Application of Divergence Entropy to Characterize the Structure of the Hydrophobic Core in DNA Interacting Proteins

Hydrophobicity-Based Force Field In Enzymes

The biocatalysis process takes place with the participation of enzymes, which, depending on the reaction carried out, require, apart from the appropriate arrangement of catalytic residues, an appropriate external force field. It is generated by the protein body. The relatively small size of the part directly involved in the process itself is supported by the presence of an often complex structure of the protein body, the purpose of which is to provide an appropriate local force field, eliminating the influence of water. Very often, the large size of the enzyme is an expression of the complex form of this field. In this paper, a comparative analysis of arbitrarily selected enzymes, representatives of different enzyme classes, was carried out, focusing on the measurement of the diversity of the force field provided by a given protein. This analysis was based on the fuzzy oil drop model (FOD) and its modified version (FOD-M), which takes into account the participation of nonaqueous external factors in shaping the structure and thus the force field within the protein. The degree and type of ordering of the hydrophobicity distribution in the protein molecule is the result of the influence of the environment but also the supplier of the local environment for a given process, including the catalysis process in particular. Determining the share of a nonaqueous environment is important due to the ubiquity of polar water, whose participation in processes with high specificity requires control. It can be assumed that some enzymes in their composition have a permanently built-in part, the role of which is reduced to that of a permanent chaperone. It provides a specific external force field needed for the process. The proposed model, generalized to other types of proteins, may also provide a form of recording the environment model for the simulation of the in silico protein folding process, taking into account the impact of its differentiation.

An Attempt of Seeking Favorable Binding Free Energy Prediction Schemes Considering the Entropic Effect on Fis-DNA Binding

Protein-DNA binding mechanisms in a complex manner are essential for understanding many biological processes. Over the past decades, numerous experiments and calculations have analyzed the specificity of protein-DNA binding. However, the accuracy of binding free energy prediction for multi-base DNA systems still needs to be improved. Fis is a DNA-binding protein that regulates various transcription and recombination reactions. In the present work, we tested several methods of predict binding free energy based on this system to find a favorable prediction scheme and explore the binding mechanism of Fis protein and DNA. Two solvent models (explicit and implicit solvent models) were chosen for the dynamics process, and the predicted binding free energy was more accurate under the explicit solvent model. When different Poisson-Boltzmann/Generalized Born (PB/GB) models were tested for DNA force fields (BSC1 and OL15), it was found that the binding free energy predicted by the selected OL15 force field performed better and the correlation between predicted and experimental values was improved with the increasing interior dielectric constant (Dk). Finally, using Dk = 8, the GB^OBC1 model combined with interaction entropy (IE), which was calculated for entropic contribution (GB^OBC1_IE_8), was screened out for the binding free energy prediction and analysis of the Fis-DNA system, and the validity of the method was further verified by testing the Cren7-DNA system. By performing conformational analysis of the minor groove, it was found that mutation of the DNA central sequence A/T to C/G and deletion of the guanine 2-amino group would change the minor groove width and thus affect the formation of the major groove, altering the interaction and atomic contact between the protein and the major groove, thus changing the binding affinity of Fis and DNA. Hopefully, the series of tests in this work can shed some light on the related studies of protein and DNA systems.

On the need to introduce environmental characteristics in ab initio protein structure prediction using a coarse-grained UNRES force field

During the protein folding process in computer simulations involving the use of a United RESidue (UNRES) force field, an additional module was introduced to represent directly the presence of a polar solvent in water form. This module implements the fuzzy oil drop model (FOD) where the 3D Gauss function expresses the presence of a polar environment which directs the polypeptide chain folding process towards the generation of a centric hydrophobic core. Sample test polypeptide chains of 8 proteins with chain lengths ranging from 37 to 75 aa were simulated in silico using the UNRES (U) package with an implicit solvent model and a built-in module expressing the FOD model (UNRES-FOD-UNRES (U + F) interleaved simulation). The protein structure obtained by both *** simulation schemes, i.e., accordingly***U and U + F, for all the analyzed protein models shows the presence of a hydrophobic core including where it is absent in the native structure. The proposed FOD-M model (M-modified) explaining the source of this phenomenon reveals the need to modify the external field expressing the role of a folding environment. The modification takes into account the influence of other than polar factors present in the folding environment.

Dependence of Protein Structure on Environment: FOD Model Applied to Membrane Proteins

The natural environment of proteins is the polar aquatic environment and the hydrophobic (amphipathic) environment of the membrane. The fuzzy oil drop model (FOD) used to characterize water-soluble proteins, as well as its modified version FOD-M, enables a mathematical description of the presence and influence of diverse environments on protein structure. The present work characterized the structures of membrane proteins, including those that act as channels, and a water-soluble protein for contrast. The purpose of the analysis was to verify the possibility that an external force field can be used in the simulation of the protein-folding process, taking into account the diverse nature of the environment that guarantees a structure showing biological activity.

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.

The Functional Significance of Hydrophobic Residue Distribution in Bacterial Beta-Barrel Transmembrane Proteins

β-barrel membrane proteins have several important biological functions, including transporting water and solutes across the membrane. They are active in the highly hydrophobic environment of the lipid membrane, as opposed to soluble proteins, which function in a more polar, aqueous environment. Globular soluble proteins typically have a hydrophobic core and a polar surface that interacts favorably with water. In the fuzzy oil drop (FOD) model, this distribution is represented by the 3D Gauss function (3DG). In contrast, membrane proteins expose hydrophobic residues on the surface, and, in the case of ion channels, the polar residues face inwards towards a central pore. The distribution of hydrophobic residues in membrane proteins can be characterized by means of 1–3DG, a complementary 3D Gauss function. Such an analysis was carried out on the transmembrane proteins of bacteria, which, despite the considerable similarities of their super-secondary structure (β-barrel), have highly differentiated properties in terms of stabilization based on hydrophobic interactions. The biological activity and substrate specificity of these proteins are determined by the distribution of the polar and nonpolar amino acids. The present analysis allowed us to compare the ways in which the different proteins interact with antibiotics and helped us understand their relative importance in the development of the resistance mechanism. We showed that beta barrel membrane proteins with a hydrophobic core interact less strongly with the molecules they transport.

Divergence Entropy-Based Evaluation of Hydrophobic Core in Aggressive and Resistant Forms of Transthyretin

The two forms of transthyretin differing slightly in the tertiary structure, despite the presence of five mutations, show radically different properties in terms of susceptibility to the amyloid transformation process. These two forms of transthyretin are the object of analysis. The search for the sources of these differences was carried out by means of a comparative analysis of the structure of these molecules in their native and early intermediate stage forms in the folding process. The criterion for assessing the degree of similarity and differences is the status of the hydrophobic core. The comparison of the level of arrangement of the hydrophobic core and its initial stages is possible thanks to the application of divergence entropy for the early intermediate stage and for the final forms. It was shown that the minimal differences observed in the structure of the hydrophobic core of the forms available in PDB, turned out to be significantly different in the early stage (ES) structure in folding process. The determined values of divergence entropy for both ES forms indicate the presence of the seed of hydrophobic core only in the form resistant to amyloid transformation. In the form of aggressively undergoing amyloid transformation, the structure lacking such a seed is revealed, being a stretched one with a high content of β-type structure. In the discussed case, the active presence of water in the structural transformation of proteins expressed in the fuzzy oil drop model (FOD) is of decisive importance for the generation of the final protein structure. It has been shown that the resistant form tends to generate a centric hydrophobic core with the possibility of creating a globular structure, i.e., a spherical micelle-like form. The aggressively transforming form reveals in the structure of its early intermediate, a tendency to form the ribbon-like micelle as observed in amyloid.

Model of Environmental Membrane Field for Transmembrane Proteins

The water environment determines the activity of biological processes. The role of such an environment interpreted in the form of an external field expressed by the 3D Gaussian distribution in the fuzzy oil drop model directs the folding process towards the generation of a centrally located hydrophobic core with the simultaneous exposure of polar residues on the surface. In addition to proteins soluble in the water environment, there is a significant group of membrane proteins that act as receptors or channels, including ion channels in particular. The change of the polar (water) environment into a highly hydrophobic (membrane) environment is quite radical, resulting in a different hydrophobicity distribution within the membrane protein. Modification of the notation of the force field expressing the presence of the hydrophobic environment has been proposed in this work. A modified fuzzy oil drop model with its adaptation to membrane proteins was used to interpret the structure of membrane proteins–mechanosensitive channel. The modified model was also used to describe the so-called negative cases—i.e., for water-soluble proteins with a clear distribution consistent with the fuzzy oil drop model.

Structure and Location of Protein Sites Binding Self-Associated Congo Red Molecules with Intercalated Drugs as Compact Ligands-Theoretical Studies

In the search for new carriers capable of transporting toxic drugs to a target, particular attention has been devoted to supramolecular systems with a ribbon-like micellar structure of which Congo red is an example. A special promise of the possible use of such systems for directing drugs to a target emerges from their particular affinity to immune complexes and as an independent property, binding many organic compounds including drugs by intercalation. Serum albumin also appeared able to bind micellar particles of such systems. It may protect them against dilution in transport. The mathematical tool, which relies on analysis of the distribution of polarity and hydrophobicity in protein molecules (fuzzy oil drop model), has been used to find the location of binding area in albumin as well as anchorage site for Congo red in heated IgG light chain used as a model presenting immunoglobulin-like structures. Results confirm the suggested formerly binding site of Congo red in V domain of IgG light chain and indicated the cleft between pseudo-symmetric domains of albumin as the area of attachment for the dye.

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.

The Structure of Amyloid Versus the Structure of Globular Proteins

The issue of changing the structure of globular proteins into an amyloid form is in the focus of researchers' attention. Numerous experimental studies are carried out, and mathematical models to define the essence of amyloid transformation are sought. The present work focuses on the issue of the hydrophobic core structure in amyloids. The form of ordering the hydrophobic core in globular proteins is described by a 3D Gaussian distribution analog to the distribution of hydrophobicity in a spherical micelle. Amyloid fibril is a ribbon-like micelle made up of numerous individual chains, each representing a flat structure. The distribution of hydrophobicity within a single chain included in the fibril describes the 2D Gaussian distribution. Such a description expresses the location of polar residues on a circle with a center with a high level of hydrophobicity. The presence of this type of order in the amyloid forms available in Preotin Data Bank (PDB) (both in proto- and superfibrils) is demonstrated in the present work. In this system, it can be assumed that the amyloid transformation is a chain transition from 3D Gauss ordering to 2D Gauss ordering. This means changing the globular structure to a ribbon-like structure. This observation can provide a simple mathematical model for simulating the amyloid transformation of proteins.

The Status of Edge Strands in Ferredoxin-Like Fold

There is an opinion in professional literature that edge-strands in β-sheet are critical to the processes of amyloid transformation. Propagation of fibrillar forms mainly takes place on the basis of β-sheet type interactions. In many proteins, the edge strands represent only a partially matched form to the β-sheet. Therefore, the edge-strand takes slightly distorted forms. The assessment of the level of arrangement can be carried out based on studying the secondary structure as well as the structure of the hydrophobic core. For this purpose, a fuzzy oil drop model was used to determine the contribution of each fragment with a specific secondary structure to the construction of the system being the effect of a certain synergy, which results in the construction of a hydrophobic core. Studying the participation of β-sheets edge fragments in the hydrophobic core construction is the subject of the current analysis. Statuses of these edge fragments in β-sheets in ferredoxin-like folds are treated as factors that disturb the symmetry of the system.

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.

Alternative Hydrophobic Core in Proteins—The Effect of Specific Synergy

Proteins with a high degree of sequence similarity representing different structures provide a key to understand how protein sequence codes for 3D structure. An analysis using the fuzzy oil drop model was carried out on two pairs of proteins with different secondary structures and with high sequence identities. It has been shown that distributions of hydrophobicity for these proteins are approximated well using single 3D Gaussian function. In other words, the similar sequences fold into different 3D structures, however, alternative structures also have symmetric and monocentric hydrophobic cores. It should be noted that a significant change in the helical to beta-structured form in the N-terminal section takes places in the fragment much preceding the location of the mutated regions. It can be concluded that the final structure is the result of a complicated synergy effect in which the whole chain participates simultaneously.

Alternative Structures of α-Synuclein

The object of our analysis is the structure of alpha-synuclein (ASyn), which, under in vivo conditions, associates with presynaptic vesicles. Misfolding of ASyn is known to be implicated in Parkinson's disease. The availability of structural information for both the micelle-bound and amyloid form of ASyn enables us to speculate on the specific mechanism of amyloid transformation. This analysis is all the more interesting given the fact that-Unlike in Aβ(1-42) amyloids-only the central fragment (30-100) of ASyn has a fibrillar structure, whereas, its N- and C-terminal fragments (1-30 and 100-140, respectively) are described as random coils. Our work addresses the following question: Can the ASyn chain-as well as the aforementioned individual fragments-adopt globular conformations? In order to provide an answer, we subjected the corresponding sequences to simulations carried out using Robetta and I-Tasser, both of which are regarded as accurate protein structure predictors. In addition, we also applied the fuzzy oil drop (FOD) model, which, in addition to optimizing the protein's internal free energy, acknowledges the presence of an external force field contributed by the aqueous solvent. This field directs hydrophobic residues to congregate near the center of the protein body while exposing hydrophilic residues on its surface. Comparative analysis of the obtained models suggests that fragments which do not participate in forming the amyloid fibril (i.e., 1-30 and 100-140) can indeed attain globular conformations. We also explain the influence of mutations observed in vivo upon the susceptibility of ASyn to undergo amyloid transformation. In particular, the 30-100 fragment (which adopts a fibrillar structure in PDB) is not predicted to produce a centralized hydrophobic core by any of the applied toolkits (Robetta, I-Tasser, and FOD). This means that in order to minimize the entropically disadvantageous contact between hydrophobic residues and the polar solvent, ASyn adopts the form of a ribbonlike micelle (rather than a spherical one). In other words, the ribbonlike micelle represents a synergy between the conformational preferences of the protein chain and the influence of its environment.

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).

Aggregation-promoting conditions necessary to create the complexes by acylphosphatase from the hyperthermophile Sulfolobus solfataricus

The structural transition from the globular to the amyloid form of proteins requires aggregation-promoting conditions. The protein example of this category is acylphosphatase from the hyperthermophile Sulfolobus solfataricus. This protein represents a structure with a well-defined hydrophobic core. This is why the complexation (including oligomerization) of this protein is of low probability. The chain fragment participating in aggregation in comparison to the status with respect to the fuzzy oil drop model is discussed in this paper.

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).

Fragment Aβ(18-41) presented within the CDR3 loop region of a shark immunoglobulin new antigen receptor single-variable domain antibody analyzed based on the fuzzy oil drop model

The structure of amyloid Aβ(1-41) is the object of many papers due to the neurodegenerative processes induced by this amyloid. One of the ways to investigate the possible structural forms other than the amyloid is to incorporate the fragment of this peptide into the chain of immunoglobulin. Fragment Aβ(18-41) presented within the CDR3 loop region of a shark immunoglobulin new antigen receptor single-variable domain antibody is the object of this analysis. The structure of this hybrid is available in the PDB and analyzed based on the fuzzy oil drop model. The aim is to define the status of this fragment, revealing the possible fitting to the ordered form of the hydrophobic core. Simultaneously, the verification of the predisposition to complexation is possible.

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.

Mechanism of ligand binding – PDZ domain taken as example

The mechanism of specific ligand binding by proteins is discussed using the PDZ domain complexing the pentapeptide. This process is critical for clustering the membrane ion channel. The traditional model based on the Beta-sheet extension by complexed pentapeptide is interpreted as a hydrophobic core extension supported by additional Beta-strand generated by complexed pentapeptide. The explanation is based on the fuzzy oil drop model applied to the crystal structure of PDZ-pentapeptide.

Chain-chain complexation and heme binding in haemoglobin with respect to the hydrophobic core structure

Heme binding by proteins and protein-protein complexation are the processes strongly related to the biological activity of proteins. The mechanism of these processes has not been still recognised. These phenomena are presented using haemoglobin as the example. Half of the mature haemoglobin (one α-chain and one β-chain) treated as a dissociation step in haemoglobin degradation reveals a specific change in heme binding after dissociation. This phenomenon is the object of analysis that interprets the structure of both complexes (tetramer and dimer) with respect to their hydrophobic core structure. The results suggest the higher stability of the complex in the form of one α-chain and one β-chain with respect to the hydrophobic core.

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.

Why do antifreeze proteins require a solenoid?

Proteins whose presence prevents water from freezing in living organisms at temperatures below 0 °C are referred to as antifreeze proteins. This group includes molecules of varying size (from 30 to over 300 aa) and variable secondary/supersecondary conformation. Some of these proteins also contain peculiar structural motifs called solenoids. We have applied the fuzzy oil drop model in the analysis of four categories of antifreeze proteins: 1 - very small proteins, i.e. helical peptides (below 40 aa); 2 - small globular proteins (40-100 aa); 3 - large globular proteins (>100 aa) and 4 - proteins containing solenoids. The FOD model suggests a mechanism by which antifreeze proteins prevent freezing. In accordance with this theory, the presence of the protein itself produces an ordering of water molecules which counteracts the formation of ice crystals. This conclusion is supported by analysis of the ordering of hydrophobic and hydrophilic residues in antifreeze proteins, revealing significant variability - from perfect adherence to the fuzzy oil drop model through structures which lack a clearly defined hydrophobic core, all the way to linear arrangement of alternating local minima and maxima propagating along the principal axis of the solenoid (much like in amyloids). The presented model - alternative with respect to the ice docking model - explains the antifreeze properties of compounds such as saccharides and fatty acids. The fuzzy oil drop model also enables differentiation between amyloids and antifreeze proteins.

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.

Structure of hydrophobic core in plant carboxylesterase

The fuzzy oil drop model was applied to characterize the hydrophobic core structure in plant carboxylesterase. The characteristics revealed the status of β-sheets in the central part of the molecule as discordant as opposed to the expected hydrophobicity distribution. Particularly, the β-strands and helices in close proximity to the enzymatic residues recognized as discordant with respect to the ideal hydrophobicity distribution of hydrophobic core are of high importance. It is assumed that this local irregularity is the form of coding the specificity of enzymes. The protein under consideration appears to be the next example proving this assumption.

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.