Understanding and controlling the director field configuration, shape, and orientation in nematic and cholesteric liquid crystals is of fundamental importance in several branches of science. Liquid crystalline droplets, also known as tactoids, which spontaneously form by nucleation and growth within the biphasic region of the phase diagram where isotropic and nematic phases coexist, challenge our current understanding of liquid crystals under confinement, due to the influence of anisotropic surface boundaries at vanishingly small interfacial tension and are mostly studied under quiescent, quasi-equilibrium conditions. Here, we show that different classes of amyloid fibril nematic and cholesteric tactoids undergo out-of-equilibrium order-order transitions by flow-induced deformations of their shape. The tactoids align under extensional flow and undergo extreme deformation into highly elongated oblate shapes, allowing the cholesteric pitch to decrease as an inverse power law of the tactoids aspect ratio. Energy functional theory and experimental measurements are combined to rationalize the critical elongation ratio above which the director-field configuration of tactoids transforms from bipolar and uniaxial cholesteric to homogenous and to debate on the thermodynamic nature of these transitions. Our findings suggest new opportunities in designing self-assembled liquid crystalline materials where structural and dynamical properties may be tuned by non-equilibrium phase transitions.
Many proteins have the potential to aggregate into amyloid fibrils, which are associated with a wide range of human disorders including Alzheimer's and Parkinson's disease. In contrast to that of folded proteins, the thermodynamic stability of amyloid fibrils is not well understood: specifically the balance between entropic and enthalpic terms, including the chain entropy and the hydrophobic effect, are poorly characterised. Using simulations of a coarse-grained protein model we delineate the enthalpic and entropic contributions dominating amyloid fibril elongation, predicting a characteristic…
Protein amyloid fibrils are a form of linear protein aggregates that are implicated in many neurodegenerative diseases. Here, we study the dynamics of amyloid fibril elongation by performing Langevin dynamic simulations on a coarse-grained model of peptides. Our simulation results suggest that the elongation process is dominated by a series of local minimum due to frustration in monomer-fibril interactions. This rugged energy landscape picture indicates that the amount of recycling of monomers at the fibrils' ends before being fibrilized is substantially reduced in comparison to the convention…
We develop a general theory for three states of equilibrium of amyloid peptides: the monomer, oligomer, and fibril. We assume that the oligomeric state is a disordered micelle-like collection of a few peptide chains held together loosely by hydrophobic interactions into a spherical hydrophobic core. We assume that fibrillar amyloid chains are aligned and further stabilized by `steric zipper' interactions -- hydrogen bonding and steric packing, in addition to specific hydrophobic sidechain contacts. The model makes a broad set of predictions, consistent with experiments: (i) Similar to surfacta…
Protein aggregation in the form of amyloid fibrils has important biological and technological implications. Although the self-assembly process is highly efficient, aggregates not in the fibrillar form would also occur and it is important to include these disordered species when discussing the thermodynamic equilibrium behavior of the system. Here, we initiate such a task by considering a mixture of monomeric proteins and the corresponding aggregates in the disordered form (micelles) and in the fibrillar form (amyloid fibrils). Starting with a model on the respective binding free energies for t…
Above a critical concentration a wide variety of peptides and proteins self-assemble into amyloid fibrils which entangle to form percolating networks called hydrogels. Such hydrogels have important applications as biomaterials and in nanotechnology, but their applicability often depends on their mechanical properties for which we currently have no predictive capability. Here we use a peptide model to simulate the formation of amyloid fibril networks, and couple these to elastic network theory to determine their mechanical properties. The simulations reveal that the time-dependence of morpholog…
Mechanical strength of amyloid beta fibrils has been known to be correlated with neuronal cell death. Here, we resorted to steered molecular dynamics (SMD) simulations to mechanically stretch a single S-shape amyloid beta Abeta11-42 dodecamer fibril in vacuum. It was found that the weakest sites at which the fibril was ruptured due to mechanical extension were exclusively at the interfaces of alanine and glutamic acid distributed throughout the fibril. It was also revealed that the free energy required to unfold the fibril to form a long linear conformation is equivalent to ~ 210 eV, being sev…
We present and study a minimal structure-based model for the self-assembly of peptides into ordered beta-sheet-rich fibrils. The peptides are represented by unit-length sticks on a cubic lattice and interact by hydrogen bonding and hydrophobicity forces. By Monte Carlo simulations with >100,000 peptides, we show that fibril formation occurs with sigmoidal kinetics in the model. To determine the mechanism of fibril nucleation, we compute the joint distribution in length and width of the aggregates at equilibrium, using an efficient cluster move and flat-histogram techniques. This analysis, base…
We consider nucleation of amyloid fibrils in the case when the process occurs by the mechanism of direct polymerization of practically fully extended protein segments, i.e. beta-strands, into beta-sheets. Applying the classical nucleation theory, we derive a general expression for the work to form a nanosized amyloid fibril (protofilament) constituted of successively layered beta-sheets. Analysis of this expression reveals that with increasing its size, the fibril transforms from one-dimensional into two-dimensional aggregate in order to preserve the equilibrium shape corresponding to minimal …
We study the two-filament insulin fibril's structure by incorporating recent simulation results and mechanical measurements. Our investigation suggests that the persistence length measurement correlates well with the previously proposed structural model, while the elasticity measurement suggests that stretching the fibril may involve hydrogen bond breakage. Our work illustrates an attempt to correlate nanoscale measurements with microscopic information on the quaternary protein structure.
Protein aggregation including the formation of dimers and multimers in solution, underlies an array of human diseases such as systemic amyloidosis which is a fatal disease caused by misfolding of native globular proteins damaging the structure and function of affected organs. Different kind of interactors can interfere with the formation of protein dimers and multimers in solution. A very special class of interactors are nanoparticles thanks to the extremely efficient extension of their interaction surface. In particular citrate-coated gold nanoparticles (cit-AuNPs) were recently investigated …
Protein fibril accumulation at interfaces is an important step in many physiological processes and neurodegenerative diseases as well as in designing materials. Here we show, using $β$-lactoglobulin fibrils as a model, that semiflexible fibrils exposed to a surface do not possess the Gaussian distribution of curvatures characteristic for wormlike chains, but instead exhibit a spontaneous curvature, which can even lead to ring-like conformations. The long-lived presence of such rings is confirmed by atomic force microscopy, cryogenic scanning electron microscopy and passive probe particle track…
Effects of green tea tannin epigallocatechin-gallate (EGCG) on thermal-stress-induced amyloid fibril formation of reduced carboxymethylated bovine milk protein $κ$-casein (RCMK) were studied by dynamical light scattering (DLS) and small angle x-rays scattering (SAXS). Two populations of aggregates, micelles and fibrils, dominated the time evolution of light scattering intensity and of effective hydrodynamic diameter. SAXS experiments allowed to resolve micelles and fibrils so that the time dependence of scattering profile revealed structural evolution of the two populations. The low-Q scatteri…
Protein oligomers have been implicated as toxic agents in a wide range of amyloid-related diseases. Yet it has remained unsolved whether the oligomers are a necessary step in the formation of amyloid fibrils, or just a dangerous by-product. Analogously, it has not been resolved if the amyloid nucleation process is a classical one-step nucleation process, or a two-step process involving pre-nucleation clusters. We use coarse-grained computer simulations to study the effect of non-specific attractions between peptides on the primary nucleation process underlying amyloid fibrillization. We find t…
The self-assembly of proteins into $β$-sheet-rich amyloid fibrils has been observed to occur with sigmoidal kinetics, indicating that the system initially is trapped in a metastable state. Here, we use a minimal lattice-based model to explore the thermodynamic forces driving amyloid formation in a finite canonical ($NVT$) system. By means of generalized-ensemble Monte Carlo techniques and a semi-analytical method, the thermodynamic properties of this model are investigated for different sets of intersheet interaction parameters. When the interactions support lateral growth into multi-layered f…
In water, networks of semi-flexible fibrils of the protein $α$-synuclein stiffen significantly with increasing temperature. We make plausible that this reversible stiffening is a result of hydrophobic contacts between the fibrils that become more prominent with increasing temperature. The good agreement of our experimentally observed temperature dependence of the storage modulus of the network with a scaling theory linking network elasticity with reversible crosslinking enables us to quantify the endothermic binding enthalpy and an estimate the effective size of hydrophobic patches on the fibr…
The classical nucleation theory finds the rate of nucleation proportional to the monomer concentration raised to the power, which is the `critical nucleaus size', ${n_c}$. The implicit assumption, that amyloids nucleate in the same way, has been recently challenged by an alternative two-step mechanism, when the soluble monomers first form a metastable aggregate (micelle), and then undergo conversion into the conformation rich in $β$-strands that are able to form a stable growing nucleus for the protofilament. Here we put together the elements of extensive knowledge about aggregation and nuclea…
Protein aggregation, linked to many of diseases, is initiated when monomers access rogue conformations that are poised to form amyloid fibrils. We show, using simulations of src SH3 domain, that mechanical force enhances the population of the aggregation prone ($N^*$) states, which are rarely populated under force free native conditions, but are encoded in the spectrum of native fluctuations. The folding phase diagrams of SH3 as a function of denaturant concentration ($[C]$), mechanical force ($f$), and temperature exhibit an apparent two-state behavior, without revealing the presence of the e…
A variety of neurodegenerative diseases are associated with the formation of amyloid plaques. Our incomplete understanding of this process underscores the need to decipher the principles governing protein aggregation. Most experimental and simulation studies have been interpreted largely from the perspective of proteins: the role of solvent has been relatively overlooked. In this Account, we provide a perspective on how interactions with water affect folding landscapes of A$β$ monomers, A$β_{16-22}$ oligomer formation, and protofilament formation in a Sup35 peptide. Simulations show that the f…
Equilibrating proteins and other biomacromolecules is cardinal for molecular dynamics simulation of such biological systems in which they perform free dynamics without any externally-applied mechanical constraint, until thermodynamic equilibrium with the surrounding is attained. However, in some important cases, we have to equilibrate the system of interest in the constant presence of certain constraints, being referred to as constrained equilibration in the present work. A clear illustration of this type is a single amyloid \b{eta}-strand or RNA, when the reaction coordinate is defined as the…
Nucleation and growth (N&G) - the emergence of a new phase within an initially homogeneous one - is one of the most important physical phenomena by which gas-liquid, liquid-liquid and solid-liquid phase separation takes place. Accordingly, thermodynamics sets the asymptotic boundaries towards which the system must evolve, while kinetics tries to cope with it by imposing the transport rates at which phase separation is realized. In all heterogeneous colloidal systems observed in nature, the composition, shape, structure and ultimately physical properties result from the trade-off between thermo…
