Fuzzy Oil Drop Model Research Articles

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.

Mechanism of ligand binding – PDZ domain taken as example

Abstract 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.

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.

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

Abstract 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.

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.

The variability of protein structure with respect to the hydrophobic core

Abstract 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.

Structure of hydrophobic core in plant carboxylesterase

Abstract 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.

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.

Influence of the Aqueous Environment on Protein Structure—A Plausible Hypothesis Concerning the Mechanism of Amyloidogenesis

The aqueous environment is a pervasive factor which, in many ways, determines the protein folding process and consequently the activity of proteins. Proteins are unable to perform their function unless immersed in water (membrane proteins excluded from this statement). Tertiary conformational stabilization is dependent on the presence of internal force fields (nonbonding interactions between atoms), as well as an external force field generated by water. The hitherto the unknown structuralization of water as the aqueous environment may be elucidated by analyzing its effects on protein structure and function. Our study is based on the fuzzy oil drop model—a mechanism which describes the formation of a hydrophobic core and attempts to explain the emergence of amyloid-like fibrils. A set of proteins which vary with respect to their fuzzy oil drop status (including titin, transthyretin and a prion protein) have been selected for in-depth analysis to suggest the plausible mechanism of amyloidogenesis.

Dissimilar sequence: similar structure of proteins

Abstract 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.

Role of Disulfide Bonds in Stabilizing the Conformation of Selected Enzymes—An Approach Based on Divergence Entropy Applied to the Structure of Hydrophobic Core in Proteins

One of the factors responsible for tertiary structural stabilization in proteins is the presence of the hydrophobic core—a result of hydrophobic interactions within the protein body. In some proteins (especially extracellular ones) additional stabilization is provided by covalent bonds between selected Cys residues, commonly referred to as disulfide bonds. The mutual interplay of both factors and their respective contributions to stabilization are the focus of this work. The assessment of the effects of disulfide bonds isinterpreted by Fuzzy Oil Drop (FOD) model in which individual polypeptide chain fragments (including fragments which participate in SS bonds) can be evaluated in the context of their influence upon tertiary structural stabilization by comparing their corresponding theoretical and idealized hydrophobicity density distributions. The proteins were identified with both factors reinforcing each other, as well as proteins where they seem to counteract each other. The analysis presents a number of enzymes, including ribonuclease, lysozyme, disulfide isomerase and phospholipase.

Sequence-to-Structure Relation in Proteins-Amyloidogenic Proteins with Chameleon Sequences

The existence of polypeptide chain fragments in which identical sequences translate into different secondary folds gives rise to questions concerning the structural variability associated with amyloidogenesis. In this paper the structural contribution of identical sequences to a common hydrophobic core is assessed on the basis of the fuzzy oil drop model. The model compares the observed hydrophobicity density distribution in a protein molecule to its idealized counterpart, where all hydrophilic residues are exposed on the surface while all hydrophobic residues are internalized. The conformational variability of such fragments is thought to be associated with their role: they either participate in the formation of a stable core, or become involved in mediating the protein’s biological function. The fuzzy oil drop model provides clues as to the role of chameleon sequences in prions, seen as potential loci of conformational changes resulting in amyloidogenesis.

Structural Role of Hydrophobic Core in Proteins-Selected Examples

This paper discusses the sequence/structure relation. The core question concerns the degree to which similar sequences produce similar structures and vice versa. A mechanism by which similar sequences may result in dissimilar structures is proposed, based on the Fuzzy Oil Drop (FOD) model in which structural similarity is estimated by analyzing the protein’s hydrophobic core. We show that local changes in amino acid sequences, in addition to producing local structural alterations at the substitution site, may also change the shape of the hydrophobic core, significantly affecting the overall tertiary conformation of the protein. Our analysis focuses on four sets of proteins: 1) Pair of designer proteins with specially prepared sequences; 2) Pair of natural proteins modified (mutated) to converge to a point of high-level sequence identity while retaining their respective wild-type tertiary folds; 3) Pair of natural proteins with common ancestry but with differing structures and biological profiles shaped by divergent evolution; and 4) Pair of natural proteins of high structural similarity with no sequence similarity and different biological function.

Contingency Table Browser - prediction of early stage protein structure.

The Early Stage (ES) intermediate represents the starting structure in protein folding simulations based on the Fuzzy Oil Drop (FOD) model. The accuracy of FOD predictions is greatly dependent on the accuracy of the chosen intermediate. A suitable intermediate can be constructed using the sequence-structure relationship information contained in the so-called contingency table − this table expresses the likelihood of encountering various structural motifs for each tetrapeptide fragment in the amino acid sequence. The limited accuracy with which such structures could previously be predicted provided the motivation for a more indepth study of the contingency table itself. The Contingency Table Browser is a tool which can visualize, search and analyze the table. Our work presents possible applications of Contingency Table Browser, among them − analysis of specific protein sequences from the point of view of their structural ambiguity.

Hydrophobic core structure of macromomycin – the apoprotein of the antitumor antibiotic auromomycin – fuzzy oil drop model applied

Abstract The fuzzy oil drop model was applied to analyze the structure of macromomycin, the apoprotein of the antitumor antibiotic auromomycin, revealing the differentiation of β-structural fragments present in β-sandwich. The seven-stranded antiparallel β-barrel and two antiparallel β-sheet ribbons represent the highly ordered geometry of the structure. However, participation in hydrophobic core formation appears different. The structure of the complete domain represents the status of the irregular hydrophobic core; however, some β-structural fragments appear to represent the hydrophobicity density distribution accordant with the idealized distribution of hydrophobicity as expected using the fuzzy oil drop model. Four β-structural fragments generating one common layer appear to be unstable in respect to the general structure of the hydrophobic core. This area is expected to be more flexible than other parts of the molecule. The protein binds the ligand – chromophore, two 2-methyl-2,4-pentanediol – in a well-defined cleft. The presence of this cleft makes the general structure of the hydrophobic core irregular (as it may be interpreted using the fuzzy oil drop model). Two short loops generated by two SS bonds fit very well to the general distribution of hydrophobicity density as expected for the model. No information about the potential amyloidogenic character of this protein is given in the literature; however, the specificity of the hydrophobicity distribution profile is found to be highly similar to the one observed in transthyretin (Banach M, Konieczny L, Roterman I. The fuzzy oil drop model, based on hydrophobicity density distribution, generalizes the influence of water environment on protein structure and function. J Theor Biol 2014;359:6–17), suggesting a possible tendency to turn to the amyloid form. A detailed analysis of macromomycin will be given, and a comparable analysis with other proteins of β-sandwich or β-barrel will be presented.

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

The fuzzy oil drop model, a tool which can be used to study the structure of the hydrophobic core in proteins, has been applied in the analysis of proteins belonging to the jumonji group—JARID2, JARID1A, JARID1B and JARID1D—proteins that share the property of being able to interact with DNA. Their ARID and PHD domains, when analyzed in the context of the fuzzy oil drop model, are found to exhibit structural variability regarding the status of their secondary folds, including the β-hairpin which determines their biological function. Additionally, the structure of disordered fragments which are present in jumonji proteins (as confirmed by the DisProt database) is explained on the grounds of the hydrophobic core model, suggesting that such fragments contribute to tertiary structural stabilization. This conclusion is supported by divergence entropy measurements, expressing the degree of ordering in each protein’s hydrophobic core.

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

In this paper we show that the fuzzy oil drop model represents a general framework for describing the generation of hydrophobic cores in proteins and thus provides insight into the influence of the water environment upon protein structure and stability. The model has been successfully applied in the study of a wide range of proteins, however this paper focuses specifically on domains representing immunoglobulin-like folds. Here we provide evidence that immunoglobulin-like domains, despite being structurally similar, differ with respect to their participation in the generation of hydrophobic core. It is shown that β-structural fragments in β-barrels participate in hydrophobic core formation in a highly differentiated manner. Quantitatively measured participation in core formation helps explain the variable stability of proteins and is shown to be related to their biological properties. This also includes the known tendency of immunoglobulin domains to form amyloids, as shown using transthyretin to reveal the clear relation between amyloidogenic properties and structural characteristics based on the fuzzy oil drop model.

Stability of Two Natural Homologous Proteins with Different Folds

Abstract The applicability of the model for protein folding process simulation is presented using as the test two homologous proteins of different fold: helical in 3BD1 and beta-structural form in 2PIJ [L. van Dorn, T. Newlove, S. Chang, W. Ingram, M. Cordes. Biochemistry 45, 10542 (2006)]. The folding process is assumed to be directed by hydrophobic core directing the hydrophobic residues toward the center of the molecule and exposing the hydrophilic residues on the surface. The fuzzy oil drop model is expressed by the 3-dimensional Gauss function which mimics the external force field. The value of Gauss function is interpreted as the hydrophobicity density calculated in any point of the space of the protein body. The accordance of idealized and observed hydrophobicity distributions (calculated according to Levitt function) measured using the Kullback-Leibler divergence entropy reveals good accordance in two homological proteins of different folds. The structural differences appeared to be easily explainable on the basis of fuzzy oil drop model.

Fuzzy oil drop model to interpret the structure of antifreeze proteins and their mutants

Mutations in proteins introduce structural changes and influence biological activity: the specific effects depend on the location of the mutation. The simple method proposed in the present paper is based on a two-step model of in silico protein folding. The structure of the first intermediate is assumed to be determined solely by backbone conformation. The structure of the second one is assumed to be determined by the presence of a hydrophobic center. The comparable structural analysis of the set of mutants is performed to identify the mutant-induced structural changes. The changes of the hydrophobic core organization measured by the divergence entropy allows quantitative comparison estimating the relative structural changes upon mutation. The set of antifreeze proteins, which appeared to represent the hydrophobic core structure accordant with “fuzzy oil drop” model was selected for analysis.