Natural compound plumbagin based inhibition of hIAPP revealed by Markov state models based on MD data along with experimental validations

Human islet amyloid polypeptide (amylin or hIAPP) is a 37 residue hormone co-secreted with insulin from β cells of the pancreas. In patients suffering from type-2 diabetes, amylin self-assembles into amyloid fibrils, ultimately leading to the death of the pancreatic cells. However, a research gap exists in preventing and treating such amyloidosis. Plumbagin, a natural compound, has previously been demonstrated to have inhibitory potential against insulin amyloidosis. Our investigation unveils collapsible regions within hIAPP that, upon collapse, facilitates hydrophobic and pi-pi interactions, ultimately leading to aggregation. Intriguingly plumbagin exhibits the ability to bind these specific collapsible regions, thereby impeding the aforementioned interactions that would otherwise drive hIAPP aggregation. We have used atomistic molecular dynamics approach to determine secondary structural changes. MSM shows metastable states forming native like hIAPP structure in presence of PGN. Our in silico results concur with in vitro results. The ThT assay revealed a striking 50% decrease in fluorescence intensity at a 1:1 ratio of hIAPP to Plumbagin. This finding suggests a significant inhibition of amyloid fibril formation by plumbagin, as ThT fluorescence directly correlates with the presence of these fibrils. Further TEM images revealed disappearance of hIAPP fibrils in plumbagin pre-treated hIAPP samples. Also, we have shown that plumbagin disrupts the intermolecular hydrogen bonding in hIAPP fibrils leading to an increase in the average beta strand spacing, thereby causing disaggregation of pre-formed fibrils demonstrating overall disruption of the aggregation machinery of hIAPP. Our work is the first to report a detailed atomistic simulation of 22 μs for hIAPP. Overall, our studies put plumbagin as a potential candidate for both preventive and therapeutic candidate for hIAPP amyloidosis.

Biophysical Principles Emerging from Experiments on Protein-Protein Association and Aggregation

Protein-protein association and aggregation are fundamental processes that play critical roles in various biological phenomena, from cellular signaling to disease progression. Understanding the underlying biophysical principles governing these processes is crucial for elucidating their mechanisms and developing strategies for therapeutic intervention. In this review, we provide an overview of recent experimental studies focused on protein-protein association and aggregation. We explore the key biophysical factors that influence these processes, including protein structure, conformational dynamics, and intermolecular interactions. We discuss the effects of environmental conditions such as temperature, pH and related buffer-specific effects, and ionic strength and related ion-specific effects on protein aggregation. The effects of polymer crowders and sugars are also addressed. We list the techniques used to study aggregation. We analyze emerging trends and challenges in the field, including the development of computational models and the integration of multidisciplinary approaches for a comprehensive understanding of protein-protein association and aggregation.

Interfacial Interaction between Functionalization of Polysulfone Membrane Materials and Protein Adsorption

This study that modified polysulfone membranes with different end-group chemical functionalities were prepared using chemical synthesis methods and experimentally characterized. The molecular dynamics (MD) method were used to discuss the adsorption mechanism of proteins on functionalized modified polysulfone membrane materials from a molecular perspective, revealing the interactions between different functionalized membrane surfaces and protein adsorption. Theoretical analysis combined with basic experiments and MD simulations were used to explore the orientation and spatial conformational changes of protein adsorption at the molecular level. The results show that BSA exhibits different variability and adsorption characteristics on membranes with different functional group modifications. On hydrophobic membrane surfaces, BSA shows the least stable configuration stability, making it prone to nonspecific structural changes. In addition, surface charge effects lead to electrostatic repulsion for BSA and reduce the protein adsorption sites. These MD simulation results are consistent with experimental findings, providing new design ideas and support for modifying blood-compatible membrane materials.

Advanced computational approaches to understand protein aggregation

Protein aggregation is a widespread phenomenon implicated in debilitating diseases like Alzheimer's, Parkinson's, and cataracts, presenting complex hurdles for the field of molecular biology. In this review, we explore the evolving realm of computational methods and bioinformatics tools that have revolutionized our comprehension of protein aggregation. Beginning with a discussion of the multifaceted challenges associated with understanding this process and emphasizing the critical need for precise predictive tools, we highlight how computational techniques have become indispensable for understanding protein aggregation. We focus on molecular simulations, notably molecular dynamics (MD) simulations, spanning from atomistic to coarse-grained levels, which have emerged as pivotal tools in unraveling the complex dynamics governing protein aggregation in diseases such as cataracts, Alzheimer's, and Parkinson's. MD simulations provide microscopic insights into protein interactions and the subtleties of aggregation pathways, with advanced techniques like replica exchange molecular dynamics, Metadynamics (MetaD), and umbrella sampling enhancing our understanding by probing intricate energy landscapes and transition states. We delve into specific applications of MD simulations, elucidating the chaperone mechanism underlying cataract formation using Markov state modeling and the intricate pathways and interactions driving the toxic aggregate formation in Alzheimer's and Parkinson's disease. Transitioning we highlight how computational techniques, including bioinformatics, sequence analysis, structural data, machine learning algorithms, and artificial intelligence have become indispensable for predicting protein aggregation propensity and locating aggregation-prone regions within protein sequences. Throughout our exploration, we underscore the symbiotic relationship between computational approaches and empirical data, which has paved the way for potential therapeutic strategies against protein aggregation-related diseases. In conclusion, this review offers a comprehensive overview of advanced computational methodologies and bioinformatics tools that have catalyzed breakthroughs in unraveling the molecular basis of protein aggregation, with significant implications for clinical interventions, standing at the intersection of computational biology and experimental research.

Multiscale Simulations to Discover Self-Assembled Oligopeptides: A Benchmarking Study

Peptide self-assembly is critical for biomedical and material discovery and production. While it is costly to experimentally test every possible peptide design, computational assessment provides an affordable solution to evaluate many designs and prioritize synthesis and characterization. Following a theoretical investigation, we present a systematic analysis of all-atom and coarse-grained simulations to predict peptide self-assembly. Benchmarking studies of two model dipeptides allow us to assess the impacts of intrinsic properties (such as amino acids and terminal modifications) and external environment (such as salinity) on the simulated aggregation. Further examination of 20 oligopeptides containing two to five amino acids shows good agreement among our theory, simulations, and prior experimental observations. The success rate of our prediction is 90%. Therefore, our theory, simulation, and analysis can be useful to identify peptide designs that can self-assemble and predict the potential nanostructures. These findings lay the ground for future virtual screening of peptide-assembled nanostructures and computer-aided biologics design.

Injectable cell-laden silk acid hydrogel

This study presents an injectable cell-laden hydrogel system based on silk acid, a carboxylated derivative of natural silk fibroin, which exhibits promising applications in biomedicine. The hydrogel is produced under physiological conditions (37 °C and pH 7.4) via physical crosslinking. Notably, the hydrogel demonstrates remarkable cytocompatibility, enabling efficient cell encapsulation, and exhibits good injectability. These promising results strongly indicate the potential of silk acid hydrogel for transformative applications, including 3D cell culture, targeted cell delivery, and tissue engineering.

Protein Association in Solution: Statistical Mechanical Modeling

Protein molecules associate in solution, often in clusters beyond pairwise, leading to liquid phase separations and high viscosities. It is often impractical to study these multi-protein systems by atomistic computer simulations, particularly in multi-component solvents. Instead, their forces and states can be studied by liquid state statistical mechanics. However, past such approaches, such as the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, were limited to modeling proteins as spheres, and contained no microscopic structure-property relations. Recently, this limitation has been partly overcome by bringing the powerful Wertheim theory of associating molecules to bear on protein association equilibria. Here, we review these developments.

Machine Learning-Guided Adaptive Parametrization for Coupling Terms in a Mixed United-Atom/Coarse-Grained Model for Diphenylalanine Self-Assembly in Aqueous Ionic Liquids

Precise regulation of the peptide self-assembly into ordered nanostructures with intriguing properties has attracted intense attention. However, predicting peptide assembly at atomic resolution is a challenge due to both the structural flexibility of peptides and the associated huge computational costs. A machine learning-guided adaptive parametrization method was proposed for developing a mixed atomic and coarse-grained (CG) model through a multiobjective optimization strategy. Our model incorporates the united-atom (UA) model for diphenylalanine (P) and the polarizable electrostatic-variable coarse-grained (VaCG) model for aqueous ionic liquid [BMIM]+[BF4]- solution. In this mixed model, the coupling van der Waals (vdW) interaction is addressed by introducing virtual sites (VS) in the UA model to interact with solvent CG beads. The coupling parameters, including the electrostatic parameter and vdW parameters, are automatically optimized through ML-guided adaptive parametrization. The performance of this model was tested by some microstructural properties, e.g., the average number of P-P intermolecular hydrogen bonds (HBs) and radius distribution functions (RDFs) between P and different fragments of IL, in comparison with all-atom (AA) simulations. The computational cost is significantly reduced using such a parametrization scheme, which could search tens of thousands of force-field parameter sets, while needing only a small fraction of them to be assessed with molecular dynamics (MD) simulations. We used such a mixed resolution model to investigate the self-assembly in IL-water mixtures with variants of IL concentration (X). The long-range-ordered fibril structure is formed in a pure water system (X = 0). With an increase of IL concentrations, the formation of an ordered self-assembly nanostructure is prohibited, instead forming branched fibril at X = 2 mol % or amorphous aggregates when X > 10 mol %, resulting from the interplay between π-stacking and HB interactions between P and IL. The qualitative agreement between the simulated structures and the observed morphologies in experiments indicates the applicability of ML-guided parametrization strategy in the study of complex systems, such as polymers, lipid bilayers, and polysaccharides.

Computational formulation study of insulin on biodegradable polymers

Insulin administered orally has a limited therapeutic profile due to factors such as digestion enzymes, pH, temperature, and acidic conditions in the gastrointestinal tract. Type 1 diabetes patients are typically restricted to use intradermal insulin injections to manage their blood sugar levels as oral administration is not available. Research has shown that polymers could enhance the oral bioavailability of therapeutic biologicals, but traditional methods for developing suitable polymers are time-consuming and resource-intensive. Although computational formulations can be used to identify the best polymers more quickly. The true potential of biological formulations has not been fully explored due to a lack of benchmarking studies. Therefore, molecular modelling techniques were used as a case study in this research to determine which polymer is most compatible among five natural biodegradable polymers to address insulin stability. Specially, molecular dynamics simulations were conducted in order to compare insulin-polymer mixtures at different pH levels and temperatures. Hormonal peptide morphological properties were analyzed in body and storage conditions to assess stability of insulin with and without polymers. According to our computational simulations and energetic analyses, polymer cyclodextrin and chitosan maintain insulin stability the most effectively, while alginate and pectin are less effective relatively. Overall, this study contributes valuable insight into the role of biopolymers in stabilizing hormonal peptides in biological and storage conditions. A study such as this could have a significant impact on the development of new drug delivery systems and encourage scientists to utilize them in the formulation of biologicals.

Electrostatics-Induced Nucleated Conformational Transition of Protein Aggregation

Despite the wide existence of protein aggregation in nature and its intimate connection to many human diseases, the underlying mechanism remains unclear. Here, we develop a molecular theory by systematically incorporating the self-consistent field theory for charged macromolecules into the dilute solution thermodynamics. The kinetic pathway is tracked without any restriction on the morphology of the aggregates. We find that protein aggregation at low salt concentrations is via a two-step nucleated process involving a conformational transition from metastable spherical oligomer to elongated fibril. The scaling analysis elucidates the electrostatic origin of the conformational transition: the fibril enters the screening region much earlier than the spherical aggregate. As salt concentration increases, the classical mode of one-step nucleation corresponding to macroscopic liquid-liquid phase separation is recovered. Our results reveal that the screened electrostatic interaction is essential for the existence of the metastable oligomer and its subsequent conformational transition to fibril. The theoretical predictions of the kinetic pathway and the morphology of the aggregates are in good agreement with the experimental observations of real proteins.

Peptide Self-Assembled Nanocarriers for Cancer Drug Delivery

The design of novel cancer drug nanocarriers is critical in the framework of cancer therapeutics. Nanomaterials are gaining increased interest as cancer drug delivery systems. Self-assembling peptides constitute an emerging novel class of highly attractive nanomaterials with highly promising applications in drug delivery, as they can be used to facilitate drug release and/or stability while reducing side effects. Here, we provide a perspective on peptide self-assembled nanocarriers for cancer drug delivery and highlight the aspects of metal coordination, structure stabilization, and cyclization, as well as minimalism. We review particular challenges in nanomedicine design criteria and, finally, provide future perspectives on addressing a portion of the challenges via self-assembling peptide systems. We consider that the intrinsic advantages of such systems, along with the increasing progress in computational and experimental approaches for their study and design, could possibly lead to novel classes of single or multicomponent systems incorporating such materials for cancer drug delivery.

Network Hamiltonian Models for Unstructured Protein Aggregates, with Application to γD-Crystallin

Network Hamiltonian models (NHMs) are a framework for topological coarse-graining of protein-protein interactions, in which each node corresponds to a protein, and edges are drawn between nodes representing proteins that are noncovalently bound. Here, this framework is applied to aggregates of γD-crystallin, a structural protein of the eye lens implicated in cataract disease. The NHMs in this study are generated from atomistic simulations of equilibrium distributions of wild-type and the cataract-causing variant W42R in solution, performed by Wong, E. K.; Prytkova, V.; Freites, J. A.; Butts, C. T.; Tobias, D. J. Molecular Mechanism of Aggregation of the Cataract-Related γD-Crystallin W42R Variant from Multiscale Atomistic Simulations. Biochemistry2019, 58 (35), 3691-3699. Network models are shown to successfully reproduce the aggregate size and structure observed in the atomistic simulation, and provide information about the transient protein-protein interactions therein. The system size is scaled from the original 375 monomers to a system of 10000 monomers, revealing a lowering of the upper tail of the aggregate size distribution of the W42R variant. Extrapolation to higher and lower concentrations is also performed. These results provide an example of the utility of NHMs for coarse-grained simulation of protein systems, as well as their ability to scale to large system sizes and high concentrations, reducing computational costs while retaining topological information about the system.

Hierarchical Materials from High Information Content Macromolecular Building Blocks: Construction, Dynamic Interventions, and Prediction

Hierarchical materials that exhibit order over multiple length scales are ubiquitous in nature. Because hierarchy gives rise to unique properties and functions, many have sought inspiration from nature when designing and fabricating hierarchical matter. More and more, however, nature's own high-information content building blocks, proteins, peptides, and peptidomimetics, are being coopted to build hierarchy because the information that determines structure, function, and interfacial interactions can be readily encoded in these versatile macromolecules. Here, we take stock of recent progress in the rational design and characterization of hierarchical materials produced from high-information content blocks with a focus on stimuli-responsive and "smart" architectures. We also review advances in the use of computational simulations and data-driven predictions to shed light on how the side chain chemistry and conformational flexibility of macromolecular blocks drive the emergence of order and the acquisition of hierarchy and also on how ionic, solvent, and surface effects influence the outcomes of assembly. Continued progress in the above areas will ultimately usher in an era where an understanding of designed interactions, surface effects, and solution conditions can be harnessed to achieve predictive materials synthesis across scale and drive emergent phenomena in the self-assembly and reconfiguration of high-information content building blocks.

Inhibition of Amyloid Nucleation by Steric Hindrance

Despite recent experiments and simulations suggesting that small-molecule inhibitors and some post-translational modifications (e.g., glycosylation and ubiquitination) can suppress the pathogenic aggregation of proteins due to steric hindrance, the effect of steric hindrance on amyloid formation has not been systematically studied. Based on Monte Carlo simulations using a coarse-grained model for amyloidogenic proteins and a hard sphere acting as steric hindrance, we investigated how steric hindrance on proteins could affect amyloid formation, particularly two steps of primary nucleation, namely, oligomerization and conformational conversion into a β-sheet-enriched nucleus. We found that steric spheres played an inhibitory role in oligomerization with the effect proportional to the sphere radius R_S, which we attributed to the decline in the nonspecific attractions between proteins. During the second step, small steric spheres facilitated the conformational conversion of proteins while large ones suppressed the conversion. The overall steric effect on amyloid nucleation was inhibitory regardless of R_S. As R_S increased, oligomeric assemblies changed from amorphous into sheet-like, structurally ordered species, reminiscent of the structure of amyloid fibrils. The oligomers with large R_S were off-pathway with their ordered structures induced by the competition between steric hindrance and nonspecific attractions of soluble proteins. Interestingly, the equimolar mixture of proteins with and without steric hindrance amplified the sterically inhibitory effect by increasing the energy barrier of protein's conformational conversion. The physical mechanisms and biological implications of the above results are discussed. Our findings improve the current understanding of how nature regulates protein aggregation and amyloid formation by steric hindrance.

Advances in the understanding of protein misfolding and aggregation through molecular dynamics simulation

Aberrant protein folding known as protein misfolding is counted as one of the striking factors of neurodegenerative diseases. The extensive range of pathologies caused by protein misfolding, aggregation and subsequent accumulation are mainly classified into either gain of function diseases or loss of function diseases. In order to seek for novel strategies for treatment and diagnosis of neurodegenerative diseases, insights into the mechanism of misfolding and aggregation is essential. A comprehensive knowledge on the factors influencing misfolding and aggregation is required as well. An extensive experimental study on protein aggregation is somewhat challenging due to the insoluble and noncrystalline nature of amyloid fibrils. Thus there has been a growing use of computational approaches including Monte Carlo simulation, docking simulation, molecular dynamics simulation in the study of protein misfolding and aggregation. The review presents a discussion on molecular dynamics simulation alone as to how it has emerged as a promising tool in the understanding of protein misfolding and aggregation in general, detailing upon three different aspects considering four misfold prone proteins in particular. It is noticeable that all four proteins considered in this review i.e prion, superoxide dismutase1, huntingtin and amyloid β are linked to chronic neurodegenerative diseases with debilitating effects. Initially the review elaborates on the factors influencing the misfolding and aggregation. Next, it addresses our current understanding of the amyloid structures and the associated aggregation mechanisms, finally, summarizing the contribution of this computational tool in the search for therapeutic strategies against the respective protein-deposition diseases.

pH Induced Switch in the Conformational Ensemble of Intrinsically Disordered Protein Prothymosin-α and Its Implications for Amyloid Fibril Formation

Aggregation of intrinsically disordered proteins (IDPs) can lead to neurodegenerative diseases. Although there is experimental evidence that acidic pH promotes IDP monomer compaction leading to aggregation, the general mechanism is unclear. We studied the pH effect on the conformational ensemble of prothymosin-α (proTα), which is involved in multiple essential functions, and probed its role in aggregation using computer simulations. We show that compaction in the proTα dimension at low pH is due to the protein's collapse in the intermediate region (E41-D80) rich in glutamic acid residues, enhancing its β-sheet content. We observed by performing dimer simulations that the conformations with high β-sheet content could act as aggregation-prone (N*) states and nucleate the aggregation process. The simulations initiated using N* states form dimers within a microsecond time scale, whereas the non-N* states do not form dimers within this time scale. This study contributes to understanding the general principles of pH-induced IDP aggregation.

A New Transfer Free Energy Based Implicit Solvation Model for the Description of Disordered and Folded Proteins

Most biological events occur on time scales that are difficult to access using conventional all-atom molecular dynamics simulations in explicit solvent. Implicit solvent techniques offer a promising solution to this problem, alleviating the computational cost associated with the simulation of large systems and accelerating the sampling compared to explicit solvent models. The substitution of water molecules by a mean field, however, introduces simplifications that may penalize accuracy and impede the prediction of certain physical properties. We demonstrate that existing implicit solvent models developed using a transfer free energy approach, while satisfactory at reproducing the folding behavior of globular proteins, fare less well in characterizing the conformational properties of intrinsically disordered proteins. We develop a new implicit solvent model that maximizes the degree of accuracy for both disordered and folded proteins. We show, by comparing the simulation outputs to experimental data, that in combination with the a99SB-disp force field, the implicit solvent model can describe both disordered (aβ40, PaaA2, and drkN SH3) and folded ((AAQAA)₃, CLN025, Trp-cage, and GTT) peptides. Our implicit solvent model permits a computationally efficient investigation of proteins containing both ordered and disordered regions, as well as the study of the transition between ordered and disordered protein states.

Antibody binding modulates the dynamics of the membrane-bound prion protein

Misfolding of the cellular prion protein (PrP^C) is associated with lethal neurodegeneration. PrP^C consists of a flexible tail (residues 23-123) and a globular domain (residues 124-231) whose C-terminal end is anchored to the cell membrane. The neurotoxic antibody POM1 and the innocuous antibody POM6 recognize the globular domain. Experimental evidence indicates that POM1 binding to PrP^C emulates the influence on PrP^C of the misfolded prion protein (PrP^Sc) while the binding of POM6 has the opposite biological response. Little is known about the potential interactions between flexible tail, globular domain, and the membrane. Here, we used atomistic simulations to investigate how these interactions are modulated by the binding of the Fab fragments of POM1 and POM6 to PrP^C and by interstitial sequence truncations to the flexible tail. The simulations show that the binding of the antibodies restricts the range of orientations of the globular domain with respect to the membrane and decreases the distance between tail and membrane. Five of the six sequence truncations influence only marginally this distance and the contact patterns between tail and globular domain. The only exception is a truncation coupled to a charge inversion mutation of four N-terminal residues, which increases the distance of the flexible tail from the membrane. The interactions of the flexible tail and globular domain are modulated differently by the two antibodies.

Computational models for studying physical instabilities in high concentration biotherapeutic formulations

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

Single-molecule Observation of Self-Propagating Amyloid Fibrils

The assembly of misfolded proteins into amyloid fibrils is associated with amyloidosis, including neurodegenerative diseases, such as Alzheimer’s, Parkinson’s, and prion diseases. The self-propagation of amyloid fibrils is widely observed in the aggregation pathways of numerous amyloidogenic proteins. This propensity with plasticity in primary nucleation allows amyloid fibril polymorphism, which is correlated with the pathology/phenotypes of patients. Because the interference with the nucleation and replication processes of amyloid fibrils can alter the amyloid structure and the outcome of the disease, these processes can be a target for developing clinical drugs. Single-molecule observation of amyloid fibril replication can be an experimental system to provide the kinetic parameters for simulation studies and confirm the effect of clinical drugs. Here, we review single-molecule observation of the amyloid fibril replication process using fluorescence microscopy and time-lapse atomic force microscopy, including high-speed atomic force microscopy. We discussed the amyloid fibril replication process and combined single-molecule observation results with molecular dynamics simulations.

Mini Abstract Structural dynamics in amyloid aggregation is related with various Alzheimer’s and Parkinson’s disease symptoms. Single-molecule observation using high-speed atomic force microscopy can directly visualize the structural dynamics of individual amyloid aggregate assemblies. Here, we review historical and recent studies of single-molecule observation of amyloid aggregation with supportive molecular dynamics simulation.

Matrin3: Disorder and ALS Pathogenesis

Amyotrophic lateral sclerosis (ALS) is a neurodegenerative disorder characterized by the degeneration of both upper and lower motor neurons in the brain and spinal cord. ALS is associated with protein misfolding and inclusion formation involving RNA-binding proteins, including TAR DNA-binding protein (TDP-43) and fused in sarcoma (FUS). The 125-kDa Matrin3 is a highly conserved nuclear DNA/RNA-binding protein that is implicated in many cellular processes, including binding and stabilizing mRNA, regulating mRNA nuclear export, modulating alternative splicing, and managing chromosomal distribution. Mutations in MATR3, the gene encoding Matrin3, have been identified as causal in familial ALS (fALS). Matrin3 lacks a prion-like domain that characterizes many other ALS-associated RNA-binding proteins, including TDP-43 and FUS, however, our bioinformatics analyses and preliminary studies document that Matrin3 contains long intrinsically disordered regions that may facilitate promiscuous interactions with many proteins and may contribute to its misfolding. In addition, these disordered regions in Matrin3 undergo numerous post-translational modifications, including phosphorylation, ubiquitination and acetylation that modulate the function and misfolding of the protein. Here we discuss the disordered nature of Matrin3 and review the factors that may promote its misfolding and aggregation, two elements that might explain its role in ALS pathogenesis.

Computational Models for the Study of Protein Aggregation

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

Computational Methods and Tools in Antimicrobial Peptide Research

The evolution of antibiotic-resistant bacteria is an ongoing and troubling development that has increased the number of diseases and infections that risk going untreated. There is an urgent need to develop alternative strategies and treatments to address this issue. One class of molecules that is attracting significant interest is that of antimicrobial peptides (AMPs). Their design and development has been aided considerably by the applications of molecular models, and we review these here. These methods include the use of tools to explore the relationships between their structures, dynamics, and functions and the increasing application of machine learning and molecular dynamics simulations. This review compiles resources such as AMP databases, AMP-related web servers, and commonly used techniques, together aimed at aiding researchers in the area toward complementing experimental studies with computational approaches.

Size-based Degradation of Therapeutic Proteins - Mechanisms, Modelling and Control

Protein therapeutics are in great demand due to their effectiveness towards hard-to-treat diseases. Despite their high demand, these bio-therapeutics are very susceptible to degradation via aggregation, fragmentation, oxidation, and reduction, all of which are very likely to affect the quality and efficacy of the product. Mechanisms and modelling of these degradation (aggregation and fragmentation) pathways is critical for gaining a deeper understanding of stability of these products. This review aims to provide a summary of major developments that have occurred towards unravelling the mechanisms of size-based protein degradation (particularly aggregation and fragmentation), modelling of these size-based degradation pathways, and their control. Major caveats that remain in our understanding and control of size-based protein degradation have also been presented and discussed.

Atomistic Modeling of Peptide Aggregation and β-Sheet Structuring in Corn Zein for Viscoelasticity

The structure-function relationships of plant-based proteins that give rise to desirable texture attributes in order to mimic meat products are generally unknown. In particular, it is not clear how to engineer viscoelasticity to impart cohesiveness and proper mouthfeel; however, it is known that intermolecular β-sheet structures have the potential to enhance the viscoelastic property. Here, we investigated the propensity of selected peptide segments within common corn α-zein variants to maintain stable aggregates and β-sheet structures. Simulations on dimer systems showed that stability was influenced by the initial orientation and the presence of contiguous small hydrophobic residues. Simulations using eight-peptide β-sheet oligomers revealed that peptide sequences without proline had higher levels of β-sheet structuring. Additionally, we identified that sequences with a dimer hydrogen-bonding density of >22% tended to have a larger percent β-sheet conformation. These results contribute to understanding how the viscoelasticity of zein can be increased for use in plant-based meat analogues.

Physics-based computational and theoretical approaches to intrinsically disordered proteins

Intrinsically disordered proteins (IDPs) are an important class of proteins that do not fold to a well-defined three-dimensional shape but rather adopt an ensemble of inter-converting conformations. This feature makes their experimental characterization challenging and invites a theoretical and computational approach to complement experimental studies. In this review, we highlight the recent progress in developing new computational and theoretical approaches to study the structure and dynamics of monomeric and order higher assemblies of IDPs, with a particular emphasis on their phase separation into protein-rich condensates.

Dissecting the role of glutamine in seeding peptide aggregation

Poly glutamine and glutamine-rich peptides play a central role in a plethora of pathological aggregation events. However, biophysical characterization of soluble oligomers -the most toxic species involved in these processes- remains elusive due to their structural heterogeneity and dynamical nature. Here, we exploit the high spatio-temporal resolution of coarse-grained simulations as a computational microscope to characterize the aggregation propensity and morphology of a series of polyglutamine and glutamine-rich peptides. Comparative analysis of ab-initio aggregation pinpointed a double role for glutamines. In the first phase, glutamines mediate seeding by pairing monomeric peptides, which serve as primers for higher-order nucleation. According to the glutamine content, these low molecular-weight oligomers may then proceed to create larger aggregates. Once within the aggregates, buried glutamines continue to play a role in their maturation by optimizing solvent-protected hydrogen bonds networks.

Defining the Neuropathological Aggresome across in Silico, in Vitro, and ex Vivo Experiments

The loss of proteostasis over the life course is associated with a wide range of debilitating degenerative diseases and is a central hallmark of human aging. When left unchecked, proteins that are intrinsically disordered can pathologically aggregate into highly ordered fibrils, plaques, and tangles (termed amyloids), which are associated with countless disorders such as Alzheimer's disease, Parkinson's disease, type II diabetes, cancer, and even certain viral infections. However, despite significant advances in protein folding and solution biophysics techniques, determining the molecular cause of these conditions in humans has remained elusive. This has been due, in part, to recent discoveries showing that soluble protein oligomers, not insoluble fibrils or plaques, drive the majority of pathological processes. This has subsequently led researchers to focus instead on heterogeneous and often promiscuous protein oligomers. Unfortunately, significant gaps remain in how to prepare, model, experimentally corroborate, and extract amyloid oligomers relevant to human disease in a systematic manner. This Review will report on each of these techniques and their successes and shortcomings in an attempt to standardize comparisons between protein oligomers across disciplines, especially in the context of neurodegeneration. By standardizing multiple techniques and identifying their common overlap, a clearer picture of the soluble neuropathological aggresome can be constructed and used as a baseline for studying human disease and aging.

Morpholino-based peptide oligomers: Synthesis and DNA binding properties

The chemical structure of oligonucleotide analogues dictates the conformation of oligonucleotide analogue oligomers, their ability to hybridize complementary DNA and RNA, their stability to degradation and their pharmacokinetic properties. In a study aimed at investigating new analogues featuring a neutral backbone, we explored the ability of oligomers containing a morpholino-peptide backbone to bind oligonucleotides. Circular Dichroism studies revealed the ability of our oligomers to interact with DNA, molecular modelling studies revealed the interaction responsible for complex stabilization.

The concept of protein folding/unfolding and its impacts on human health

Proteins have evolved in specific 3D structures and play different functions in cells and determine various reactions and pathways. The newly synthesized amino acid chains once depart ribosome must crumple into three-dimensional structures so can be biologically active. This process of protein that makes a functional molecule is called protein folding. The protein folding is both a biological and a physicochemical process that depends on the sequence of it. In fact, this process occurs more complicated and in some cases and in exposure to some molecules like glucose (glycation), mistaken folding leads to amyloid structures and fatal disorders called conformational diseases. Such conditions are detected by the quality control system of the cell and these abnormal proteins undergo renovation or degradation. This scenario takes place by the chaperones, chaperonins, and Ubiquitin-proteasome complex. Understanding of protein folding mechanisms from different views including experimental and computational approaches has revealed some intermediate ensembles such as molten globule and has been subjected to biophysical and molecular biology attempts to know more about prevalent conformational diseases.

Fundamental Challenges and Outlook in Simulating Liquid-Liquid Phase Separation of Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDPs) populate an ensemble of dynamic conformations, making their structural characterization by experiments challenging. Many IDPs undergo liquid-liquid phase separation into dense membraneless organelles with myriad cellular functions. Multivalent interactions in low-complexity IDPs promote the formation of these subcellular coacervates. While solution NMR, Förster resonance energy transfer (FRET), and small-angle X-ray scattering (SAXS) studies on IDPs have their own challenges, recent computational methods draw a rational trade-off to characterize the driving forces underlying phase separation. In this Perspective, we critically evaluate the scope of approximation-free field theoretic simulations, well-tempered ensemble methods, enhanced sampling techniques, coarse-grained force fields, and slab simulation approaches to offer an improved understanding of phase separation. A synergy between simulation length scale and model resolution would reduce the existing caveats and enable theories of polymer physics to elucidate finer details of liquid-liquid phase separation (LLPS). These computational advances offer promise for rigorous characterization of the IDP proteome and designing peptides with tunable material and self-assembly properties.

Protein aggregation: in silico algorithms and applications

Protein aggregation is a topic of immense interest to the scientific community due to its role in several neurodegenerative diseases/disorders and industrial importance. Several in silico techniques, tools, and algorithms have been developed to predict aggregation in proteins and understand the aggregation mechanisms. This review attempts to provide an essence of the vast developments in in silico approaches, resources available, and future perspectives. It reviews aggregation-related databases, mechanistic models (aggregation-prone region and aggregation propensity prediction), kinetic models (aggregation rate prediction), and molecular dynamics studies related to aggregation. With a multitude of prediction models related to aggregation already available to the scientific community, the field of protein aggregation is rapidly maturing to tackle new applications.

The F19W mutation reduces the binding affinity of the transmembrane Aβ11-40 trimer to the membrane bilayer

Alzheimer's disease is linked to the aggregation of the amyloid-β protein (Aβ) of 40 or 42 amino acids. Lipid membranes are known to modulate the rate and mechanisms of the Aβ aggregation. Point mutations in Aβ can alter these rates and mechanisms. In particular, experiments show that F19 mutations influence the aggregation rate, but maintain the fibril structures. Here, we used molecular dynamics simulations to examine the effect of the F19W mutation in the 3Aβ11-40 trimer immersed in DPPC lipid bilayers submerged in aqueous solution. Substituting Phe by its closest (non-polar) aromatic amino acid Trp has a dramatic reduction in binding affinity to the phospholipid membrane (measured with respect to the solvated protein) compared to the wild type: the binding free energy of the protein-DPPC lipid bilayer increases by 40-50 kcal mol-1 over the wild-type. This is accompanied by conformational changes and loss of salt bridges, as well as a more complex free energy surface, all indicative of a more flexible and less stable mutated trimer. These results suggest that the impact of mutations can be assessed, at least partially, by evaluating the interaction of the mutated peptides with the lipid membranes.

Studying the mechanism of phase separation in aqueous solutions of globular proteins via molecular dynamics computer simulations

Proteins are the most abundant biomacromolecules in living cells, where they perform vital roles in virtually every biological process. To maintain their function, proteins need to remain in a stable (native) state. Inter- and intramolecular interactions in aqueous protein solutions govern the fate of proteins, as they can provoke their unfolding or association into aggregates. The initial steps of protein aggregation are difficult to capture experimentally, therefore we used molecular dynamics simulations in this study. We investigated the initial phase of aggregation of two different lysozymes, hen egg-white (HEWL) and T4 WT* lysozyme and also human lens γ-D crystallin by using atomistic simulations. We monitored the phase stability of their aqueous solutions by calculating time-dependent density fluctuations. We found that all proteins remained in their compact form despite aggregation. With an extensive analysis of intermolecular residue-residue interactions we discovered that arginine is of paramount importance in the initial stage of aggregation of HEWL and γ-D crystallin, meanwhile lysine was found to be the most involved amino acid in forming initial contacts between T4 WT* molecules.

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.

A Perspective on Biophysical Studies of Crystallin Aggregation and Implications for Cataract Formation

Lens crystallins are subject to various types of damage during their lifetime which triggers protein misfolding and aggregation, ultimately causing cataracts. There are several models for crystallin aggregation, but a comprehensive picture of the mechanism of cataract is still underway. The complex biomolecular interactions underlying crystallin aggregation have motivated major efforts to resolve the structural details and mechanism of aggregation using multiple biophysical techniques at different resolutions. Together, experimental and computational approaches identify and characterize both amyloidogenic and amorphous aggregates leading to an improved understanding of crystallin aggregation. A rigorous characterization of the aggregation-prone intermediates is crucial in cataract-mediated drug discovery. This Perspective summarizes recent biophysical studies on lens crystallin aggregation. We evaluate the outstanding challenges, future outlook, and rewards in this fertile field of research. With lessons learned from protein folding and multiple pathways of aggregation, we highlight the differences in the overall mechanisms of age-related and congenital cataracts. We expect that a correlation between the existing and developing biophysical techniques would provide a platform to study amyloid architecture in the eye lens and reduce the existing gaps in our understanding of crystallin biophysics.

The Early Phase of β2-Microglobulin Aggregation: Perspectives From Molecular Simulations

Protein β2-microglobulin is the causing agent of two amyloidosis, dialysis related amyloidosis (DRA), affecting the bones and cartilages of individuals with chronic renal failure undergoing long-term hemodialysis, and a systemic amyloidosis, found in one French family, which impairs visceral organs. The protein’s small size and its biomedical significance attracted the attention of theoretical scientists, and there are now several studies addressing its aggregation mechanism in the context of molecular simulations. Here, we review the early phase of β2-microglobulin aggregation, by focusing on the identification and structural characterization of monomers with the ability to trigger aggregation, and initial small oligomers (dimers, tetramers, hexamers etc.) formed in the so-called nucleation phase. We focus our analysis on results from molecular simulations and integrate our views with those coming from in vitro experiments to provide a broader perspective of this interesting field of research. We also outline directions for future computer simulation studies.

Using the generalized Born surface area model to fold proteins yields more effective sampling while qualitatively preserving the folding landscape

Protein folding is a long-standing problem and has been widely investigated using molecular dynamics simulations with both explicit and implicit solvents. However, to what extent the folding mechanisms observed in two water models agree remains an open question. In this study, ab initio folding simulations of ten proteins with different topologies are performed in two combinations of force fields and water models (ff14SB+TIP3P and ff14SBonlysc+GB-Neck2). Interestingly, the latter combination not only folds more proteins but also provides a better balance of different secondary structures than the former in the same number of integration time steps. More importantly, the folding pathways found in the two types of simulations are conserved and they may only differ in their weights. Our results suggest that simulations with an implicit solvent may also be suitable for the investigation of the mechanism of protein folding.

How Does the Mono-Triazole Derivative Modulate Aβ42 Aggregation and Disrupt a Protofibril Structure: Insights from Molecular Dynamics Simulations

Clinical studies have identified that abnormal self-assembly of amyloid-β (Aβ) peptide into toxic fibrillar aggregates is associated with the pathology of Alzheimer's disease (AD). The most acceptable therapeutic approach to stop the progression of AD is to inhibit the formation of β-sheet-rich structures. Recently, we designed and evaluated a series of novel mono-triazole derivatives 4(a-x), where compound 4v was identified as the most potent inhibitor of Aβ₄₂ aggregation and disaggregates preformed Aβ₄₂ fibrils significantly. Moreover, 4v strongly averts the Cu²⁺-induced Aβ₄₂ aggregation and disaggregates the preformed Cu²⁺-induced Aβ₄₂ fibrils, halts the generation of reactive oxygen species, and shows neuroprotective effects in SH-SY5Y cells. However, the underlying molecular mechanism of inhibition of Aβ₄₂ aggregation by 4v and disaggregation of preformed Aβ₄₂ fibrils remains obscure. In this work, molecular dynamics (MD) simulations have been performed to explore the conformational ensemble of the Aβ₄₂ monomer and a pentameric protofibril structure of Aβ₄₂ in the presence of 4v. The MD simulations highlighted that 4v binds preferentially at the central hydrophobic core region of the Aβ₄₂ monomer and chains D and E of the Aβ₄₂ protofibril. The dictionary of secondary structure of proteins analysis indicated that 4v retards the conformational conversion of the helix-rich structure of the Aβ₄₂ monomer into the aggregation-prone β-sheet conformation. The binding free energy calculated by the molecular mechanics Poisson-Boltzmann surface area method revealed an energetically favorable process with ΔG _binding = -44.9 ± 3.3 kcal/mol for the Aβ₄₂ monomer-4v complex. The free energy landscape analysis highlighted that the Aβ₄₂ monomer-4v complex sampled conformations with significantly higher helical contents (35 and 49%) as compared to the Aβ₄₂ monomer alone (17%). Compound 4v displayed hydrogen bonding with Gly37 (chain E) and π-π interactions with Phe19 (chain D) of the Aβ₄₂ protofibril. Further, the per-residue binding free energy analysis also highlighted that Phe19 (chain D) and Gly37 (chain E) of the Aβ₄₂ protofibril showed the maximum contribution in the binding free energy. The decreased binding affinity and residue-residue contacts between chains D and E of the Aβ₄₂ protofibril in the presence of 4v indicate destabilization of the Aβ₄₂ protofibril structure. Overall, the structural information obtained through MD simulations indicated that 4v stabilizes the native helical conformation of the Aβ₄₂ monomer and persuades a destabilization in the protofibril structure of Aβ₄₂. The results of the study will be useful in the rational design of potent inhibitors against amyloid aggregation.

On the Conformational Dynamics of β-Amyloid Forming Peptides: A Computational Perspective

Understanding the conformational dynamics of proteins and peptides involved in important functions is still a difficult task in computational structural biology. Because such conformational transitions in β-amyloid (Aβ) forming peptides play a crucial role in many neurological disorders, researchers from different scientific fields have been trying to address issues related to the folding of Aβ forming peptides together. Many theoretical models have been proposed in the recent years for studying Aβ peptides using mathematical, physicochemical, and molecular dynamics simulation, and machine learning approaches. In this article, we have comprehensively reviewed the developmental advances in the theoretical models for Aβ peptide folding and interactions, particularly in the context of neurological disorders. Furthermore, we have extensively reviewed the advances in molecular dynamics simulation as a tool used for studying the conversions between polymorphic amyloid forms and applications of using machine learning approaches in predicting Aβ peptides and aggregation-prone regions in proteins. We have also provided details on the theoretical advances in the study of Aβ peptides, which would enhance our understanding of these peptides at the molecular level and eventually lead to the development of targeted therapies for certain acute neurological disorders such as Alzheimer's disease in the future.

Variance of Atomic Coordinates as a Dynamical Metric to Distinguish Proteins and Protein-Protein Interactions in Molecular Dynamics Simulations

Protein dynamics is a manifestation of the complex trajectories of these biomolecules on a multidimensional rugged potential energy surface (PES) driven by thermal energy. At present, computational methods such as atomistic molecular dynamics (MD) simulations can describe thermal protein conformational changes in fully solvated environments over millisecond timescales. Despite these advances, a quantitative assessment of protein dynamics remains a complicated topic, intricately linked to issues such as sampling convergence and the identification of appropriate reaction coordinates/structural features to describe protein conformational states and motions. Here, we present the cumulative variance of atomic coordinate fluctuations (CVCF) along trajectories as an intuitive PES sensitive metric to assess both the extent of sampling and protein dynamics captured in MD simulations. We first examine the sampling problem in model one- (1D) and two-dimensional (2D) PES to demonstrate that the CVCF when traced as a function of the sampling variable (time in MD simulations) can identify local and global equilibria. Further, even far from global equilibrium, a situation representative of standard MD trajectories of proteins, the CVCF can distinguish different PES and therefore resolve the resultant protein dynamics. We demonstrate the utility of our CVCF analysis by applying it to distinguish the dynamics of structurally homologous proteins from the ubiquitin family (ubiquitin, SUMO1, SUMO2) and ubiquitin protein-protein interactions. Our CVCF analysis reveals that differential side-chain dynamics from the structured part of the protein (the conserved β-grasp fold) present distinct protein PES to distinguish ubiquitin from SUMO isoforms. Upon binding to two functionally distinct protein partners (UBCH5A and UEV), intrinsic ubiquitin dynamics changes to reflect the binding context even though the two proteins have similar binding modes, which lead to negligible (sub-angstrom scale) structural changes.

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.

Amyloid assembly is dominated by misregistered kinetic traps on an unbiased energy landscape

Atomistic description of protein fibril formation has been elusive due to the complexity and long time scales of the conformational search. Here, we develop a multiscale approach combining numerous atomistic simulations in explicit solvent to construct Markov State Models (MSMs) of fibril growth. The search for the in-register fully bound fibril state is modeled as a random walk on a rugged two-dimensional energy landscape defined by β-sheet alignment and hydrogen-bonding states, whereas transitions involving states without hydrogen bonds are derived from kinetic clustering. The reversible association/dissociation of an incoming peptide and overall growth kinetics are then computed from MSM simulations. This approach is applied to derive a parameter-free, comprehensive description of fibril elongation of Aβ_16-22 and how it is modulated by phenylalanine-to-cyclohexylalanine (CHA) mutations. The trajectories show an aggregation mechanism in which the peptide spends most of its time trapped in misregistered β-sheet states connected by weakly bound states twith short lifetimes. Our results recapitulate the experimental observation that mutants CHA19 and CHA1920 accelerate fibril elongation but have a relatively minor effect on the critical concentration for fibril growth. Importantly, the kinetic consequences of mutations arise from cumulative effects of perturbing the network of productive and nonproductive pathways of fibril growth. This is consistent with the expectation that nonfunctional states will not have evolved efficient folding pathways and, therefore, will require a random search of configuration space. This study highlights the importance of describing the complete energy landscape when studying the elongation mechanism and kinetics of protein fibrils.

Exploring the interplay between fibrillization and amorphous aggregation channels on the energy landscapes of tau repeat isoforms

Filaments made up of different isoforms of tau protein are associated with a variety of neurodegenerative diseases. Filaments made up of the 4R-tau isoform, which has four repeat regions (R1 to R4), are found in patients suffering from Alzheimer's disease, while filaments made of the 3R-tau isoform, which contains only three repeat units (R1, R3, and R4), are found in patients with Pick's disease (frontotemporal dementia). In this work, a predictive coarse-grained protein force field, the associative memory water-mediated structure and energy model (AWSEM), is used to study the energy landscapes of nucleation of the two different fibrils derived from patients with Pick's and Alzheimer's diseases. The landscapes for nucleating both fibril types contain amorphous oligomers leading to branched structures as well as prefibrillar oligomers. These two classes of oligomers differ in their structural details: The prefibrillar oligomers have more parallel in-register β-strands, which ultimately lead to amyloid fibrils, while the amorphous oligomers are characterized by a near random β-strand stacking, leading to a distinct amorphous phase. The landscape topography suggests that there must be significant structural reordering, or "backtracking," to transit from the amorphous aggregation channel to the fibrillization channel. Statistical mechanical perturbation theory allows us to evaluate the effects of changing concentration on the aggregation free-energy landscapes and to predict the effects of phosphorylation, which is known to facilitate the aggregation of tau repeats.