model proteins, cytochrome c, ovalbumin and azocasein. Phase diagrams were established for the ATPS, as well as co-existence curves for the AMTPS. Then, by scanning and choosing the most promising systems, the separation of the three model proteins was performed. The aqueous systems based on Pluronic L-35 and potassium phosphate buffer (pH = 6.6) proved to be the most selective platform to separate the proteins (SAzo/Cyt = 1667; SOva/Cyt = 5.33 e SAzo/Ova = 1676). The consecutive fractionation of these proteins as well as their isolation from the aqueous phases was proposed, envisaging the industrial application of this downstream strategy. The environmental impact of this downstream process was studied, considering the carbon footprint as the final output. The main contribution to the total carbon footprint comes from the ultrafiltration (~ 49%) and the acid precipitation (~ 33%) due to the energy consumption in the centrifugation. The ATPS step contributes to ~ 17% while the AMTPS only accounts for 0.30% of the total carbon footprint.

Extraction of glycyrrhizic acid by aqueous two-phase system formed by PEG and two environmentally friendly organic acid salts - sodium citrate and sodium tartrate

Abstract Two aqueous two-phase systems (ATPS’s) formed by using PEG and sodium citrate/sodium tartrate are applied and compared for extraction of glycyrrhizic acid (GA) from its stock solution. Their binodal curves and tie-lines are studied firstly. Influence of usage amount of the salt and the PEG on the partition coefficient and extraction efficiency is investigated. The highest extraction efficiency and partition coefficient achieved is 73% and 6.5, when the sodium citrate and PEG concentration is 15% and 20% respectively. It is also found that the ATPS based on sodium citrate is better than sodium tartrate for GA extraction. The present study indicates that ATPS formed by biodegradable organic acid salts could be feasible and environment-friendly technique for GA and other bioactive compounds.

Experimental study of choline chloride and K2HPO4 aqueous two-phase system, and its application in the partitioning of penicillin G

Aqueous two-phase systems are useful for separating biological materials. In this study, the phase diagram of the ternary system of choline chloride, K2HPO4 and water was determined at 298.15K and 0.1MPa. In this regard, the binodal curves between the single liquid phase, liquid-liquid two-phase region, solid-liquid-liquid three-phase region, and solid-liquid two-phase region were determined experimentally. Then, the liquid-liquid two-phase region as an aqueous two-phase system was studied in more details and tie lines of the aqueous two-phase system were obtained. Finally, the partition coefficient of penicillin-G was measured in this aqueous two-phase system. The effect of concentration of the constituents of the aqueous two-phase system on the partition coefficient of penicillin G was investigated. The results show that >96% of penicillin-G extracted to the top phase that is rich in choline chloride. Also, the maximum experimental partition coefficient of penicillin-G was found to be 323.5 that indicates the high capability of the current system in the separation of penicillin G.

Partitioning of cefazolin in aqueous two-phase systems containing poly (ethylene glycol) and sodium salts (citrate, tartrate, and sulphate)

Aqueous two-phase systems (ATPSs) have been recognized as potential alternative techniques for extraction or purification of biomolecules. In this work, partitioning behavior of cefazolin has been investigated in polymer-salt ATPSs. Thus, systems containing polyethylene glycol (PEG) with two different molecular weights (6000 and 8000) and three forms of sodium salts, including sodium citrate, sodium tartrate, and sodium sulfate were examined. Firstly, the binodal curves were determined at 300 K and then correlated with Merchuk equation. Results indicate that the system PEG8000/sulfate owns a wider two-phase area. Then, the tie-lines were plotted for the systems under study, and their validity was evaluated using the Othmer-Tobias and Bancroft equations. Finally, the partition coefficient of cefazolin was investigated in 6 different two-phase systems and 28 tie-lines overall. Effect of salt type, polymer molecular weight and its concentration on partition coefficient were discussed. On the basis of the results it can be declared that as the polymer concentration increases, the partition coefficient increases but the increase of polymer molecular weight leads to partition coefficient reduction. Sodium citrate was better than the other salts used for studying the cefazolin partitioning, that is in good accordance with the excluded volume theory. The maximum amount of partition coefficient equals to 13.4 with a 90.5 recovery percentage in the top phase which belongs to the system combined of PEG6000 (16% w/w) and sodium citrate (14% w/w).

Thermodynamic Investigation of the Aqueous Two-Phase Systems Formed by PEG 400 + Water + Either Sodium Carbonate or Potassium Carbonate at Different Temperatures: Experimental and Correlational Approaches

Systems composed of poly(ethylene)glycol (PEG 400) + water + either potassium carbonate or sodium carbonate were studied at 283.15, 298.15, and 313.15 K. The effects of temperature and the electrolyte on phase segregation were evaluated. The phase segregation process was endothermic and entropically driven. The efficacy of the cations in inducing phase formation with PEG 400 followed the order K2CO3 < Na2CO3. The binodal curves were successfully described using the empirical equation suggested by Merchuk and modified to include the effect of temperature. Tie-line compositions were correlated using the Othmer–Tobias, Bancroft, and Hand equations. The experimental tie-line data for PEG 400 + K2CO3 + water and PEG 400 + Na2CO3 + water were also correlated using the nonrandom two liquid model. The use of this thermodynamic model resulted in reliable data for the system while reducing the number of experiments needed. All of the correlations indicated satisfactory fits between the calculated and experimental data.

Development and application of a high density ratio pseudopotential based two-phase LBM solver to study cavitating bubble dynamics in pressure driven channel flow at low Reynolds number

Abstract A pseudo-potential based single component multiphase Lattice Boltzmann flow solver was developed. Peng–Robinson equation of state was coupled with Exact Difference Method to incorporate interaction forces. This solver was developed for a D2Q9 lattice structure. The solver was thoroughly validated against several canonical problems like estimation of coexistence curve, surface tension estimation from Laplace Law and growth of a cavitating bubble in quiescent flow. The solver was found to be numerically stable for density ratios up to 103. The solver was then used to simulate bubble dynamics for cavitating flows in different flow configurations. Fluid flow characteristics of a single cavitating bubble for Poiseuille flow with stationary and non-stationary walls at Reynolds number of 1 and 10 were investigated. Temporal evolution of the bubble when it is placed along the channel centreline and at an offset is presented here.

Effects of the polymer molecular weight and type of cation on phase diagrams of polythylene glycol + sulfate salts aqueous two-phase systems

Phase diagrams and liquid ? liquid equilibrium (LLE) data for aqueous two-phase systems (ATPSs) containing zinc sulfate, magnesium sulfate or aluminium sulfate and polyethylene glycols PEG 300, 400 and 600 have been determined at 298.15 K. It was attempted to show how the PEG molecular weight and the type of cation influence the binodal curve, tie line length (TLL) and slope of the tie line (STL). The results have shown that as the PEG molecular weight increases, the two-phase region becomes extended and the binodal curve shifts to the origin. The refractive index and density of ternary (PEG 300,400 and 600 + zinc sulfate/magnesium sulfate/aluminium sulfate + water) systems have been measured to achieve the phase composition and the tie lines. Finally, the effective excluded volume (EEV) model was applied to describe the salting-out ability of the systems. The LLE data from this research may be potentially used for recovering biological molecules like proteins.

Prediction of Thermodynamic Properties of Levulinic Acid via Molecular Simulation Techniques.

Second-generation biofuels are a complex mixture of organic compounds that can be further processed to hydrocarbon fuels and other valuable chemicals. One such chemical is levulinic acid (IUPAC name: 4-oxo pentanoic acid), which is a highly versatile ketoacid obtained from cellulose present in agricultural byproducts. For oxygen-containing compounds that decompose at elevated temperatures and pressures, determining the vapor–liquid equilibria data at high temperatures via the experimental route may be challenging. The molecular simulation approach is a cost-effective tool to obtain the necessary data while also allowing us to understand the microscopic origins of macroscopic observable properties. We have employed the transferable potential for phase equilibria-united atom force field to describe the interactions in this system with the parameters for a torsional interaction that are not reported in the literature (levulinic acid is a ketoacid) being determined from density functional theory calculations. We have verified our parameterization via density computations in the isothermal–isobaric ensemble and by comparing our simulation results with the corresponding data from experiments reported in the literature. We have performed grand-canonical transition-matrix Monte Carlo simulations in the temperature range from 580 to 690 K to estimate the vapor–liquid coexistence curves in the temperature–density plane and the Clapeyron plots. From this data, the critical point (TC = 755 K, ρC = 285.4 kg/m3, and PC = 30.57 bar) has been estimated, and this may be used as input to the equations of state employed in process simulation software for design of industrial separation processes including those for “biorefining”. As levulinic acid is a “ketoacid”, hydrogen bonding occurs, and the liquid phase structure has also been studied using radial distribution functions.

P‐Wave Superfluid Phases of Fermi Molecules in a Bilayer Lattice Array

AbstractThe superfluid phases in an ultracold gas of dipolar Fermi molecules lying in two parallel square lattices in 2D are investigated. As shown by a two‐body study, dipole moments oriented in opposite directions in each layer are the key ingredients in our mean‐field analysis from which unconventional superfluidity is predicted. The phase diagram summarizes our findings: stable and metastable superfluid phases appear as a function of both, the dipole–dipole interaction coupling parameter and filling factor. A first‐order phase transition, and thus a mixture of superfluid phases at different densities, is revealed from the coexistence curves in the metastable region. The model predicts that these superfluid phases can be observed experimentally at 10 nK in molecules of NaK confined in optical lattices of size nm. Other routes to reach higher temperatures require the use of subwavelength confinement technique.

Phase equilibria of aqueous mixtures of PEG with formate salt: Effects of pH, type of cation, polymer molecular weight and temperature

Liquid-liquid equilibrium (LLE) data for poly (ethylene glycol) (PEG) of different molecular weights (600, 1500, 3000, 6000) + sodium formate (NaCHO2), potassium formate (KCHO2) + water at different temperatures (298.15 and 308.15 K) and for PEG (1500) + sodium formate + water at different pH values (8.05, 9.06, 10.92), were determined experimentally. The tie lines and plait point are reported at different PEG molecular weight, pH, temperature and type of cation. Furthermore, the effect of those parameters on binodal curve, tie-line length (TLL) and slope of tie line (STL) are discussed in detail by comparing the results to that of literature data. The effective excluded volume (EEV) values obtained from the LLE data were used to study the effect of the parameters on the binodal curves. The phase composition and the tie-lines’ ends were obtained by measuring the density (ρ) and refractive index (nD). Furthermore, the binodal curves and the tie-line compositions were well-fitted by using some semi empirical equations.

Solubility, liquid-liquid equilibrium and critical states for the quaternary system formic acid – ethanol – ethyl formate – water at 298.15 K and 308.15 K

Solubility, critical states and liquid-liquid equilibrium (LLE) in the quaternary reacting system formic acid – ethanol – ethyl formate – water and in the ternary subsystems formic acid – ethyl formate – water and ethanol – ethyl formate – water were studied experimentally at 298.15 K and 308.15 K and atmospheric pressure. Binodal curves, binodal surfaces, tie-lines and critical manifolds were determined. In order to construct binodal surfaces and critical curves of the quaternary system, five cutting planes with several different ratios of concentration of formic acid to ethanol were studied. Experimental LLE data were compared with the data calculated by NRTL model, and it was found that experimental and calculated data are in a good agreement.

Relation between a heterogeneous percolation model for cylinders and phase separation in the lattice fluid problem

A relationship based upon analogy is explored between (i) a lattice-based model for percolation by cylinders that employs distinct site types with unequal occupation probabilities in order to capture heterogeneities in the particle dispersion, and (ii) the well-studied mean-field lattice gas model. The strength of the correlation that sites in the percolation model that have distinct occupation probabilities are adjacent to each other maps into the coupling constant for the associated lattice fluid problem. Pursuing the analogy further, the vapor-liquid coexistence curve for the lattice gas translates into a phase boundary for the percolation problem, in terms of a locus of correlation strengths that demarcate a region of phase separation into sites with different occupation probabilities and distinct percolation thresholds. The dependence of the percolation thresholds in the one- and two-phase regions as delineated by this analogy are calculated as functions of the degree of disparity between site occupation probabilities and the strength of the correlation between adjacent site types.

Liquid–Liquid–Solid Equilibria in the Ternary System Water–Phosphoric Acid–Cyclohexane at 25 and 35 °C: Stability Domain of Hemihydrate and Anhydrous Phosphoric Acid

The water–phosphoric acid–cyclohexane ternary system was studied at 25 and 35 °C under atmospheric pressure, and the binodal curve was determined by the cloud-point method. In addition, the isoplethic section between 2H3PO4·H2O–cyclohexane was investigated using a Tammann diagram based on the thermal analysis of different samples with the determination of hemihydrate melting temperature. The concentration of phosphoric acid and cyclohexane was assayed by volumetric titration and gas chromatography, respectively; the amount of water was calculated by the material balance equation. The miscibility between phosphoric acid and cyclohexane was found to be very low with the appearance of a three-phase stability domain liquid–liquid–solid by the presence of phosphoric acid crystals: hemihydrate (2H3PO4·H2O) and anhydrous phosphoric acid (H3PO4).

Phase Transition of RN-AdS Black Hole with Fixed Electric Charge and Topological Charge

Phase transition of RN-AdS black hole is investigated from a new perspective. Not only is the cosmological constant treated as pressure but also the spatial curvature of black hole is treated as topological charge ϵ. We obtain the extended thermodynamic first law from which the mass is naturally viewed as enthalpy rather than internal energy. In canonical ensemble with fixed topological charge and electric charge Q, interesting van der Waals like oscillatory behavior in T-S and P-V graphs and swallow tail behavior in G-T and G-P graphs is observed. By applying the Maxwell equal area law and analysing the Gibbs free energy, we obtain analytical phase transition coexistence curves which are consistent with each other. The phase diagram is four dimensional with T,P,Q,ϵ.

Thermodynamics of supersaturated steam: Towards an equation of state

Thermodynamics of supersaturated (supercooled) steam at conditions occurring in steam turbines, and inaccessible thus to experiments, has been studied by a number of theoretical and semi-theoretical methods with the goal to assess available theoretical tools for developing an equation of state. Extended virial expansions with different reference systems have been used along with two, qualitatively different equations of state. According to the proposed strategy, all equations were first used for the vapor-liquid coexistence curve and then extended to the metastable region and tested against computer simulation data. Despite the fact that no specificities of supersaturated steam have been accounted for, all the considered methods provide results with deviations from (pseudo)experimental data up to about 5% over the entire range of thermodynamic conditions except the critical region. It turns out that the perturbed virial expansion with a suitably chosen reference system outperforms other methods, including equations of state originally developed for liquid water.

Critical phase behavior in multi-component fluid mixtures: Complete scaling analysis.

We analyze the critical gas-liquid phase behavior of arbitrary fluid mixtures in their coexistence region. We focus on the setting relevant for polydisperse colloids, where the overall density and composition of the system are being controlled, in addition to temperature. Our analysis uses the complete scaling formalism and thus includes pressure mixing effects in the mapping from thermodynamic fields to the effective fields of 3D Ising criticality. Because of fractionation, where mixture components are distributed unevenly across coexisting phases, the critical behavior is remarkably rich. We give scaling laws for a number of important loci in the phase diagram. These include the cloud and shadow curves, which characterise the onset of phase coexistence, a more general set of curves defined by fixing the fractional volumes of the coexisting phases to arbitrary values, and conventional coexistence curves of the densities of coexisting phases for fixed overall density. We identify suitable observables (distinct from the Yang-Yang anomalies discussed in the literature) for detecting pressure mixing effects. Our analytical predictions are checked against numerics using a set of mapping parameters fitted to simulation data for a polydisperse Lennard-Jones fluid, allowing us to highlight crossovers where pressure mixing becomes relevant close to the critical point.

Purification of a Bacteriocin-Like Inhibitory Substance Derived from Pediococcus acidilactici Kp10 by an Aqueous Micellar Two-Phase System.

Aqueous micellar two-phase system (AMTPS) is an extractive technique of biomolecule, where it is based on the differential partitioning behavior of biomolecule between a micelle-rich and a micelle-poor phase. In this study, an AMTPS composed of a nonionic surfactant, Triton X-100 (TX-100) was used for purifying a bacteriocin-like inhibitory substance (BLIS) derived from Pediococcus acidilactici Kp10. The influences of the surfactant concentration and the effect of additives on the partitioning behavior and activity yield of the BLIS were investigated. The obtained coexistence curves showed that the mixtures of solutions composed of different surfactant concentrations (5-30% w/w) and 50% w/w crude load were able to separate into two phases at temperatures of above 60 °C. The optimum conditions for BLIS partitioning using the TX-100-based AMTPS were: TX-100 concentration of 22.5% w/w, CFCS load of 50% w/w, incubation time of 30 min at 75 °C, and back-extraction using acetone precipitation. This optimal partitioning resulted in an activity yield of 64.3% and a purification factor of 5.8. Moreover, the addition of several additives, such as sorbitol, KCl, dioctyl sulfosuccinate sodium salt, and Coomassie® Brilliant Blue, demonstrated no improvement in the BLIS separation, except for Amberlite® resin XAD-4, where the activity yield was improved to 70.3% but the purification factor was reduced to 2.3. Results from this study have demonstrated the potential and applicability of TX-100-based AMTPS as a primary recovery method for the BLIS from a complex fermentation broth of P. acidilactici Kp10. © 2018 American Institute of Chemical Engineers Biotechnol. Prog., 35: e2719, 2019.

Three-phase equilibrium curve shift for methane hydrate in oceanic conditions calculated from Molecular Dynamics simulations

This paper presents an analysis using molecular simulation of the phase equilibrium of methane hydrates under the oceanic crust conditions. Although there is a number of works dealing with computational simulation of gas hydrates, obtaining their phase diagrams using different techniques, simulations under realistic conditions and environments are not available yet. As the first step in this direction, we have added Na+ and Cl− ions to the water liquid phase in a model of the hydrate (S)–water (L)–methane (G) three-phase system, with the aim to simulate the system behaviour using classical Molecular Dynamics with the direct coexistence technique. The results are in good agreement with other simulations and experimental measurements reported in literature. Coexistence curves are well defined including a proper shift between water with and without NaCl. Additionally, water solvation of ions was found to interfere with crystallization process, slowing it down and preventing the incorporation of all liquid molecules to the hydrate phase.

Propanol – Sugar aqueous biphasic systems as a suitable platform for biomolecules extraction

Aiming at designing efficient extraction processes, this work proposes the novel aqueous biphasic systems (ABS) composed of sugars and alcohols. The complete liquid-liquid phase diagrams (binodal curves and tie-lines) for several ternary systems of {water + 1-propanol / 2-propanol + sugar (mono- and di-saccharides, and their polyols)} were determined, for the first time. The main factors which affect the phase separation ability of these systems, such as temperature, structure and stereochemistry of sugars, and the alcohol type were discussed. In all the studied ABS, the top phase is alcohol-rich with lower water content, while the bottom phase is sugar-rich with higher water content. The partitioning behavior of two alkaloids (caffeine and codeine) and a flavoring antioxidant (vanillin) in the produced ABS was evaluated. In all the partitioning experiments, caffeine and vanillin have a preferable tendency to concentrate in the more hydrophobic alcohol-rich phase, however, codeine preferentially migrate to the more hydrophilic sugar-rich phase. The selectivity index of the alcohol-sugar ABS to separate compounds of the same family (caffeine and codeine) was calculated and found to be higher than 25 at optimum conditions. In general, the more soluting-out ability of sugars, the more difference in the water content of the coexisting phases, and the longer tie-line length lead to the better extraction performance of the propanol-sugar ABS. Heating has a favorable effect on the preferential partitioning of caffeine and codeine, but it is unfavorable for extraction of vanillin. From the results gathered, the novel ABS produced in this work provide efficient and money-saving extraction platforms, and can selectively separate similar biomolecules.