Time evolution of amyloid fibril length distribution described by a population balance model

Surface-catalyzed liquid-liquid phase separation and amyloid-like assembly in microscale compartments

Liquid-liquid phase separation is a key phenomenon in the formation of membrane-less structures within the cell, appearing as liquid biomolecular condensates. Protein condensates are the most studied for their biological relevance, and their tendency to evolve, resulting in the formation of aggregates with a high level of order called amyloid. In this study, it is demonstrated that Human Insulin forms micrometric, round amyloid-like structures at room temperature within sub-microliter scale aqueous compartments. These distinctive particles feature a solid core enveloped by a fluid-like corona and form at the interface between the aqueous compartment and the glass coverslip upon which they are cast. Quantitative fluorescence microscopy is used to study in real-time the formation of amyloid-like superstructures. Their formation results driven by liquid-liquid phase separation process that arises from spatially heterogeneous distribution of nuclei at the glass-water interface. The proposed experimental setup allows modifying the surface-to-volume ratio of the aqueous compartments, which affects the aggregation rate and particle size, while also inducing fine alterations in the molecular structures of the final assemblies. These findings enhance the understanding of the factors governing amyloid structure formation, shedding light on the catalytic role of surfaces in this process.

Morphological integrity of insulin amyloid-like aggregates depends on preparation methods and post-production treatments

Protein aggregates are often varying extensively in their morphological characteristics, which may lead to various biological outcomes, such as increased immunogenicity risk. However, isolation of aggregates with a specific morphology within an ensemble is often challenging. To gain vital knowledge on the effects of aggregate characteristics, samples containing a single morphology must be produced by direct control of the aggregation process. Moreover, the formed aggregates need to be in an aqueous solution suitable for biological assays, while keeping their morphology intact. Here we evaluated the dependence of morphology and integrity of amyloid-like fibrils and spherulites on preparation conditions and post-treatment methods. Samples containing either amyloid-like fibrils or spherulites produced from human insulin in acetic acid solutions are dependent on the presence of salt (NaCl). Moreover, mechanical shaking (600 rpm) inhibits spherulite formation, while only affecting the length of the formed fibrils compared to quiescent conditions. Besides shaking, the initial protein concentration in the formulation was found to control fibril length. Surprisingly, exchanging the solution used for aggregate formation to a physiologically relevant buffer, had a striking effect on the morphological integrity of the fibril and spherulite samples. Especially the secondary structure of one of our spherulite samples presented dramatic changes of the aggregated β-sheet content after exchanging the solution, emphasizing the importance of the aggregate stability. These results and considerations have profound implications on the data interpretation and should be implemented in the workflow for both fundamental characterization of aggregates as well as assays for evaluation of their corresponding biological effects.

Multiscale Model for Quantitative Prediction of Insulin Aggregation Nucleation Kinetics

We combined kinetic, thermodynamic, and structural information from single-molecule (protein folding) and two-molecule (association) explicit-solvent simulations for determination of kinetic parameters in protein aggregation nucleation with insulin as the model protein. A structural bioinformatics approach was developed to account for heterogeneity of aggregation-prone species, with the transition complex theory found applicable in modeling association kinetics involving non-native species. Specifically, the kinetic pathway for formation of aggregation-prone oligomeric species was found to contain a structurally specific dominant binding mode, making the kinetic process similar to native protein association. The kinetic parameters thus obtained were used in a population balance model, and accurate predictions for aggregation nucleation time varying over 2 orders of magnitude with changes in either insulin concentration or an aggregation-inhibitor ligand concentration were obtained, while an empirical parameter set was not found to be transferable for prediction of ligand effects. Further, this physically determined kinetic parameter set provided several mechanistic insights, such as identification of the rate-limiting step in aggregation nucleation and a quantitative explanation for the switch from Arrhenius to non-Arrhenius aggregation kinetics around the melting temperature of insulin.

Kinetics of aggregation of amyloid β under different shearing conditions: Experimental and modelling analyses

Amyloid β (Aβ40) is a class of amyloidogenic proteins known to aggregate into a fibrillar network. The rate of aggregation and fibril yield is sensitive to external energy input, such as shear. In this work, simple shear and shaking experiments are performed on Aβ40 solution using a Couette cell and an orbital shaker, respectively. Experiments show that, under uniform shear, both the mass of fibrils and aggregation rate increase with the shear rate. In the case of orbital shaking, the lag time decreases with the rotational speed of the shaker, but the final fibril mass is the same for all agitation speeds. To explain this contrasting behavior of aggregation kinetics, a population balance model is developed to account for the effect of shear on the aggregation of Aβ. The kinetic model includes primary nucleation, secondary nucleation, elongation, fragmentation, and depolymerization steps. The effect of steady uniform shear is encoded in the depolymerization rate constant (k_d), and it is shown that k_d decreases with shear rate initially and saturates at high shear rates. A competition between elongation and depolymerization rates yields different equilibrium masses of fibril at different shear rates. The model results agree quantitatively well with experimental data on the rate of aggregation and mass of fibrils as a function of shear rate. The modeling framework can be used to explain the shear rate-dependent aggregation of other amyloidogenic proteins.

Computational Model for Studying Breakage-Dependent Amyloid Growth

Amyloid fibrils are typically associated with neurodegenerative diseases. Recent studies have suggested that, similar to prions, many amyloid proteins are infectious in nature and may cause spreading and dissemination of diseases. Typical amyloid infection propagates by recruiting functional proteins into amyloidogenic form and multiplying by breaking the existing fibril. In this study, we model the kinetics of fibril growth through breakage and the subsequent elongation process, similar to the prion infection process. Using kinetic Monte Carlo simulations as well as mathematical counting methods, we show how the measurable quantities like the 50% aggregation time (T₅₀) and the maximum growth rate (V_max) scale with various parameters in the problem. This study has a direct application where it can be used to understand experiments that amplify the minute amount of amyloid seeds present in biological fluid for early detection of human disease. Using the knowledge from our simulations, we can predict the initial seed concentration, known as the filament kinetics.

Investigating the Effects of Molecular Crowding on the Kinetics of Protein Aggregation

The thermodynamics and kinetics of protein folding and protein aggregation in vivo are of great importance in numerous scientific areas including fundamental biophysics research, nanotechnology, and medicine. However, these processes remain poorly understood in both in vivo and in vitro systems. Here we extend an established model for protein aggregation that is based on the kinetic equations for the moments of the polymer size distribution by introducing macromolecular crowding particles into the model using scaled-particle and transition-state theories. The model predicts that the presence of crowders can either speed up, cause no change to, or slow down the progress of the aggregation compared to crowder-free solutions, in striking agreement with experimental results from nine different amyloid-forming proteins that utilized dextran as the crowder. These different dynamic effects of macromolecular crowding can be understood in terms of the change of excluded volume associated with each reaction step.

Is a cross-β-sheet structure of low molecular weight peptides necessary for the formation of fibrils and peptide hydrogels?

Short peptides have emerged as versatile building blocks for supramolecular structures and hydrogels. In particular, the presence of aromatic amino acid residues and/or aromatic end groups is generally considered to be a prerequisite for initiating aggregation of short peptides into nanotubes or cross β-sheet type fibrils. However, the cationic GAG tripeptide surprisingly violates these rules. Specifically, in water/ethanol mixtures, GAG peptides aggregate into very long crystalline fibrils at temperatures below 35 °C where they eventually form a spanning network structure and, thus, a hydrogel. Two gel phases are formed in this network, and they differ substantially in chirality and thickness of the underlying fibrils, their rheological parameters, and the kinetics of oligomerization, fibrilization, and gel formation. The spectroscopic data strongly suggests that the observed fibrils do not exhibit canonical cross β-sheet structures and are indicative of a yet unknown secondary conformation. To complement our unusual experimental observations in this perspective article, we performed large-scale DFT calculations to probe the geometry and spectroscopic properties of these GAG oligomers. Most importantly, our experimental and computational results yield rather unconventional structures that are not reminiscent of classical cross-β-sheet structures, and we give two extremely likely candidates for oligomer structures that are consistent with experimental amide I' profiles in IR and vibrational circular dichroism (VCD) spectra of the two gel phases.

Biomolecular Assemblies: Moving from Observation to Predictive Design

Biomolecular assembly is a key driving force in nearly all life processes, providing structure, information storage, and communication within cells and at the whole organism level. These assembly processes rely on precise interactions between functional groups on nucleic acids, proteins, carbohydrates, and small molecules, and can be fine-tuned to span a range of time, length, and complexity scales. Recognizing the power of these motifs, researchers have sought to emulate and engineer biomolecular assemblies in the laboratory, with goals ranging from modulating cellular function to the creation of new polymeric materials. In most cases, engineering efforts are inspired or informed by understanding the structure and properties of naturally occurring assemblies, which has in turn fueled the development of predictive models that enable computational design of novel assemblies. This Review will focus on selected examples of protein assemblies, highlighting the story arc from initial discovery of an assembly, through initial engineering attempts, toward the ultimate goal of predictive design. The aim of this Review is to highlight areas where significant progress has been made, as well as to outline remaining challenges, as solving these challenges will be the key that unlocks the full power of biomolecules for advances in technology and medicine.

High-Throughput Image Analysis of Fibrillar Materials: A Case Study on Polymer Nanofiber Packing, Alignment, and Defects in Organic Field Effect Transistors

High-throughput discovery of process-structure-property relationships in materials through an informatics-enabled empirical approach is an increasingly utilized technique in materials research due to the rapidly expanding availability of data. Here, process-structure-property relationships are extracted for the nucleation, growth, and deposition of semiconducting poly(3-hexylthiophene) (P3HT) nanofibers used in organic field effect transistors, via high-throughput image analysis. This study is performed using an automated image analysis pipeline combining existing open-source software and new algorithms, enabling the rapid evaluation of structural metrics for images of fibrillar materials, including local orientational order, fiber length density, and fiber length distributions. We observe that microfluidic processing leads to fibers that pack with unusually high density, while sonication yields fibers that pack sparsely with low alignment. This is attributed to differences in their crystallization mechanisms. P3HT nanofiber packing during thin film deposition exhibits behavior suggesting that fibers are confined to packing in two-dimensional layers. We find that fiber alignment, a feature correlated with charge carrier mobility, is driven by increasing fiber length, and that shorter fibers tend to segregate to the buried dielectric interface during deposition, creating potentially performance-limiting defects in alignment. Another barrier to perfect alignment is the curvature of P3HT fibers; we propose a mechanistic simulation of fiber growth that reconciles both this curvature and the log-normal distribution of fiber lengths inherent to the fiber populations under consideration.

Self-assembling peptide and protein amyloids: from structure to tailored function in nanotechnology

Self-assembled peptide and protein amyloid nanostructures have traditionally been considered only as pathological aggregates implicated in human neurodegenerative diseases. In more recent times, these nanostructures have found interesting applications as advanced materials in biomedicine, tissue engineering, renewable energy, environmental science, nanotechnology and material science, to name only a few fields. In all these applications, the final function depends on: (i) the specific mechanisms of protein aggregation, (ii) the hierarchical structure of the protein and peptide amyloids from the atomistic to mesoscopic length scales and (iii) the physical properties of the amyloids in the context of their surrounding environment (biological or artificial). In this review, we will discuss recent progress made in the field of functional and artificial amyloids and highlight connections between protein/peptide folding, unfolding and aggregation mechanisms, with the resulting amyloid structure and functionality. We also highlight current advances in the design and synthesis of amyloid-based biological and functional materials and identify new potential fields in which amyloid-based structures promise new breakthroughs.

Measurement of amyloid formation by turbidity assay-seeing through the cloud

Detection of amyloid growth is commonly carried out by measurement of solution turbidity, a low-cost assay procedure based on the intrinsic light scattering properties of the protein aggregate. Here, we review the biophysical chemistry associated with the turbidimetric assay methodology, exploring the reviewed literature using a series of pedagogical kinetic simulations. In turn, these simulations are used to interrogate the literature concerned with in vitro drug screening and the assessment of amyloid aggregation mechanisms.

Dynamics of protein aggregation and oligomer formation governed by secondary nucleation

The formation of aggregates in many protein systems can be significantly accelerated by secondary nucleation, a process where existing assemblies catalyse the nucleation of new species. In particular, secondary nucleation has emerged as a central process controlling the proliferation of many filamentous protein structures, including molecular species related to diseases such as sickle cell anemia and a range of neurodegenerative conditions. Increasing evidence suggests that the physical size of protein filaments plays a key role in determining their potential for deleterious interactions with living cells, with smaller aggregates of misfolded proteins, oligomers, being particularly toxic. It is thus crucial to progress towards an understanding of the factors that control the sizes of protein aggregates. However, the influence of secondary nucleation on the time evolution of aggregate size distributions has been challenging to quantify. This difficulty originates in large part from the fact that secondary nucleation couples the dynamics of species distant in size space. Here, we approach this problem by presenting an analytical treatment of the master equation describing the growth kinetics of linear protein structures proliferating through secondary nucleation and provide closed-form expressions for the temporal evolution of the resulting aggregate size distribution. We show how the availability of analytical solutions for the full filament distribution allows us to identify the key physical parameters that control the sizes of growing protein filaments. Furthermore, we use these results to probe the dynamics of the populations of small oligomeric species as they are formed through secondary nucleation and discuss the implications of our work for understanding the factors that promote or curtail the production of these species with a potentially high deleterious biological activity.

Analysis of the length distribution of amyloid fibrils by centrifugal sedimentation

The aggregation of normally soluble peptides and proteins into amyloid fibrils is a process associated with a wide range of pathological conditions, including Alzheimer's and Parkinson's diseases. It has become apparent that aggregates of different sizes possess markedly different biological effects, with aggregates of lower relative molecular weight being associated with stronger neurotoxicity. Yet, although many approaches exist to measure the total mass concentration of aggregates, the ability to probe the length distribution of growing aggregates in solution has remained more elusive. In this work, we applied a differential centrifugation technique to measure the sedimentation coefficients of amyloid fibrils produced during the aggregation process of the amyloid β (M1-42) peptide (Aβ42). The centrifugal method has the advantage of providing structural information on the fibril distribution directly in solution and affording a short analysis time with respect to alternative imaging and analytical centrifugation approaches. We show that under quiescent conditions interactions between Aβ42 fibrils lead to lateral association and to the formation of entangled clusters. By contrast, aggregation under shaking generates a population of filaments characterized by shorter lengths. The results, which have been validated by cryogenic transmission electron microscopy (cryo-TEM) analysis, highlight the important role that fibril-fibril assembly can play in the deposition of aggregation-prone peptides.

A minimal conformational switching-dependent model for amyloid self-assembly

Amyloid formation is associated with various pathophysiological conditions like Alzheimer’s and Parkinson’s diseases as well as many useful functions. The hallmark of amyloid assemblies is a conformational transition of the constituent proteins into a β - sheet rich filament. Accounting for this conformational transition in amyloidogenic proteins, we develop an analytically solvable model that can probe the dynamics of an ensemble of single filaments. Using the theory and Monte Carlo simulations, we show the presence of two kinetic regimes for the growth of a self-assembling filament – switching-dependent and –independent growth regimes. We observe a saturation in fibril elongation velocities at higher concentrations in the first regime, providing a novel explanation to the concentration-independence of growth velocities observed experimentally. We also compute the length fluctuation of the filaments to characterize aggregate heterogeneity. From the early velocities and length fluctuation, we propose a novel way of estimating the conformational switching rate. Our theory predicts a kinetic phase diagram that has three distinct phases – short oligomers/monomers, disordered aggregates and β -rich filaments. The model also predicts the force generation potential and the intermittent growth of amyloid fibrils evident from single molecular experiments. Our model could contribute significantly to the physical understanding of amyloid aggregation.

Role of filament annealing in the kinetics and thermodynamics of nucleated polymerization

The formation of nanoscale protein filaments from soluble precursor molecules through nucleated polymerization is a common form of supra-molecular assembly phenomenon. This process underlies the generation of a range of both functional and pathological structures in nature. Filament breakage has emerged as a key process controlling the kinetics of the growth reaction since it increases the number of filament ends in the system that can act as growth sites. In order to ensure microscopic reversibility, however, the inverse process of fragmentation, end-to-end annealing of filaments, is a necessary component of a consistent description of such systems. Here, we combine Smoluchowski kinetics with nucleated polymerization models to generate a master equation description of protein fibrillization, where filamentous structures can undergo end-to-end association, in addition to elongation, fragmentation, and nucleation processes. We obtain self-consistent closed-form expressions for the growth kinetics and discuss the key physics that emerges from considering filament fusion relative to current fragmentation only models. Furthermore, we study the key time scales that describe relaxation to equilibrium.

Fragmentation of amyloid fibrils occurs in preferential positions depending on the environmental conditions

Understanding the mechanism of amyloid fibril breakage is of fundamental importance in various research fields including biomedicine and bionanotechnology. The aim of this work is to clarify the impact of temperature and agitation speed on the fibril breakage rate constant, which depends both on the fibril length as well as on the position of fragmentation along the fibril longitudinal axis. In particular, we intend to discriminate between three fibril fragmentation mechanisms: erosion (i.e., breakage occurs preferentially at the ends of the fibril), random (i.e., breakage occurs with the same likelihood at any position), or central (i.e., breakage occurs preferentially at the center of the fibril). To do so, we compare the time evolution of the fibril length distribution followed with atomic force microscopy with simulations from a kinetic model based on population balance equations (PBE). In this frame, we investigate the breakage mechanism of insulin fibrils, which turns out to be affected by the operative conditions employed. Moreover, we compare our findings with literature data obtained with β-lactoglobulin and β2-microglobulin. It is observed that high temperature drives the breakage toward an erosion mechanism, while a high agitation rate rather induces a central breakage.

A monomer-trimer model supports intermittent glucagon fibril growth

We investigate in vitro fibrillation kinetics of the hormone peptide glucagon at various concentrations using confocal microscopy and determine the glucagon fibril persistence length 60μm. At all concentrations we observe that periods of individual fibril growth are interrupted by periods of stasis. The growth probability is large at high and low concentrations and is reduced for intermediate glucagon concentrations. To explain this behavior we propose a simple model, where fibrils come in two forms, one built entirely from glucagon monomers and one entirely from glucagon trimers. The opposite building blocks act as fibril growth blockers, and this generic model reproduces experimental behavior well.

Chemical kinetics for drug discovery to combat protein aggregation diseases

Protein misfolding diseases are becoming increasingly prevalent, yet there are very few effective pharmacological treatments. The onset and progression of these diseases is associated with the aberrant aggregation of normally soluble proteins and peptides into amyloid fibrils. Because genetic and physiological findings suggest that protein aggregation is a key event in pathogenesis, an attractive therapeutic strategy against this class of disorders is the search for compounds able to interfere with this process, in particular by suppressing the formation of soluble toxic oligomeric aggregates. In this review, we discuss how chemical kinetics can contribute to the fundamental understanding of the molecular mechanism of aggregation, and speculate on the implications for the development of therapeutic molecules that inhibit specific steps in the aggregation pathway that are crucial for preventing toxicity.

Modelling amyloid fibril formation kinetics: mechanisms of nucleation and growth

Amyloid and amyloid-like fibrils are self-assembling protein nanostructures, of interest for their robust material properties and inherent biological compatibility as well as their putative role in a number of debilitating mammalian disorders. Understanding fibril formation is essential to the development of strategies to control, manipulate or prevent fibril growth. As such, this area of research has attracted significant attention over the last half century. This review describes a number of different models that have been formulated to describe the kinetics of fibril assembly. We describe the macroscopic implications of mechanisms in which secondary processes such as secondary nucleation, fragmentation or branching dominate the assembly pathway, compared to mechanisms dominated by the influence of primary nucleation. We further describe how experimental data can be analysed with respect to the predictions of kinetic models.

The self-assembly, aggregation and phase transitions of food protein systems in one, two and three dimensions

The aggregation of proteins is of fundamental relevance in a number of daily phenomena, as important and diverse as blood coagulation, medical diseases, or cooking an egg in the kitchen. Colloidal food systems, in particular, are examples that have great significance for protein aggregation, not only for their importance and implications, which touches on everyday life, but also because they allow the limits of the colloidal science analogy to be tested in a much broader window of conditions, such as pH, ionic strength, concentration and temperature. Thus, studying the aggregation and self-assembly of proteins in foods challenges our understanding of these complex systems from both the molecular and statistical physics perspectives. Last but not least, food offers a unique playground to study the aggregation of proteins in three, two and one dimensions, that is to say, in the bulk, at air/water and oil/water interfaces and in protein fibrillation phenomena. In this review we will tackle this very ambitious task in order to discuss the current understanding of protein aggregation in the framework of foods, which is possibly one of the broadest contexts, yet is of tremendous daily relevance.