The physics of protein self-assembly

Layered self-assemblies for controlled drug delivery: A translational overview

Self-assembly is a prominent phenomenon observed in nature. Inspired by this thermodynamically favorable approach, several natural and synthetic materials have been investigated to develop functional systems for various biomedical applications, including drug delivery. Furthermore, layered self-assembled systems provide added advantages of tunability and multifunctionality which are crucial for controlled and targeted drug release. Layer-by-layer (LbL) deposition has emerged as one of the most popular, well-established techniques for tailoring such layered self-assemblies. This review aims to provide a brief overview of drug delivery applications using LbL deposition, along with a discussion of associated scalability challenges, technological innovations to overcome them, and prospects for commercial translation of this versatile technique. Additionally, alternative self-assembly techniques such as metal-phenolic networks (MPNs) and Liesegang rings are also reviewed in the context of their recent utilization for controlled drug delivery. Blending the sophistication of these self-assembly phenomena with material science and technological advances can provide a powerful tool to develop smart drug carriers in a scalable manner.

Potential and limits of a colloid approach to protein solutions

Looking at globular proteins with the eyes of a colloid scientist has a long tradition, in fact a significant part of the early colloid literature was focused on protein solutions. However, it has also been recognized that proteins are much more complex than the typical hard sphere-like synthetic model colloids. Proteins are not perfect spheres, their interaction potentials are in general not isotropic, and using theories developed for such particles are thus clearly inadequate in many cases. In this perspective article, we now take a closer look at the field. In particular, we reflect on the fact that modern colloid science has been undergoing a tremendous development, where a multitude of novel systems have been developed in the lab and in silico. During the last decade we have seen a rapidly increasing number of reports on the synthesis of anisotropic, patchy and/or responsive synthetic colloids, that start to resemble their complex biological counterparts. This experimental development is also reflected in a corresponding theoretical and simulation effort. The experimental and theoretical toolbox of colloid science has thus rapidly expanded, and there is obviously an enormous potential for an application of these new concepts to protein solutions, which has already been realized and harvested in recent years. In this perspective article we make an attempt to critically discuss the exploitation of colloid science concepts to better understand protein solutions. We not only consider classical applications such as the attempt to understand and predict solution stability and phase behaviour, but also discuss new challenges related to the dynamics, flow behaviour and liquid-solid transitions found in concentrated or crowded protein solutions. It not only aims to provide an overview on the progress in experimental and theoretical (bio)colloid science, but also discusses current shortcomings in our ability to correctly reproduce and predict the structural and dynamic properties of protein solutions based on such a colloid approach.

A comparative study of the self-assembly of achiral and chiral hairy nanoparticles with polystyrene cores and poly(2-hydroxyethylmethacrylate) hairs

Hairy nanoparticles with polystyrene cores (PS cores) and poly(2-hydroxyethylmethacrylate) (PHEMA) shells were synthesized by combining living anionic polymerization and atom transfer radical polymerization (ATRP). The structural characterization was carried out by FT-IR and NMR spectroscopy (¹H NMR, ¹³C NMR, APT ¹³C NMR and ¹H ¹³C HMQC). The thermal stability of the PS cores was not affected by grafting PHEMA on their surfaces. A differential scanning calorimetry (DSC) thermogram of the HNPs showed two distinct transition temperatures indicating microphase separation. Chiral HNPs were prepared by inducing chirality in the achiral HNPs by complexation with R- or S-mandelic acid. The circular dichroism (CD) spectroscopy of complexes of the HNPs/R- or S-mandelic acid indicated the formation of enantiomeric chiral structures. The self-assembled structures formed from the achiral HNPs show different surface morphologies, porous and zigzag, dependent on the solvents used. Blends of polystyrene functionalized with hydroxyl groups and PHEMA show different morphology and thermal properties compared with the core–shell HNP system. The chiral HNPs self-assembled into donut like structures or toroids with sizes in the range between 200 to 5000 nm. The study suggests that chirality can be utilized to develop interesting self-assembled structures.

Chiral hairy nanoparticles (HNP), prepared by complexation of achiral HNPs with R- or S-mandelic acid, self-assemble into toroidal or donut like structures.

Label-Free Analysis of Protein Aggregation and Phase Behavior

Phase transitions of protein molecules are central to biological function and malfunction. One such transition commonly encountered in nature is the conversion of soluble monomeric states into solid phases, which include crystals and amyloid fibrils, the latter of which are associated with the onset and development of neurodegenerative diseases. Monitoring aggregate formation and protein phase behavior is essential in gaining mechanistic insights into these fundamental processes. Fluorescence techniques have proven invaluable in observing biological molecules; yet, most such approaches rely on the use of an extrinsic fluorophore that binds to the molecule of interest, the installation of which can perturb the molecular systems under study. However, most proteins also possess aromatic amino acids within their peptide sequence and therefore exhibit intrinsic fluorescence. Here, we show that by measuring in space and time tryptophan autofluorescence for three proteins, reconstituted silk fibroin, β-lactoglobulin, and lysozyme, fibrillar self-assembly can be monitored accurately and without the need for extrinsic dyes. When fibrillar protein self-assembly takes place, hydrophobic burial occurs, resulting in the minimization of exposed tryptophan residues to the solvent and consequently leading to an increase in protein autofluorescence. Moreover, by employing a droplet-microfluidic approach to confine protein self-assembly in space, we demonstrate that intrinsic fluorescence can be used to image protein nanofibrils in a label-free manner and that the microstructural analysis obtained from intrinsic fluorescence microscopy correlates well with that from samples treated with extrinsic dyes. Finally, our results show that protein autofluorescence is not limited to the observation of β-sheet-rich structures, but can also be used to distinguish between different types of solid phases including spherulites and crystals, making this approach suitable for overall characterization of protein phase transition phenomena.

Evidence of Structural Inhomogeneities in Hard-Soft Dimeric Particles without Attractive Interactions

We perform Monte Carlo simulations of a simple hard-soft dimeric model constituted by two tangent spheres experiencing different interactions. Specifically, two hard spheres belonging to different dimers interact via a bare hard-core repulsion, whereas two soft spheres experience a softly repulsive Hertzian interaction. The cross correlations are soft as well. By exploring a wide range of temperatures and densities we investigate the capability of this model to document the existence of structural inhomogeneities indicating the possible onset of aggregates, even if no attraction is set. The fluid phase behavior is studied by analyzing structural and thermodynamical properties of the observed structures, in particular by computing radial distribution functions, structure factors and cluster size distributions. The numerical results are supported by integral equation theories of molecular liquids which allow for a finer and faster spanning of the temperature-density diagram. Our results may serve as a framework for a more systematic investigation of self-assembled structures of functionalized hard-soft dimers able to aggregate in a variety of structures widely oberved in colloidal dispersion.

Amyloid cross-seeding raises new dimensions to understanding of amyloidogenesis mechanism

Hallmarks of most of the amyloid pathologies are surprisingly found to be heterocomponent entities such as inclusions and plaques which contain diverse essential proteins and metabolites. Experimental studies have already revealed the occurrence of coaggregation and cross-seeding during amyloid formation of several proteins and peptides, yielding multicomponent assemblies of amyloid nature. Further, research reports on the co-occurrence of more than one type of amyloid-linked pathologies in the same individual suggest the possible cross-talk among the disease related amyloidogenic protein species during their amyloid growth. In this review paper, we have tried to gain more insight into the process of coaggregation and cross-seeding during amyloid aggregation of proteins, particularly focusing on their relevance to the pathogenesis of the protein misfolding diseases. Revelation of amyloid cross-seeding and coaggregation seems to open new dimensions in our mechanistic understanding of amyloidogenesis and such knowledge may possibly inspire better designing of anti-amyloid therapeutics.

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.

A Multiscale Model for the Self-Assembly of Coat Proteins in Bacteriophage MS2

The self-assembly of viral capsids is an essential step to the formation of infectious viruses. Elucidating the kinetic mechanisms of how a capsid or virus-like particle assembles could advance our knowledge about the viral lifecycle, as well as the general principles in self-assembly of biomaterials. However, current understanding of capsid assembly remains incomplete for many viruses due to the fact that the transient intermediates along the assembling pathways are experimentally difficult to be detected. In this paper, we constructed a new multiscale computational framework to simulate the self-assembly of virus-like particles. We applied our method to the coat proteins of bacteriophage MS2 as a specific model system. This virus-like particle of bacteriophage MS2 has a unique feature that its 90 sequence-identical dimers can be classified into two structurally various groups: one is the symmetric CC dimer, and the other is the asymmetric AB dimer. The homotypic interactions between AB dimers result in a 5-fold symmetric contact, while the heterotypic interactions between AB and CC dimers result in 6-fold symmetric contact. We found that the assembly can be described as a physical process of phase transition that is regulated by various factors such as concentration and specific stoichiometry between AB and CC dimers. Our simulations also demonstrate that heterotypic and homotypic interfaces play distinctive roles in modulating the assembling kinetics. The interaction between AB and CC dimers is much more dynamic than that between two AB dimers. We therefore suggest that the alternate growth of viral capsid through the heterotypic dimer interactions dominates the assembling pathways. This is, to the best of our knowledge, the first multiscale model to simulate the assembling process of coat proteins in bacteriophage MS2. The generality of this approach opens the door to its further applications in assembly of other viral capsids, virus-like particles, and novel drug delivery systems.

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.

Surface heterogeneity affects percolation and gelation of colloids: dynamic simulations with random patchy spheres

Surface heterogeneity of colloidal particles has a significant impact on their structure in solution and their rheological properties. During particle synthesis, heterogeneous chemical functionalization, processes of self-assembly, or phase separation, can all lead to heterogeneous colloidal surfaces which impart anisotropic interactions to suspended particles. Additionally, an important class of colloids, biological macromolecules, exhibit similar localized, short-ranged, anisotropic interactions, which have a significant impact on their solution properties. Therefore, understanding the assembly and rheology of such colloids can provide insight into a wide variety of relevant physical systems. In this computational study, we investigate dispersions of particles having surface patches with randomized functionality as a model for heterogeneous colloids. We use Brownian dynamics simulations with hydrodynamic interactions to explore the differences between these random patchy particles and homogeneous (or isotropic) particles. The common basis used for comparing dispersions of particles with different surface functionality is equality of the second virial coefficient, so that dispersions of particles with different patterns of surface heterogeneity are similar thermodynamically at low particle concentrations. We show that at modest particle concentrations, significant deviations from the isotropic model are evident in the dispersion micro-structure, giving drastically different percolation transition points depending on the degree of surface heterogeneity. However, these deviations can be rationalized and a universal percolation criteria derived in terms of the osmotic pressure of the dispersion. Heterogeneous interactions also impose extra constraints on the relative translation and rotation between neighboring particles, which increase the viscosity and elastic modulus of aggregated dispersions and gels built from heterogeneous colloids and shifts the gel point measurably.

Breakdown of the law of rectilinear diameter and related surprises in the liquid-vapor coexistence in systems of patchy particles

The phase diagram of molecular or colloidal systems depends strongly on the range and angular dependence of the interactions between the constituent particles. For instance, it is well known that the critical density of particles with "patchy" interactions shifts to lower values as the number of patches is decreased [see Bianchi et al. Phys. Rev. Lett. 97, 168301 (2006)]. Here, we present simulations that show that the phase behavior of patchy particles is even more interesting than had been appreciated. In particular, we find that, upon cooling below the critical point, the width of the liquid-vapor coexistence region of a system of particles with tetrahedrally arranged patches first increases, then decreases, and finally increases again. In other words, this system exhibits a doubly re-entrant liquid-vapor transition. As a consequence, the system exhibits a very large deviation from the law of rectilinear diameter, which assumes that the critical density can be obtained by linear extrapolation of the averages of the densities of the coexisting liquid and vapor phases. We argue that the unusual behavior of this system has the same origin as the density maximum in liquid water and is not captured by the Wertheim theory. The Wertheim theory also cannot account for our observation that the phase diagram of particles with three patches depends strongly on the geometrical distribution of the patches and on the degree to which their position on the particle surface is rigidly constrained. However, the phase diagram is less sensitive to small angular spreads in the patch locations. We argue that the phase behavior reported in this paper should be observable in experiments on patchy colloids and may be relevant for the liquid-liquid equilibrium in solutions of properly functionalized dendrimers.

A molecular model for self-assembly of the synaptonemal complex protein SYCE3

The synaptonemal complex (SC) is a supramolecular protein assembly that mediates homologous chromosome synapsis during meiosis. This zipper-like structure assembles in a continuous manner between homologous chromosome axes, enforcing a 100-nm separation along their entire length and providing the necessary three-dimensional framework for cross-over formation. The mammalian SC comprises eight components-synaptonemal complex protein 1-3 (SYCP1-3), synaptonemal complex central element protein 1-3 (SYCE1-3), testis-expressed 12 (TEX12), and six6 opposite strand transcript 1 (SIX6OS1)-arranged in transverse and longitudinal structures. These largely α-helical, coiled-coil proteins undergo heterotypic interactions, coupled with recursive self-assembly of SYCP1, SYCE2-TEX12, and SYCP2-SYCP3, to achieve the vast supramolecular SC structure. Here, we report a novel self-assembly mechanism of the SC central element component SYCE3, identified through multi-angle light scattering and small-angle X-ray scattering (SAXS) experiments. These analyses revealed that SYCE3 adopts a dimeric four-helical bundle structure that acts as the building block for concentration-dependent self-assembly into a series of discrete higher-order oligomers. We observed that this is achieved through staggered lateral interactions between self-assembly surfaces of SYCE3 dimers and through end-on interactions that likely occur through intermolecular domain swapping between dimer folds. These mechanisms are combined to achieve potentially limitless SYCE3 assembly, particularly favoring formation of dodecamers of three laterally associated end-on tetramers. Our findings extend the family of self-assembling proteins within the SC and reveal additional means for structural stabilization of the SC central element.

A Colloid Approach to Self-Assembling Antibodies

Concentrated solutions of monoclonal antibodies have attracted considerable attention due to their importance in pharmaceutical formulations; yet, their tendency to aggregate and the resulting high viscosity pose considerable problems. Here we tackle this problem by a soft condensed matter physics approach, which combines a variety of experimental measurements with a patchy colloid model, amenable of analytical solution. We thus report results of structural antibodies and dynamic properties obtained through scattering methods and microrheological experiments. We model the data using a colloid-inspired approach, explicitly taking into account both the anisotropic shape of the molecule and its charge distribution. Our simple patchy model is able to disentangle self-assembly and intermolecular interactions and to quantitatively describe the concentration-dependence of the osmotic compressibility, collective diffusion coefficient, and zero shear viscosity. Our results offer new insights on the key problem of antibody formulations, providing a theoretical and experimental framework for a quantitative assessment of the effects of additional excipients or chemical modifications and a prediction of the resulting viscosity.

Twisted Ribbon Aggregates in a Model Peptide System

The model peptides A₈K and A₁₀K self-assemble in water into ca. 100 nm long ribbon-like aggregates. These structures can be described as β-sheets laminated into a ribbon structure with a constant elliptical cross-section of 4 by 8 nm, where the longer axis corresponds to a finite number, N ≈ 15, of laminated sheets, and 4 nm corresponds to a stretched peptide length. The ribbon cross-section is strikingly constant and independent of the peptide concentration. High-contrast transmission electron microscopy shows that the ribbons are twisted with a pitch λ ≈ 15 nm. The self-assembly is analyzed within a simple model taking into account the interfacial free energy of the hydrophobic β-sheets and a free energy penalty arising from an increased stretching of hydrogen bonds within the laminated β-sheets, arising from the twist of the ribbons. The model predicts an optimal value N, in agreement with the experimental observations.

Directing curli polymerization with DNA origami nucleators

The physiological or pathological formation of fibrils often relies on molecular-scale nucleators that finely control the kinetics and structural features. However, mechanistic understanding of how protein nucleators mediate fibril formation in cells remains elusive. Here, we develop a CsgB-decorated DNA origami (CB-origami) to mimic protein nucleators in Escherichia coli biofilm that direct curli polymerization. We show that CB-origami directs curli subunit CsgA monomers to form oligomers and then accelerates fibril formation by increasing the proliferation rate of primary pathways. Fibrils grow either out from (departure mode) or towards the nucleators (arrival mode), implying two distinct roles of CsgB: as nucleation sites and as trap sites to capture growing nanofibrils in vicinity. Curli polymerization follows typical stop-and-go dynamics but exhibits a higher instantaneous elongation rate compared with independent fibril growth. This origami nucleator thus provides an in vitro platform for mechanistically probing molecular nucleation and controlling directional fibril polymerization for bionanotechnology.

Controlling the Self-Assembly of Biomolecules into Functional Nanomaterials through Internal Interactions and External Stimulations: A Review

Biomolecular self-assembly provides a facile way to synthesize functional nanomaterials. Due to the unique structure and functions of biomolecules, the created biological nanomaterials via biomolecular self-assembly have a wide range of applications, from materials science to biomedical engineering, tissue engineering, nanotechnology, and analytical science. In this review, we present recent advances in the synthesis of biological nanomaterials by controlling the biomolecular self-assembly from adjusting internal interactions and external stimulations. The self-assembly mechanisms of biomolecules (DNA, protein, peptide, virus, enzyme, metabolites, lipid, cholesterol, and others) related to various internal interactions, including hydrogen bonds, electrostatic interactions, hydrophobic interactions, π⁻π stacking, DNA base pairing, and ligand⁻receptor binding, are discussed by analyzing some recent studies. In addition, some strategies for promoting biomolecular self-assembly via external stimulations, such as adjusting the solution conditions (pH, temperature, ionic strength), adding organics, nanoparticles, or enzymes, and applying external light stimulation to the self-assembly systems, are demonstrated. We hope that this overview will be helpful for readers to understand the self-assembly mechanisms and strategies of biomolecules and to design and develop new biological nanostructures or nanomaterials for desired applications.

The crystal structures of benzyl-ammonium phenyl-acetate and its hydrate

The title compounds benzyl-ammonium phenyl-acetate, C7H10N+·C8H7O2 - (1), and its monohydrate, C7H10N+·C8H7O2 -·H2O (2), can be obtained by evaporating methano-lic solutions containing equimolar amounts of benzyl-amine and phenyl-acetic acid in the absence and presence of water, respectively. N-H⋯O hydrogen bonds in the crystal structure of 1 lead to the formation of hydro-philic channels running along the b-axis direction. The hydrogen-bonding system is best described by fused R 3 4(10) ring patterns, often observed in ammonium carboxyl-ate salts. In 2, the presence of the crystal water leads to the formation of a two-dimensional hydrogen-bonding network. The benzyl moieties in 1 and 2 form hydro-phobic layers in the crystal structures with the aromatic rings adopting edge-to-face arrangements.

Life under Continuous Streaming: Recrystallization of Low Concentrations of Bacterial SbpA in Dynamic Flow Conditions

The well-known bacterial S-layer protein SbpA from Lysinibacillus sphaericus CCM2177 induces spontaneous crystal formation via cooperative self-assembly of the protein subunits into an ordered supramolecular structure. Recrystallization occurs in the presence of divalent cations (i.e., Ca2+) and finally leads to producing smooth 2-D crystalline coatings composed of squared (p4) lattice structures. Among the factors interfering in such a process, the rate of protein supply certainly plays an important role since a limited number of accessible proteins might turn detrimental for film completion. Studies so far have mostly focused on high SbpA concentrations provided under stopped-flow or dynamic-flow conditions, thus omitting the possibility of investigating intermediate states, in which dynamic flow is applied for more critical concentrations of SbpA (i.e., 25, 10, and 5 µg/mL). In this work, we have characterized both physico-chemical and topographical aspects of the assembly and recrystallization of SbpA protein in such low concentration conditions by means of in situ Quartz Crystal Microbalance with Dissipation (QCMD) and atomic force microscopy (AFM) measurements, respectively. On the basis of these experiments, we can confirm how the application of a dynamic flow influences the formation of a closed and crystalline protein film from low protein concentrations (i.e., 10 µg/mL), which otherwise would not be formed.

Soft-Matter Approaches for Controlling Food Protein Interactions and Assembly

Animal- and plant-based proteins are present in a wide variety of raw and processed foods. They play an important role in determining the final structure of food matrices. Food proteins are diverse in terms of their biological origin, molecular structure, and supramolecular assembly. This diversity has led to segmented experimental studies that typically focus on one or two proteins but hinder a more general understanding of food protein structuring as a whole. In this review, we propose a unified view of how soft-matter physics can be used to control food protein assembly. We discuss physical models from polymer and colloidal science that best describe and predict the phase behavior of proteins. We explore the occurrence of phase transitions along two axes: increasing protein concentration and increasing molecular attraction. This review provides new perspectives on the link between the interactions, phase transitions, and assembly of proteins that can help in designing new food products and innovative food processing operations.

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.

The physiology of impenetrable skin: Colossus of the X-Men

The X-Men are an ensemble of superheroes whose powers are associated with the X-Gene, a mutant genetic factor. The powers exhibited by each character differ and are dependent on how the X-Gene has modified their individual genomes. For instance, Wolverine possesses regenerative healing, Storm can control local weather systems, and Colossus can create an impenetrable "organic steel" layer around his body. Thanks to the establishment of the superhero genre in modern cinema, audiences are familiar with Colossus from films such as X-Men: Days of Future Past and Deadpool. While attaining this power might be attractive to many people, there are innumerate scientific obstacles to be overcome to replicate this "organic steel" layer. Due to its unique combination of high strength and flexibility, a graphene-based layer might be a more realistic material for Colossus' impenetrable skin and would also address a number of physiological issues associated with an "organic steel" layer. The actualization of this layer would depend on complex processes associated with protein folding, protein self-assembly, and changing the structure of his skin. In the classroom, Colossus can foster a multidisciplinary learning environment where concepts in physiology can overlap with topics in physics, engineering, and materials science. Just like other superheroes, Colossus can also be used to promote scientific content in outreach for the general public.

Controlling the viscosities of antibody solutions through control of their binding sites

For biotechnological drugs, it is desirable to formulate antibody solutions with low viscosities. We go beyond previous colloid theories in treating protein-protein self-association of molecules that are antibody-shaped and flexible and have spatially specific binding sites. We consider interactions either through fragment antigen (Fab-Fab) or fragment crystalizable (Fab-Fc) binding. Wertheim's theory is adapted to compute the cluster-size distributions, viscosities, second virial coefficients, and Huggins coefficients, as functions of antibody concentration. We find that the aggregation properties of concentrated solutions can be anticipated from simpler-to-measure dilute solutions. A principal finding is that aggregation is controllable, in principle, through modifying the antibody itself, and not just the solution it is dissolved in. In particular: (i) monospecific antibodies having two identical Fab arms can form linear chains with intermediate viscosities. (ii) Bispecific antibodies having different Fab arms can, in some cases, only dimerize, having low viscosities. (iii) Arm-to-Fc binding allows for three binding partners, leading to networks and high viscosities.

Fibrous Protein Self-Assembly in Biomimetic Materials

Protein self-assembly processes, by which polypeptides interact and independently form multimeric structures, lead to a wide array of different endpoints. Structures formed range from highly ordered molecular crystals to amorphous aggregates. Order arises in the system from a balance between many low-energy processes occurring due to a set of interactions between residues in a chain, between residues in different chains, and between solute and solvent. In Nature, self-assembling protein systems have evolved over millions of years to organize into supramolecular structures, optimized for specific functions, with this propensity determined by the sequence of their constituent amino acids, of which only 20 are encoded in DNA. The structural materials that arise from biological self-assembly can display remarkable mechanical properties, often as a result of hierarchical structure on the nano- and microscales, and much research has been devoted to mimicking and exploiting these properties for a variety of end uses. This work presents a review of a range of studies in which biological functions are effectively reproduced through the design of self-assembling fibrous protein systems.

Understanding the Interplay between Self-Assembling Peptides and Solution Ions for Tunable Protein Nanoparticle Formation

Protein-based nanomaterials are gaining importance in biomedical and biosensor applications where tunability of the protein particle size is highly desirable. Rationally designed proteins and peptides offer control over molecular interactions between monomeric protein units to modulate their self-assembly and thus particle formation. Here, using an example enzyme-peptide system produced as a single construct by bacterial expression, we explore how solution conditions affect the formation and size of protein nanoparticles. We found two independent routes to particle formation, one facilitated by charge interactions between protein-peptide and peptide-peptide exemplified by pH change or the presence of NO₃^- or NH₄⁺ and the second route via metal-ion coordination ( e.g., Mg²⁺) within peptides. We further demonstrate that the two independent factors of pH and Mg²⁺ ions can be combined to regulate nanoparticle size. Charge interactions between protein-peptide monomers play a key role in either promoting or suppressing protein assembly; the intermolecular contact points within protein-peptide monomers involved in nanoparticle formation were identified by chemical cross-linking mass spectrometry. Importantly, the protein nanoparticles retain their catalytic activities, suggesting that their native structures are unaffected. Once formed, protein nanoparticles remain stable over long periods of storage or with changed solution conditions. Nevertheless, formation of nanoparticles is also reversible-they can be disassembled by desalting the buffer to remove complexing agents ( e.g., Mg²⁺). This study defines the factors controlling formation of protein nanoparticles driven by self-assembly peptides and an understanding of complex ion-peptide interactions involved within, offering a convenient approach to tailor protein nanoparticles without changing amino acid sequence.

Self-assembly of toroidal proteins explored using native mass spectrometry

The peroxiredoxins are a well characterised family of toroidal proteins which can self-assemble into a striking array of quaternary structures, including protein nanotubes, making them attractive as building blocks for nanotechnology.

The peroxiredoxins are a well characterised family of toroidal proteins which can self-assemble into a striking array of quaternary structures, including protein nanotubes, making them attractive as building blocks for nanotechnology. Tools to characterise these assemblies are currently scarce. Here, assemblies of peroxiredoxin proteins were examined using native mass spectrometry and complementary solution techniques. We demonstrated unequivocally that tube formation is fully reversible, a useful feature in a molecular switch. Simple assembly of individual toroids was shown to be tunable by pH and the presence of a histidine tag. Collision induced dissociation experiments on peroxiredoxin rings revealed a highly unusual symmetrical disassembly pathway, consistent with the structure disassembling as a hexamer of dimers. This study provides the foundation for the rational design and precise characterisation of peroxiredoxin protein structures where self-assembly can be harnessed as a key feature for applications in nanotechnology.

Theory for the Liquid-Liquid Phase Separation in Aqueous Antibody Solutions

This study presents the theory for liquid-liquid phase separation for systems of molecules modeling monoclonal antibodies. Individual molecule is depicted as an assembly of seven hard spheres, organized to mimic the Y-shaped antibody. We consider the antibody-antibody interactions either through Fab, Fab' (two Fab fragments may be different), or Fc domain. Interaction between these three domains of the molecule (hereafter denoted as A, B, and C, respectively) is modeled by a short-range square-well attraction. To obtain numerical results for the model under study, we adapt Wertheim's thermodynamic perturbation theory. We use this model to calculate the liquid-liquid phase separation curve and the second virial coefficient B2. Various interaction scenarios are examined to see how the strength of the site-site interactions and their range shape the coexistence curve. In the asymmetric case, where an attraction between two sites is favored and the interaction energies for the other sites kept constant, critical temperature first increases and than strongly decreases. Some more microscopic information, for example, the probability for the particular two sites to be connected, has been calculated. Analysis of the experimental liquid-liquid phase diagrams, obtained from literature, is presented. In addition, we calculate the second virial coefficient under conditions leading to the liquid-liquid phase separation and present this quantity on the graph B2 versus protein concentration.

Mimicking Pathogenic Invasion with the Complexes of Au22(SG)18-Engineered Assemblies and Folic Acid

Biological systems provide the richest spectrum of sophisticated design for materials engineering. We herein provide a paradigm of Au₂₂(SG)₁₈-engineered (SG, glutathione thiolate) and hydrogen bonds engaged assemblies for mimicking capsid protein self-assembly. The water-evaporation-induced self-assembly method allows discrete ultrasmall gold nanoclusters (GNCs) to be self-assembled into super-GNCs assemblies (SGNCs) ranging from nano-, meso- to microscale in water-dimethyl sulfoxide binary solvents in a template-free manner. After removing free and hydration layer water molecules, the formation of SGNCs is engaged by the collective cohesion of hydrogen bonds between glutathione ligands of gradually approaching GNCs. Then, a series of tightly orchestrated cellular events induced by the complexes of Au₂₂(SG)₁₈-engineered assemblies and folic acid are demonstrated to mimic the invasion of eukaryotic cells by pathogens. First, the activation of macropinocytosis mimics the macropinocytic entry used by the pathogens to invade host cells. Then the cytoplasmic vacuolization is a mimicry of vacuolating effects induced by the oligomeric vacuolating toxins secreted by some bacteria. Lastly, the escaping from macropinosomes into cytosol is in a vacuolating toxin's strategy. The findings demonstrate the capabilities of artificial pathogens to emulate the structures and functions of natural pathogens.

Self-Assembly of Ionic Microgels Driven by an Alternating Electric Field: Theory, Simulations, and Experiments

The structural properties of a system of ionic microgels under the influence of an alternating electric field are investigated both theoretically and experimentally. This combined investigation aims to shed light on the structural transitions that can be induced by changing either the driving frequency or the strength of the applied field, which range from string-like formation along the field to crystal-like structures across the orthogonal plane. In order to highlight the physical mechanisms responsible for the observed particle self-assembly, we develop a coarse-grained description, in which effective interactions among the charged microgels are induced by both equilibrium ionic distributions and their time-averaged hydrodynamic responses to the applied field. These contributions are modeled by the buildup of an effective dipole moment at the microgels backbones, which is partially screened by their ionic double layer. We show that this description is able to capture the structural properties of this system, allowing for very good agreement with the experimental results. The model coarse-graining parameters are indirectly obtained via the measured pair distribution functions and then further assigned with a clear physical interpretation, allowing us to highlight the main physical mechanisms accounting for the observed self-assembly behavior.

How to simulate patchy particles⋆

Patchy particles is the name given to a large class of systems of mesoscopic particles characterized by a repulsive core and a discrete number of short-range and highly directional interaction sites. Numerical simulations have contributed significantly to our understanding of the behaviour of patchy particles, but, although simple in principle, advanced simulation techniques are often required to sample the low temperatures and long time-scales associated with their self-assembly behaviour. In this work we review the most popular simulation techniques that have been used to study patchy particles, with a special focus on Monte Carlo methods. We cover many of the tools required to simulate patchy systems, from interaction potentials to biased moves, cluster moves, and free-energy methods. The review is complemented by an educationally oriented Monte Carlo computer code that implements all the techniques described in the text to simulate a well-known tetrahedral patchy particle model.

Self assembled linear polymeric chains with tuneable semiflexibility using isotropic interactions

We propose a two-body spherically symmetric (isotropic) potential such that particles interacting by the potential self-assemble into linear semiflexible polymeric chains without branching. By suitable control of the potential parameters, we can control the persistence length of the polymer and can even introduce a controlled number of branches. Thus we show how to achieve effective directional interactions starting from spherically symmetric potentials. The self-assembled polymers have an exponential distribution of chain lengths akin to what is observed for worm-like micellar systems. On increasing particle density, the polymeric chains self-organize to an ordered line-hexagonal phase where every chain is surrounded by six parallel chains, the transition is first order. On further increase in monomer density, the order is destroyed and we get a branched gel-like phase. This potential can be used to model semi-flexible equilibrium polymers with tunable semiflexibility and excluded volume. The use of the potential is computationally cheap and hence can be used to simulate and probe equilibrium polymer dynamics with long chains. The potential also gives a plausible method of tuning colloidal interactions in experiments such that one can obtain self-assembling polymeric chains made up of colloids and probe polymer dynamics using an optical microscope. Furthermore, we show how a modified potential leads to the observation of an intermediate nematic phase of self-assembled chains in between the low density disordered phase and the line-ordered hexagonal phase.

Creation of artificial protein-protein interactions using α-helices as interfaces

Designing novel protein-protein interactions (PPIs) with high affinity is a challenging task. Directed evolution, a combination of randomization of the gene for the protein of interest and selection using a display technique, is one of the most powerful tools for producing a protein binder. However, the selected proteins often bind to the target protein at an undesired surface. More problematically, some selected proteins bind to their targets even though they are unfolded. Current state-of-the-art computational design methods have successfully created novel protein binders. These computational methods have optimized the non-covalent interactions at interfaces and thus produced artificial protein complexes. However, to date there are only a limited number of successful examples of computationally designed de novo PPIs. De novo design of coiled-coil proteins has been extensively performed and, therefore, a large amount of knowledge of the sequence-structure relationship of coiled-coil proteins has been accumulated. Taking advantage of this knowledge, de novo design of inter-helical interactions has been used to produce artificial PPIs. Here, we review recent progress in the in silico design and rational design of de novo PPIs and the use of α-helices as interfaces.

Valence, loop formation and universality in self-assembling patchy particles

Patchy particles have emerged as an attractive model to mimic phase separation and self-assembly of globular proteins solutions, colloidal patchy particles, and molecular fluids where directional interactions are operative. In our previous work, we extensively explored the coupling of directional and isotropic interactions on both the phase separation and self-assembly in a system of patchy particles with five spots. Here, we extend this work to consider different patch valences and isotropic interaction strengths with an emphasis on self-assembly. Although the location of self-assembly transition lines in the temperature-density plane depend on a number of parameters, we find universal behavior of cluster size that is dependent only on the probability of a spot being bound, the patch valence, and the density. Using these principles, we quantify both the mass distribution and the shape for all clusters, as well as clusters containing loops. Following the logical implications of these results, combined with a simplified version of a mean-field theory that incorporates Flory-Stockmayer theory, we find a universal curve for the temperature dependence of cluster mass and a universal curve for the fraction of clusters that contain loops. As the curves are dependent on the particle valence, such results provide a method for parameterizing patchy particle models using experimental data.

Complex patchy colloids shaped from deformable seed particles through capillary interactions

We investigate the mechanisms underlying the reconfiguration of random aggregates of spheres through capillary interactions, the so-called "colloidal recycling" method, to fabricate a wide variety of patchy particles. We explore the influence of capillary forces on clusters of deformable seed particles by systematically varying the crosslink density of the spherical seeds. Spheres with a poorly crosslinked polymer network strongly deform due to capillary forces and merge into large spheres. With increasing crosslink density and therefore rigidity, the shape of the spheres is increasingly preserved during reconfiguration, yielding patchy particles of well-defined shape for up to five spheres. In particular, we find that the aspect ratio between the length and width of dumbbells, L/W, increases with the crosslink density (cd) as L/W = B - A·exp(-cd/C). For clusters consisting of more than five spheres, the particle deformability furthermore determines the patch arrangement of the resulting particles. The reconfiguration pathway of clusters of six densely or poorly crosslinked seeds leads to octahedral and polytetrahedral shaped patchy particles, respectively. For seven particles several geometries were obtained with a preference for pentagonal dipyramids by the rigid spheres, while the soft spheres do rarely arrive in these structures. Even larger clusters of over 15 particles form non-uniform often aspherical shapes. We discuss that the reconfiguration pathway is largely influenced by confinement and geometric constraints. The key factor which dominates during reconfiguration depends on the deformability of the spherical seed particles.

Nuclear spin singlet states as magnetic on/off probes in self-assembling systems

Nuclear singlet states in thermo-responsive peptides are introduced as magnetic on/off switches.

Non-ideal behavior of binary aqueous mixtures of some urea derivatives and their capacity to induce lysozyme gelation

The urea derivatives, namely, ethylurea (EU), 1,3 dimethylurea (1,3-DMU) and 1,1 diethylurea (1,1-DEU), in the limiting regions of their solubilities in water, and tetramethylurea (TMU) at w≥0.65 were investigated in relation to their capacity of inducing hen egg white lysozyme (HEWL) physical (non-covalent) gelation. Protein transparent gels were generated out of TMU/H₂O and 1,1-DEU/H₂O, respectively, whereas an intensively turbid gel resulted from sol-gel transition taking place in EU/H₂O. Oscillatory rheology revealed distinctions in the gels' structural and dynamic characteristics. Hydration patterns of the derivatives in solution, sizes of their non-polar domains and supramolecular symmetry features played a central role in their capacity of gel formation and in the gels' rheological behavior and morphology. Effects on gel characteristics of distinctively positioned ions in the Hofmeister series showed that SCN^- disrupted water H-bonding interconnectivity in TMU lysozyme gel, strengthening gel structure, yet maintaining gel transparency. Citrate enhanced system elasticity albeit causing intense turbidity and leading to phase separation. Larger values of the storage modulus, G', were verified for gels generated from binary mixtures containing urea derivatives with higher dipole moments.

pH Dependence of Charge Multipole Moments in Proteins

Electrostatic interactions play a fundamental role in the structure and function of proteins. Due to ionizable amino acid residues present on the solvent-exposed surfaces of proteins, the protein charge is not constant but varies with the changes in the environment-most notably, the pH of the surrounding solution. We study the effects of pH on the charge of four globular proteins by expanding their surface charge distributions in terms of multipoles. The detailed representation of the charges on the proteins is in this way replaced by the magnitudes and orientations of the multipole moments of varying order. Focusing on the three lowest-order multipoles-the total charge, dipole, and quadrupole moment-we show that the value of pH influences not only their magnitudes, but more notably and importantly also the spatial orientation of their principal axes. Our findings imply important consequences for the study of protein-protein interactions and the assembly of both proteinaceous shells and patchy colloids with dissociable charge groups.

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.

Orbitals for classical arbitrary anisotropic colloidal potentials

Coarse-grained potentials are ubiquitous in mesoscale simulations. While various methods to compute effective interactions for spherically symmetric particles exist, anisotropic interactions are seldom used, due to their complexity. Here we describe a general formulation, based on a spatial decomposition of the density fields around the particles, akin to atomic orbitals. We show that anisotropic potentials can be efficiently computed in numerical simulations using Fourier-based methods. We validate the field formulation and characterize its computational efficiency with a system of colloids that have Gaussian surface charge distributions. We also investigate the phase behavior of charged Janus colloids immersed in screened media, with screening lengths comparable to the colloid size. The system shows rich behaviors, exhibiting vapor, liquid, gel, and crystalline morphologies, depending on temperature and screening length. The crystalline phase only appears for symmetric Janus particles. For very short screening lengths, the system undergoes a direct transition from a vapor to a crystal on cooling; while, for longer screening lengths, a vapor-liquid-crystal transition is observed. The proposed formulation can be extended to model force fields that are time or orientation dependent, such as those in systems of polymer-grafted particles and magnetic colloids.

Geometrical frustration yields fiber formation in self-assembly

Controlling the self-assembly of supramolecular structures is vital for living cells, and a central challenge for engineering at the nano- and microscales [1, 2]. Nevertheless, even particles without optimized shapes can robustly form well-defined morphologies. This is the case in numerous medical conditions where normally soluble proteins aggregate into fibers [3, 4]. Beyond the diversity of molecular mechanisms involved [5, 6], we propose that fibers generically arise from the aggregation of irregular particles with short-range interactions. Using a minimal model of ill-fitting, sticky particles, we demonstrate robust fiber formation for a variety of particle shapes and aggregation conditions. Geometrical frustration plays a crucial role in this process, and accounts for the range of parameters in which fibers form as well as for their metastable character.