Characterizing protein crystal contacts and their role in crystallization: rubredoxin as a case study

Insights into the solubility of γ $$ \gamma $$ D-crystallin from multiscale atomistic simulations

The molecular basis underlying the rich phase behavior of globular proteins remains poorly understood. We use atomistic multiscale molecular simulations to model the solution-state conformational dynamics and interprotein interactions of γ $$ \gamma $$ D-crystallin and its P23T-R36S mutant, which drastically limits the protein solubility, at both infinite dilution and at a concentration where the mutant fluid phase and crystalline phase coexist. We find that while the mutant conserves the protein fold, changes to the surface exposure of residues in the neighborhood of residue-36 enhance protein-protein interactions and develop specific protein-protein contacts found in the protein crystal lattice.

Surface Exposed Free Cysteine Suppresses Crystallization of Human γD-Crystallin

Human γD-crystallin (HGD) has remarkable stability against condensation in the human lens, sometimes over a whole lifetime. The native protein has a surface exposed free cysteine that forms dimers (Benedek, 1997; Ramkumar et al., 1864)^1,2 without specific biological function and leads to further protein association and/or aggregation, which creates a paradox for understanding its stability. Previous work has demonstrated that chemical modification of the protein at the free cysteine (C110), increases the temperature at which liquid-liquid phase separation occurs (LLPS), lowers protein solubility and suggests an important role for this amino acid in maintaining its long-term resistance to condensation. Here we demonstrate that mutation of the cysteine does not alter the structure or solubility (liquidus) line for the protein, but dramatically increases the protein crystal nucleation rate following LLPS, suggesting that the free cysteine has a vital role in suppressing crystallization in the human lens.

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.

The role of complementary shape in protein dimerization

Shape guides colloidal nanoparticles to form complex assemblies, but its role in defining interfaces in biomolecular complexes is less clear. In this work, we isolate the role of shape in protein complexes by studying the reversible binding processes of 46 protein dimer pairs, and investigate when entropic effects from shape complementarity alone are sufficient to predict the native protein binding interface. We employ depletants using a generic, implicit depletion model to amplify the magnitude of the entropic forces arising from lock-and-key binding and isolate the effect of shape complementarity in protein dimerization. For 13% of the complexes studied here, protein shape is sufficient to predict native complexes as equilibrium assemblies. We elucidate the results by analyzing the importance of competing binding configurations and how it affects the assembly. A machine learning classifier, with a precision of 89.14% and a recall of 77.11%, is able to identify the cases where shape alone predicts the native protein interface.

Decorated networks of native proteins: nanomaterials with tunable mesoscopic domain size

Natural and artificial proteins with designer properties and functionalities offer unparalleled opportunity for functional nanoarchitectures formed through self-assembly. However, to exploit this potential we need to design the system such that assembly results in desired architecture forms while avoiding denaturation and therefore retaining protein functionality. Here we address this challenge with a model system of fluorescent proteins. By manipulating self-assembly using techniques inspired by soft matter where interactions between the components are controlled to yield the desired structure, we have developed a methodology to assemble networks of proteins of one species which we can decorate with another, whose coverage we can tune. Consequently, the interfaces between domains of each component can also be tuned, with potential applications for example in energy - or electron - transfer. Our model system of eGFP and mCherry with tuneable interactions reveals control over domain sizes in the resulting networks.

Streamlined purification and characterization of Pyrococcus furiosus rubredoxins with different N-terminal modifications by reversed-phase HPLC

Rubredoxins (Rds), like those from Pyrococcus furious (Pf), have largely been found to be expressed in Escherichia coli (E. coli) as a mixture of different N-terminal forms, which may affect the properties of the protein. The typical procedures for the purification of Rds are cumbersome and usually with low yield. We present herein a streamlined purification strategy based on the reversed-phase high performance liquid chromatography (RP-HPLC), which offers high yield and high resolution after simply one-step purification following pre-treatment. We also show that RP-HPLC can be a valuable tool to gain information related to the thermal decomposition pathway of Pf-Rds.

Obtaining Soft Matter Models of Proteins and their Phase Behavior

Globular proteins are roughly spherical biomolecules with attractive and highly directional interactions. This microscopic observation motivates describing these proteins as patchy particles: hard spheres with attractive surface patches. Mapping a biomolecule to a patchy model requires simplifying effective protein-protein interactions, which in turn provides a microscopic understanding of the protein solution behavior. The patchy model can indeed be fully analyzed, including its phase diagram. In this chapter, we detail the methodology of mapping a given protein to a patchy model and of determining the phase diagram of the latter. We also briefly describe the theory upon which the methodology is based, provide practical information, and discuss potential pitfalls. Data and scripts relevant to this work have been archived and can be accessed at https://doi.org/10.7924/r4ww7bs1p .

Using Schematic Models to Understand the Microscopic Basis for Inverted Solubility in γD-Crystallin

Inverted solubility-melting a crystal by cooling-is observed in a handful of proteins, such as carbomonoxy hemoglobin C and γD-crystallin. In human γD-crystallin, the phenomenon is associated with the mutation of the 23rd residue, a proline, to a threonine, serine, or valine. One proposed microscopic mechanism entails an increase in surface hydrophobicity upon mutagenesis. Recent crystal structures of a double mutant that includes the P23T mutation allow for a more careful investigation of this proposal. Here, we first measure the surface hydrophobicity of various mutant structures of γD-crystallin and discern no notable increase in hydrophobicity upon mutating the 23rd residue. We then investigate the solubility inversion regime with a schematic patchy particle model that includes one of three variants of temperature-dependent patch energies: two of the hydrophobic effect, and one of a more generic nature. We conclude that, while solubility inversion due to the hydrophobic effect may be possible, microscopic evidence to support it in γD-crystallin is weak. More generally, we find that solubility inversion requires a fine balance between patch strengths and their temperature-dependent component, which may explain why inverted solubility is not commonly observed in proteins. We also find that the temperature-dependent interaction has only a negligible impact on liquid-liquid phase boundaries of γD-crystallin, in line with previous experimental observations.

Toward the computational design of protein crystals with improved resolution

Substantial advances have been made in the computational design of protein interfaces over the last 20 years. However, the interfaces targeted by design have typically been stable and high-affinity. Here, we report the development of a generic computational design method to stabilize the weak interactions at crystallographic interfaces. Initially, we analyzed structures reported in the Protein Data Bank to determine whether crystals with more stable interfaces result in higher resolution structures. We found that for 22 variants of a single protein crystallized by a single individual, the Rosetta-calculated `crystal score' correlates with the reported diffraction resolution. We next developed and tested a computational design protocol, seeking to identify point mutations that would improve resolution in a highly stable variant of staphylococcal nuclease (SNase). Using a protocol based on fixed protein backbones, only one of the 11 initial designs crystallized, indicating modeling inaccuracies and forcing us to re-evaluate our strategy. To compensate for slight changes in the local backbone and side-chain environment, we subsequently designed on an ensemble of minimally perturbed protein backbones. Using this strategy, four of the seven designed proteins crystallized. By collecting diffraction data from multiple crystals per design and solving crystal structures, we found that the designed crystals improved the resolution modestly and in unpredictable ways, including altering the crystal space group. Post hoc, in silico analysis of the three observed space groups for SNase showed that the native space group was the lowest scoring for four of six variants (including the wild type), but that resolution did not correlate with crystal score, as it did in the preliminary results. Collectively, our results show that calculated crystal scores can correlate with reported resolution, but that the correlation is absent when the problem is inverted. This outcome suggests that more comprehensive modeling of the crystallographic state is necessary to design high-resolution protein crystals from poorly diffracting crystals.

Temperature-Dependent Interactions Explain Normal and Inverted Solubility in a γD-Crystallin Mutant

Protein crystal production is a major bottleneck in the structural characterization of proteins. To advance beyond large-scale screening, rational strategies for protein crystallization are crucial. Understanding how chemical anisotropy (or patchiness) of the protein surface, due to the variety of amino-acid side chains in contact with solvent, contributes to protein-protein contact formation in the crystal lattice is a major obstacle to predicting and optimizing crystallization. The relative scarcity of sophisticated theoretical models that include sufficient detail to link collective behavior, captured in protein phase diagrams, and molecular-level details, determined from high-resolution structural information, is a further barrier. Here, we present two crystal structures for the P23T + R36S mutant of γD-crystallin, each with opposite solubility behavior: one melts when heated, the other when cooled. When combined with the protein phase diagram and a tailored patchy particle model, we show that a single temperature-dependent interaction is sufficient to stabilize the inverted solubility crystal. This contact, at the P23T substitution site, relates to a genetic cataract and reveals at a molecular level the origin of the lowered and retrograde solubility of the protein. Our results show that the approach employed here may present a productive strategy for the rationalization of protein crystallization.

Protein and RNA dynamical fingerprinting

Protein structural vibrations impact biology by steering the structure to functional intermediate states; enhancing tunneling events; and optimizing energy transfer. Strong water absorption and a broad continuous vibrational density of states have prevented optical identification of these vibrations. Recently spectroscopic signatures that change with functional state were measured using anisotropic terahertz microscopy. The technique however has complex sample positioning requirements and long measurement times, limiting access for the biomolecular community. Here we demonstrate that a simplified system increases spectroscopic structure to dynamically fingerprint biomacromolecules with a factor of 6 reduction in data acquisition time. Using this technique, polarization varying anisotropy terahertz microscopy, we show sensitivity to inhibitor binding and unique vibrational spectra for several proteins and an RNA G-quadruplex. The technique’s sensitivity to anisotropic absorbance and birefringence provides rapid assessment of macromolecular dynamics that impact biology.

The characterization of biomacromolecule structural vibrations has been impeded by a broad continuous vibrational density of states obscuring molecule specific vibrations. A terahertz microscopy system using polarization control produces signatures to dynamically fingerprint proteins and a RNA G-quadruplex.

Calixarene-mediated assembly of a small antifungal protein

Synthetic macrocycles such as calixarenes and cucurbiturils are increasingly applied as mediators of protein assembly and crystallization. The macrocycle can facilitate assembly by providing a surface on which two or more proteins bind simultaneously. This work explores the capacity of the sulfonato-calix[n]arene (sclx n ) series to effect crystallization of PAF, a small, cationic antifungal protein. Co-crystallization with sclx4, sclx6 or sclx8 led to high-resolution crystal structures. In the absence of sclx n , diffraction-quality crystals of PAF were not obtained. Interestingly, all three sclx n were bound to a similar patch on PAF. The largest and most flexible variant, sclx8, yielded a dimer of PAF. Complex formation was evident in solution via NMR and ITC experiments, showing more pronounced effects with increasing macrocycle size. In agreement with the crystal structure, the ITC data suggested that sclx8 acts as a bidentate ligand. The contributions of calixarene size/conformation to protein recognition and assembly are discussed. Finally, it is suggested that the conserved binding site for anionic calixarenes implicates this region of PAF in membrane binding, which is a prerequisite for antifungal activity.

Measuring Nonspecific Protein-Protein Interactions by Dynamic Light Scattering

Dynamic light scattering has become a method of choice for measuring and quantifying weak, nonspecific protein-protein interactions due to its ease of use, minimal sample consumption, and amenability to high-throughput screening via plate readers. A procedure is given on how to prepare protein samples, carry out measurements by commonly used experimental setups including flow through systems, plate readers, and cuvettes, and analyze the correlation functions to obtain diffusion coefficient data. The chapter concludes by a theoretical section that derives and rationalizes the correlation between diffusion coefficient measurements and protein-protein interactions.

Patchy Particle Models to Understand Protein Phase Behavior

In this chapter we describe numerical procedures to evaluate the phase behavior of coarse-grained models for globular proteins. Specifically we focus on models based on hard spheres complemented with "patchy-like" anisotropic interactions that mimic the attractive regions on the surface of the proteins. We introduce the basic elements of grand canonical Monte Carlo simulations for these types of models in which rotational and translational moves need to be accounted for. We describe the techniques for the estimation of the fluid-fluid critical point, coexistence curve, and fluid-crystal boundaries. We also discuss an efficient method for the evaluation of the fluid-fluid phase diagram: the successive umbrella sampling technique. Finally we briefly describe how to exploit the same tools for the calculation of the phase behavior of protein binary mixtures.

Peculiarities of Protein Crystal Nucleation and Growth

This paper reviews investigations on protein crystallization. It aims to present a comprehensive rather than complete account of recent studies and efforts to elucidate the most intimate mechanisms of protein crystal nucleation. It is emphasized that both physical and biochemical factors are at play during this process. Recently-discovered molecular scale pathways for protein crystal nucleation are considered first. The bond selection during protein crystal lattice formation, which is a typical biochemically-conditioned peculiarity of the crystallization process, is revisited. Novel approaches allow us to quantitatively describe some protein crystallization cases. Additional light is shed on the protein crystal nucleation in pores and crevices by employing the so-called EBDE method (equilibration between crystal bond and destructive energies). Also, protein crystal nucleation in solution flow is considered.

Two time scales for self and collective diffusion near the critical point in a simple patchy model for proteins with floating bonds

Using dynamic Monte Carlo and Brownian dynamics, we investigate a floating bond model in which particles can bind through mobile bonds. The maximum number of bonds (here fixed to 4) can be tuned by appropriately choosing the repulsive, nonadditive interactions among bonds and particles. We compute the static and dynamic structure factor (intermediate scattering function) in the vicinity of the gas-liquid critical point. The static structure exhibits a weak tetrahedral network character. The intermediate scattering function shows a temporal decay deviating from a single exponential, which can be described by a double exponential decay where the two time scales differ approximately by one order of magnitude. This time scale separation is robust over a range of wave numbers. The analysis of clusters in real space indicates the formation of noncompact clusters and shows a considerable stretch in the instantaneous size distribution when approaching the critical point. The average time evolution of the largest subcluster of given initial clusters with 10 or more particles also shows a double exponential decay. The observation of two time scales in the intermediate scattering function at low packing fractions is consistent with similar findings in globular protein solutions with trivalent metal ions that act as bonds between proteins.

Nonclassical nucleation pathways in protein crystallization

Classical nucleation theory (CNT), which was established about 90 years ago, has been very successful in many research fields, and continues to be the most commonly used theory in describing the nucleation process. For a fluid-to-solid phase transition, CNT states that the solute molecules in a supersaturated solution reversibly form small clusters. Once the cluster size reaches a critical value, it becomes thermodynamically stable and favored for further growth. One of the most important assumptions of CNT is that the nucleation process is described by one reaction coordinate and all order parameters proceed simultaneously. Recent studies in experiments, computer simulations and theory have revealed nonclassical features in the early stage of nucleation. In particular, the decoupling of order parameters involved during a fluid-to-solid transition leads to the so-called two-step nucleation mechanism, in which a metastable intermediate phase (MIP) exists between the initial supersaturated solution and the final crystals. Depending on the exact free energy landscapes, the MIPs can be a high density liquid phase, mesoscopic clusters, or a pre-ordered state. In this review, we focus on the studies of nonclassical pathways in protein crystallization and discuss the applications of the various scenarios of two-step nucleation theory. In particular, we focus on protein solutions in the presence of multivalent salts, which serve as a model protein system to study the nucleation pathways. We wish to point out the unique features of proteins as model systems for further studies.

A density functional theory for association of fluid molecules with a functionalized surface: fluid-wall single and double bonding

In this manuscript we extend Wertheim's two-density formalism beyond its first order to model a system of fluid molecules with a single association site close to a planar hard wall with association sites on its surface in a density functional theory framework. The association sites of the fluid molecules are small enough that they can form only one bond, while the wall association sites are large enough to bond with more than one fluid molecule. The effects of temperature and of bulk fluid and wall site densities on the fluid density profile, extent of association, and competition between single and double bonding of fluid segments at the wall sites versus distance from the wall are presented. The theory predictions are compared with new Monte Carlo simulation results and they are in good agreement. The theory captures the surface coverage over wide ranges of temperature and bulk density by introducing the effect of steric hindrance in fluid association at a wall site.

The "Sticky Patch" Model of Crystallization and Modification of Proteins for Enhanced Crystallizability

Crystallization of macromolecules has long been perceived as a stochastic process, which cannot be predicted or controlled. This is consistent with another popular notion that the interactions of molecules within the crystal, i.e., crystal contacts, are essentially random and devoid of specific physicochemical features. In contrast, functionally relevant surfaces, such as oligomerization interfaces and specific protein-protein interaction sites, are under evolutionary pressures so their amino acid composition, structure, and topology are distinct. However, current theoretical and experimental studies are significantly changing our understanding of the nature of crystallization. The increasingly popular "sticky patch" model, derived from soft matter physics, describes crystallization as a process driven by interactions between select, specific surface patches, with properties thermodynamically favorable for cohesive interactions. Independent support for this model comes from various sources including structural studies and bioinformatics. Proteins that are recalcitrant to crystallization can be modified for enhanced crystallizability through chemical or mutational modification of their surface to effectively engineer "sticky patches" which would drive crystallization. Here, we discuss the current state of knowledge of the relationship between the microscopic properties of the target macromolecule and its crystallizability, focusing on the "sticky patch" model. We discuss state-of-the-art in silico methods that evaluate the propensity of a given target protein to form crystals based on these relationships, with the objective to design variants with modified molecular surface properties and enhanced crystallization propensity. We illustrate this discussion with specific cases where these approaches allowed to generate crystals suitable for structural analysis.

Minimal Positive Design for Self-Assembly of the Archimedean Tilings

A challenge of molecular self-assembly is to understand how to design particles that self-assemble into a desired structure and not any of a potentially large number of undesired structures. Here we use simulation to show that a strategy of minimal positive design allows the self-assembly of networks equivalent to the 8 semiregular Archimedean tilings of the plane, structures not previously realized in simulation. This strategy consists of identifying the fewest distinct types of interparticle interaction that appear in the desired structure, and does not require enumeration of the many possible undesired structures. The resulting particles, which self-assemble into the desired networks, possess DNA-like selectivity of their interactions. Assembly of certain molecular networks may therefore require such selectivity.

Effect of the surface charge distribution on the fluid phase behavior of charged colloids and proteins

A generic but simple model is presented to evaluate the effect of the heterogeneous surface charge distribution of proteins and zwitterionic nanoparticles on their thermodynamic phase behavior. By considering surface charges as continuous "patches," the rich set of surface patterns that is embedded in proteins and charged patchy particles can readily be described. This model is used to study the fluid phase separation of charged particles where the screening length is of the same order of magnitude as the particle size. In particular, two types of charged particles are studied: dipolar fluids and protein-like fluids. The former represents the simplest case of zwitterionic particles, whose charge distribution can be described by their dipole moment. The latter system corresponds to molecules/particles with complex surface charge arrangements such as those found in biomolecules. The results for both systems suggest a relation between the critical region, the strength of the interparticle interactions, and the arrangement of charged patches, where the critical temperature is strongly correlated to the magnitude of the dipole moment. Additionally, competition between attractive and repulsive charge-charge interactions seems to be related to the formation of fluctuating clusters in the dilute phase of dipolar fluids, as well as to the broadening of the binodal curve in protein-like fluids. Finally, a variety of self-assembled architectures are detected for dipolar fluids upon small changes to the charge distribution, providing the groundwork for studying the self-assembly of charged patchy particles.

A density functional theory for colloids with two multiple bonding associating sites

Wertheim's multi-density formalism is extended for patchy colloidal fluids with two multiple bonding patches. The theory is developed as a density functional theory to predict the properties of an associating inhomogeneous fluid. The equation of state developed for this fluid depends on the size of the patch, and includes formation of cyclic, branched and linear clusters of associated species. The theory predicts the density profile and the fractions of colloids in different bonding states versus the distance from one wall as a function of bulk density and temperature. The predictions from our theory are compared with previous results for a confined fluid with four single bonding association sites. Also, comparison between the present theory and Monte Carlo simulation indicates a good agreement.

Structural evidence for solvent-stabilisation by aspartic acid as a mechanism for halophilic protein stability in high salt concentrations

Halophilic organisms have adapted to survive in high salt environments, where mesophilic organisms would perish. One of the biggest challenges faced by halophilic proteins is the ability to maintain both the structure and function at molar concentrations of salt. A distinct adaptation of halophilic proteins, compared to mesophilic homologues, is the abundance of aspartic acid on the protein surface. Mutagenesis and crystallographic studies of halophilic proteins suggest an important role for solvent interactions with the surface aspartic acid residues. This interaction, between the regions of the acidic protein surface and the solvent, is thought to maintain a hydration layer around the protein at molar salt concentrations thereby allowing halophilic proteins to retain their functional state. Here we present neutron diffraction data of the monomeric zwitterionic form of aspartic acid solutions at physiological pH in 0.25 M and 2.5 M concentration of potassium chloride, to mimic mesophilic and halophilic-like environmental conditions. We have used isotopic substitution in combination with empirical potential structure refinement to extract atomic-scale information from the data. Our study provides structural insights that support the hypothesis that carboxyl groups on acidic residues bind water more tightly under high salt conditions, in support of the residue-ion interaction model of halophilic protein stabilisation. Furthermore our data show that in the presence of high salt the self-association between the zwitterionic form of aspartic acid molecules is reduced, suggesting a possible mechanism through which protein aggregation is prevented.

Computational crystallization

Crystallization is a key step in macromolecular structure determination by crystallography. While a robust theoretical treatment of the process is available, due to the complexity of the system, the experimental process is still largely one of trial and error. In this article, efforts in the field are discussed together with a theoretical underpinning using a solubility phase diagram. Prior knowledge has been used to develop tools that computationally predict the crystallization outcome and define mutational approaches that enhance the likelihood of crystallization. For the most part these tools are based on binary outcomes (crystal or no crystal), and the full information contained in an assembly of crystallization screening experiments is lost. The potential of this additional information is illustrated by examples where new biological knowledge can be obtained and where a target can be sub-categorized to predict which class of reagents provides the crystallization driving force. Computational analysis of crystallization requires complete and correctly formatted data. While massive crystallization screening efforts are under way, the data available from many of these studies are sparse. The potential for this data and the steps needed to realize this potential are discussed.

The self assembly of proteins; probing patchy protein interactions

The ability to control the self-assembly of biological molecules to form defined structures, with a high degree of predictability is a central aim for soft matter science and synthetic biology. Several examples of this are known for synthetic systems, such as anisotropic colloids. However, for biomacromolecules, such as proteins, success has been more limited, since aeolotopic (or anisotropic) interactions between protein molecules are not easily predicted. We have created three double mutants of human γD-crystallin for which the phase diagrams for singly mutated proteins can be used to predict the behavior of the double mutants. These proteins provide a robust mechanism to examine the kinetic and thermodynamic properties of proteins in which competing interactions exist due to the anisotropic or patchy nature of the protein surface.

Simulation of protein association: Kinetic pathways towards crystal contacts

We conducted molecular dynamics simulations combined with distance-based umbrella sampling and forward flux sampling to investigate the early stages of protein crystallization. Formation of contacts with long-range interactions and/or an exposed position on the protein surface was kinetically preferred over more stable hydrophobic contacts with a shorter attractive range, while the thermodynamic stability of the protein crystal was provided by hydrophobic interactions. Contacts with a large interaction area showed complex dissociation pathways that were not detected by distance-based umbrella sampling. Instead, forward flux sampling simulations of contact dissociation identified long-range attractive interactions.

How fluorescent labelling alters the solution behaviour of proteins

The impact of adding a fluorescent dye to a protein is examined using protein phase diagrams and numerical simulations. The addition of the dye is the equivalent of adding a large attractive patch to the surface of the protein, which results in significant changes to the protein solution behaviour.

Charge-induced patchy attractions between proteins

Static light scattering (SLS) combined with structure-based Monte Carlo (MC) simulations provide new insights into mechanisms behind anisotropic, attractive protein interactions. A nonmonotonic behavior of the osmotic second virial coefficient as a function of ionic strength is here shown to originate from a few charged amino acids forming an electrostatic attractive patch, highly directional and complementary. Together with Coulombic repulsion, this attractive patch results in two counteracting electrostatic contributions to the interaction free energy which, by operating over different length scales, is manifested in a subtle, salt-induced minimum in the second virial coefficient as observed in both experiment and simulations.

Utilisation of adsorption and desorption for simultaneously improving protein crystallisation success rate and crystal quality

High-quality protein crystals of suitable size are an important prerequisite for applying X-ray crystallography to determine the 3-dimensional structure of proteins. However, it is often difficult to obtain protein crystals of appropriate size and quality because nucleation and growth processes can be unsuccessful. Here, we show that by adsorbing proteins onto porous polystyrene-divinylbenzene microspheres (SDB) floating on the surface of the crystallisation solution, a localised high supersaturation region at the surface of the microspheres and a low supersaturation region below the microspheres can coexist in a single solution. The crystals will easily nucleate in the region of high supersaturation, but when they grow to a certain size, they will sediment to the region of low supersaturation and continue to grow. In this way, the probability of crystallisation and crystal quality can be simultaneously increased in a single solution without changing other crystallisation parameters.

Ion-activated attractive patches as a mechanism for controlled protein interactions

The understanding of protein interactions to control phase and nucleation behavior of protein solutions is an important challenge for soft matter, biological and medical research. Here, we present ion bridges of multivalent cations between proteins as an ion-activated mechanism for patchy interaction that is directly supported by experimental findings in protein crystals. A deep understanding of experimentally observed phenomena in protein solutions--including charge reversal, reentrant condensation, metastable liquid-liquid phase separation, cluster formation and different pathways of crystallization--is gained by an analytic model that directly displays parameter dependencies and physical connections. The direct connection between experiment and theory provides a conceptual framework for future experimental, computational and theoretical research on topics such as rational design of phase behavior and crystallization pathways on the basis of the statistical physics of patchy particles.

Thermodynamic perturbation theory for self-assembling mixtures of divalent single patch colloids

In this work we extend Wertheim's thermodynamic perturbation theory (TPT) to binary mixtures (species A and species B) of patchy colloids were each species has a single patch which can bond a maximum of twice (divalent). Colloids are treated as hard spheres with a directional conical association site. We restrict the system such that only patches between unlike species share attractions; meaning there are AB attractions but no AA or BB attractions. The theory is derived in Wertheim's two density formalism for one site associating fluids. Since the patches are doubly bondable, associated chains, of all chain lengths, as well as 4-mer rings consisting of two species A and two species B colloids are accounted for. With the restriction of only AB attractions, triatomic rings of doubly bonded colloids, which dominate in the corresponding pure component case, cannot form. The theory is shown to be in good agreement with Monte Carlo simulation data for the structure and thermodynamics of these patchy colloid mixtures as a function of temperature, density, patch size and composition. It is shown that 4-mer rings dominate at low temperature, inhibiting the polymerization of the mixture into long chains. Mixtures of this type have been recently synthesized by researchers. This work provides the first theory capable of accurately modeling these mixtures.

Statistical analysis of crystallization database links protein physico-chemical features with crystallization mechanisms

X-ray crystallography is the predominant method for obtaining atomic-scale information about biological macromolecules. Despite the success of the technique, obtaining well diffracting crystals still critically limits going from protein to structure. In practice, the crystallization process proceeds through knowledge-informed empiricism. Better physico-chemical understanding remains elusive because of the large number of variables involved, hence little guidance is available to systematically identify solution conditions that promote crystallization. To help determine relationships between macromolecular properties and their crystallization propensity, we have trained statistical models on samples for 182 proteins supplied by the Northeast Structural Genomics consortium. Gaussian processes, which capture trends beyond the reach of linear statistical models, distinguish between two main physico-chemical mechanisms driving crystallization. One is characterized by low levels of side chain entropy and has been extensively reported in the literature. The other identifies specific electrostatic interactions not previously described in the crystallization context. Because evidence for two distinct mechanisms can be gleaned both from crystal contacts and from solution conditions leading to successful crystallization, the model offers future avenues for optimizing crystallization screens based on partial structural information. The availability of crystallization data coupled with structural outcomes analyzed through state-of-the-art statistical models may thus guide macromolecular crystallization toward a more rational basis.

Collective translational and rotational Monte Carlo moves for attractive particles

Virtual move Monte Carlo is a Monte Carlo (MC) cluster algorithm forming clusters via local energy gradients and approximating the collective kinetic or dynamic motion of attractive colloidal particles. We carefully describe, analyze, and test the algorithm. To formally validate the algorithm through highlighting its symmetries, we present alternative and compact ways of selecting and accepting clusters which illustrate the formal use of abstract concepts in the design of biased MC techniques: the superdetailed balance and the early rejection scheme. A brief and comprehensive summary of the algorithms is presented, which makes them accessible without needing to understand the details of the derivation.