Rapid amyloid fiber formation from the fast-folding WW domain FBP28

Structure of Amyloid Peptide Ribbons Characterized by Electron Microscopy, Atomic Force Microscopy, and Solid-State Nuclear Magnetic Resonance

Polypeptides often self-assemble to form amyloid fibrils, which contain cross-β structural motifs and are typically 5-15 nm in width and micrometers in length. In many cases, short segments of longer amyloid-forming protein or peptide sequences also form cross-β assemblies but with distinctive ribbon-like morphologies that are characterized by a well-defined thickness (on the order of 5 nm) in one lateral dimension and a variable width (typically 10-100 nm) in the other. Here, we use a novel combination of data from solid-state nuclear magnetic resonance (ssNMR), dark-field transmission electron microscopy (TEM), atomic force microscopy (AFM), and cryogenic electron microscopy (cryoEM) to investigate the structures within amyloid ribbons formed by residues 14-23 and residues 11-25 of the Alzheimer's disease-associated amyloid-β peptide (Aβ14-23 and Aβ11-25). The ssNMR data indicate antiparallel β-sheets with specific registries of intermolecular hydrogen bonds. Mass-per-area values are derived from dark-field TEM data. The ribbon thickness is determined from AFM images. For Aβ14-23 ribbons, averaged cryoEM images show a periodic spacing of β-sheets. The combined data support structures in which the amyloid ribbon growth direction is the direction of intermolecular hydrogen bonds between β-strands, the ribbon thickness corresponds to the width of one β-sheet (i.e., approximately the length of one molecule), and the variable ribbon width is a variable multiple of the thickness of one β-sheet (i.e., a multiple of the repeat distance in a stack of β-sheets). This architecture for a cross-β assembly may generally exist within amyloid ribbons.

Uncovering the universality of self-replication in protein aggregation and its link to disease

Fibrillar protein aggregates are a hallmark of a range of human disorders, from prion diseases to dementias, but are also encountered in several functional contexts. Yet, the fundamental links between protein assembly mechanisms and their functional or pathological roles have remained elusive. Here, we analyze the aggregation kinetics of a large set of proteins that self-assemble by a nucleated-growth mechanism, from those associated with disease, over those whose aggregates fulfill functional roles in biology, to those that aggregate only under artificial conditions. We find that, essentially, all such systems, regardless of their biological role, are capable of self-replication. However, for aggregates that have evolved to fulfill a structural role, the rate of self-replication is too low to be significant on the biologically relevant time scale. By contrast, all disease-related proteins are able to self-replicate quickly compared to the time scale of the associated disease. Our findings establish the ubiquity of self-replication and point to its potential importance across aggregation-related disorders.

Amyloidogenic Properties of Peptides Derived from the VHL Tumor Suppressor Protein

The von Hippel-Lindau tumor suppressor protein (pVHL) is involved in maintaining cellular oxygen homeostasis through the regulated degradation of HIF-α. The intrinsically disordered nature of pVHL makes it prone to aggregation that impairs its function, and this is further aggravated in mutant versions of the protein, thus promoting tumor development. By using in silico analysis, we predicted six peptide fragments from pVHL to be amyloidogenic. This was verified for two of the peptides by biophysical approaches, which demonstrated self-assembly and formation of β-sheet-rich aggregates, which, under transmission electron microscopy, atomic force microscopy, and X-ray diffraction, displayed typical fibrillar amyloid characteristics. These motifs may serve as proxies for exploring the nature of pVHL aggregation.

Statistical Learning from Single-Molecule Experiments: Support Vector Machines and Expectation-Maximization Approaches to Understanding Protein Unfolding Data

Single-molecule force spectroscopy has become a powerful tool for the exploration of dynamic processes that involve proteins; yet, meaningful interpretation of the experimental data remains challenging. Owing to low signal-to-noise ratio, experimental force-extension spectra contain force signals due to nonspecific interactions, tip or substrate detachment, and protein desorption. Unravelling of complex protein structures results in the unfolding transitions of different types. Here, we test the performance of Support Vector Machines (SVM) and Expectation Maximization (EM) approaches in statistical learning from dynamic force experiments. When the output from molecular modeling in silico (or other studies) is used as a training set, SVM and EM can be applied to understand the unfolding force data. The maximal margin or maximum likelihood classifier can be used to separate experimental test observations into the unfolding transitions of different types, and EM optimization can then be utilized to resolve the statistics of unfolding forces: weights, average forces, and standard deviations. We designed an EM-based approach, which can be directly applied to the experimental data without data classification and division into training and test observations. This approach performs well even when the sample size is small and when the unfolding transitions are characterized by overlapping force ranges.

New Insights into Folding, Misfolding, and Nonfolding Dynamics of a WW Domain

Intermediate states in protein folding are associated with formation of amyloid fibrils, which are responsible for a number of neurodegenerative diseases. Therefore, prevention of the aggregation of folding intermediates is one of the most important problems to overcome. Recently, we studied the origins and prevention of formation of intermediate states with the example of the Formin binding protein 28 (FBP28) WW domain. We demonstrated that the replacement of Leu26 by Asp26 or Trp26 (in ∼15% of the folding trajectories) can alter the folding scenario from three-state folding, a major folding scenario for the FBP28 WW domain (WT) and its mutants, toward two-state or downhill folding at temperatures below the melting point. Here, for a better understanding of the physics of the formation/elimination of intermediates, (i) the dynamics and energetics of formation of β-strands in folding, misfolding, and nonfolding trajectories of these mutants (L26D and L26W) is investigated; (ii) the experimental structures of WT, L26D, and L26W are analyzed in terms of a kink (heteroclinic standing wave solution) of a generalized discrete nonlinear Schrödinger equation. We show that the formation of each β-strand in folding trajectories is accompanied by the emergence of kinks in internal coordinate space as well as a decrease in local free energy. In particular, the decrease in downhill folding trajectory is ∼7 kcal/mol, while it varies between 31 and 48 kcal/mol for the three-state folding trajectory. The kink analyses of the experimental structures give new insights into formation of intermediates, which may become a useful tool for preventing aggregation.

Universality of filamentous aggregation phenomena

We use perturbative renormalization group theory to study the kinetics of protein aggregation phenomena in a unified manner across multiple timescales. Using this approach, we find that, irrespective of the specific molecular details or experimental conditions, filamentous assembly systems display universal behavior in time. Moreover, we show that the universality classes for protein aggregation correspond to simple autocatalytic processes and that the diversity of behavior in these systems is determined solely by the reaction order for secondary nucleation with respect to the protein concentration, which labels all possible universality classes. We validate these predictions on experimental data for the aggregation of several different proteins at several different initial concentrations, which by appropriate coordinate transformations we are able to collapse onto universal kinetic growth curves. These results establish the power of the perturbative renormalization group in distilling the ultimately simple temporal behavior of complex protein aggregation systems, creating the possibility to study the kinetics of general self-assembly phenomena in a unified fashion.

Prediction of amyloid aggregation rates by machine learning and feature selection

A novel data-based machine learning algorithm for predicting amyloid aggregation rates is reported in this paper. Based on a highly nonlinear projection from 16 intrinsic features of a protein and 4 extrinsic features of the environment to the protein aggregation rate, a feedforward fully connected neural network (FCN) with one hidden layer is trained on a dataset composed of 21 different kinds of amyloid proteins and tested on 4 rest proteins. FCN shows a much better performance than traditional algorithms, such as multivariable linear regression and support vector regression, with an average accuracy higher than 90%. Furthermore, by the correlation analysis and the principal component analysis, seven key features, folding energy, HP patterns for helix, sheet and helices cross membrane, pH, ionic strength, and protein concentration, are shown to constitute a minimum feature set for characterizing the amyloid aggregation kinetics.

Polymeric microfluidic continuous flow mixer combined with hyperspectral FT-IR imaging for studying rapid biomolecular events

Early reaction intermediates in protein folding, such as those resulting in β-amyloid formation due to transient misfolding, emerge within a few hundred microseconds. Here, we report a method to obtain sub-millisecond temporal resolution and molecular structural information of protein (mis-)folding events by using a microfluidic continuous-flow mixer (MCFM) in combination with Fourier transform infrared (FT-IR) imaging. The MCFMs are made out of cyclic olefin copolymer (COC) films, because this approach allows for rapid prototyping of different mixer designs. Furthermore, COC offers high IR transparency between 1500 and 2500 cm^-1, thus maximizing the signal to noise ratio of the IR data obtained from a sample of interest. By combining narrow and wide channel widths in MCFM design, the platform provides fast mixing (460 μs) to induce protein (mis-)folding, and it maximizes the residence time in the observing area, so a wide range of reaction timescales can be captured in a single image. We validated the platform for its ability to induce and observe sub-millisecond processes by studying two systems: (i) the mixing of H₂O and D₂O and (ii) the mixing induced deprotonation of carboxylic acid. First, we observed excellent agreement between simulated and experimental data of the on-chip mixing of H₂O and D₂O, which verifies the distance-reaction time relationships based on simulation. Second, deprotonation of carboxylic acid by on-chip mixing with sodium hydroxide solution validates the ability of the platform to induce rapid pH jump that is needed for some biomolecular reactions. Finally, we studied the methanol-induced partial-unfolding of ubiquitin to show that our platform can be used to study biomolecular events 'on-pathway' using FT-IR imaging. We successfully extracted kinetic and structural details of the conformational changes along the channel. Our results are in agreement with prior studies that required more elaborate stopped flow approaches to acquire data for different time points. In summary, the reported method uses an easy-to-fabricate microfluidic mixer platform integrated with hyperspectral FT-IR imaging for rapid acquisition of structural details and kinetic parameters of biomolecular reactions. This approach does not need stopped flow or molecular imaging probes, as required respectively for alternative FT-IR spectroscopy and fluorescence approaches.

A quantitative connection of experimental and simulated folding landscapes by vibrational spectroscopy

We break the barrier between simulation and experiment by comparing identical computed and experimental infrared observables.

For small molecule reaction kinetics, computed reaction coordinates often mimic experimentally measured observables quite accurately. Although nowadays simulated and measured biomolecule kinetics can be compared on the same time scale, a gap between computed and experimental observables remains. Here we directly compared temperature-jump experiments and molecular dynamics simulations of protein folding dynamics using the same observable: the time-dependent infrared spectrum. We first measured the stability and folding kinetics of the fastest-folding β-protein, the GTT35 WW domain, using its structurally specific infrared spectrum. The relaxation dynamics of the peptide backbone, β-sheets, turn, and random coil were measured independently by probing the amide I′ region at different frequencies. Next, the amide I′ spectra along folding/unfolding molecular dynamics trajectories were simulated by accurate mixed quantum/classical calculations. The simulated time dependence and spectral amplitudes at the exact experimental probe frequencies provided relaxation and folding rates in agreement with experimental observations. The calculations validated by experiment yield direct structural evidence for a rate-limiting reaction step where an intermediate state with either the first or second hairpin is formed. We show how folding switches from a more homogeneous (apparent two-state) process at high temperature to a more heterogeneous process at low temperature, where different parts of the WW domain fold at different rates.

Proline Restricts Loop I Conformation of the High Affinity WW Domain from Human Nedd4-1 to a Ligand Binding-Competent Type I β-Turn

Sequence alignment of the four WW domains from human Nedd4-1 (neuronal precursor cell expressed developmentally down-regulated gene 4-1) reveals that the highest sequence diversity exists in loop I. Three residues in this type I β-turn interact with the PPxY motif of the human epithelial Na⁺ channel (hENaC) subunits, indicating that peptide affinity is defined by the loop I sequence. The third WW domain (WW3*) has the highest ligand affinity and unlike the other three hNedd4-1 WW domains or other WW domains studied contains the highly statistically preferred proline at the ( i + 1) position found in β-turns. In this report, molecular dynamics simulations and experimental data were combined to characterize loop I stability and dynamics. Exchange of the proline to the equivalent residue in WW4 (Thr) results in the presence of a predominantly open seven residue Ω loop rather than the type I β-turn conformation for the wild-type apo-WW3*. In the presence of the ligand, the structure of the mutated loop I is locked into a type I β-turn. Thus, proline in loop I ensures a stable peptide binding-competent β-turn conformation, indicating that amino acid sequence modulates local flexibility to tune binding preferences and stability of dynamic interaction motifs.

Thioflavin T as an amyloid dye: fibril quantification, optimal concentration and effect on aggregation

Formation of amyloid fibrils underlies a wide range of human disorders, including Alzheimer's and prion diseases. The amyloid fibrils can be readily detected thanks to thioflavin T (ThT), a small molecule that gives strong fluorescence upon binding to amyloids. Using the amyloid fibrils of Aβ40 and Aβ42 involved in Alzheimer's disease, and of yeast prion protein Ure2, here we study three aspects of ThT binding to amyloids: quantification of amyloid fibrils using ThT, the optimal ThT concentration for monitoring amyloid formation and the effect of ThT on aggregation kinetics. We show that ThT fluorescence correlates linearly with amyloid concentration over ThT concentrations ranging from 0.2 to 500 µM. At a given amyloid concentration, the plot of ThT fluorescence versus ThT concentration exhibits a bell-shaped curve. The maximal fluorescence signal depends mostly on the total ThT concentration, rather than amyloid to ThT ratio. For the three proteins investigated, the maximal fluorescence is observed at ThT concentrations of 20-50 µM. Aggregation kinetics experiments in the presence of different ThT concentrations show that ThT has little effect on aggregation at concentrations of 20 µM or lower. ThT at concentrations of 50 µM or more could affect the shape of the aggregation curves, but this effect is protein-dependent and not universal.

Thioflavin T as an amyloid dye: fibril quantification, optimal concentration and effect on aggregation

Formation of amyloid fibrils underlies a wide range of human disorders, including Alzheimer's and prion diseases. The amyloid fibrils can be readily detected thanks to thioflavin T (ThT), a small molecule that gives strong fluorescence upon binding to amyloids. Using the amyloid fibrils of Aβ40 and Aβ42 involved in Alzheimer's disease, and of yeast prion protein Ure2, here we study three aspects of ThT binding to amyloids: quantification of amyloid fibrils using ThT, the optimal ThT concentration for monitoring amyloid formation and the effect of ThT on aggregation kinetics. We show that ThT fluorescence correlates linearly with amyloid concentration over ThT concentrations ranging from 0.2 to 500 µM. At a given amyloid concentration, the plot of ThT fluorescence versus ThT concentration exhibits a bell-shaped curve. The maximal fluorescence signal depends mostly on the total ThT concentration, rather than amyloid to ThT ratio. For the three proteins investigated, the maximal fluorescence is observed at ThT concentrations of 20-50 µM. Aggregation kinetics experiments in the presence of different ThT concentrations show that ThT has little effect on aggregation at concentrations of 20 µM or lower. ThT at concentrations of 50 µM or more could affect the shape of the aggregation curves, but this effect is protein-dependent and not universal.

Transcriptional Elongation Regulator 1 Affects Transcription and Splicing of Genes Associated with Cellular Morphology and Cytoskeleton Dynamics and Is Required for Neurite Outgrowth in Neuroblastoma Cells and Primary Neuronal Cultures

TCERG1 is a highly conserved human protein implicated in interactions with the transcriptional and splicing machinery that is associated with neurodegenerative disorders. Biochemical, neuropathological, and genetic evidence suggests an important role for TCERG1 in Huntington's disease (HD) pathogenesis. At present, the molecular mechanism underlying TCERG1-mediated neuronal effects is unknown. Here, we show that TCERG1 depletion led to widespread alterations in mRNA processing that affected different types of alternative transcriptional or splicing events, indicating that TCERG1 plays a broad role in the regulation of alternative splicing. We observed considerable changes in the transcription and alternative splicing patterns of genes involved in cytoskeleton dynamics and neurite outgrowth. Accordingly, TCERG1 depletion in the neuroblastoma SH-SY5Y cell line and primary mouse neurons affected morphogenesis and resulted in reduced dendritic outgrowth, with a major effect on dendrite ramification and branching complexity. These defects could be rescued by ectopic expression of TCERG1. Our results indicate that TCERG1 affects expression of multiple mRNAs involved in neuron projection development, whose misregulation may be involved in TCERG1-linked neurological disorders.

The Role of Electrostatic Interactions in Folding of β-Proteins

Atomic-level molecular dynamic simulations are capable of fully folding structurally diverse proteins; however, they are limited in their ability to accurately represent electrostatic interactions. Here we have experimentally tested the role of charged residues on stability and folding kinetics of one of the most widely simulated β-proteins, the WW domain. The folding of wild type Pin1 WW domain, which has two positively charged residues in the first turn, was compared to the fast folding mutant FiP35 Pin1, which introduces a negative charge into the first turn. A combination of FTIR spectroscopy and laser-induced temperature-jump coupled with infrared spectroscopy was used to probe changes in the amide I region. The relaxation dynamics of the peptide backbone, β-sheets and β-turns, and negatively charged aspartic acid side chain of FiP35 were measured independently by probing the corresponding bands assigned in the amide I region. Folding is initiated in the turns and the β-sheets form last. While the global folding mechanism is in good agreement with simulation predictions, we observe changes in the protonation state of aspartic acid during folding that have not been captured by simulation methods. The protonation state of aspartic acid is coupled to protein folding; the apparent pKa of aspartic acid in the folded protein is 6.4. The dynamics of the aspartic acid follow the dynamics of the intermediate phase, supporting assignment of this phase to formation of the first hairpin. These results demonstrate the importance of electrostatic interactions in turn stability and formation of extended β-sheet structures.

Preventing fibril formation of a protein by selective mutation

The origins of formation of an intermediate state involved in amyloid formation and ways to prevent it are illustrated with the example of the Formin binding protein 28 (FBP28) WW domain, which folds with biphasic kinetics. Molecular dynamics of protein folding trajectories are used to examine local and global motions and the time dependence of formation of contacts between C(α)s and C(β)s of selected pairs of residues. Focus is placed on the WT FBP28 WW domain and its six mutants (L26D, L26E, L26W, E27Y, T29D, and T29Y), which have structures that are determined by high-resolution NMR spectroscopy. The origins of formation of an intermediate state are elucidated, viz. as formation of hairpin 1 by a hydrophobic collapse mechanism causing significant delay of formation of both hairpins, especially hairpin 2, which facilitates the emergence of an intermediate state. It seems that three-state folding is a major folding scenario for all six mutants and WT. Additionally, two-state and downhill folding scenarios were identified in ∼ 15% of the folding trajectories for L26D and L26W, in which both hairpins are formed by the Matheson-Scheraga mechanism much faster than in three-state folding. These results indicate that formation of hairpins connecting two antiparallel β-strands determines overall folding. The correlations between the local and global motions identified for all folding trajectories lead to the identification of the residues making the main contributions in the formation of the intermediate state. The presented findings may provide an understanding of protein folding intermediates in general and lead to a procedure for their prevention.

SOD1 aggregation in ALS mice shows simplistic test tube behavior

A longstanding challenge in studies of neurodegenerative disease has been that the pathologic protein aggregates in live tissue are not amenable to structural and kinetic analysis by conventional methods. The situation is put in focus by the current progress in demarcating protein aggregation in vitro, exposing new mechanistic details that are now calling for quantitative in vivo comparison. In this study, we bridge this gap by presenting a direct comparison of the aggregation kinetics of the ALS-associated protein superoxide dismutase 1 (SOD1) in vitro and in transgenic mice. The results based on tissue sampling by quantitative antibody assays show that the SOD1 fibrillation kinetics in vitro mirror with remarkable accuracy the spinal cord aggregate buildup and disease progression in transgenic mice. This similarity between in vitro and in vivo data suggests that, despite the complexity of live tissue, SOD1 aggregation follows robust and simplistic rules, providing new mechanistic insights into the ALS pathology and organism-level manifestation of protein aggregation phenomena in general.

A Q-switched Ho:YAG laser assisted nanosecond time-resolved T-jump transient mid-IR absorbance spectroscopy with high sensitivity

Knowledge of dynamical structure of protein is an important clue to understand its biological function in vivo. Temperature-jump (T-jump) time-resolved transient mid-IR absorbance spectroscopy is a powerful tool in elucidating the protein dynamical structures and the folding/unfolding kinetics of proteins in solution. A home-built setup of T-jump time-resolved transient mid-IR absorbance spectroscopy with high sensitivity is developed, which is composed of a Q-switched Cr, Tm, Ho:YAG laser with an output wavelength at 2.09 μm as the T-jump heating source, and a continuous working CO laser tunable from 1580 to 1980 cm(-1) as the IR probe. The results demonstrate that this system has a sensitivity of 1 × 10(-4) ΔOD for a single wavelength detection, and 2 × 10(-4) ΔOD for spectral detection in amide I' region, as well as a temporal resolution of 20 ns. Moreover, the data quality coming from the CO laser is comparable to the one using the commercial quantum cascade laser.

Folding kinetics of WW domains with the united residue force field for bridging microscopic motions and experimental measurements

To demonstrate the utility of the coarse-grained united-residue (UNRES) force field to compare experimental and computed kinetic data for folding proteins, we have performed long-time millisecond-timescale canonical Langevin molecular dynamics simulations of the triple β-strand from the Formin binding protein 28 WW domain and six nonnatural variants, using UNRES. The results have been compared with available experimental data in both a qualitative and a quantitative manner. Complexities of the folding pathways, which cannot be determined experimentally, were revealed. The folding mechanisms obtained from the simulated folding kinetics are in agreement with experimental results, with a few discrepancies for which we have accounted. The origins of single- and double-exponential kinetics and their correlations with two- and three-state folding scenarios are shown to be related to the relative barrier heights between the various states. The rate constants obtained from time profiles of the fractions of the native, intermediate, and unfolded structures, and the kinetic equations fitted to them, correlate with the experimental values; however, they are about three orders of magnitude larger than the experimental ones for most of the systems. These differences are in agreement with the timescale extension derived by scaling down the friction of water and averaging out the fast degrees of freedom when passing from all-atom to a coarse-grained representation. Our results indicate that the UNRES force field can provide accurate predictions of folding kinetics of these WW domains, often used as models for the study of the mechanisms of proein folding.

WW domain folding complexity revealed by infrared spectroscopy

Although the intrinsic tryptophan fluorescence of proteins offers a convenient probe of protein folding, interpretation of the fluorescence spectrum is often difficult because it is sensitive to both global and local changes. Infrared (IR) spectroscopy offers a complementary measure of structural changes involved in protein folding, because it probes changes in the secondary structure of the protein backbone. Here we demonstrate the advantages of using multiple probes, infrared and fluorescence spectroscopy, to study the folding of the FBP28 WW domain. Laser-induced temperature jumps coupled with fluorescence or infrared spectroscopy have been used to probe changes in the peptide backbone on the submillisecond time scale. The relaxation dynamics of the β-sheets and β-turn were measured independently by probing the corresponding IR bands assigned in the amide I region. Using these wavelength-dependent measurements, we observe three kinetics phases, with the fastest process corresponding to the relaxation kinetics of the turns. In contrast, fluorescence measurements of the wild-type WW domain and tryptophan mutants exhibit single-exponential kinetics with a lifetime that corresponds to the slowest phase observed by infrared spectroscopy. Mutant sequences provide evidence of an intermediate dry molten globule state. The slowest step in the folding of this WW domain is the tight packing of the side chains in the transition from the dry molten globule intermediate to the native structure. This study demonstrates that using multiple complementary probes enhances the interpretation of protein folding dynamics.

Order statistics inference for describing topological coupling and mechanical symmetry breaking in multidomain proteins

Cooperativity is a hallmark of proteins, many of which show a modular architecture comprising discrete structural domains. Detecting and describing dynamic couplings between structural regions is difficult in view of the many-body nature of protein-protein interactions. By utilizing the GPU-based computational acceleration, we carried out simulations of the protein forced unfolding for the dimer WW - WW of the all-β-sheet WW domains used as a model multidomain protein. We found that while the physically non-interacting identical protein domains (WW) show nearly symmetric mechanical properties at low tension, reflected, e.g., in the similarity of their distributions of unfolding times, these properties become distinctly different when tension is increased. Moreover, the uncorrelated unfolding transitions at a low pulling force become increasingly more correlated (dependent) at higher forces. Hence, the applied force not only breaks "the mechanical symmetry" but also couples the physically non-interacting protein domains forming a multi-domain protein. We call this effect "the topological coupling." We developed a new theory, inspired by order statistics, to characterize protein-protein interactions in multi-domain proteins. The method utilizes the squared-Gaussian model, but it can also be used in conjunction with other parametric models for the distribution of unfolding times. The formalism can be taken to the single-molecule experimental lab to probe mechanical cooperativity and domain communication in multi-domain proteins.

Dynamics of an ultrafast folding subdomain in the context of a larger protein fold

Small fast folding subdomains with low contact order have been postulated to facilitate the folding of larger proteins. We have tested this idea by determining how the fastest folding linear β-hairpin, CLN025, which folds on the nanosecond time scale, folds within the context of a two-hairpin WW domain system, which folds on the microsecond time scale. The folding of the wild type FBP28 WW domain was compared to constructs in which each of the loops was replaced by CLN025. A combination of FTIR spectroscopy and laser-induced temperature-jump coupled with infrared spectroscopy was used to probe changes in the peptide backbone. The relaxation dynamics of the β-sheets and β-turn were measured independently by probing the corresponding bands assigned in the amide I region. The folding rate of the CLN025 β-hairpin is unchanged within the larger protein. Insertion of the β-hairpin into the second loop results in an overall stabilization of the WW domain and a relaxation lifetime five times faster than the parent WW domain. In both mutants, folding is initiated in the turns and the β-sheets form last. These results demonstrate that fast folding subdomains can be used to speed the folding of more complex proteins, and that the folding dynamics of the subdomain is unchanged within the context of the larger protein.

Simple moment-closure model for the self-assembly of breakable amyloid filaments

In this work, we derive a simple mathematical model from mass-action equations for amyloid fiber formation that takes into account the primary nucleation, elongation, and length-dependent fragmentation. The derivation is based on the principle of minimum free energy under certain constraints and is mathematically related to the partial equilibrium approximation. Direct numerical comparisons confirm the usefulness of our simple model. We further explore its basic kinetic and equilibrium properties, and show that the current model is a straightforward generalization of that with constant fragmentation rates.

Local vs global motions in protein folding

It is of interest to know whether local fluctuations in a polypeptide chain play any role in the mechanism by which the chain folds to the native structure of a protein. This question is addressed by analyzing folding and non-folding trajectories of a protein; as an example, the analysis is applied to the 37-residue triple β-strand WW domain from the Formin binding protein 28 (FBP28) (PDB ID: 1E0L). Molecular dynamics (MD) trajectories were generated with the coarse-grained united-residue force field, and one- and two-dimensional free-energy landscapes (FELs) along the backbone virtual-bond angle θ and backbone virtual-bond-dihedral angle γ of each residue, and principal components, respectively, were analyzed. The key residues involved in the folding of the FBP28 WW domain are elucidated by this analysis. The correlations between local and global motions are found. It is shown that most of the residues in the folding trajectories of the system studied here move in a concerted fashion, following the dynamics of the whole system. This demonstrates how the choice of a pathway has to involve concerted movements in order for this protein to fold. This finding also sheds light on the effectiveness of principal component analysis (PCA) for the description of the folding dynamics of the system studied. It is demonstrated that the FEL along the PCs, computed by considering only several critically-placed residues, can correctly describe the folding dynamics.

Kinetics of amyloid aggregation: a study of the GNNQQNY prion sequence

The small amyloid-forming GNNQQNY fragment of the prion sequence has been the subject of extensive experimental and numerical studies over the last few years. Using unbiased molecular dynamics with the OPEP coarse-grained potential, we focus here on the onset of aggregation in a 20-mer system. With a total of 16.9 of simulations at 280 K and 300 K, we show that the GNNQQNY aggregation follows the classical nucleation theory (CNT) in that the number of monomers in the aggregate is a very reliable descriptor of aggregation. We find that the critical nucleus size in this finite-size system is between 4 and 5 monomers at 280 K and 5 and 6 at 300 K, in overall agreement with experiment. The kinetics of growth cannot be fully accounted for by the CNT, however. For example, we observe considerable rearrangements after the nucleus is formed, as the system attempts to optimize its organization. We also clearly identify two large families of structures that are selected at the onset of aggregation demonstrating the presence of well-defined polymorphism, a signature of amyloid growth, already in the 20-mer aggregate.

Protein aggregation plays an important pathological role in numerous neurodegenerative diseases such as Alzheimer's, Parkinson's, Creutzfeldt-Jakob, the Prion disease and diabetes mellitus. In most cases, misfolded proteins are involved and aggregate irreversibly to form highly ordered insoluble macrostructures, called amyloid fibrils, which deposit in the brain. Studies have revealed that all proteins are capable of forming amyloid fibrils that all share common structural features and therefore aggregation mechanisms. The toxicity of amyloid aggregates is however not attributed to the fibrils themselves but rather to smaller more disordered aggregates, oligomers, forming parallel to or prior to fibrils. Understanding the assembly process of these amyloid oligomers is key to understanding their toxicity mechanism in order to devise a possible treatment strategy targeting these toxic aggregates. Our approach here is to computationally study the aggregation dynamics of a 20-mer of an amyloid peptide GNNQQNY from a prion protein. Our findings suggest that the assembly is a spontaneous process that can be described as a complex nucleation and growth mechanism and which can lead to two classes of morphologies for the aggregates, one of which resembles a protofibril-like structure. Such numerical studies are crucial to understanding the details of fast biological processes and complement well experimental studies.

Effects of mutation, truncation, and temperature on the folding kinetics of a WW domain

The purpose of this work is to show how mutation, truncation, and change of temperature can influence the folding kinetics of a protein. This is accomplished by principal component analysis of molecular-dynamics-generated folding trajectories of the triple β-strand WW domain from formin binding protein 28 (FBP28) (Protein Data Bank ID: 1E0L) and its full-size, and singly- and doubly-truncated mutants at temperatures below and very close to the melting point. The reasons for biphasic folding kinetics [i.e., coexistence of slow (three-state) and fast (two-state) phases], including the involvement of a solvent-exposed hydrophobic cluster and another delocalized hydrophobic core in the folding kinetics, are discussed. New folding pathways are identified in free-energy landscapes determined in terms of principal components for full-size mutants. Three-state folding is found to be a main mechanism for folding the FBP28 WW domain and most of the full-size and truncated mutants. The results from the theoretical analysis are compared to those from experiment. Agreements and discrepancies between the theoretical and experimental results are discussed. Because of its importance in understanding protein kinetics and function, the diffusive mechanism by which the FBP28 WW domain and its full-size and truncated mutants explore their conformational space is examined in terms of the mean-square displacement and principal component analysis eigenvalue spectrum analyses. Subdiffusive behavior is observed for all studied systems.

From macroscopic measurements to microscopic mechanisms of protein aggregation

The ability to relate bulk experimental measurements of amyloid formation to the microscopic assembly processes that underlie protein aggregation is critical in order to achieve a quantitative understanding of this complex phenomenon. In this review, we focus on the insights from classical and modern theories of linear growth phenomena and discuss how theory allows the roles of growth and nucleation processes to be defined through the analysis of experimental in vitro time courses of amyloid formation. Moreover, we discuss the specific signatures in the time course of the reactions that correspond to the actions of primary and secondary nucleation processes, and outline strategies for identifying and characterising the nature of the dominant process responsible in each case for the generation of new aggregates. We highlight the power of a global analysis of experimental time courses acquired under different conditions, and discuss how such an analysis allows a rigorous connection to be established between the macroscopic measurements and the rates of the individual microscopic processes that underlie the phenomenon of amyloid formation.

Dissecting the kinetic process of amyloid fiber formation through asymptotic analysis

Amyloids are insoluble fibrous protein aggregates which, when abnormally accumulated in the body, can result in amyloidosis and various neurodegenerative diseases. In this work, we describe a new approach to the asymptotic solution of the master equation of amyloid fiber aggregations. It is found that four distinct and successive stages (lag phase, exponential growth phase, breaking phase, and static phase) dominate the fiber formation process. On the basis of the distinctive power-law dependence of the half-time and apparent growth rate of the fiber formation on the initial protein concentration, we propose a novel classification for amyloid proteins theoretically.

The ensemble folding kinetics of the FBP28 WW domain revealed by an all-atom Monte Carlo simulation in a knowledge-based potential

In this work, we apply a detailed all-atom model with a transferable knowledge-based potential to study the folding kinetics of Formin-Binding protein, FBP28, which is a canonical three-stranded β-sheet WW domain. Replica exchange Monte Carlo simulations starting from random coils find native-like (Cα RMSD of 2.68 Å) lowest energy structure. We also study the folding kinetics of FBP28 WW domain by performing a large number of ab initio Monte Carlo folding simulations. Using these trajectories, we examine the order of formation of two β-hairpins, the folding mechanism of each individual β-hairpin, and transition state ensemble (TSE) of FBP28 WW domain and compare our results with experimental data and previous computational studies. To obtain detailed structural information on the folding dynamics viewed as an ensemble process, we perform a clustering analysis procedure based on graph theory. Further, a rigorous P(fold) analysis is used to obtain representative samples of the TSEs showing good quantitative agreement between experimental and simulated Φ values. Our analysis shows that the turn structure between first and second β strands is a partially stable structural motif that gets formed before entering the TSE in FBP28 WW domain and there exist two major pathways for the folding of FBP28 WW domain, which differ in the order and mechanism of hairpin formation.

Order statistics theory of unfolding of multimeric proteins

Dynamic force spectroscopy has become indispensable for the exploration of the mechanical properties of proteins. In force-ramp experiments, performed by utilizing a time-dependent pulling force, the peak forces for unfolding transitions in a multimeric protein (D)(N) are used to map the free energy landscape for unfolding for a protein domain D. We show that theoretical modeling of unfolding transitions based on combining the observed first (f(1)), second (f(2)), …, N(th) (f(N)) unfolding forces for a protein tandem of fixed length N, and pooling the force data for tandems of different length, n(1) <n(2) < … <N, leads to an inaccurate estimation of the distribution of unfolding forces for the protein D, ψ(D)(f). This problem can be overcome by using Order statistics theory, which, in conjunction with analytically tractable models, can be used to resolve the molecular characteristics that determine the unfolding micromechanics. We present a simple method of estimation of the parent distribution, ψ(D)(f), based on analyzing the force data for a tandem (D)(n) of arbitrary length n. Order statistics theory is exemplified through a detailed analysis and modeling of the unfolding forces obtained from pulling simulations of the monomer and oligomers of the all-β-sheet WW domain.

Structural characterization of GNNQQNY amyloid fibrils by magic angle spinning NMR

Several human diseases are associated with the formation of amyloid aggregates, but experimental characterization of these amyloid fibrils and their oligomeric precursors has remained challenging. Experimental and computational analysis of simpler model systems has therefore been necessary, for instance, on the peptide fragment GNNQQNY7−13 of yeast prion protein Sup35p. Expanding on a previous publication, we report here a detailed structural characterization of GNNQQNY fibrils using magic angle spinning (MAS) NMR. On the basis of additional chemical shift assignments we confirm the coexistence of three distinct peptide conformations within the fibrillar samples, as reflected in substantial chemical shift differences. Backbone torsion angle measurements indicate that the basic structure of these coexisting conformers is an extended β-sheet. We structurally characterize a previously identified localized distortion of the β-strand backbone specific to one of the conformers. Intermolecular contacts are consistent with each of the conformers being present in its own parallel and in-register sheet. Overall the MAS NMR data indicate a substantial difference between the structure of the fibrillar and crystalline forms of these peptides, with a clearly increased complexity in the GNNQQNY fibril structure. These experimental data can provide guidance for future work, both experimental and theoretical, and provide insights into the distinction between fibril growth and crystal formation.

(Un)Folding mechanisms of the FBP28 WW domain in explicit solvent revealed by multiple rare event simulation methods

We report a numerical study of the (un)folding routes of the truncated FBP28 WW domain at ambient conditions using a combination of four advanced rare event molecular simulation techniques. We explore the free energy landscape of the native state, the unfolded state, and possible intermediates, with replica exchange molecular dynamics. Subsequent application of bias-exchange metadynamics yields three tentative unfolding pathways at room temperature. Using these paths to initiate a transition path sampling simulation reveals the existence of two major folding routes, differing in the formation order of the two main hairpins, and in hydrophobic side-chain interactions. Having established that the hairpin strand separation distances can act as reasonable reaction coordinates, we employ metadynamics to compute the unfolding barriers and find that the barrier with the lowest free energy corresponds with the most likely pathway found by transition path sampling. The unfolding barrier at 300 K is approximately 17 k(B)T approximately 42 kJ/mol, in agreement with the experimental unfolding rate constant. This work shows that combining several powerful simulation techniques provides a more complete understanding of the kinetic mechanism of protein folding.

An analytical solution to the kinetics of breakable filament assembly

We present an analytical treatment of a set of coupled kinetic equations that governs the self-assembly of filamentous molecular structures. Application to the case of protein aggregation demonstrates that the kinetics of amyloid growth can often be dominated by secondary rather than by primary nucleation events. Our results further reveal a range of general features of the growth kinetics of fragmenting filamentous structures, including the existence of generic scaling laws that provide mechanistic information in contexts ranging from in vitro amyloid growth to the in vivo development of mammalian prion diseases.

Simulations of nucleation and elongation of amyloid fibrils

We present a coarse-grained model for the growth kinetics of amyloid fibrils from solutions of peptides and address the fundamental mechanism of nucleation and elongation by using a lattice Monte Carlo procedure. We reproduce the three main characteristics of nucleation of amyloid fibrils: (1) existence of lag time, (2) occurrence of a critical concentration, and (3) seeding. We find the nucleation of amyloid fibrils to require a quasi-two-dimensional configuration, where a second layer of beta sheet must be formed adjunct to a first layer, which in turn leads to a highly cooperative nucleation barrier. The elongation stage is found to involve the Ostwald ripening (evaporation-condensation) mechanism, whereby bigger fibrils grow at the expense of smaller ones. This new mechanism reconciles the debate as to whether protofibrils are precursors or monomer reservoirs. We have systematically investigated the roles of time, peptide concentration, temperature, and seed size. In general, we find that there are two kinds of lag time arising from two different mechanisms. For higher temperatures or low enough concentrations close to the disassembly boundary, the fibrillization follows the nucleation mechanism. However, for low temperatures, where the nucleation time is sufficiently short, there still exists an apparent lag time due to slow Ostwald ripening mechanism. Consequently, the lag time is nonmonotonic with temperature, with the shortest lag time occurring at intermediate temperatures, which in turn depend on the peptide concentration. While the nucleation dominated regime can be controlled by seeding, the Ostwald ripening regime is insensitive to seeding. Simulation results from our coarse-grained model on the fibril size, lag time, elongation rate, and solubility are consistent with available experimental observations on many specific amyloid systems.

Ab initio folding of proteins with all-atom discrete molecular dynamics

Discrete molecular dynamics (DMD) is a rapid sampling method used in protein folding and aggregation studies. Until now, DMD was used to perform simulations of simplified protein models in conjunction with structure-based force fields. Here, we develop an all-atom protein model and a transferable force field featuring packing, solvation, and environment-dependent hydrogen bond interactions. We performed folding simulations of six small proteins (20-60 residues) with distinct native structures by the replica exchange method. In all cases, native or near-native states were reached in simulations. For three small proteins, multiple folding transitions are observed, and the computationally characterized thermodynamics are in qualitative agreement with experiments. The predictive power of all-atom DMD highlights the importance of environment-dependent hydrogen bond interactions in modeling protein folding. The developed approach can be used for accurate and rapid sampling of conformational spaces of proteins and protein-protein complexes and applied to protein engineering and design of protein-protein interactions.