Protein crystallization induced by polyethylene glycol: A model study using apoferritin

Freezing-mediated formation of supraproteins using depletion forces

Hypothesis Long-acting formulations such as microparticles, injectable depots and implantable devices can realize spatiotemporally controlled delivery of protein drugs to extend their therapeutic in vivo half-lives. To efficiently encapsulate the protein drugs into such drug delivery systems, (sub)micron-sized protein particles are needed. The formation of micronized supraproteins can be induced through the synergistic combination of attractive depletion forces and freezing. The size of the supraproteins can be fine-tuned from submicron to several microns by adjusting the ice crystallization rate through the freeze-quench depth, which is set by the target temperature. Methods Supraprotein micron structures were prepared from protein solutions under various conditions in the presence and absence of nonadsorbing polyethylene glycol. Scanning electron microscopy and dynamic light scattering were employed to determine the sizes of the supraproteins and real-time total internal reflection fluorescent microscopy was used to follow the supraprotein formation during freezing. The protein secondary structure was measured before and after micronization by circular dichroism. A phase diagram of a protein-polyethylene glycol mixture was theoretically predicted to investigate whether the depletion interaction can elucidate the phase behavior. Findings Micronized protein supraparticles could be prepared in a controlled manner by rapid freeze-drying of aqueous mixtures of bovine serum albumin, horseradish peroxidase and lysozyme mixed with polyethylene glycol. Upon freezing, the temperature quench initiates a phase separation process which is reminiscent of spinodal decomposition. This demixing is subsequently arrested during droplet phase separation to form protein-rich microstructures. The final size of the generated protein microparticles is determined by a competition between phase separation and cooling rate, which can be controlled by target temperature. The experimental phase diagram of the aqueous protein-polyethylene glycol dispersion aligns with predictions from depletion theory for charged colloids and nonadsorbing polymers.

Assembling Inorganic Nanocrystal Gels

Inorganic nanocrystal gels retain distinct properties of individual nanocrystals while offering tunable, network-structure-dependent characteristics. We review different mechanisms for assembling gels from colloidal nanocrystals including (1) controlled destabilization, (2) direct bridging, (3) depletion, as well as linking mediated by (4) coordination bonding or (5) dynamic covalent bonding, and we highlight how each impacts gel properties. These approaches use nanocrystal surface chemistry or the addition of small molecules to mediate inter-nanocrystal attractions. Each method offers advantages in terms of gel stability, reversibility, or tunability and presents new opportunities for the design of reconfigurable materials and fueled assemblies.

Revisit PEG-Induced Precipitation Assay for Protein Solubility Assessment of Monoclonal Antibody Formulations

PURPOSE

Protein solubility is an important attribute of pharmaceutical monoclonal antibody (MAb) formulations, particularly at high MAb concentrations. PEG-induced protein precipitation has been routinely used to assess protein solubility. To provide insights for better understanding and implementation of PEG-induced protein precipitation assay, this work compares different solubility measures and examines their relevance to loss of protein solubility in concentrated formulations.

METHODS

Solubility of a MAb in 15 formulations was evaluated using PEG-induced precipitation assay. Three apparent protein solubility measures, the middle-point and onset PEG concentrations (c_mid and c_onset) as well as the binding free energy (μ_B), were obtained from the PEG-induced protein precipitation assay and compared to the DLS protein interaction parameter (k_D). Visual inspection of loss of protein solubility in concentrated formulations during storage was used to further examine the discrepancy of protein solubility ranking by these measures.

RESULTS

PEG-induced precipitation assay predicted overall protein solubility ranking similar to that by DLS k_D. However, for three formulations with ionic excipients NaCl, Arg·Cl, and Arg·Glu·Cl, PEG-induced precipitation assay yielded more accurate predictions compared to DLS k_D measurements. Furthermore, μ_B showed superior ability in distinguishing protein solubility for these formulations.

CONCLUSIONS

This study demonstrated good correlations between the protein solubility measures obtained from PEG-induced precipitation experiments and DLS k_D measurement. It also provides one example in which protein solubility ranking by binding free energy is more accurate than the other measures. The results support the theoretical proposition that μ_B has a potential to serve as standard protein solubility measure.

Protein-polymer mixtures in the colloid limit: Aggregation, sedimentation, and crystallization

While proteins have been treated as particles with a spherically symmetric interaction, of course in reality, the situation is rather more complex. A simple step toward higher complexity is to treat the proteins as non-spherical particles and that is the approach we pursue here. We investigate the phase behavior of the enhanced green fluorescent protein (eGFP) under the addition of a non-adsorbing polymer, polyethylene glycol. From small angle x-ray scattering, we infer that the eGFP undergoes dimerization and we treat the dimers as spherocylinders with aspect ratio L/D - 1 = 1.05. Despite the complex nature of the proteins, we find that the phase behavior is similar to that of hard spherocylinders with an ideal polymer depletant, exhibiting aggregation and, in a small region of the phase diagram, crystallization. By comparing our measurements of the onset of aggregation with predictions for hard colloids and ideal polymers [S. V. Savenko and M. Dijkstra, J. Chem. Phys. 124, 234902 (2006) and Lo Verso et al., Phys. Rev. E 73, 061407 (2006)], we find good agreement, which suggests that the behavior of the eGFP is consistent with that of hard spherocylinders and ideal polymers.

Colloidal Nanocrystal Gels from Thermodynamic Principles

Gels assembled from solvent-dispersed nanocrystals are of interest for functional materials because they promise the opportunity to retain distinctive properties of individual nanocrystals combined with tunable, structure-dependent collective behavior. By incorporating stimuli-responsive components, these materials could also be dynamically reconfigured between structurally distinct states. However, nanocrystal gels have so far been formed mostly through irreversible aggregation, which has limited the realization of these possibilities. Meanwhile, gelation strategies for larger colloidal microparticles have been developed using reversible physical or chemical interactions. These approaches have enabled the experimental navigation of theoretically predicted phase diagrams, helping to establish an understanding of how thermodynamic behavior can guide gel formation in these materials. However, the translation of these principles to the nanoscale poses both practical and fundamental challenges. The molecules guiding assembly can no longer be safely assumed to be vanishingly small compared to the particles nor large compared to the solvent.In this Account, we discuss recent progress toward the assembly of tunable nanocrystal gels using two strategies guided by equilibrium considerations: (1) reversible chemical bonding between functionalized nanocrystals and difunctional linker molecules and (2) nonspecific, polymer-induced depletion attractions. The effective nanocrystal attractions, mediated in both approaches by a secondary molecule, compete against stabilizing repulsions to promote reversible assembly. The structure and properties of the nanocrystal gels are controlled microscopically by the design of the secondary molecule and macroscopically by its concentration. This mode of control is compelling because it largely decouples nanocrystal synthesis and functionalization from the design of interactions that drive assembly. Statistical thermodynamic theory and computer simulation have been applied to simple models that describe the bonding motifs in these assembling systems, furnish predictions for conditions under which gelation is likely to occur, and suggest strategies for tuning and disassembling the gel networks. Insights from these models have guided experimental realizations of reversible gels with optical properties in the infrared range that are sensitive to the gel structure. This process avoids time-consuming and costly trial-and-error experimental investigations to accelerate the development of nanocrystal gel assemblies.These advances highlight the need to better understand interactions between nanocrystals, how interactions give rise to gel structure, and properties that emerge. Such an understanding could suggest new approaches for creating stimuli-responsive and dissipative assembled materials whose properties are tunable on demand through directed reconfiguration of the underlying gel microstructure. It may also make nanocrystal gels amenable to computationally guided design using inverse methods to rapidly optimize experimental parameters for targeted functionalities.

Methods for Obtaining Better Diffractive Protein Crystals: From Sample Evaluation to Space Crystallization

In this paper, we present a summary on how to obtain protein crystals from which better diffraction images can be produced. In particular, we describe, in detail, quality evaluation of the protein sample, the crystallization conditions and methods, flash-cooling protection of the crystal, and crystallization under a microgravity environment. Our approach to protein crystallization relies on a theoretical understanding of the mechanisms of crystal growth. They are useful not only for space experiments, but also for crystallization in the laboratory.

Enhancement of Macromolecular Ice Recrystallization Inhibition Activity by Exploiting Depletion Forces

Antifreeze (glyco) proteins (AF(G)Ps) are potent inhibitors of ice recrystallization and may have biotechnological applications. The most potent AF(G)Ps function at concentrations a thousand times lower than synthetic mimics such as poly(vinyl alcohol), PVA. Here, we demonstrate that PVA’s ice recrystallization activity can be rescued at concentrations where it does not normally function, by the addition of noninteracting polymeric depletants, due to PVA forming colloids in the concentrated saline environment present between ice crystals. These depletants shift the equilibrium toward ice binding and, hence, enable PVA to inhibit ice growth at lower concentrations. Using theory and experiments, we show this effect requires polymeric depletants, not small molecules, to enhance activity. These results increase our understanding of how to design new ice growth inhibitors, but also offer opportunities to enhance activity by exploiting depletion forces, without re-engineering ice-binding materials. It also shows that when screening for IRI activity that polymer contaminants in buffers may give rise to false positive results.

Defined PEG smears as an alternative approach to enhance the search for crystallization conditions and crystal-quality improvement in reduced screens

The quest for an optimal limited set of effective crystallization conditions remains a challenge in macromolecular crystallography, an issue that is complicated by the large number of chemicals which have been deemed to be suitable for promoting crystal growth. The lack of rational approaches towards the selection of successful chemical space and representative combinations has led to significant overlapping conditions, which are currently present in a multitude of commercially available crystallization screens. Here, an alternative approach to the sampling of widely used PEG precipitants is suggested through the use of PEG smears, which are mixtures of different PEGs with a requirement of either neutral or cooperatively positive effects of each component on crystal growth. Four newly defined smears were classified by molecular-weight groups and enabled the preservation of specific properties related to different polymer sizes. These smears not only allowed a wide coverage of properties of these polymers, but also reduced PEG variables, enabling greater sampling of other parameters such as buffers and additives. The efficiency of the smear-based screens was evaluated on more than 220 diverse recombinant human proteins, which overall revealed a good initial crystallization success rate of nearly 50%. In addition, in several cases successful crystallizations were only obtained using PEG smears, while various commercial screens failed to yield crystals. The defined smears therefore offer an alternative approach towards PEG sampling, which will benefit the design of crystallization screens sampling a wide chemical space of this key precipitant.

Polymer-mediated interactions and their effect on the coagulation-fragmentation of nano-colloids: a self-consistent field theory approach

This feature paper reviews our recent efforts to theoretically model the effect of polymer mediated interactions on the coagulation-fragmentation of nano-colloids in different settings encountered in practical systems. The polymer-mediated interactions among nanoparticles play a key role in many biological and technological processes such as red blood cell aggregation, protein crystallization, self-healing of polymer composites, filler reinforcement of rubbers used in tire technology, etc. By developing and making use of the novel potential theory, we investigate several important cases of these interactions acting between nanoparticles in diverse nano-polymer composites. As a demonstration of its practical applicability, we use the developed theory to investigate the effect of polymer mediated interactions on the coagulation-fragmentation of fillers and their kinetic stability in the presence of non-adsorbing and adsorbing polymers. In particular, we use our findings to develop a pragmatic way of evaluating the kinetic stability of nano-filler agglomerates critical for understanding the filler reinforcement of rubbers. Finally, we perform thorough comparison of the present theoretical findings with the available experimental data and simulations.

Influence of macromolecular precipitants on phase behavior of monoclonal antibodies

For the successful application of protein crystallization as a downstream step, a profound knowledge of protein phase behavior in solutions is needed. Therefore, a systematic screening was conducted to analyze the influence of macromolecular precipitants in the form of polyethylene glycol (PEG). First, the influence of molecular weight and concentration of PEG at different pH-values were investigated and analyzed in three-dimensional (3-D) phase diagrams to find appropriate conditions in terms of a fast kinetic and crystal size for downstream processing. In comparison to the use of salts as precipitant, PEG was more suitable to obtain compact 3-D crystals over a broad range of conditions, whereby the molecular weight of PEG is, besides the pH-value, the most important parameter. Second, osmotic second virial coefficients as parameters for protein interactions are experimentally determined with static light scattering to gain a deep insight view in the phase behavior on a molecular basis. The PEG-protein solutions were analyzed as a pseudo-one-compartment system. As the precipitant is also a macromolecule, the new approach of analyzing cross-interactions between the protein and the macromolecule PEG in form of the osmotic second cross-virial coefficient (B23 ) was applied. Both parameters help to understand the protein phase behavior. However, a predictive description of protein phase behavior for systems consisting of monoclonal antibodies and PEG as precipitant is not possible, as kinetic phenomena and concentration dependencies were not taken into account.

Method and apparatus for characterization of electric field-induced aggregation in pre-crystalline protein solutions

The article presents a method and an apparatus for the characterization of protein aggregation under an applied internal electric field. The method is based on a forward light scattering technique that is highly sensitive to aggregates in pre-crystalline protein solutions. Transparent conductive films are used as electrodes for a planar thin sample cell, which enables precise measurement of the forward light scattering at small angles through the electrodes. Evaluation of the protein aggregation under applied electric fields was demonstrated for a model lysozyme protein. In situ measurements of crystallizing lysozyme solutions under a low applied voltage revealed that the forward static light scattering profiles changed with time into power law profiles. This indicates the formation of lysozyme fractal clusters under applied electric fields in the pre-crystalline state. The method and the apparatus presented here can sensitively evaluate the promotion process in protein crystallization under an applied electric field.

Size selectivity in the confined ternary colloidal mixtures: the depletion in the competition

Based on classical density functional theory, we study the size selectivity for ternary colloidal mixtures in the presence of a Gauss barrier. The competition between the external potential and the depletion potential is also investigated. The effects of bulk fraction of each species, the size asymmetry, and the strength and width of the Gauss barrier on the selectivity of the big species are calculated and analyzed in detail. The results in different conditions of bulk fraction suggest that the larger the bulk fraction for the small species, the stronger selectivity of big particles. On the contrary, increase of bulk fraction for the big species leads to a reduction in selectivity. In addition, results under different conditions of size asymmetry suggest that the medium particles can also be selected by the Gauss barrier when they are sufficiently large in comparison to the small particles. We also demonstrate the effect of barrier geometry on the selectivity of the big species and the competition between the depletion and the external potential.

PEG-protein interaction induced contraction of NalD chains

In a recent attempt to crystallize a regulator of MexAB-OprM multi-drug efflux systems in Pseudomonas aeruginosa (NalD), we found that adding polyethylene glycol (PEG3350, Mw = 3,350 g/mol) into the protein solution increases the speed of NalD migration in gel electrophoresis, signaling a smaller hydrodynamic size. At first we conjectured that NalD was degraded unexpectedly by PEG; however, we found that there was no change in its molar mass by MALDI-TOF characterization. Moreover, we found that adding polyacrylic acid (PAA) into the solution mixture returned the NalD migration to its normal speed. Furthermore, our analytic ultracentrifugation and dynamic laser light scattering results directly reveal that NalD interacts with PEG so that individual NalD chains gradually shrink as more PEG chains are added in the range of 10-50 mg/mL. Size exclusion chromatography also confirms that the NalD chain shrinks in the presence of PEG. A combination of these results indicates that PEG3350 chains can complex with NalD to induce an intra-protein chain contraction, presumably via the formation of hydrogen bond between -C-O-C- on PEG and -COOH on NalD, resulting in a smaller hydrodynamic size (faster migration) and a higher apparent molar mass. Note that because the presence of PEG affects osmotic pressure, it is considered to be a precipitator of protein crystallization. Our current finding reveals that the interaction of PEG/protein may play a significant role in protein crystallization. The complexation potentially makes the protein chain segments less flexible, and consequently makes crystallization easier. Hopefully, our current results will stimulate further studies in this direction.

Analysis of conformational variation in macromolecular structural models

Experimental conditions or the presence of interacting components can lead to variations in the structural models of macromolecules. However, the role of these factors in conformational selection is often omitted by in silico methods to extract dynamic information from protein structural models. Structures of small peptides, considered building blocks for larger macromolecular structural models, can substantially differ in the context of a larger protein. This limitation is more evident in the case of modeling large multi-subunit macromolecular complexes using structures of the individual protein components. Here we report an analysis of variations in structural models of proteins with high sequence similarity. These models were analyzed for sequence features of the protein, the role of scaffolding segments including interacting proteins or affinity tags and the chemical components in the experimental conditions. Conformational features in these structural models could be rationalized by conformational selection events, perhaps induced by experimental conditions. This analysis was performed on a non-redundant dataset of protein structures from different SCOP classes. The sequence-conformation correlations that we note here suggest additional features that could be incorporated by in silico methods to extract dynamic information from protein structural models.

Effect of PEG end-group hydrophobicity on lysozyme interactions in solution characterized by light scattering

We compare protein-protein and protein-polymer osmotic virial coefficients measured by static light scattering for aqueous solutions of lysozyme with low-molecular-weight, hydroxy-terminated (hPEG) and methyl-terminated (mPEG) poly(ethylene glycol) at two solution conditions: pH 7.0 and 0.01 M ionic strength, and pH 6.2 and 0.8 M ionic strength. We find that adding PEG to aqueous lysozyme solutions makes a net repulsive contribution to lysozyme-lysozyme interactions, independent of ionic strength and PEG end-group hydrophobicity. PEG end-group hydrophobicity has a profound effect on the magnitude of this contribution, however, at low ionic strength where mPEG-lysozyme attractive interactions become significant. The enhanced attractions promote mPEG-lysozyme preferential interactions at the expense of lysozyme self-interactions, which leads to lysozyme-lysozyme interactions that are more repulsive in the presence of mPEG. These preferential interactions also lead to the preferential exclusion of diffusable ions locally around the protein, which results in a pronounced ionic strength dependence of mPEG-mediated lysozyme-lysozyme interactions.

Common crowding agents have only a small effect on protein-protein interactions

Studies of protein-protein interactions, carried out in polymer solutions, are designed to mimic the crowded environment inside living cells. It was shown that crowding enhances oligomerization and polymerization of macromolecules. Conversely, we have shown that crowding has only a small effect on the rate of association of protein complexes. Here, we investigated the equilibrium effects of crowding on protein heterodimerization of TEM1-beta-lactamase with beta-lactamase inhibitor protein (BLIP) and barnase with barstar. We also contrasted these with the effect of crowding on the weak binding pair CyPet-YPet. We measured the association and dissociation rates as well as the affinities and thermodynamic parameters of these interactions in polyethylene glycol and dextran solutions. For TEM1-BLIP and for barnase-barstar, only a minor reduction in association rate constants compared to that expected based on solution viscosity was found. Dissociation rate constants showed similar levels of reduction. Overall, this resulted in a binding affinity that is quite similar to that in aqueous solutions. On the other hand, for the CyPet-YPet pair, aggregation, and not enhanced dimerization, was detected in polyethylene glycol solutions. The results suggest that typical crowding agents have only a small effect on specific protein-protein dimerization reactions. Although crowding in the cell results from proteins and other macromolecules, one may still speculate that binding in vivo is not very different from that measured in dilute solutions.

Low energy methods of phase separation in colloidal dispersions and microemulsions

The majority of work on phase separation of colloidal systems has been concerned with the energy intensive approaches such as ultracentrifugation, solvent evaporation, changes of temperature and pressure etc. However, in modern nanotechnology it is desirable to minimize environmental impact in order to achieve separation and recovery of colloidal products. In this review recent research on phase separation methods, requiring relatively lower energy consumption are summarized. These include polymer-, solvent- and photo-induced approaches to phase separation.

Effects of ammonium sulfate and sodium chloride concentration on PEG/protein liquid-liquid phase separation

When added to protein solutions, poly(ethylene glycol) (PEG) creates an effective attraction between protein molecules due to depletion forces. This effect has been widely used to crystallize proteins, and PEG is among the most successful crystallization agents in current use. However, PEG is almost always used in combination with a salt at either low or relatively high concentrations. Here the effects of sodium chloride and ammonium sulfate concentration on PEG 8000/ovalbumin liquid-liquid (L-L) phase separation are investigated. At low salt the L-L phase separation occurs at decreasing protein concentration with increasing salt concentration, presumably due to repulsive electrostatic interactions between proteins. At high salt concentration, the behavior depends on the nature of the salt. Sodium chloride has little effect on the L-L phase separation, but ammonium sulfate decreases the protein concentration at which the L-L phase separation occurs. This trend is attributed to the effects of critical fluctuations on depletion forces. The implications of these results for designing solution conditions optimal for protein crystallization are discussed.

Analytical phase diagram for colloid-polymer mixtures

We present a theoretical analysis of the phase behavior of colloid-polymer mixtures which applies to all polymer/colloid size ratios q. It accounts for the crossover from a constant length scale R (radius of gyration) in the colloid limit (small q) to the concentration-dependent correlation length xi in the protein limit (q>1). We obtain predictions that fully agree with observations and simulations. In the protein limit the colloid concentrations eta along the binodals become independent of q and the polymer concentrations phi scale as q1/gamma, where gamma=0.77 is the scaling exponent in xi approximately phi(-gamma):phase diagrams plotted as phiq(-1/gamma) vs eta are then independent of q. The liquid window in the protein limit is narrow.

Intermolecular interaction of actin revealed by a dynamic light scattering technique

The intermolecular interaction force of actin was studied by a dynamic light scattering technique. The mutual diffusion coefficients (D) of monomeric actin were accurately determined in a G-buffer with a low concentration of KCl from 0 to 10 mM. The translational diffusion coefficient was obtained as D(0) = (87 +/- 3) x 10(-12) m(2).s(-1) at 25 degrees C and pH 7.4, which gives a hydrodynamic radius of monomeric actin of r(H) = 2.8 +/- 0.1 nm. The Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, assuming electrostatic and van der Waals potentials, failed to describe the change in interaction parameter (lambda) with KCl concentration, but the extended DLVO theory succeeded if an additional repulsive potential was assumed. The Hamaker constant of actin in the Ca(2+)-ATP bound state was determined for the first time as A(H) = 10.4 +/- 0.6 k(B)T.

Influence of Poly(ethylene glycol) Molecular Mass on Separation and Ordering in Solutions of CiEj Nonionic Surfactants: Depletion Interactions and Steric Effects

We study ternary mixtures of nonionic surfactants C(i)E(j) (i = 12; j = 5, 6, 8) and poly(ethylene glycol) (PEG) in water. For sufficiently large molecular mass of PEG (M >M(sep) approximately 600), we observe a lowering of phase separation temperature with an increase in polymer concentration. The value of M(sep) is consistent with the analysis based on depletion interactions between micelles induced by polymer chains. We also demonstrate that there is another critical molecular mass of PEG (M = M* approximately 2000) necessary to induce ordering in the surfactant-rich phase. This critical molecular mass follows from two requirements: (a) PEG has to reduce the separation temperature below a temperature of hexagonal-isotropic phase transition in a binary surfactant-water mixture and (b) the PEG radius of gyration has to be larger than the size of the water channels in the hexagonal phase.

Association Kinetics of Wild- and Mutant-Type Ynd1p in Relation to Quality of Grown Crystals

The intermolecular interaction and association dynamics of the Ynd1p protein were investigated using dynamic and time-resolved static light scattering measurements. The mutual diffusion coefficients of wild- and mutant-type (a single amino acid substitution) Ynd1p monomer were measured in 50 mM 2-(N-morpholino)ethanesulfonic acid (MES) buffer with 5 mM MnCl2 and 7.5% (v/v) ethylene glycol. Both translational diffusion coefficients at a zero protein concentration were (40.3 +/- 0.2) x 10(-12) m2/s at 20 degrees C and a pH of 7.0, so the hydrodynamic radius of the monomers was 4.1 +/- 0.1 nm. The measured intermolecular interaction between monomers, however, showed that the mutant-type Ynd1p had a stronger attractive force. Time-resolved static light scattering measurements showed that the association of mutant-type Ynd1p yielded a larger number of aggregates than that of wild-type Ynd1p. The time dependence of aggregate gyration radius differed between the two types. Fractal dimension analysis using scattering intensity data suggested that the inner structure of the aggregates changed from loose to rigid with time. Although this phenomenon is common for wild and mutant types, the differences in the number of aggregates yielded in the initial stages and in the intermolecular interaction affected the quality of the final grown crystals. That is, single crystals of Ynd1p grew in the mutant-type protein solution and polycrystals of Ynd1p grew in the wild-type protein solution.

Multiple extrema in the intermolecular potential and the phase diagram of protein solutions

Recent experiments have revealed several surprising features of the phase equilibria in protein solutions: liquid-liquid phase separation which is, in some cases, metastable with respect to the liquid-solid equilibrium, and in others-unobservable; widely varying crystallization enthalpies, including completely athermal crystallization; the co-existence of several crystalline polymorphs; and others. Other studies have shown that the solvent molecules at the hydrophobic and polar patches on the protein molecular surfaces are structured, introducing repulsive forces at surface separations equal to several water molecule sizes. In search of a causal link between the latter and former findings, we apply Monte Carlo simulation techniques in the investigation of phase diagrams associated with globular biological molecules in solution. We account for the solvent structuring via short-range isotropic two-body intermolecular potentials exhibiting multiple extrema. We show that the introduction of a repulsive maximum or a secondary attractive minimum at separations longer than the primary attractive minimum has dramatic effects on the phase diagram: liquid-liquid separation curves are driven to lower or higher temperatures, the sensitivity of the solubility curve (liquidus) to temperature, i.e., the enthalpy of crystallization, is significantly reduced or enhanced, metastable liquid-liquid separation may become stable and vice versa, and both low- and high-density crystalline phases are observed. The similarity of these features of the simulated phase behavior to those observed experimentally suggests that at least some of the mysteries of the protein phase equilibria may be due to the structuring of the solvent around the protein molecular surfaces. Another conclusion is that at least some of the dense liquids seen in protein solutions may be stable and not metastable with respect to a solid phase.

Depletion and pair interactions of proteins in polymer solutions

We study the depletion, pair interaction, and phase behavioral characteristics of proteins in polymer solutions. We use a McMillan-Mayer-like approach [W. G. McMillan, Jr. and J. E. Mayer, J. Chem. Phys. 13, 276 (1945)] to suggest that the depletion characteristics should be studied at an effective polymer concentration which is a function of both the average polymer and the protein concentrations. In the protein limit, we show that the volume of the polymer depletion layers exceeds the size of the proteins, leading to effective polymer concentrations typically in the semidilute and concentrated regimes even when the average polymer concentrations are in the dilute regimes. We propose an approximate approach that accounts for the multibody depletion overlaps, and use an accurate numerical solution of polymer mean-field theory to address depletion characteristics in these regimes which are characterized by both the importance of polymer interactions as well as the curvature of the proteins relative to the correlation length of polymers. We show that the depletion characteristics of the protein-polymer mixture can be quite different when viewed in this framework, and this can have profound consequences for the phase behavior of the mixture. Our theoretical predictions for the phase diagram match semiquantitatively with published experimental results.

Liquid-liquid phase separation in hemoglobins: distinct aggregation mechanisms of the beta6 mutants

Reversible liquid-liquid (L-L) phase separation in the form of high concentration hemoglobin (Hb) solution droplets is favored in an equilibrium with a low-concentration Hb solution when induced by inositol-hexaphosphate in the presence of polyethylene glycol 4000 at pH 6.35 HEPES (50 mM). The L-L phase separation of Hb serves as a model to elucidate intermolecular interactions that may give rise to accelerated nucleation kinetics of liganded HbC (beta6 Lys) compared to HbS (beta6 Val) and HbA (beta6 Glu). Under conditions of low pH (pH 6.35) in the presence of inositol-hexaphosphate, COHb assumes an altered R-state. The phase lines for the three Hb variants in concentration and temperature coordinates indicate that liganded HbC exhibits a stronger net intermolecular attraction with a longer range than liganded HbS and HbA. Over time, L-L phase separation gives rise to amorphous aggregation and subsequent formation of crystals of different kinetics and habits, unique to the individual Hb. The composite of R- and T-like solution aggregation behavior indicates that this is a conformationally driven event. These results indicate that specific contact sites, thermodynamics, and kinetics all play a role in L-L phase separation and differ for the beta6 mutant hemoglobins compared to HbA. In addition, the dense liquid droplet interface or aggregate interface noticeably participates in crystal nucleation.

Hydration of proteins: SAXS study of native and methoxy polyethyleneglycol (mPEG)-modifiedL-asparaginase and bovine serum albumin in mPEG solutions

Two mPEG-modified globular proteins [mPEG: methoxy poly(ethylene glycol)], and their native unmodified forms, were examined by small-angle x-ray scattering to evaluate the extent of their surface hydration. The effects of free and protein-bound mPEG on the hydration shell were modeled with discrete electron density profiles. We show that an mPEG-depleted layer can account for the decrease in the measured radius of gyration R(g) from 34.1 to 31.1 A in native L-asparaginase, and from 32.4 to 31.0 A in native bovine serum albumin (BSA) in mPEG-containing solvents. For mPEG-modified proteins in mPEG-free solvents, we attribute the observed increase in the R(g) over that of the native proteins (approximately 3% in L-asparaginase, and 10% in BSA) to the presence of mPEG on the protein surface. The R(g) of the mPEG-modified proteins in mPEG solutions generally decrease with mPEG concentration. Relative to the corresponding unmodified protein, this decrease in R(g) is much larger in BSA (from 35.6 to 31.2 A) but much smaller (from 34.9 to 34.3 A) in L-asparaginase. From these studies, the thickness of the hydration layer around L-asparaginase and BSA is estimated to be approximately 15 A. Exclusion of polyols from the protein domain could be related to the presence of the hydration shell around the protein.

Control of the Geometry of the Adsorbed Thin Layer by the Depletion Interaction

The depletion interaction was reported to drive the mixtures of rodlike colloids and polymer coils into a variety of phase transitions such as isotropic-nematic, nematic-smectic, and so forth. We describe in this Communication a convenient preparation of the self-assembled monolayer of the platelike porphyrin molecules by the depletion interaction between the absorbent and the metal substrates. After the depletant, low molecular weight poly(ethylene oxide) (PEO), was added into the porphyrin/ethanol solution, random oriented porphyrin was then regulated to lie parallel to the adjacent metal substrates, forming the self-assembled monolayer.

Rationalization of membrane protein crystallization with polyethylene glycol using a simple depletion model

Based on the importance of crystallizing membrane proteins in a rational way, cytochrome bc(1) complex (BC1) was crystallized using polyethylene glycol (PEG) as a sole crystallization agent. Interaction between protein-detergent complexes of BC1 was estimated by dynamic light scattering, and was compared with the numerical calculation using the Derjaguin-Landau-Verwey-Overbeek potential plus a depletion potential, without considering specific surface properties of the protein-detergent complexes. The experiments and calculation were found to be consistent and we obtained a relation between PEG molecular weight M and the range of depletion zone delta as delta approximately M(0.48+/-0.02). The stability of liquid phase of BC1 solutions was controlled by a ratio of (the range of depletion zone)/(the radius of a BC1 particle), which was consistent with recent theoretical predictions. The crystallization was most successful under a condition where the stability of the liquid phase changed from stable to unstable. The PEG molecular weight that fulfilled this condition coincided with the one used empirically to crystallize BC1 in the past by a number of groups. These results are compared to the fact that membrane proteins were often successfully crystallized close to the detergent cloud point.

Colloid-polymer mixtures in the protein limit

We computed the phase-separation behavior and effective interactions of colloid-polymer mixtures in the "protein limit," where the polymer radius of gyration is much larger than the colloid radius. For ideal polymers, the critical colloidal packing fraction tends to zero, whereas for interacting polymers in a good solvent the behavior is governed by a universal binodal, implying a constant critical colloid packing fraction. In both systems the depletion interaction is not well described by effective pair potentials but requires the incorporation of many-body contributions.