The fuzzy oil drop model, based on hydrophobicity density distribution, generalizes the influence of water environment on protein structure and function

Improved Assessment of Globularity of Protein Structures and the Ellipsoid Profile of the Biological Assemblies from the PDB

In this paper, we present an update to the ellipsoid profile algorithm (EP), a simple technique for the measurement of the globularity of protein structures without the calculation of molecular surfaces. The globularity property is understood in this context as the ability of the molecule to fill a minimum volume enclosing ellipsoid (MVEE) that approximates its assumed globular shape. The more of the interior of this ellipsoid is occupied by the atoms of the protein, the better are its globularity metrics. These metrics are derived from the comparison of the volume of the voxelized representation of the atoms and the volume of all voxels that can fit inside that ellipsoid (a uniform unit Å cube lattice). The so-called ellipsoid profile shows how the globularity changes with the distance from the center. Two of its values, the so-called ellipsoid indexes, are used to classify the structure as globular, semi-globular or non-globular. Here, we enhance the workflow of the EP algorithm via an improved outlier detection subroutine based on principal component analysis. It is capable of robust distinguishing between the dense parts of the molecules and, for example, disordered chain fragments fully exposed to the solvent. The PCA-based method replaces the current approach based on kernel density estimation. The improved EP algorithm was tested on 2124 representatives of domain superfamilies from SCOP 2.08. The second part of this work is dedicated to the survey of globularity of 3594 representatives of biological assemblies from molecules currently deposited in the PDB and analyzed by the 3DComplex database (monomers and complexes up to 60 chains).

In Silico Modeling of the Influence of Environment on Amyloid Folding Using FOD-M Model

The role of the environment in amyloid formation based on the fuzzy oil drop model (FOD) is discussed here. This model assumes that the hydrophobicity distribution within a globular protein is consistent with a 3D Gaussian (3DG) distribution. Such a distribution is interpreted as the idealized effect of the presence of a polar solvent-water. A chain with a sequence of amino acids (which are bipolar molecules) determined by evolution recreates a micelle-like structure with varying accuracy. The membrane, which is a specific environment with opposite characteristics to the polar aquatic environment, directs the hydrophobic residues towards the surface. The modification of the FOD model to the FOD-M form takes into account the specificity of the cell membrane. It consists in "inverting" the 3DG distribution (complementing the Gaussian distribution), which expresses the exposure of hydrophobic residues on the surface. It turns out that the influence of the environment for any protein (soluble or membrane-anchored) is the result of a consensus factor expressing the participation of the polar environment and the "inverted" environment. The ratio between the proportion of the aqueous and the "reversed" environment turns out to be a characteristic property of a given protein, including amyloid protein in particular. The structure of amyloid proteins has been characterized in the context of prion, intrinsically disordered, and other non-complexing proteins to cover a wider spectrum of molecules with the given characteristics based on the FOD-M model.

Downhill, Ultrafast and Fast Folding Proteins Revised

Research on the protein folding problem differentiates the protein folding process with respect to the duration of this process. The current structure encoded in sequence dogma seems to be clearly justified, especially in the case of proteins referred to as fast-folding, ultra-fast-folding or downhill. In the present work, an attempt to determine the characteristics of this group of proteins using fuzzy oil drop model is undertaken. According to the fuzzy oil drop model, a protein is a specific micelle composed of bi-polar molecules such as amino acids. Protein folding is regarded as a spherical micelle formation process. The presence of covalent peptide bonds between amino acids eliminates the possibility of free mutual arrangement of neighbors. An example would be the construction of co-micelles composed of more than one type of bipolar molecules. In the case of fast folding proteins, the amino acid sequence represents the optimal bipolarity system to generate a spherical micelle. In order to achieve the native form, it is enough to have an external force field provided by the water environment which directs the folding process towards the generation of a centric hydrophobic core. The influence of the external field can be expressed using the 3D Gaussian function which is a mathematical model of the folding process orientation towards the concentration of hydrophobic residues in the center with polar residues exposed on the surface. The set of proteins under study reveals a hydrophobicity distribution compatible with a 3D Gaussian distribution, taken as representing an idealized micelle-like distribution. The structure of the present hydrophobic core is also discussed in relation to the distribution of hydrophobic residues in a partially unfolded form.

Structure of the Hydrophobic Core Determines the 3D Protein Structure-Verification by Single Mutation Proteins

Four de novo proteins differing in single mutation positions, with a chain length of 56 amino acids, represent diverse 3D structures: monomeric 3α and 4β + α folds. The reason for this diversity is seen in the different structure of the hydrophobic core as a result of synergy leading to the generation of a system in which the polypeptide chain as a whole participates. On the basis of the fuzzy oil drop model, where the structure of the hydrophobic core is expressed by means of the hydrophobic distribution function in the form of a 3D Gaussian distribution, it has been shown that the composition of the hydrophobic core in these two structural forms is different. In addition, the use of a model to determine the structure of the early intermediate in the folding process allows to indicate differences in the polypeptide chain geometry, which, combined with the construction of a common hydrophobic nucleus as an effect of specific synergy, may indicate the reason for the diversity of the folding process of the polypeptide chain. The results indicate the need to take into account the presence of an external force field originating from the water environment and that its active impact on the formation of a hydrophobic core whose participation in the stabilization of the tertiary structure is fundamental.

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.

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).

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.

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.

Towards the design of anti-amyloid short peptide helices

A set of short peptide sequences susceptible to fibrillar aggregation produces sequneces capable of arresting elongation of amyloid fibrils. The "stop" signals are short helices customized for each individual target. Such a helix should exhibit high amphiphilicity, with differing conditions present on each side (one side should be highly hydrophilic to enable water to interact with the aggregate, while the other side must retain a local distribution of hydrophobicity which matches that of the terminal portion of the fibril). The emergence and elongation of fibrillary forms resulting from linear propagation of local hydrophobicity peaks is shown using the fuzzy oil drop model.

Is the hydrophobic core a universal structural element in proteins?

The hydrophobic core, when subjected to analysis based on the fuzzy oil drop model, appears to be a universal structural component of proteins irrespective of their secondary, supersecondary, and tertiary conformations. A study has been performed on a set of nonhomologous proteins representing a variety of CATH categories. The presence of a well-ordered hydrophobic core has been confirmed in each case, regardless of the protein’s biological function, chain length or source organism. In light of fuzzy oil drop (FOD) analysis, various supersecondary forms seem to share a common structural factor in the form of a hydrophobic core, emerging either as part of the whole protein or a specific domain. The variable status of individual folds with respect to the FOD model reflects their propensity for conformational changes, frequently associated with biological function. Such flexibility is expressed as variable stability of the hydrophobic core, along with specific encoding of potential conformational changes which depend on the properties of helices and β-folds.

Determining protein similarity by comparing hydrophobic core structure

Formal assessment of structural similarity is - next to protein structure prediction - arguably the most important unsolved problem in proteomics. In this paper we propose a similarity criterion based on commonalities between the proteins' hydrophobic cores. The hydrophobic core emerges as a result of conformational changes through which each residue reaches its intended position in the protein body. A quantitative criterion based on this phenomenon has been proposed in the framework of the CASP challenge. The structure of the hydrophobic core - including the placement and scope of any deviations from the idealized model - may indirectly point to areas of importance from the point of view of the protein's biological function. Our analysis focuses on an arbitrarily selected target from the CASP11 challenge. The proposed measure, while compliant with CASP criteria (70-80% correlation), involves certain adjustments which acknowledge the presence of factors other than simple spatial arrangement of solids.

The variability of protein structure with respect to the hydrophobic core

The application of the fuzzy oil drop model to the analysis of protein structure is shown using two proteins. The selection of these two examples is due to their opposite character. Two proteins were selected representing very high order and very high disorder with respect to the organized uni-central hydrophobic core in proteins (one centrally localized concentration of high hydrophobicity). These two cases are to show examples of the large spectrum of variability of local organization of the hydrophobic core in proteins. The importance of the observation presented in this paper is significant with respect to large sets of proteins discussed in separate publications.

Role of the hydrophobic core in cytoskeleton protein: cardiac myosin binding protein C

Cardiac myosin binding protein C is the object of analysis presented in this paper. The fuzzy oil drop model was applied to analyze the status of the hydrophobic core in two forms of this protein: WT and R502W mutant. The status of the mutant is revealed to be of lower stability than the WT form. The high order of the hydrophobic core is interpreted as the factor of stability of the tertiary structure. The muscle proteins, which undergo significant structural changes as the consequence of external stretching forces, are expected to return to initial structures after the release of an external force. The mutant R502W appears to represent lower stability; thus, the return to the initial structure may be of lower probability. The comparable analysis to other muscle domains (titin) and immunoglobulin domains suggests the very subtle relation to the biological activity of these proteins.

Structural Interface Forms and Their Involvement in Stabilization of Multidomain Proteins or Protein Complexes

The presented analysis concerns the inter-domain and inter-protein interface in protein complexes. We propose extending the traditional understanding of the protein domain as a function of local compactness with an additional criterion which refers to the presence of a well-defined hydrophobic core. Interface areas in selected homodimers vary with respect to their contribution to share as well as individual (domain-specific) hydrophobic cores. The basic definition of a protein domain, i.e., a structural unit characterized by tighter packing than its immediate environment, is extended in order to acknowledge the role of a structured hydrophobic core, which includes the interface area. The hydrophobic properties of interfaces vary depending on the status of interacting domains—In this context we can distinguish: (1) Shared hydrophobic cores (spanning the whole dimer); (2) Individual hydrophobic cores present in each monomer irrespective of whether the dimer contains a shared core. Analysis of interfaces in dystrophin and utrophin indicates the presence of an additional quasi-domain with a prominent hydrophobic core, consisting of fragments contributed by both monomers. In addition, we have also attempted to determine the relationship between the type of interface (as categorized above) and the biological function of each complex. This analysis is entirely based on the fuzzy oil drop model.

Dissimilar sequence: similar structure of proteins

Sequence-to-structure relation is one of the major objects of the analysis of protein folding problem. The pair of two small proteins (domains) of similar structure (β-hairpin/α-helix/β-hairpin) generated by the chains of similar length (about 60 amino acids) with very low sequence similarity (15%) is the object of the comparable analysis of 3D structure. The criterion for similarity estimation is the status of polypeptide chain with respect to the hydrophobic core structure. The fuzzy oil drop model is applied to reveal the differentiated status of fragments of the well-defined secondary structure. This analysis allows the interpretation of the structure in other than the geometric form as it is made based on secondary structure classification. The two compared highly similar proteins appear to be different with respect to the hydrophobic core structure.