Applications of the second virial coefficient: protein crystallization and solubility

The Effects of Electric Fields on Protein Phase Behavior and Protein Crystallization Kinetics

We experimentally studied the effects of an externally applied electric field on protein crystallization and liquid-liquid phase separation (LLPS) and its crystallization kinetics. For a surprisingly weak alternating current (AC) electric field, crystallization was found to occur in a wider region of the phase diagram, while nucleation induction times were reduced, and crystal growth rates were enhanced. LLPS on the contrary was suppressed, which diminishes the tendency for a two-step crystallization scenario. The effect of the electric field is ascribed to a change in the protein-protein interaction potential.

Inverse design of triblock Janus spheres for self-assembly of complex structures in the crystallization slot via digital alchemy

The digital alchemy framework is an extended ensemble simulation technique that incorporates particle attributes as thermodynamic variables, enabling the inverse design of colloidal particles for desired behavior. Here, we extend the digital alchemy framework for the inverse design of patchy spheres that self-assemble into target crystal structures. To constrain the potentials to non-trivial solutions, we conduct digital alchemy simulations with constant second virial coefficient. We optimize the size, range, and strength of patchy interactions in model triblock Janus spheres to self-assemble the 2D kagome and snub square lattices and the 3D pyrochlore lattice, and demonstrate self-assembly of all three target structures with the designed models. The particles designed for the kagome and snub square lattices assemble into high quality clusters of their target structures, while competition from similar polymorphs lower the yield of the pyrochlore assemblies. We find that the alchemically designed potentials do not always match physical intuition, illustrating the ability of the method to find nontrivial solutions to the optimization problem. We identify a window of second virial coefficients that result in self-assembly of the target structures, analogous to the crystallization slot in protein crystallization.

Instabilities of complex fluids with partially structured and partially random interactions

We develop a theory for thermodynamic instabilities of complex fluids composed of many interacting chemical species organised in families. This model includes partially structured and partially random interactions and can be solved exactly using tools from random matrix theory. The model exhibits three kinds of fluid instabilities: one in which the species form a condensate with a local density that depends on their family (family condensation); one in which species demix in two phases depending on their family (family demixing); and one in which species demix in a random manner irrespective of their family (random demixing). We determine the critical spinodal density of the three types of instabilities and find that the critical spinodal density is finite for both family condensation and family demixing, while for random demixing the critical spinodal density grows as the square root of the number of species. We use the developed framework to describe phase-separation instability of the cytoplasm induced by a change in pH.

Probing interactions of therapeutic antibodies with serum via second virial coefficient measurements

Antibody-based therapeutics are the fastest-growing drug class on the market, used to treat aggressive forms of cancer, chronic autoimmune conditions, and numerous other disease states. Although the specificity, affinity, and versatility of therapeutic antibodies can provide an advantage over traditional small-molecule drugs, their development and optimization can be much more challenging and time-consuming. This is, in part, because the ideal formulation buffer systems used for in vitro characterization inadequately reflect the crowded biological environments (serum, endosomal lumen, etc.) that these drugs experience once administered to a patient. Such environments can perturb the binding of antibodies to their antigens and receptors, as well as homo- and hetero-aggregation, thereby altering therapeutic effect and disposition in ways that are incompletely understood. Although excluded volume effects are classically thought to favor binding, weak interactions with co-solutes in crowded conditions can inhibit binding. The second virial coefficient (B₂) parameter quantifies such weak interactions and can be determined by a variety of techniques in dilute solution, but analogous methods in complex biological fluids are not well established. Here, we demonstrate that fluorescence correlation spectroscopy is able to measure diffusive B₂-values directly in undiluted serum. Apparent second virial coefficient (B_2,app) measurements of antibodies in serum reveal that changes in the balance between attractive and repulsive interactions can dramatically impact global nonideality. Furthermore, our findings suggest that the approach of isolating specific components and completing independent cross-term virial coefficient measurements may not be an effective approach to characterizing nonideality in serum. The approach presented here could enrich our understanding of the effects of biological environments on proteins in general and advance the development of therapeutic antibodies and other protein-based therapeutics.

Improved adsorption reactions, kinetics and stability for model and therapeutic proteins immobilised on affinity resins

Protein adsorption on solid state media is important for the industrial affinity chromatography of biotherapeutics and for preparing materials for self-interaction chromatography where fundamental protein solution thermodynamic properties are measured. The adsorption of three model proteins (lysozyme, catalase and BSA) and two antibodies (a monoclonal and a polyclonal antibody) have been investigated on commercial affinity chromatography media with different surface functionalities (Formyl, Tresyl and Amino). Both the extent of protein immobilised (mg protein/ml media) and the reaction kinetics are reported for a range of reaction conditions, including pH, differing buffers as well as the presence of secondary reactants (glutaraldehyde, sodium cyanoborohydride, EDC and NHS). Compared to the reaction conditions recommended by manufacturers as well as those reported in previous published work, significant increases in the extent of protein immobilisation and reaction kinetics are reported here. The addition of glutaraldehyde or sodium cyanoborohydride was found to be especially effective even when not directly needed for the adsorption to happen. For mAb and pIgG, immobilisation levels of 50 and 31 mg of protein/ml of resin respectively were achieved, which are 100% or more than previously reported. Enhanced levels were achieved for lysozyme of 120 mg/ml with very rapid reaction kinetics (< 1 h) with sodium cyanoborohydride. It can be concluded that specific chromatography resins with Tresyl activated support offered enhanced levels of protein immobilisation due to their ability to react to form amine or thio-ether linkages with proteins. Additionally, glutaraldehyde can result in higher immobilisation levels whilst it can also accelerate immobilisation reaction kinetics.

In silico prediction of monovalent and chimeric tetravalent vaccines for prevention and treatment of dengue fever

Reverse vaccinology method was used to predict the monovalent peptide vaccine candidate to produce antibodies for therapeutic purpose and to predict tetravalent vaccine candidate to act as a common vaccine to cover all the fever dengue virus serotypes. Envelope (E)-proteins of DENV-1-4 serotypes were used for vaccine prediction using NCBI, Uniprot/Swissprot, Swiss-prot viewer, VaxiJen V2.0, TMHMM, BCPREDS, Propred-1, Propred and MHC Pred,. E-proteins of DENV-1-4 serotypes were identified as antigen from which T cell epitopes, through B cell epitopes, were predicted to act as peptide vaccine candidates. Each selected T cell epitope of E-protein was confirmed to act as vaccine and to induce complementary antibody against particular serotype of dengue virus. Chimeric tetravalent vaccine was formed by the conjugation of four vaccines, each from four dengue serotypes to act as a common vaccine candidate for all the four dengue serotypes. It can be justifiably concluded that the monovalent 9-mer T cell epitope for each DENV serotypes can be used to produce specific antibody agaomst dengue virus and a chimeric common tetravalent vaccine candidate to yield a comparative vaccine to cover any of the four dengue virus serotype. This vaccine is expected to act as highly immunogenic against preventing dengue fever.

Characterization of New Detergents and Detergent Mimetics by Scattering Techniques for Membrane Protein Crystallization

Membrane proteins are difficult to manipulate and stabilize once they have been removed from their native membranes. However, despite these difficulties, successes in membrane-protein structure determination have continued to accumulate for over two decades, thanks to advances in chemistry and technology. Many of these advances have resulted from efforts focused on protein engineering, high-throughput expression, and development of detergent screens, all with the aim of enhancing protein stability for biochemistry and biophysical studies. In contrast, considerably less work has been done to decipher the basic mechanisms that underlie the structure of protein-detergent complexes and to describe the influence of detergent structure on stabilization and crystallization. These questions can be addressed using scattering techniques (employing light, X-rays, and/or neutrons), which are suitable to describe the structure and conformation of macromolecules in solution, as well as to assess weak interactions between particles, both of which are clearly germane to crystallization. These techniques can be used either in batch modes or coupled to size-exclusion chromatography, and offer the potential to describe the conformation of a detergent-solubilized membrane protein and to quantify and model detergent bound to the protein in order to optimize crystal packing. We will describe relevant techniques and present examples of scattering experiments, which allow one to explore interactions between micelles and between membrane protein complexes, and relate these interactions to membrane protein crystallization.

Applications of the second virial coefficient: protein crystallization and solubility. Corrigendum

A number of citations in the article by Wilson & DeLucas [(2014). Acta Cryst. F70, 543-554] are corrected.

Lessons from ten years of crystallization experiments at the SGC

Although protein crystallization is generally considered more art than science and remains significantly trial-and-error, large-scale data sets hold the promise of providing general learning. Observations are presented here from retrospective analyses of the strategies actively deployed for the extensive crystallization experiments at the Oxford site of the Structural Genomics Consortium (SGC), where comprehensive annotations by SGC scientists were recorded on a customized database infrastructure. The results point to the importance of using redundancy in crystallizing conditions, specifically by varying the mixing ratios of protein sample and precipitant, as well as incubation temperatures. No meaningful difference in performance could be identified between the four most widely used sparse-matrix screens, judged by the yield of crystals leading to deposited structures; this suggests that in general any comparison of screens will be meaningless without extensive cross-testing. Where protein sample is limiting, exploring more conditions has a higher likelihood of being informative by yielding hits than does redundancy of either mixing ratio or temperature. Finally, on the logistical question of how long experiments should be stored, 98% of all crystals that led to deposited structures appeared within 30 days. Overall, these analyses serve as practical guidelines for the design of initial screening experiments for new crystallization targets.

Crystallization of lysozyme with (R)-, (S)- and (RS)-2-methyl-2,4-pentanediol

Chiral control of crystallization has ample precedent in the small-molecule world, but relatively little is known about the role of chirality in protein crystallization. In this study, lysozyme was crystallized in the presence of the chiral additive 2-methyl-2,4-pentanediol (MPD) separately using the R and S enantiomers as well as with a racemic RS mixture. Crystals grown with (R)-MPD had the most order and produced the highest resolution protein structures. This result is consistent with the observation that in the crystals grown with (R)-MPD and (RS)-MPD the crystal contacts are made by (R)-MPD, demonstrating that there is preferential interaction between lysozyme and this enantiomer. These findings suggest that chiral interactions are important in protein crystallization.

Origin and use of crystallization phase diagrams

Crystallization phase diagrams are frequently used to conceptualize the phase relations and also the processes taking place during the crystallization of macromolecules. While a great deal of freedom is given in crystallization phase diagrams owing to a lack of specific knowledge about the actual phase boundaries and phase equilibria, crucial fundamental features of phase diagrams can be derived from thermodynamic first principles. Consequently, there are limits to what can be reasonably displayed in a phase diagram, and imagination may start to conflict with thermodynamic realities. Here, the commonly used `crystallization phase diagrams' are derived from thermodynamic excess properties and their limitations and appropriate use is discussed.

Large-scale crystallization of proteins for purification and formulation

Since about 170 years, salts were used to create supersaturated solutions and crystallize proteins. The dehydrating effect of salts as well as their kosmotropic or chaotropic character was revealed. Even the suitability of organic solvents for crystallization was already recognized. Interestingly, what was performed during the early times is still practiced today. A lot of effort was put into understanding the underlying physico-chemical interaction mechanisms leading to protein crystallization. However, it was understood that already the solvation of proteins is a highly complex process not to mention the intricate interrelation of electrostatic and hydrophobic interactions taking place. Although many basic questions are still unanswered, preparative protein crystallization was attempted as illustrated in the presented case studies. Due to the highly variable nature of crystallization, individual design of the crystallization process is needed in every single case. It was shown that preparative crystallization from impure protein solutions as a capture step is possible after applying adequate pre-treatment procedures like precipitation or extraction. Protein crystallization can replace one or more chromatography steps. It was further shown that crystallization can serve as an attractive alternative means for formulation of therapeutic proteins. Crystalline proteins can offer enhanced purity and enable highly concentrated doses of the active ingredient. Easy scalability of the proposed protein crystallization processes was shown using the maximum local energy dissipation as a suitable scale-up criterion. Molecular modeling and target-oriented protein engineering may allow protein crystallization to become part of a platform purification process in the near future.

Membrane proteins, detergents and crystals: what is the state of the art?

At the time when the first membrane-protein crystal structure was determined, crystallization of these molecules was widely perceived as extremely arduous. Today, that perception has changed drastically, and the process is regarded as routine (or nearly so). On the occasion of the International Year of Crystallography 2014, this review presents a snapshot of the current state of the art, with an emphasis on the role of detergents in this process. A survey of membrane-protein crystal structures published since 2012 reveals that the direct crystallization of protein-detergent complexes remains the dominant methodology; in addition, lipidic mesophases have proven immensely useful, particularly in specific niches, and bicelles, while perhaps undervalued, have provided important contributions as well. Evolving trends include the addition of lipids to protein-detergent complexes and the gradual incorporation of new detergents into the standard repertoire. Stability has emerged as a critical parameter controlling how a membrane protein behaves in the presence of detergent, and efforts to enhance stability are discussed. Finally, although discovery-based screening approaches continue to dwarf mechanistic efforts to unravel crystallization, recent technical advances offer hope that future experiments might incorporate the rational manipulation of crystallization behaviors.

Protein solubilization: a novel approach

Formulation development presents significant challenges with respect to protein therapeutics. One component of these challenges is to attain high protein solubility (>50mg/ml for immunoglobulins) with minimal aggregation. Protein-protein interactions contribute to aggregation and the integral sum of these interactions can be quantified by a thermodynamic parameter known as the osmotic second virial coefficient (B-value). The method presented here utilizes high-throughput measurement of B-values to identify the influence of additives on protein-protein interactions. The experiment design uses three tiers of screens to arrive at final solution conditions that improve protein solubility. The first screen identifies individual additives that reduce protein interactions. A second set of B-values are then measured for different combinations of these additives via an incomplete factorial screen. Results from the incomplete factorial screen are used to train an artificial neural network (ANN). The "trained" ANN enables predictions of B-values for more than 4000 formulations that include additive combinations not previously experimentally measured. Validation steps are incorporated throughout the screening process to ensure that (1) the protein's thermal and aggregation stability characteristics are not reduced and (2) the artificial neural network predictive model is accurate. The ability of this approach to reduce aggregation and increase solubility is demonstrated using an IgG protein supplied by Minerva Biotechnologies, Inc.

Identifying, studying and making good use of macromolecular crystals

As technology advances, the crystal volume that can be used to collect useful X-ray diffraction data decreases. The technologies available to detect and study growing crystals beyond the optical resolution limit and methods to successfully place the crystal into the X-ray beam are discussed.

Structural biology has contributed tremendous knowledge to the understanding of life on the molecular scale. The Protein Data Bank, a depository of this structural knowledge, currently contains over 100 000 protein structures, with the majority stemming from X-ray crystallography. As the name might suggest, crystallography requires crystals. As detectors become more sensitive and X-ray sources more intense, the notion of a crystal is gradually changing from one large enough to embellish expensive jewellery to objects that have external dimensions of the order of the wavelength of visible light. Identifying these crystals is a prerequisite to their study. This paper discusses developments in identifying these crystals during crystallization screening and distinguishing them from other potential outcomes. The practical aspects of ensuring that once a crystal is identified it can then be positioned in the X-ray beam for data collection are also addressed.