Minimal model of self-assembly: emergence of diversity and complexity

Protein aggregation in health and disease: A looking glass of two faces

Protein molecules organize into an intricate alphabet of twenty amino acids and five architecture levels. The jargon "one structure, one functionality" has been challenged, considering the amount of intrinsically disordered proteins in the human genome and the requirements of hierarchical hetero- and homo-protein complexes in cell signaling. The assembly of large protein structures in health and disease is now viewed through the lens of phase separation and transition phenomena. What drives protein misfolding and aggregation? Or, more fundamentally, what hinders proteins from maintaining their native conformations, pushing them toward aggregation? Here, we explore the principles of protein folding, phase separation, and aggregation, which hinge on crucial events such as the reorganization of solvents, the chemical properties of amino acids, and their interactions with the environment. We focus on the dynamic shifts between functional and dysfunctional states of proteins and the conditions that promote protein misfolding, often leading to disease. By exploring these processes, we highlight potential therapeutic avenues to manage protein aggregation and reduce its harmful impacts on health.

Pore Formation by Amyloid-like Peptides: Effects of the Nonpolar-Polar Sequence Pattern

One of the mechanisms accounting for the toxicity of amyloid peptides in diseases like Alzheimer's and Parkinson's is the formation of pores on the plasma membrane of neurons. Here, we perform unbiased all-atom simulations of the full membrane damaging pathway, which includes adsorption, aggregation, and perforation of the lipid bilayer accounting for pore-like structures. Simulations are performed using four peptides made with the same amino acids. Differences in the nonpolar-polar sequence pattern of these peptides prompt them to adsorb into the membrane with the extended conformations oriented either parallel [peptide labeled F1, Ac-(FKFE)2-NH2], perpendicular (F4, Ac-FFFFKKEE-NH2), or with an intermediate orientation (F2, Ac-FFKKFFEE-NH2, and F3, Ac-FFFKFEKE-NH2) in regard to the membrane surface. At the water-lipid interface, only F1 fully self-assembles into β-sheets, and F2 peptides partially fold into an α-helical structure. The β-sheets of F1 emerge as electrostatic interactions attract neighboring peptides to intermediate distances where nonpolar side chains can interact within the dry core of the bilayer. This complex interplay between electrostatic and nonpolar interactions is not observed for the other peptides. Although β-sheets of F1 peptides are mostly parallel to the membrane, some of their edges penetrate deep inside the bilayer, dragging water molecules with them. This precedes pore formation, which starts with the flow of two water layers through the membrane that expand into a stable cylindrical pore delimited by polar faces of β-sheets spanning both leaflets of the bilayer.

Exploring changes in aggregation and gel network morphology of soybean protein isolate induced by pH, NaCl, and temperature in view of interactions

The texture of soybean protein-based products is primarily influenced by the aggregation and gel morphology of the protein, which is modulated by manufacturing factors. Interactions involved in protein morphology changes include disulfide bonds, hydrophobic interactions, electrostatic interactions, and hydrogen bonds. Notably, an interaction perspective probably provides a new way to explaining the aggregation and gel morphology, which could help overcome the hurdle of developing a textured product. Based on the interaction perspective, this review provides detailed information and evidence on aggregation, conformational stability, and gel network morphology of soybean protein and its components induced by pH, NaCl, and temperature. pH-induced electrostatic interactions and hydrogen bonds, NaCl-induced electrostatic interactions, and temperature-induced hydrophobic interactions and disulfide linkages are the main motivations responsible for changes in soybean aggregation and gel morphology. By reducing the proportion of strong-interactions, such as disulfide linkages and hydrophobic interactions, and increasing the proportion of weak-interactions, such as electrostatic interactions and hydrogen bonds, the protein total surface area expands, indicating increased conformational stretching and decreased cohesion. This possibly results in reduced hardness and increased toughness of textured proteins. The opposite effect can be observed when the proportion of strong interactions is increased and that of weak interactions is decreased.

Oligomer Formation by Physiologically Relevant C-Terminal Isoforms of Amyloid β-Protein

Alzheimer's disease (AD) is a neurological disorder associated with amyloid β-protein (Aβ) assembly into toxic oligomers. In addition to the two predominant alloforms, Aβ1-40 and Aβ1-42, other C-terminally truncated Aβ peptides, including Aβ1-38 and Aβ1-43, are produced in the brain. Here, we use discrete molecular dynamics (DMD) and a four-bead protein model with amino acid-specific hydropathic interactions, DMD4B-HYDRA, to examine oligomer formation of Aβ1-38, Aβ1-40, Aβ1-42, and Aβ1-43. Self-assembly of 32 unstructured monomer peptides into oligomers is examined using 32 replica DMD trajectories for each of the four peptides. In a quasi-steady state, Aβ1-38 and Aβ1-40 adopt similar unimodal oligomer size distributions with a maximum at trimers, whereas Aβ1-42 and Aβ1-43 oligomer size distributions are multimodal with the dominant maximum at trimers or tetramers, and additional maxima at hexamers and unidecamers (for Aβ1-42) or octamers and pentadecamers (for Aβ1-43). The free energy landscapes reveal isoform- and oligomer-order specific structural and morphological features of oligomer ensembles. Our results show that oligomers of each of the four isoforms have unique features, with Aβ1-42 alone resulting in oligomers with disordered and solvent-exposed N-termini. Our findings help unravel the structure-function paradigm governing oligomers formed by various Aβ isoforms.

Peptide Self-Assembly into Amyloid Fibrils: Unbiased All-Atom Simulations

Protein self-assembly plays an important role in biological systems, accounting for the formation of mesoscopic structures that can be highly symmetric as in the capsid of viruses or disordered as in molecular condensates or exhibit a one-dimensional fibrillar morphology as in amyloid fibrils. Deposits of the latter in tissues of individuals with degenerative diseases like Alzheimer's and Parkinson's has motivated extensive efforts to understand the sequence of molecular events accounting for their formation. These studies aim to identify on-pathway intermediates that may be the targets for therapeutic intervention. This detailed knowledge of fibril formation remains obscure, in part due to challenges with experimental analyses of these processes. However, important progress is being achieved for short amyloid peptides due to advances in our ability to perform completely unbiased all-atom simulations of the self-assembly process. This perspective discusses recent developments, their implications, and the hurdles that still need to be overcome to further advance the field.

Multimode microdimer robot for crossing tissue morphological barrier

Swimming microrobot energized by magnetic fields exhibits remotely propulsion and modulation in complex biological experiment with high precision. However, achieving high environment adaptability and multiple tasking capability in one configuration is still challenging. Here, we present a strategy that use oriented magnetized Janus spheres to assemble the microdimer robots with two magnetic distribution configurations of head-to-side configuration (HTS-config) and head-to-head configuration (HTH-config), achieving performance of multiple tasks through multimode transformation and locomotion. Modulating the magnetic frequency enables multimode motion transformation between tumbling, rolling, and swing motion with different velocities. The dual-asynchronization mechanisms of HTS-config and HTH-config robot dependent on magnetic dipole-dipole angle are investigated by molecular dynamic simulation. In addition, the microdimer robot can transport cell crossing morphological rugae or complete drug delivery on tissues by switching motion modes. This microdimer robot can provide versatile motion modes to address environmental variations or multitasking requirements.

Amyloid Aggregation and Liquid-Liquid Phase Separation from the Perspective of Phase Transitions

Amyloid aggregation describes the aberrant self-assembly of peptides into ordered fibrils characterized by cross-β spine cores and is associated with many neurodegenerative diseases and Type 2 diabetes. Oligomers, populated during the early stage of aggregation, are found to be more cytotoxic than mature fibrils. Recently, many amyloidogenic peptides have been reported to undergo liquid-liquid phase separation (LLPS)─a biological process important for the compartmentalization of biomolecules in living cells─prior to fibril formation. Understanding the relationship between LLPS and amyloid aggregation, especially the formation of oligomers, is essential for uncovering disease mechanisms and mitigating amyloid toxicity. In this Perspective, available theories and models of amyloid aggregation and LLPS are first briefly reviewed. By drawing analogies to gas, liquid, and solid phases in thermodynamics, a phase diagram of protein monomer, droplet, and fibril states separated by coexistence lines can be inferred. Due to the high free energy barrier of fibrillization kinetically delaying the formation of fibril seeds out of the droplets, a "hidden" monomer-droplet coexistence line extends into the fibril phase. Amyloid aggregation can then be described as the equilibration process from the initial "out-of-equilibrium" state of a homogeneous solution of monomers to the final equilibrium state of stable amyloid fibrils coexisting with monomers and/or droplets via the formation of metastable or stable droplets as the intermediates. The relationship between droplets and oligomers is also discussed. We suggest that the droplet formation of LLPS should be considered in future studies of amyloid aggregation, which may help to better understand the aggregation process and develop therapeutic strategies to mitigate amyloid toxicity.

Protein quality control and aggregation in the endoplasmic reticulum: From basic to bedside

Endoplasmic reticulum (ER) is the largest membrane-bound compartment in all cells and functions as a key regulator in protein biosynthesis, lipid metabolism, and calcium balance. Mammalian endoplasmic reticulum has evolved with an orchestrated protein quality control system to handle defective proteins and ensure endoplasmic reticulum homeostasis. Nevertheless, the accumulation and aggregation of misfolded proteins in the endoplasmic reticulum may occur during pathological conditions. The inability of endoplasmic reticulum quality control system to clear faulty proteins and aggregates from the endoplasmic reticulum results in the development of many human disorders. The efforts to comprehensively understand endoplasmic reticulum quality control network and protein aggregation will benefit the diagnostics and therapeutics of endoplasmic reticulum storage diseases. Herein, we overview recent advances in mammalian endoplasmic reticulum protein quality control system, describe protein phase transition model, and summarize the approaches to monitor protein aggregation. Moreover, we discuss the therapeutic applications of enhancing endoplasmic reticulum protein quality control pathways in endoplasmic reticulum storage diseases.

Transferable and Polarizable Coarse Grained Model for Proteins─ProMPT

The application of classical molecular dynamics (MD) simulations at atomic resolution (fine-grained level, FG), to most biomolecular processes, remains limited because of the associated computational complexity of representing all the atoms. This problem is magnified in the presence of protein-based biomolecular systems that have a very large conformational space, and MD simulations with fine-grained resolution have slow dynamics to explore this space. Current transferable coarse grained (CG) force fields in literature are either limited to only peptides with the environment encoded in an implicit form or cannot capture transitions into secondary/tertiary peptide structures from a primary sequence of amino acids. In this work, we present a transferable CG force field with an explicit representation of the environment for accurate simulations with proteins. The force field consists of a set of pseudoatoms representing different chemical groups that can be joined/associated together to create different biomolecular systems. This preserves the transferability of the force field to multiple environments and simulation conditions. We have added electronic polarization that can respond to environmental heterogeneity/fluctuations and couple it to protein's structural transitions. The nonbonded interactions are parametrized with physics-based features such as solvation and partitioning free energies determined by thermodynamic calculations and matched with experiments and/or atomistic simulations. The bonded potentials are inferred from corresponding distributions in nonredundant protein structure databases. We present validations of the CG model with simulations of well-studied aqueous protein systems with specific protein fold types─Trp-cage, Trpzip4, villin, WW-domain, and β-α-β. We also explore the applications of the force field to study aqueous aggregation of Aβ 16-22 peptides.

Computational models for studying physical instabilities in high concentration biotherapeutic formulations

Computational prediction of the behavior of concentrated protein solutions is particularly advantageous in early development stages of biotherapeutics when material availability is limited and a large set of formulation conditions needs to be explored. This review provides an overview of the different computational paradigms that have been successfully used in modeling undesirable physical behaviors of protein solutions with a particular emphasis on high-concentration drug formulations. This includes models ranging from all-atom simulations, coarse-grained representations to macro-scale mathematical descriptions used to study physical instability phenomena of protein solutions such as aggregation, elevated viscosity, and phase separation. These models are compared and summarized in the context of the physical processes and their underlying assumptions and limitations. A detailed analysis is also given for identifying protein interaction processes that are explicitly or implicitly considered in the different modeling approaches and particularly their relations to various formulation parameters. Lastly, many of the shortcomings of existing computational models are discussed, providing perspectives and possible directions toward an efficient computational framework for designing effective protein formulations.

Computational Models for the Study of Protein Aggregation

Protein aggregation has been studied by many groups around the world for many years because it can be the cause of a number of neurodegenerative diseases that have no effective treatment. Obtaining the structure of related fibrils and toxic oligomers, as well as describing the pathways and main factors that govern the self-organization process, is of paramount importance, but it is also very difficult. To solve this problem, experimental and computational methods are often combined to get the most out of each method. The effectiveness of the computational approach largely depends on the construction of a reasonable molecular model. Here we discussed different versions of the four most popular all-atom force fields AMBER, CHARMM, GROMOS, and OPLS, which have been developed for folded and intrinsically disordered proteins, or both. Continuous and discrete coarse-grained models, which were mainly used to study the kinetics of aggregation, are also summarized.

Soluble State of Villin Headpiece Protein as a Tool in the Assessment of MD Force Fields

Protein self-assembly plays an important role in cellular processes. Whereas molecular dynamics (MD) represents a powerful tool in studying assembly mechanisms, its predictions depend on the accuracy of underlying force fields, which are known to overly promote protein assembly. We here examine villin headpiece domain, HP36, which remains soluble at concentrations amenable to MD studies. The experimental characterization of soluble HP36 at concentrations of 0.05 to 1 mM reveals concentration-independent 90% monomeric and 10% dimeric populations. Extensive all-atom MD simulations at two protein concentrations, 0.9 and 8.5 mM, probe the HP36 dimer population, stability, and kinetics of dimer formation within two MD force fields, Amber ff14SB and CHARMM36m. MD results demonstrate that whereas CHARMM36m captures experimental HP36 monomer populations at the lower concentration, both force fields overly promote HP36 association at the higher concentration. Moreover, contacts stabilizing HP36 dimers are force-field-dependent. CHARMM36m produces consistently higher HP36 monomer populations, lower association rates, and weaker dependence of these quantities on the protein concentration than Amber ff14SB. Nonetheless, the highest monomer populations and dissociation constants are observed when the TIP3P water model in Amber ff14SB is replaced by TIP4P/2005, showcasing the critical role of the water model in addressing the protein solubility problem in MD.

Amyloid-Like Peptide Aggregates

Self-assembly of proteins and peptides into the amyloid fold is a widespread phenomenon in the natural world. The structural hallmark of self-assembly into amyloid fibrillar assemblies is the cross-beta motif, which conveys distinct morphological and mechanical properties. The amyloid fibril formation has contrasting results depending on the organism, in the sense that it can bestow an organism with the advantages of mechanical strength and improved functionality or, on the contrary, could give rise to pathological states. In this chapter we review the existing information on amyloid-like peptide aggregates, which could either be derived from protein sequences, but also could be rationally or de novo designed in order to self-assemble into amyloid fibrils under physiological conditions. Moreover, the development of self-assembled fibrillar biomaterials that are tailored for the desired properties towards applications in biomedical or environmental areas is extensively analyzed. We also review computational studies predicting the amyloid propensity of the natural amino acid sequences and the structure of amyloids, as well as designing novel functional amyloid materials.

Amyloid-β (Aβ42) Peptide Aggregation Rate and Mechanism on Surfaces with Widely Varied Properties: Insights from Brownian Dynamics Simulations

Amyloid-β (Aβ) plaques, which form by aggregation of harmless Aβ peptide monomers into larger fibrils, are characteristic of neurodegenerative disorders such as Alzheimer's disease. Efforts to treat Alzheimer's disease focus on stopping or reversing the aggregation process that leads to fibril formation. However, effective treatments are elusive due to certain unknown aspects of the process. Many hypotheses point to disruption of cell membranes by adsorbed Aβ monomers or oligomers, but how Aβ behaves and aggregates on surfaces of widely varying properties, such as those present in a cell, is unclear. Elucidating the effects of various surfaces on the dynamics of Aβ and the kinetics of the aggregation process from bulk solution to a surface-adsorbed multimer can help identify what drives aggregation, leading to new methods of intervention by inhibitory drugs or other means. In this work, we used all-atom Brownian dynamics simulations to study the association of two distinct Aβ42 monomer conformations with a surface-adsorbed or free-floating Aβ42 dimer. We calculated the association time, surface interaction energy, surface diffusion coefficient, surface residence time, and the mechanism of association on four different surfaces and two different bulk solution scenarios. In the presence of a surface, the majority of monomers underwent a two-dimensional surface-mediated association that depended primarily on an Aβ42 electrostatic interaction with the self-assembled monolayer (SAM) surfaces. Moreover, aggregation could be inhibited greatly by surfaces with high affinity for Aβ42 and heterogeneous charge distribution. Our results can be used to identify new opportunities for disrupting or reversing the Aβ42 aggregation process.

Disorder at the Tips of a Disease-Relevant Aβ42 Amyloid Fibril: A Molecular Dynamics Study

We present a simulation study of the early events of peptide dissociation from a fibril of the Alzheimer's Aβ42 peptide. The fibril consists of layers of two adjacent Aβ42 peptides each folded in an S-shaped structure which has been determined by solid state NMR spectroscopy of a monomorphic disease-relevant species. Multiple molecular dynamics runs (16 at 310 K and 15 at 370 K) were carried out starting from an 18-peptide protofibril for a cumulative sampling of about 15 μs. The simulations show structural stability of the fibrillar core and an overall increase in the twist to about 3 degrees. The N-terminal segment 1-14 is disordered in all peptides. At both ends of the fibril, the central segment 21-29, which includes part of the β₂ strand, dissociates in some of the simulations. The β₁ and β₃ strands, residues 15-20 and 35-41, respectively, are structurally stable. The transient binding of the N-terminal stretch to the β₃ strand of the adjacent peptide at the tip is likely to contribute to the arrest phase of the stop-and-go mechanism.

The attachment of α-synuclein to a fiber: A coarse-grain approach

We present simulations of the amyloidogenic core of α-synuclein, the protein causing Parkinson's disease, as a short chain of coarse-grain patchy particles. Each particle represents a sequence of about a dozen amino acids. The fluctuating secondary structure of this intrinsically disordered protein is modelled by dynamic variations of the shape and interaction characteristics of the patchy particles, ranging from spherical with weak isotropic attractions for the disordered state to spherocylindrical with strong directional interactions for a β-sheet. Flexible linkers between the particles enable sampling of the tertiary structure. This novel model is applied here to study the growth of an amyloid fibril, by calculating the free energy profile of a protein attaching to the end of a fibril. The simulation results suggest that the attaching protein readily becomes trapped in a mis-folded state, thereby inhibiting further growth of the fibril until the protein has readjusted to conform to the fibril structure, in line with experimental findings and previous simulations on small fragments of other proteins.

Assembly of Stefin B into Polymorphic Oligomers Probed by Discrete Molecular Dynamics

Assembly of an amyloidogenic protein stefin B into molten globule oligomers is studied by efficient discrete molecular dynamics. Consistent with in vitro findings, tetramers form primarily through dimer association, resulting in a decreased trimer abundance. Oligomers up to heptamers display elongated rod-like morphologies akin to protofibrils, whereas larger oligomers, decamers through dodecamers, form elongated, branched, as well as annular structures, providing structural insights into pore forming ability and toxicity of amyloidogenic proteins.

Self-assembly of trimer colloids: effect of shape and interaction range

Trimers with one attractive bead and two repulsive beads, similar to recently synthesized trimer patchy colloids, were simulated with flat-histogram Monte Carlo methods to obtain the stable self-assembled structures for different shapes and interaction potentials. Extended corresponding states principle was successfully applied to self-assembling systems in order to approximately collapse the results for models with the same shape, but different interaction range. This helps us directly compare simulation results with previous experiment, and good agreement was found between the two. In addition, a variety of self-assembled structures were observed by varying the trimer geometry, including spherical clusters, elongated clusters, monolayers, and spherical shells. In conclusion, our results help to compare simulations and experiments, via extended corresponding states, and we predict the formation of self-assembled structures for trimer shapes that have not been experimentally synthesized.

Prediction and clarification of structures of (bio)molecules on surfaces

The design of future materials for biotechnological applications via deposition of molecules on surfaces will require not only exquisite control of the deposition procedure, but of equal importance will be our ability to predict the shapes and stability of individual molecules on various surfaces. Furthermore, one will need to be able to predict the structure patterns generated during the self-organization of whole layers of (bio)molecules on the surface. In this review, we present an overview over the current state of the art regarding the prediction and clarification of structures of biomolecules on surfaces using theoretical and computational methods.

Computational study of trimer self-assembly and fluid phase behavior

The fluid phase diagram of trimer particles composed of one central attractive bead and two repulsive beads was determined as a function of simple geometric parameters using flat-histogram Monte Carlo methods. A variety of self-assembled structures were obtained including spherical micelle-like clusters, elongated clusters, and densely packed cylinders, depending on both the state conditions and shape of the trimer. Advanced simulation techniques were employed to determine transitions between self-assembled structures and macroscopic phases using thermodynamic and structural definitions. Simple changes in particle geometry yield dramatic changes in phase behavior, ranging from macroscopic fluid phase separation to molecular-scale self-assembly. In special cases, both self-assembled, elongated clusters and bulk fluid phase separation occur simultaneously. Our work suggests that tuning particle shape and interactions can yield superstructures with controlled architecture.

Stabilization of native amyloid β-protein oligomers by Copper and Hydrogen peroxide Induced Cross-linking of Unmodified Proteins (CHICUP)

Oligomeric assemblies are postulated to be proximate neurotoxic species in human diseases associated with aberrant protein aggregation. Their heterogeneous and transient nature makes their structural characterization difficult. Size distributions of oligomers of several amyloidogenic proteins, including amyloid β-protein (Aβ) relevant to Alzheimer's disease (AD), have been previously characterized in vitro by photo-induced cross-linking of unmodified proteins (PICUP) followed by sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE). Due to non-physiological conditions associated with the PICUP chemistry, Aβ oligomers cross-linked by PICUP may not be representative of in vivo conditions. Here, we examine an alternative Copper and Hydrogen peroxide Induced Cross-linking of Unmodified Proteins (CHICUP), which utilizes naturally occurring divalent copper ions and hydrogen peroxide and does not require photo activation. Our results demonstrate that CHICUP and PICUP applied to the two predominant Aβ alloforms, Aβ40 and Aβ42, result in similar oligomer size distributions. Thioflavin T fluorescence data and atomic force microscopy images demonstrate that both CHICUP and PICUP stabilize Aβ oligomers and attenuate fibril formation. Relative to noncross-linked peptides, CHICUP-treated Aβ40 and Aβ42 cause prolonged disruption to biomimetic lipid vesicles. CHICUP-stabilized Aβ oligomers link the amyloid cascade, metal, and oxidative stress hypotheses of AD into a more comprehensive understanding of the molecular basis of AD pathology. Because copper and hydrogen peroxide are elevated in the AD brain, CHICUP-stabilized Aβ oligomers are biologically relevant and should be further explored as a new therapeutic target.