Application of the Fuzzy Oil Drop Model Describes Amyloid as a Ribbonlike Micelle

On the Dependence of Prion and Amyloid Structure on the Folding Environment

Currently available analyses of amyloid proteins reveal the necessity of the existence of radical structural changes in amyloid transformation processes. The analysis carried out in this paper based on the model called fuzzy oil drop (FOD) and its modified form (FOD-M) allows quantifying the role of the environment, particularly including the aquatic environment. The starting point and basis for the present presentation is the statement about the presence of two fundamentally different methods of organizing polypeptides into ordered conformations—globular proteins and amyloids. The present study shows the source of the differences between these two paths resulting from the specificity of the external force field coming from the environment, including the aquatic and hydrophobic one. The water environment expressed in the fuzzy oil drop model using the 3D Gauss function directs the folding process towards the construction of a micelle-like system with a hydrophobic core in the central part and the exposure of polarity on the surface. The hydrophobicity distribution of membrane proteins has the opposite characteristic: Exposure of hydrophobicity at the surface of the membrane protein with an often polar center (as in the case of ion channels) is expected. The structure of most proteins is influenced by a more or less modified force field generated by water through the appropriate presence of a non-polar (membrane-like) environment. The determination of the proportion of a factor different from polar water enables the assessment of the protein status by indicating factors favoring the structure it represents.

Model of Early Stage Intermediate in Respect to Its Final Structure

The model, describing a method of determining the structure of an early intermediate in the process of protein folding to analyze nonredundant PDB protein bases, allows determining the relationship between the sequence of tetrapeptides and their structural forms expressed by structural codes. The contingency table expressing such a relationship can be used to predict the structure of polypeptides by proposing a structural form with a precision limited to the structural code. However, by analyzing structural forms in native forms of proteins based on the fuzzy oil drop model, one can also determine the status of polypeptide chain fragments with respect to the assumptions of this model. Whether the probability distributions for both compliant and noncompliant forms were similar or whether the tetrapeptide sequences showed some differences at a level of a set of structural codes was investigated. The analysis presented here indicated that some sequences in both forms revealed differences in probability distributions expressed as a negative statistically significant correlation coefficient. This meant that the identified sections (tetrapeptides) took different forms against the fuzzy oil drop model. It may suggest that the information of the final status with respect to hydrophobic core formation is already carried by the structure of the early-stage intermediate.

The Amyloid as a Ribbon-Like Micelle in Contrast to Spherical Micelles Represented by Globular Proteins

Selected amyloid structures available in the Protein Data Bank have been subjected to a comparative analysis. Classification is based on the distribution of hydrophobicity in amyloids that differ with respect to sequence, chain length, the distribution of beta folds, protofibril structure, and the arrangement of protofibrils in each superfibril. The study set includes the following amyloids: Aβ (1-42), which is listed as Aβ (15-40) and carries the D23N mutation, and Aβ (11-42) and Aβ (1-40), both of which carry the E22Δ mutation, tau amyloid, and α-synuclein. Based on the fuzzy oil drop model (FOD), we determined that, despite their conformational diversity, all presented amyloids adopt a similar structural pattern that can be described as a ribbon-like micelle. The same model, when applied to globular proteins, results in structures referred to as "globular micelles," emerging as a result of interactions between the proteins' constituent residues and the aqueous solvent. Due to their composition, amyloids are unable to attain entropically favorable globular forms and instead attempt to limit contact between hydrophobic residues and water by producing elongated structures. Such structures typically contain quasi hydrophobic cores that stretch along the fibril's long axis. Similar properties are commonly found in ribbon-like micelles, with alternating bands of high and low hydrophobicity emerging as the fibrils increase in length. Thus, while globular proteins are generally consistent with a 3D Gaussian distribution of hydrophobicity, the distribution instead conforms to a 2D Gaussian distribution in amyloid fibrils.

Symmetry and Dissymmetry in Protein Structure—System-Coding Its Biological Specificity

The solenoid is a highly ordered structure observed in proteins, characterized by a set of symmetries. A group of enzymes—lyases containing solenoid fragments—was subjected to analysis with focus on their distribution of hydrophobicity/hydrophilicity, applying the fuzzy oil drop model. The model differentiates between a monocentric distribution hydrophobic core (spherical symmetry—mathematically modeled by a 3D Gaussian) and linear propagation of hydrophobicity (symmetry based on translation of structural units, i.e., chains—evident in amyloids). The linearly ordered solenoid carries information that affects the structure of the aqueous solvent in its neighborhood. Progressive disruption of its symmetry (via incorporation of asymmetrical fragments of varying size) appears to facilitate selective interaction with the intended substrate during enzymatic catalysis.

Different Synergy in Amyloids and Biologically Active Forms of Proteins

Protein structure is the result of the high synergy of all amino acids present in the protein. This synergy is the result of an overall strategy for adapting a specific protein structure. It is a compromise between two trends: The optimization of non-binding interactions and the directing of the folding process by an external force field, whose source is the water environment. The geometric parameters of the structural form of the polypeptide chain in the form of a local radius of curvature that is dependent on the orientation of adjacent peptide bond planes (result of the respective Phi and Psi rotation) allow for a comparative analysis of protein structures. Certain levels of their geometry are the criteria for comparison. In particular, they can be used to assess the differences between the structural form of biologically active proteins and their amyloid forms. On the other hand, the application of the fuzzy oil drop model allows the assessment of the role of amino acids in the construction of tertiary structure through their participation in the construction of a hydrophobic core. The combination of these two models-the geometric structure of the backbone and the determining of the participation in the construction of the tertiary structure that is applied for the comparative analysis of biologically active and amyloid forms-is presented.

Structural analysis of the Aβ(11-42) amyloid fibril based on hydrophobicity distribution

The structure of the Aβ(11–42) amyloid available in PDB makes possible the molecular analysis of the specificity of amyloid formation. This molecule (PDB ID 2MVX) is the object of analysis. This work presents the outcome of in silico experiments involving various alternative conformations of the Aβ(11–42) sequence, providing clues as to the amylodogenecity of its constituent fragments. The reference structure (PDB) has been compared with folds generated using I-Tasser and Robetta—the strongest contenders in the CASP challenge. Additionally, a polypeptide which matches the Aβ(11–42) sequence has been subjected to folding simulations based on the fuzzy oil drop model, which favors the production of a monocentric hydrophobic core. Computer simulations yielded 15 distinct structural forma (five per software package), which, when compared to the experimentally determined structure, allow us to study the role of structural elements which cause an otherwise globular protein to transform into an amyloid. The unusual positions of hydrophilic residues disrupting the expected hydrophobic core and propagating linearly along the long axis of fibril is recognized as the seed for amyloidogenic transformation in this polypeptide. This paper discusses the structure of the Aβ(11–42) amyloid fibril, listed in PDB under ID 2MXU (fragment od Aβ(1–42) amyloid).

Mechanisms of Strain Diversity of Disease-Associated in-Register Parallel β-Sheet Amyloids and Implications About Prion Strains

The mechanism of prion strain diversity remains unsolved. Investigation of inheritance and diversification of protein-based pathogenic information demands the identification of the detailed structures of abnormal isoforms of the prion protein (PrPSc); however, achieving purification is difficult without affecting infectivity. Similar prion-like properties are recognized also in other disease-associated in-register parallel β-sheet amyloids including Tau and α-synuclein (αSyn) amyloids. Investigations into structures of those amyloids via solid-state nuclear magnetic resonance spectroscopy and cryo-electron microscopy recently made remarkable advances due to their relatively small sizes and lack of post-translational modifications. Herein, we review advances regarding pathogenic amyloids, particularly Tau and αSyn, and discuss implications about strain diversity mechanisms of prion/PrPSc from the perspective that PrPSc is an in-register parallel β-sheet amyloid. Additionally, we present our recent data of molecular dynamics simulations of αSyn amyloid, which suggest significance of compatibility between β-sheet propensities of the substrate and local structures of the template for stability of amyloid structures. Detailed structures of αSyn and Tau amyloids are excellent models of pathogenic amyloids, including PrPSc, to elucidate strain diversity and pathogenic mechanisms.

Secondary and Supersecondary Structure of Proteins in Light of the Structure of Hydrophobic Cores

The traditional classification of protein structures (with regard to their supersecondary and tertiary conformation) is based on an assessment of conformational similarities between various polypeptide chains and particularly on the presence of specific secondary structural motifs. Mutual relations between secondary folds determine the overall shape of the protein and may be used to assign proteins to specific families (such as the immunoglobulin-like family). An alternative means of conducting structural assessment focuses on the structure of the protein's hydrophobic core. In this case, the protein is treated as a quasi-micelle, which exposes hydrophilic residues on its surface while internalizing hydrophobic residues. The accordance between the actual distribution of hydrophobicity in a protein and its corresponding theoretical ("idealized") distribution can be determined quantitatively, which, in turn, enables comparative analysis of structures regarded as geometrically similar (as well as geometrically divergent structures which are nevertheless regarded as similar in the sense of the fuzzy oil drop model). In this scope, the protein may be compared to an "intelligent micelle," where local disorder is often intentional and related to biological function-unlike traditional surfactant micelles which remain highly symmetrical throughout and do not carry any encoded information.

The aqueous environment as an active participant in the protein folding process

Existing computational models applied in the protein structure prediction process do not sufficiently account for the presence of the aqueous solvent. The solvent is usually represented by a predetermined number of H₂O molecules in the bounding box which contains the target chain. The fuzzy oil drop (FOD) model, presented in this paper, follows an alternative approach, with the solvent assuming the form of a continuous external hydrophobic force field, with a Gaussian distribution. The effect of this force field is to guide hydrophobic residues towards the center of the protein body, while promoting exposure of hydrophilic residues on its surface. This work focuses on the following sample proteins: Engrailed homeodomain (RCSB: 1enh), Chicken villin subdomain hp-35, n68h (RCSB: 1yrf), Chicken villin subdomain hp-35, k65(nle), n68h, k70(nle) (RCSB: 2f4k), Thermostable subdomain from chicken villin headpiece (RCSB: 1vii), de novo designed single chain three-helix bundle (a3d) (RCSB: 2a3d), albumin-binding domain (RCSB: 1prb) and lambda repressor-operator complex (RCSB: 1lmb).

Filamentous Aggregates of Tau Proteins Fulfil Standard Amyloid Criteria Provided by the Fuzzy Oil Drop (FOD) Model

Abnormal filamentous aggregates that are formed by tangled tau protein turn out to be classic amyloid fibrils, meeting all the criteria defined under the fuzzy oil drop model in the context of amyloid characterization. The model recognizes amyloids as linear structures where local hydrophobicity minima and maxima propagate in an alternating manner along the fibril's long axis. This distribution of hydrophobicity differs greatly from the classic monocentric hydrophobic core observed in globular proteins. Rather than becoming a globule, the amyloid instead forms a ribbonlike (or cylindrical) structure.

Comparison of the structure of Aβ(1-40) amyloid with the one in complex with polyphenol ε-viniferin glucoside (EVG)

The analysis of amyloid structures is much easier recently due to the availability of the solid-state nuclear magnetic resonance technique, which allows the determination of the 3D structure of amyloid forms. The amyloidogenic polypeptide Aβ(1-40) (PDB ID 2M9R, 2M9S) in its soluble form is the object of analysis in this paper. The solubility of this polypeptide is reached due to the presence of a complexed ligand: polyphenol ε-viniferin glucoside. Two forms of complexes available in the PDB were taken for analysis with respect to the presence of a hydrophobic core in the 3D structure of these complexes. The idealized hydrophobic core structure assumed to be accordant with the 3D Gauss function distribution was taken as the pattern. The aim of this analysis is the possible further comparison to the structures of the hydrophobic core present in amyloids. It is shown that the discordant (versus the 3D Gauss function) fragments present in amyloids appear accordant in the discussed complexes.

Propagation of Fibrillar Structural Forms in Proteins Stopped by Naturally Occurring Short Polypeptide Chain Fragments

Amyloids characterized by unbounded growth of fibrillar structures cause many pathological processes. Such unbounded propagation is due to the presence of a propagating hydrophobicity field around the fibril's main axis, preventing its closure (unlike in globular proteins). Interestingly, similar fragments, commonly referred to as solenoids, are present in many naturally occurring proteins, where their propagation is arrested by suitably located "stopper" fragments. In this work, we analyze the distribution of hydrophobicity in solenoids and in their corresponding "stoppers" from the point of view of the fuzzy oil drop model (called FOD in this paper). This model characterizes the unique linear propagation of local hydrophobicity in the solenoid fragment and allows us to pinpoint "stopper" sequences, where local hydrophobicity quite closely resembles conditions encountered in globular proteins. Consequently, such fragments perform their function by mediating entropically advantageous contact with the water environment. We discuss examples of amyloid-like structures in solenoids, with particular attention to "stop" segments present in properly folded proteins found in living organisms.