Empirical Phase Diagram Research Articles

Interpretable Machine Learning Models for Phase Prediction in Polymerization-Induced Self-Assembly.

While polymerization-induced self-assembly (PISA) has become a preferred synthetic route toward amphiphilic block copolymer self-assemblies, predicting their phase behavior from experimental design is extremely challenging, requiring time and work-intensive creation of empirical phase diagrams whenever self-assemblies of novel monomer pairs are sought for specific applications. To alleviate this burden, we develop here the first framework for a data-driven methodology for the probabilistic modeling of PISA morphologies based on a selection and suitable adaption of statistical machine learning methods. As the complexity of PISA precludes generating large volumes of training data with in silico simulations, we focus on interpretable low variance methods that can be interrogated for conformity with chemical intuition and that promise to work well with only 592 training data points which we curated from the PISA literature. We found that among the evaluated linear models, generalized additive models, and rule and tree ensembles, all but the linear models show a decent interpolation performance with around 0.2 estimated error rate and 1 bit expected cross entropy loss (surprisal) when predicting the mixture of morphologies formed from monomer pairs already encountered in the training data. When considering extrapolation to new monomer combinations, the model performance is weaker but the best model (random forest) still achieves highly nontrivial prediction performance (0.27 error rate, 1.6 bit surprisal), which renders it a good candidate to support the creation of empirical phase diagrams for new monomers and conditions. Indeed, we find in three case studies that, when used to actively learn phase diagrams, the model is able to select a smart set of experiments that lead to satisfactory phase diagrams after observing only relatively few data points (5-16) for the targeted conditions. The data set as well as all model training and evaluation codes are publicly available through the GitHub repository of the last author.

Effect of Al/Ni ratio on phase, microstructure and mechanical properties of the AlxCrFeMnNi2-x high entropy alloys

In this work, the as-cast AlxCrFeMnNi2-x (x = 0.3, 0.7, 1.0) high-entropy alloys (HEAs) were designed via the empirical criterion and equilibrium phase diagrams, and the effect of Al/Ni ratio on the microstructure and mechanical properties was investigated and discussed. An increase of Al/Ni ratio promotes the matrix phase transition from FCC to BCC phase, this mainly is attributed to the decrease of VEC. No matter it is in FCC- or BCC-dominant HEAs, the ordered B2 phase (rich-Al and Ni) always appears together with the BCC phase, but the morphology of which translates from spherical-shape to cubical-shape, and to the weave-like microstructure due to the increase of the lattice misfit constant ε. The alloy (x = 0.3) is composed of FCC matrix phase with a small amount of BCC and spherical B2 precipitates, which exhibits favorable total ductility (∼80 %), but low yield strength (∼304 MPa); An increase of Al/Ni ratio results in the increase of the yield strength, but the decrease of the ductility. The alloy (x = 0.7) consists of the BCC matrix phase with trimodal (r-p, c-p, and s-p) distribution of B2 precipitates, which exhibits the optimal mechanical properties with the yield strength (∼1158 MPa) and a relatively high total ductility (∼50 %). Further increase of Al/Ni ratio does not influence the strength considerably, but decreases the total ductility sharply. The alloy (x = 1.0) presents a yield strength (∼1119 MPa) close to that of the alloy (x = 0.7), while the ductility is very low (∼10 %). It is mainly attributed to the spinodal weave-like microstructure, which is prone to the initiation and propagation of cracks.

Shape-Mediated Oriented Assembly of Concave Nanoparticles under Cylindrical Confinement.

This contribution describes the self-assembly of colloidal nanodumbbells (NDs) with tunable shapes within cylindrical channels. We present that the intrinsic concave geometry of NDs endows them with peculiar packing and interlocking behaviors, which, in conjunction with the adjustable confinement constraint, leads to a variety of superstructures such as tilted-ladder chains and crossed-chain superlattices. A mechanistic investigation, corroborated by geometric calculations, reveals that the phase behavior of NDs under strong confinement can be rationalized by the entropy-driven maximization of the packing efficiency. Based on the experimental results, an empirical phase diagram is generated, which could provide general guidance in the design of intended superstructures from NDs. This study provides essential insight into how the interplay between the particle shape and confinement conditions can be exploited to direct the orientationally ordered assembly of concave nanoparticles into unusual superlattices.

Comprehensive Screening of Halogen-Containing Oxide Double Perovskites A2BXO6 (X = Cl, Br, and I) for Photovoltaic Applications.

The new halogen-containing oxide double perovskites A2BXO6 (X = Cl, Br, and I) have attracted much attention because of their superb electronic properties in halide double perovskites and their high stability in oxide double perovskites. Herein, 408 A2BXO6 double perovskites have been systematically screened by high-throughput computation. Refer to the empirical structural factors phase diagram (t-u), which uses large-scale first-principles calculations. Fourteen stable perovskites are finally confirmed; moreover, 11 of them have never been reported before. Our results show that Ba2AgIO6 and Sr2AgIO6 are the most preferable candidates for photovoltaic applications, of which Sr2AgIO6 has balanceable electron and hole effective masses, a quasi-direct band gap, and strong optical absorption. Importantly, Sr2AgIO6 was successfully synthesized by the solution method. Our work enriches the family of double perovskites, and the tentative experimental evidence undoubtedly hints at their great potential applications in the near future.

PH-Dependent Phase Behavior and Stability of Cationic Lipid–mRNA Nanoparticles

Lipid nanoparticles (LNPs) containing mRNA can deliver genetic material to cells for use as vaccines or protein replacement therapies. We characterized the effect of solution pH on cationic LNPs containing green fluorescent protein (EGFP) mRNA and their transfection efficiency. We compared the structural and colloidal properties of mRNA LNPs with LNPs not containing mRNA and mRNA free in solution. We used a combination of biophysical technique to build a picture of the structure of the lipids and mRNA across pH and temperature in the form of an empirical phase diagram (EPD). A combination of Fourier-transform infrared (FTIR) spectroscopy and differential scanning calorimetry was used to investigate lipid phase behavior.The mRNA–LNPs transition from an inverse hexagonal phase at pH values below the pKa of the cationic lipid to a lamellar phase above the pKa. At higher temperatures the mRNA–LNPs also transitioned from an inverse hexagonal phase to a lamellar phase indicating the inverse hexagonal phase is more thermodynamically favorable. Based on circular dichroism, the mRNA within the LNP has more A form structure at pH values below the lipid pKa than above it.Optical density, zeta potential and dynamic light scattering measurements were used to probe the colloidal stability of the mRNA–LNPs. The particles were larger and more prone to aggregation below the pKa. A stability study was performed to relate the biophysical characteristics to the storage of the particles in solution at 4 and 25 °C. mRNA–LNPs had the highest transfection efficiency and stability at pH values below the pKa. However, there was a trade-off between the stability and aggregation propensity since at very low pH the particles were most prone to aggregation. We performed kinetic experiments to show that the time scale of the pH-dependent phase behavior is slow (6 hour transition) and the transition from lamellar to inverse hexagonal phases is irreversible. This suggests that the lamellar phase is less stable and kinetically trapped. Our findings deepen our structural understanding of mRNA–LNPs and will aid the development of related formulations.

Two‐Dimensional (2D) or Quasi‐2D Superstructures from DNA‐Coated Colloidal Particles

AbstractThis contribution describes the synthesis of colloidal di‐patch particles functionalized with DNA on the patches and their assembly into colloidal superstructures via cooperative depletion and DNA‐mediated interactions. The assembly into flower‐like Kagome, brick‐wall like monolayer, orthogonal packed single or double layers, wrinkled monolayer, and colloidal honeycomb superstructures can be controlled by tuning the particles’ patch sizes and assembly conditions. Based on these experimental results, we generate an empirical phase diagram. The principles revealed by the phase diagram provide guidance in the design of two‐dimensional (2D) materials with desired superstructures. Our strategy might be translatable to the assembly of three‐dimensional (3D) colloidal structures.

Crumples as a Generic Stress-Focusing Instability in Confined Sheets

Thin elastic solids are easily deformed into a myriad of three-dimensional shapes, which may contain sharp localized structures as in a crumpled candy wrapper, or have smooth and diffuse features like the undulating edge of a flower. Anticipating and controlling these morphologies is crucial to a variety of applications involving textiles, synthetic skins, and inflatable structures. Here we show that a "wrinkle-to-crumple" transition, previously observed in specific settings, is a ubiquitous response for confined sheets. This unified picture is borne out of a suite of model experiments on polymer films confined to liquid interfaces with spherical, hyperbolic, and cylindrical geometries, which are complemented by experiments on macroscopic membranes inflated with gas. We use measurements across this wide range of geometries, boundary conditions, and lengthscales to quantify several robust morphological features of the crumpled phase, and we build an empirical phase diagram for crumple formation that disentangles the competing effects of curvature and compression. Our results suggest that crumples are a generic microstructure that emerge at large curvatures due to a competition of elastic and substrate energies.

Redesigning food protein formulations with empirical phase diagrams: A case study on glycerol-poor and glycerol-free formulations

Redesigning existing food protein formulations is necessary in situations where food authorities propose dose adjustments or removal of currently employed additives. Redesigning formulations involves evaluating substitute additives to obtain similar long-term physical stability as the original formulation. Such formulation screening experiments benefit from comprehensive data visualization, understanding the effects of substitute additives on long-term physical stability, and identification of short-term optimization targets. This work employs empirical phase diagrams to reach these benefits by combining multidimensional long-term protein physical stability data with short-term empirical protein properties. A case study was performed where multidimensional protein phase diagrams (1152 formulations) allowed for identification of stabilizing effects as a result of pH, methionine, sugars, salt, and minimized glycerol content. Corresponding empirical protein property diagrams (144 formulations) resulted in the identification of normalized surface tension as a short-term empirical protein property to reach long-term physical stability presumably similar to the original product, namely via preferential hydration. Additionally, changes in pH and salt were identified as environmental optimization targets to reach stability via repulsive electrostatic forces. This case study shows the applicability of the empirical phase diagram method to rationally perform formulation redesign screenings, while simultaneously expanding knowledge on protein long-term physical stability.

Correlating multidimensional short-term empirical protein properties to long-term protein physical stability data via empirical phase diagrams

Identification of long-term stable biopharmaceutical formulations is essential for biopharmaceutical product development. Reduction of the number of long-term storage experiments and a well-defined formulation search space requires knowledge-based formulation screenings and a detailed protein phase behavior understanding. To achieve this, short-term analytical techniques can serve as predictors for long-term protein phase behavior. Protein phase behavior studies that investigate this concept commonly display shortcomings such as limited and small datasets, sample adjustments, or simplistic data analysis. To overcome these shortcomings, 150 unique lysozyme solutions were analyzed using six different short-term analytical techniques. Lysozyme’s structural properties, conformational stability, colloidal stability, surface charge, and surface hydrophobicity were obtained directly after formulation preparation. Employing the empirical phase diagram method, this short-term data was correlated to long-term physical stability data obtained during 40 days of storage. Short-term protein properties showed partial correlation to long-term phase behavior. Structural differences, changing surface properties, colloidal stability, and conformation stability as a function of formulation conditions were observed. This study contributes to long-term protein phase behavior research by presenting a systematic, data-dependent, and multidimensional data evaluation workflow to create a comprehensive overview of short-term protein analytics in relation to long-term protein phase behavior.

Application of Empirical Phase Diagrams for Multidimensional Data Visualization of High-Throughput Microbatch Crystallization Experiments

Protein phase diagrams are a tool to investigate the cause and consequence of solution conditions on protein phase behavior. The effects are scored according to aggregation morphologies such as crystals or amorphous precipitates. Solution conditions affect morphologic features, such as crystal size, as well as kinetic features, such as crystal growth time. Commonly used data visualization techniques include individual line graphs or phase diagrams based on symbols. These techniques have limitations in terms of handling large data sets, comprehensiveness or completeness. To eliminate these limitations, morphologic and kinetic features obtained from crystallization images generated with high throughput microbatch experiments have been visualized with radar charts in combination with the empirical phase diagram method. Morphologic features (crystal size, shape, and number, as well as precipitate size) and kinetic features (crystal and precipitate onset and growth time) are extracted for 768 solutions with varying chicken egg white lysozyme concentration, salt type, ionic strength, and pH. Image-based aggregation morphology and kinetic features were compiled into a single and easily interpretable figure, thereby showing that the empirical phase diagram method can support high-throughput crystallization experiments in its data amount as well as its data complexity.

Bilateral Effects of Excipients on Protein Stability: Preferential Interaction Type of Excipient and Surface Aromatic Hydrophobicity of Protein.

Understanding the mechanism of protein-excipient interaction and illuminating the influencing factors on protein stability are key steps in the rational design of protein formulations. The objective of this study was to assess effects of preferential interaction type of excipient and surface aromatic hydrophobicity of protein on protein solution stability. The preferential interaction between excipient and aromatic hydrophobic area of protein was investigated by solubility and fluorescence studies of amino acid derivatives in excipient solutions. We examined conformational, colloidal and mechanical stabilities of model proteins with different surface aromatic hydrophobicities, including bovine serum albumin (BSA) and ovalbumin (OVA), and then stability data were visualized by three-index empirical phase diagram. The result showed that preferentially excluded excipients (trehalose, sucrose and sorbitol) protected protein conformation against damage, but they could accelerate mechanical stress-induced aggregation. Preferentially bound excipients (propanediol and arginine) suppressed BSA aggregation, but arginine failed to inhibit OVA aggregation, which might be attributed to the disparate conformational perturbing effects of arginine on aromatic hydrophobic regions of BSA and OVA. These findings provided strong evidence that excipient possessed bilateral effects, and its application should be determined on different preferential interaction behaviors of excipients with protein, especially with the aromatic hydrophobic region.

Molecular Beam Epitaxy of lithium niobium oxide multifunctional materials

The role of stoichiometry and growth temperature in the preferential nucleation of material phases in the Li-Nb-O family are explored yielding an empirical growth phase diagram. It is shown that while single parameter variation often produces multi-phase films, combining substrate temperature control with the previously published lithium flux limited growth allows the repeatable growth of high quality single crystalline films of many different oxide phases. Higher temperatures (800–1050°C) than normally used in MBE were necessary to achieve high quality materials. At these temperatures the desorption of surface species is shown to play an important role in film composition. Using this method single phase films of NbO, NbO2, LiNbO2, Li3NbO4, LiNbO3, and LiNb3O8 have been achieved in the same growth system, all on c-plane sapphire. Finally, the future of these films in functional oxide heterostructures is briefly discussed.

Preformulation Characterization, Stabilization, and Formulation Design for the Acrylodan-Labeled Glucose-Binding Protein SM4-AC

This study describes the physicochemical characterization, stabilization, and formulation design of SM4-AC, an acrylodan-labeled glucose/galactose-binding protein for use in a continuous glucose monitoring device. The physical stability profile of SM4-AC as a function of pH and temperature was monitored using a combination of biophysical techniques and the resulting physical stability profile was visualized using an empirical phase diagram. Forced degradation chemical stability studies (Asn deamidation, Met oxidation) of SM4-AC were performed using a combination of capillary isoelectric focusing, peptide mapping, and reversed-phase HPLC. Differential scanning fluorimetry was then employed to screen various pharmaceutical excipients for their ability to physically stabilize SM4-AC. An optimized formulation of 20% sucrose and 2.5 mM calcium chloride in 10 mM MES buffer, 150 mM NaCl at pH 6.0 increased the conformational stability of SM4-AC by 15°C. Accelerated and real-time stability studies were setup to compare the SM4-AC protein’s physicochemical stability and glucose-binding activity in 2 formulations for up to 12 months. SM4-AC in an optimized formulation (vs the original formulation) showed improved physical stability, and similar chemical stability and glucose binding activity profiles during storage up to 52 weeks at various temperatures.

Correlating the Impact of Well-Defined Oligosaccharide Structures on Physical Stability Profiles of IgG1-Fc Glycoforms

As part of a series of articles in this special issue describing 4 well-defined IgG1-Fc glycoforms as a model system for biosimilarity analysis (high mannose-Fc, Man5-Fc, GlcNAc-Fc and N297Q-Fc aglycosylated), the focus of this work is comparisons of their physical properties. A trend of decreasing apparent solubility (thermodynamic activity) by polyethylene glycol precipitation (pH 4.5, 6.0) and lower conformational stability by differential scanning calorimetry (pH 4.5) was observed with reducing size of the N297-linked oligosaccharide structures. Using multiple high-throughput biophysical techniques, the physical stability of the Fc glycoproteins was then measured in 2 formulations (NaCl and sucrose) across a wide range of temperatures (10°C-90°C) and pH (4.0-7.5) conditions. The data sets were used to construct 3-index empirical phase diagrams and radar charts to visualize the regions of protein structural stability. Each glycoform showed improved stability in the sucrose (vs. salt) formulation. The HM-Fc and Man5-Fc displayed the highest relative stability, followed by GlcNAc-Fc, with N297Q-Fc being the least stable. Thus, the overall physical stability profiles of the 4 IgG1-Fc glycoforms also show a correlation with oligosaccharide structure. These data sets are used to develop a mathematical model for biosimilarity analysis (as described in a companion article by Kim et al. in this issue).

Biophysical Characterization of the Type III Secretion System Translocator Proteins and the Translocator Proteins Attached to Bacterium-Like Particles

Diarrhea caused by Shigella, Salmonella, and Yersinia is an important public health problem, but development of safe and effective vaccines against such diseases is challenging. A new antigen delivery platform called bacterium-like particles (BLPs) was explored as a means for delivering protective antigens from the type III secretion systems (T3SS) of these pathogens. BLPs are peptidoglycan skeletons derived from Lactococcus lactis that are safe for newborns and can carry multiple antigens. Hydrophobic T3SS translocator proteins were fused to a peptidoglycan anchor (PA) for BLP attachment. The proteins and protein-BLP complexes associated with BLPs were characterized and the resulting data used to create three-index empirical phase diagrams (EPDs). On the basis of these EPDs, IpaB (Shigella) and SipB (Salmonella) behave distinctly from YopB (Yersinia) under different environmental stresses. Adding the PA domain appears to enhance the stability of both the PA and translocator proteins, which was confirmed using differential scanning calorimetry, and although the particles dominated the spectroscopic signals in the protein-loaded BLPs, structural changes in the proteins were still detected. The protein-BLPs were most stable near neutral pH, but these proteins' hydrophobicity made them sensitive to environmental stresses.

Biophysical Characterization of the Type III Secretion Tip Proteins and the Tip Proteins Attached to Bacterium-Like Particles

Bacterium-like particles (BLPs), derived from Lactococcus lactis, offer a self-adjuvanting delivery vehicle for subunit protein vaccines. Proteins can be specifically loaded onto the BLPs via a peptidoglycan anchoring (PA) domain. In this study, the tip proteins IpaD, SipD, and LcrV belonging to type III secretion systems of Shigella flexneri, Salmonella enterica, and Yersinia enterocolitica, respectively, were fused to the PA and loaded onto the BLPs. Herein, we biophysically characterized these nine samples and condensed the spectroscopic results into three-index empirical phase diagrams (EPDs). The EPDs show distinctions between the IpaD/SipD and LcrV subfamilies of tip proteins, based on their physical stability, even upon addition of the PA. Upon attachment to the BLPs, the BLPs become defining moiety in the spectroscopic measurements, leaving the tip proteins to have a subtle yet modulating effect on the structural integrity of the tip proteins-BLPs binding. In summary, this work provides a comprehensive view of physical stability of the tip proteins and tip protein-BLPs and serves as a baseline for screening of excipients to increase the stability of the tip protein-BLPs for future vaccine formulation.

Characterization of an Oncolytic Herpes Simplex Virus Drug Candidate

The structural integrity and conformational stability of a genetically modified live, oncolytic herpes simplex virus (o-HSV) were investigated across a wide pH (5.5-8.0) and temperature (10°C-87.5°C) range. A combination of circular dichroism, intrinsic and extrinsic fluorescence, and static light scattering results was visualized using an empirical phase diagram approach to provide a global assessment of physical stability. Distinct phases were identified including the native state of the virus, an intermediate phase that could represent gradual swelling and/or shedding of the viral envelope, and a highly disrupted, aggregated phase. The nature of these altered forms of the virus was further evaluated by transmission electron microscopy and viral plaque assays. The effect of freeze-thaw (F/T) stress on o-HSV was also examined. After one F/T cycle, a loss of infectious virus titers was observed. In addition, the monomeric virus particle concentration decreased during F/T stress, whereas there was a concurrent increase in larger particles (2-10 μm). The comprehensive biophysical characterization of viral stability conducted in this study identified major degradation events leading to loss of infectivity of o-HSV and represents an important step toward stabilization of the virus against thermal and F/T stresses.

Effect of polyethylene glycol conjugation on conformational and colloidal stability of a monoclonal antibody antigen-binding fragment (Fab').

We have investigated the effects of site specific "hinge" polyethylene glycol conjugation (PEGylation) on thermal, pH, and colloidal stability of a monoclonal antibody antigen-binding fragment (Fab') using a variety of biophysical techniques. The results obtained by circular dichroism (CD), ultraviolet (UV) absorbance, and fluorescence spectroscopy suggested that the physical stability of the Fab' is maximized at pH 6-7 with no apparent differences due to PEGylation. Temperature-induced aggregation experiments revealed that PEGylation was able to increase the transition temperature, as well as prevent the formation of visible and subvisible aggregates. Statistical comparison of the three-index empirical phase diagram (EPD) revealed significant differences in thermal and pH stability signatures between Fab' and PEG-Fab'. Upon mechanical stress, micro-flow imaging (MFI) and measurement of the optical density at 360 nm showed that the PEG-Fab' had significantly higher resistance to surface-induced aggregation compared to the Fab'. Analysis of the interaction parameter, kD, indicated repulsive intermolecular forces for PEG-Fab' and attractive forces for Fab'. In conclusion, PEGylation appears to protect Fab' against thermal and mechanical stress-induced aggregation, likely due to a steric hindrance mechanism.

Impact of detergent on biophysical properties and immune response of the IpaDB fusion protein, a candidate subunit vaccine against Shigella species.

Shigella spp. are causative agents of bacillary dysentery, a human illness with high global morbidity levels, particularly among elderly and infant populations. Shigella infects via the fecal-oral route, and its virulence is dependent upon a type III secretion system (T3SS). Two components of the exposed needle tip complex of the Shigella T3SS, invasion plasmid antigen D (IpaD) and IpaB, have been identified as broadly protective antigens in the mouse lethal pneumonia model. A recombinant fusion protein (DB fusion) was created by joining the coding sequences of IpaD and IpaB. The DB fusion is coexpressed with IpaB's cognate chaperone, IpgC, for proper recombinant expression. The chaperone can then be removed by using the mild detergents octyl oligooxyethelene (OPOE) or N,N-dimethyldodecylamine N-oxide (LDAO). The DB fusion in OPOE or LDAO was used for biophysical characterization and subsequent construction of an empirical phase diagram (EPD). The EPD showed that the DB fusion in OPOE is most stable at neutral pH below 55 °C. In contrast, the DB fusion in LDAO exhibited remarkable thermal plasticity, since this detergent prevents the loss of secondary and tertiary structures after thermal unfolding at 90 °C, as well as preventing thermally induced aggregation. Moreover, the DB fusion in LDAO induced higher interleukin-17 secretion and provided a higher protective efficacy in a mouse challenge model than did the DB fusion in OPOE. These data indicate that LDAO might introduce plasticity to the protein, promoting thermal resilience and enhanced protective efficacy, which may be important in its use as a subunit vaccine.

The effect of fiber truncations on the stability of adenovirus type 5.

While fiberless adenovirus has the potential for use as a vaccine or gene delivery vector, some groups have observed instability issues associated with the modified virus. To investigate the effect of fiber modification on adenovirus stability, we produced mutant adenovirus particles that contained the tail and a portion of the shaft domain without the knob. The shaft domain was either completely removed (i.e., fiberless) or truncated to 7-, 14-, or 21-repeats. The mutants were evaluated by biophysical characterization techniques to determine their relative stabilities based on temperature-induced changes to the secondary, tertiary, and quaternary structures of the virus and its constituent proteins. Data acquired using circular dichroism, intrinsic/extrinsic fluorescence, and static/dynamic light scattering were compiled into a comprehensive empirical phase diagram, which showed that native adenovirus was the most stable followed by fiberless adenovirus and then the mutants with truncated fiber protein. In summary, the individual biophysical measurements and the empirical phase diagram showed that providing several repeats of shaft protein negatively impacted the structural stability of the virus more so than completely removing the fiber protein.