Insights into the variability of nucleated amyloid polymerization by a minimalistic model of stochastic protein assembly

Data-driven Stochastic Model for Quantifying the Interplay Between Amyloid-beta and Calcium Levels in Alzheimer's Disease

The abnormal aggregation of extracellular amyloid-β ( A β ) in senile plaques resulting in calcium C a + 2 dyshomeostasis is one of the primary symptoms of Alzheimer's disease (AD). Significant research efforts have been devoted in the past to better understand the underlying molecular mechanisms driving A β deposition and C a + 2 dysregulation. Importantly, synaptic impairments, neuronal loss, and cognitive failure in AD patients are all related to the buildup of intraneuronal A β accumulation. Moreover, increasing evidence show a feed-forward loop between A β and C a + 2 levels, i.e. A β disrupts neuronal C a + 2 levels, which in turn affects the formation of A β . To better understand this interaction, we report a novel stochastic model where we analyze the positive feedback loop between A β and C a + 2 using ADNI data. A good therapeutic treatment plan for AD requires precise predictions. Stochastic models offer an appropriate framework for modelling AD since AD studies are observational in nature and involve regular patient visits. The etiology of AD may be described as a multi-state disease process using the approximate Bayesian computation method. So, utilizing ADNI data from 2-year visits for AD patients, we employ this method to investigate the interplay between A β and C a + 2 levels at various disease development phases. Incorporating the ADNI data in our physics-based Bayesian model, we discovered that a sufficiently large disruption in either A β metabolism or intracellular C a + 2 homeostasis causes the relative growth rate in both C a + 2 and A β , which corresponds to the development of AD. The imbalance of C a + 2 ions causes A β disorders by directly or indirectly affecting a variety of cellular and subcellular processes, and the altered homeostasis may worsen the abnormalities of C a + 2 ion transportation and deposition. This suggests that altering the C a + 2 balance or the balance between A β and C a + 2 by chelating them may be able to reduce disorders associated with AD and open up new research possibilities for AD therapy.

Lipid-induced polymorphic amyloid fibril formation by α-synuclein

Many proteins that self-assemble into amyloid and amyloid-like fibers can adopt diverse polymorphic forms. These forms have been observed both in vitro and in vivo and can arise through variations in the steric-zipper interactions between β-sheets, variations in the arrangements between protofilaments, and differences in the number of protofilaments that make up a given fiber class. Different polymorphs arising from the same precursor molecule not only exhibit different levels of toxicity, but importantly can contribute to different disease conditions. However, the factors which contribute to formation of polymorphic forms of amyloid fibrils are not known. In this work, we show that in the presence of 1,2-dimyristoyl-sn-glycero-3-phospho-L-serine, a highly abundant lipid in the plasma membrane of neurons, the aggregation of α-synuclein is markedly accelerated and yields a diversity of polymorphic forms under identical experimental conditions. This morphological diversity includes thin and curly fibrils, helical ribbons, twisted ribbons, nanotubes, and flat sheets. Furthermore, the amyloid fibrils formed incorporate lipids into their structures, which corroborates the previous report of the presence of α-synuclein fibrils with high lipid content in Lewy bodies. Thus, the present study demonstrates that an interface, such as that provided by a lipid membrane, can not only modulate the kinetics of α-synuclein amyloid aggregation but also plays an important role in the formation of morphological variants by incorporating lipid molecules in the process of amyloid fibril formation.

The hydrophobic effect characterises the thermodynamic signature of amyloid fibril growth

Many proteins have the potential to aggregate into amyloid fibrils, protein polymers associated with a wide range of human disorders such as Alzheimer’s and Parkinson’s disease. The thermodynamic stability of amyloid fibrils, in contrast to that of folded proteins, is not well understood: the balance between entropic and enthalpic terms, including the chain entropy and the hydrophobic effect, are poorly characterised. Using a combination of theory, in vitro experiments, simulations of a coarse-grained protein model and meta-data analysis, we delineate the enthalpic and entropic contributions that dominate amyloid fibril elongation. Our prediction of a characteristic temperature-dependent enthalpic signature is confirmed by the performed calorimetric experiments and a meta-analysis over published data. From these results we are able to define the necessary conditions to observe cold denaturation of amyloid fibrils. Overall, we show that amyloid fibril elongation is associated with a negative heat capacity, the magnitude of which correlates closely with the hydrophobic surface area that is buried upon fibril formation, highlighting the importance of hydrophobicity for fibril stability.

Most proteins fold in the cell into stable, compact structures. Nevertheless, many proteins also have the ability to stick together, forming long fibrillar structures that are associated with a wide range of human disorders including Alzheimer’s and Parkinson’s disease. The exact nature of the amyloid-causing stickiness is not well understood, nevertheless amyloid fibrils show some very specific thermodynamic characteristics. Some fibrils even destabilise at low temperatures. In this work we translate hydrophobic theory previously used to model protein folding to fibril formation. We combine this theory with experimental measurements, simulations and meta-data analysis of different types of fibrils. This allowed us to unravel the nature of the stickiness in amyloid fibrils by observing the effect of temperature changes, specifically at low temperatures, on hydrophobicity.

Kinetic Variability in Seeded Formation of ALS-Linked SOD1 Fibrils Across Multiple Generations

The unseeded aggregation of superoxide dismutase-1 (SOD1) into amyloid-like fibrils occurs stochastically in vitro and in vivo, that is, isolated populations of SOD1 proteins (within microplate wells or living cells) self-assemble into amyloid at rates that span a probability distribution. This stochasticity has been attributed to variable degrees of monomer depletion by competing pathways of amorphous and fibrillar aggregation (inter alia). Here, microplate-based thioflavin-T (ThT) fluorescence assays were performed at high iteration (∼300) to establish whether this observed stochasticity persists when progenitor ("parent") SOD1 fibrils are used to seed the formation of multiple generations of progeny fibrils (daughter, granddaughter, and great-granddaughter fibrils). Populations of progenitor fibrils formed stochastically at different rates and fluorescence intensity, however, progeny fibrils formed at more similar rates regardless of the formation rate of the progenitor fibril. For example, populations of progenitor fibrils that formed with a lag time of ∼30 h or ∼15 h both produced progeny fibrils with lag times of ∼8 h. Likewise, populations of progenitor fibrils with high or low maximum fluorescence (e.g., ∼450 or ∼75 A.U.) both produced progeny fibrils with more similar maximum fluorescence (∼125 A.U.). The rate of propagation was found to be more dependent on monomer concentration than seed concentration. These results can be rationalized by classical rate laws for primary nucleation and monomer-dependent secondary nucleation. We also find that the seeding propensity of some "families" of in vitro grown fibrils exhibit a finite lifetime (similar to that observed in the seeding of small molecule crystals and colloids). The single biological takeaway of this study is that the concentration of native SOD1 in a cell can have a stronger effect on rates of seeded aggregation than the concentration of prion-like seed that infected the cell.

Bidirectional sliding of two parallel microtubules generated by multiple identical motors

It is often assumed in biophysical studies that when multiple identical molecular motors interact with two parallel microtubules, the microtubules will be crosslinked and locked together. The aim of this study is to examine this assumption mathematically. We model the forces and movements generated by motors with a time-continuous Markov process and find that, counter-intuitively, a tug-of-war results from opposing actions of identical motors bound to different microtubules. The model shows that many motors bound to the same microtubule generate a great force applied to a smaller number of motors bound to another microtubule, which increases detachment rate for the motors in minority, stabilizing the directional sliding. However, stochastic effects cause occasional changes of the sliding direction, which has a profound effect on the character of the long-term microtubule motility, making it effectively diffusion-like. Here, we estimate the time between the rare events of switching direction and use them to estimate the effective diffusion coefficient for the microtubule pair. Our main result is that parallel microtubules interacting with multiple identical motors are not locked together, but rather slide bidirectionally. We find explicit formulae for the time between directional switching for various motor numbers.

Sensitivity analysis of the variability of amyloid aggregation profiles

The variability of amyloid aggregation profiles is linearly proportional to the duration of the aggregation process, and arises from a perturbation of one or more of the initial conditions.

Observation of molecular self-assembly events in massively parallel microdroplet arrays

The self-assembly of peptide and protein molecules into nanoscale filaments is a process associated with both biological function and malfunction. Microfluidic techniques can provide powerful tools in the study of such aggregation phenomena while providing access to exploring the role of molecular interactions in disease development. Yet, a common challenge encountered in the study of protein aggregation is the difficulty in achieving spatial and temporal control of the underlying processes. Here, we present a planar (2-D) device allowing for both the generation and confinement of 10 000 monodisperse water-in-oil droplets in an array of chambers with a trapping efficiency of 99%. Due to the specific geometry of the device, droplets can be formed and immediately trapped on the same chip, without the need for continuous flow of the oil phase. Furthermore, we demonstrate the capability of this device as a platform to study the aggregation kinetics and determine stochastic molecular nanoscale self-assembly events in a highly parallel manner for the aggregation of the dipeptide, diphenylalanine, the core recognition motif of the Aβ-42 peptide associated with Alzheimer's disease. The ability to reproducibly generate and confine monodisperse water-in-oil droplets with an extremely high trapping efficiency while maintaining entrapment under zero-flow conditions, on timescales compatible with observing molecular self-assembly events, renders it promising for numerous potential further applications in the biological and biophysical fields.