Fuzzy Oil Drop Model Research Articles

Protein folding: Funnel model revised

The spatial structure of proteins, largely determined by their amino acid sequences, is also dependent on the environmental conditions under which the folding process takes place. In aqueous environments, exposure of polar amino acids is the driving factor, whereas protein stabilization in amphipathic membranes requires exposure to hydrophobic residues. This observation can be extended to all other environmental conditions under which proteins exhibit biological activity and, most importantly, to the folding process. The fuzzy oil drop (FOD) model assumes a centric location of hydrophobic residues (hydrophobic core) with exposure of polar residues towards the aqueous environment, as the influence of the aqueous environment is extended to include the contribution of other non-aqueous factors, enabling the assessment of their influence on protein structuring. The application of the modified FOD model (FOD-M) we have developed allows the environment to be represented as an external force field in the form of a continuum. The role of environmental conditions allows modification of the funnel model expressing the localization of the energy minimum as dependent on external conditions expressed by the K scale, where K measures the degree of other than polar water factors participating in folding process.

Chameleon Sequences-Structural Effects in Proteins Characterized by Hydrophobicity Disorder.

Repeated protein folding processes both in vivo and in vitro leading to the same structure for a specific amino acid sequence prove that the amino acid sequence determines protein structuring. This is also evidenced by the variability of structuring, dependent on the introduced mutations. An important phenomenon in this regard is the presence of a differentiated secondary structure for chain fragments of identical sequence representing distinct forms of the secondary-order structure. Proteins termed chameleon proteins contain polypeptide chain fragments of identical sequence (length 6-12 aa) showing structural differentiation: helix versus β-structure. In the present paper, it was shown that these fragments represent components matching the structural status dictated by the physicochemical properties of the entire structural unit. This structural matching is related to achieving the goal of the biological function of the structural unit. The corresponding secondary structure represents a means to achieving this goal, not an end in itself. A selected set of proteins from the ChSeq database have been analyzed using a fuzzy oil drop model (FOD-M) identifying the uniqueness of the hydrophobicity distribution taken as a medium for recording the specificity of a given protein and a given chameleon section in particular. It was shown that in the vast majority, the status of chameleon sections turns out to be comparable regardless of the represented secondary structure.

The outer-membrane componentof the multi-drug efflux system –a structural analysis based onhydrophobicity distribution

The structure of a multi-drug efflux system (specifically the outer membrane part) is the focus of our analysis. The role of electrostatic interactions in the efflux process is well understood. The distribution of hydrophobicity in the periplasmic and membrane domains plays a significant role in both stabilisation within the membrane and in tunnel formation, which facilitates the transport of antibiotics. The analysis presented in this paper reveals the specificity of hydrophobicity distribution in relation to biological activity, as well as a possible mechanism for the folding process of proteins involved in multi-drug efflux. Our analysis is made possible by the application of the fuzzy oil drop model in its modified form (FOD-M).

External Force Field for Protein Folding in Chaperonins-Potential Application in In Silico Protein Folding.

The present study discusses the influence of the TRiC chaperonin involved in the folding of the component of reovirus mu1/σ3. The TRiC chaperone is treated as a provider of a specific external force field in the fuzzy oil drop model during the structural formation of a target folded protein. The model also determines the status of the final product, which represents the structure directed by an external force field in the form of a chaperonin. This can be used for in silico folding as the process is environment-dependent. The application of the model enables the quantitative assessment of the folding dependence of an external force field, which appears to have universal application.

Transmembrane proteins-Different anchoring systems.

Transmembrane proteins are active in amphipathic environments. To stabilize the protein in such surrounding the exposure of hydrophobic residues on the protein surface is required. Transmembrane proteins are responsible for the transport of various molecules. Therefore, they often represent structures in the form of channels. This analysis focused on the stability and local flexibility of transmembrane proteins, particularly those related to their biological activity. Different forms of anchorage were identified using the fuzzy oil-drop model (FOD) and its modified form, FOD-M. The mainly helical as well as β-barrel structural forms are compared with respect to the mechanism of stabilization in the cell membrane. The different anchoring system was found to stabilize protein molecules with possible local fluctuation.

Role of environmental specificity in CASP results

BackgroundRecently, significant progress has been made in the field of protein structure prediction by the application of artificial intelligence techniques, as shown by the results of the CASP13 and CASP14 (Critical Assessment of Structure Prediction) competition. However, the question of the mechanism behind the protein folding process itself remains unanswered. Correctly predicting the structure also does not solve the problem of, for example, amyloid proteins, where a polypeptide chain with an unaltered sequence adopts a different 3D structure.ResultsThis work was an attempt at explaining the structural variation by considering the contribution of the environment to protein structuring. The application of the fuzzy oil drop (FOD) model to assess the validity of the selected models provided in the CASP13, CASP14 and CASP15 projects reveals the need for an environmental factor to determine the 3D structure of proteins. Consideration of the external force field in the form of polar water (Fuzzy Oil Drop) and a version modified by the presence of the hydrophobic compounds, FOD-M (FOD-Modified) reveals that the protein folding process is environmentally dependent. An analysis of selected models from the CASP competitions indicates the need for structure prediction as dependent on the consideration of the protein folding environment.ConclusionsThe conditions governed by the environment direct the protein folding process occurring in a certain environment. Therefore, the variation of the external force field should be taken into account in the models used in protein structure prediction.

Ab initio protein structure prediction: the necessary presence of external force field as it is delivered by Hsp40 chaperone

BackgroundThe aqueous environment directs the protein folding process towards the generation of micelle-type structures, which results in the exposure of hydrophilic residues on the surface (polarity) and the concentration of hydrophobic residues in the center (hydrophobic core). Obtaining a structure without a hydrophobic core requires a different type of external force field than those generated by a water. The examples are membrane proteins, where the distribution of hydrophobicity is opposite to that of water-soluble proteins. Apart from these two extreme examples, the process of protein folding can be directed by chaperones, resulting in a structure devoid of a hydrophobic core.ResultsThe current work presents such example: DnaJ Hsp40 in complex with alkaline phosphatase PhoA-U (PDB ID—6PSI)—the client molecule. The availability of WT form of the folding protein—alkaline phosphatase (PDB ID—1EW8) enables a comparative analysis of the structures: at the stage of interaction with the chaperone and the final, folded structure of this biologically active protein. The fuzzy oil drop model in its modified FOD-M version was used in this analysis, taking into account the influence of an external force field, in this case coming from a chaperone.ConclusionsThe FOD-M model identifies the external force field introduced by chaperon influencing the folding proces. The identified specific external force field can be applied in Ab Initio protein structure prediction as the environmental conditioning the folding proces.

Engagement of intrinsic disordered proteins in protein-protein interaction.

Proteins from the intrinsically disordered group (IDP) focus the attention of many researchers engaged in protein structure analysis. The main criteria used in their identification are lack of secondary structure and significant structural variability. This variability takes forms that cannot be identified in the X-ray technique. In the present study, different criteria were used to assess the status of IDP proteins and their fragments recognized as intrinsically disordered regions (IDRs). The status of the hydrophobic core in proteins identified as IDPs and in their complexes was assessed. The status of IDRs as components of the ordering structure resulting from the construction of the hydrophobic core was also assessed. The hydrophobic core is understood as a structure encompassing the entire molecule in the form of a centrally located high concentration of hydrophobicity and a shell with a gradually decreasing level of hydrophobicity until it reaches a level close to zero on the protein surface. It is a model assuming that the protein folding process follows a micellization pattern aiming at exposing polar residues on the surface, with the simultaneous isolation of hydrophobic amino acids from the polar aquatic environment. The use of the model of hydrophobicity distribution in proteins in the form of the 3D Gaussian distribution described on the protein particle introduces the possibility of assessing the degree of similarity to the assumed micelle-like distribution and also enables the identification of deviations and mismatch between the actual distribution and the idealized distribution. The FOD (fuzzy oil drop) model and its modified FOD-M version allow for the quantitative assessment of these differences and the assessment of the relationship of these areas to the protein function. In the present work, the sections of IDRs in protein complexes classified as IDPs are analyzed. The classification "disordered" in the structural sense (lack of secondary structure or high flexibility) does not always entail a mismatch with the structure of the hydrophobic core. Particularly, the interface area, often consisting of IDRs, in many analyzed complexes shows the compliance of the hydrophobicity distribution with the idealized distribution, which proves that matching to the structure of the hydrophobic core does not require secondary structure ordering.

New insights on the catalytic center of proteins from peptidylprolyl isomerase group based on the FOD-M model.

Generating the structure of the hydrophobic core is based on the orientation of hydrophobic residues towards the central part of the protein molecule with the simultaneous exposure of polar residues. Such a course of the protein folding process takes place with the active participation of the polar water environment. While the self-assembly process leading to the formation of micelles concerns freely moving bi-polar molecules, bipolar amino acids in polypeptide chain have limited mobility due to the covalent bonds. Therefore, proteins form a more or less perfect micelle-like structure. The criterion is the hydrophobicity distribution, which to a greater or lesser extent reproduces the distribution expressed by the 3D Gaussian function on the protein body. The vast majority of proteins must ensure solubility, so a certain part of it-as it is expected-should reproduce the structuring of micelles. The biological activity of proteins is encoded in the part that does not reproduce the micelle-like system. The location and quantitative assessment of the contribution of orderliness to disorder is of critical importance for the determination of biological activity. The form of maladjustment to the 3D Gauss function may be varied-hence the obtained high diversity of specific interactions with strictly defined molecules: ligands or substrates. The correctness of this interpretation was verified on the basis of the group of enzymes Peptidylprolyl isomerase-E.C.5.2.1.8. In proteins representing this class of enzymes, zones responsible for solubility-micelle-like hydrophobicity system-the location and specificity of the incompatible part in which the specific activity of the enzyme is located and coded were identified. The present study showed that the enzymes of the discussed group show two different schemes of the structure of catalytic center (taking into account the status as defined by the fuzzy oil drop model).

Structural Specificity of Polymorphic Forms of α-Synuclein Amyloid.

The structural transformation producing amyloids is a phenomenon that sheds new light on the protein folding problem. The analysis of the polymorphic structures of the α-synuclein amyloid available in the PDB database allows analysis of the amyloid-oriented structural transformation itself, but also the protein folding process as such. The polymorphic amyloid structures of α-synuclein analyzed employing the hydrophobicity distribution (fuzzy oil drop model) reveal a differentiation with a dominant distribution consistent with the micelle-like system (hydrophobic core with polar shell). This type of ordering of the hydrophobicity distribution covers the entire spectrum from the example with all three structural units (single chain, proto-fibril, super-fibril) exhibiting micelle-like form, through gradually emerging examples of local disorder, to structures with an extremely different structuring pattern. The water environment directing protein structures towards the generation of ribbon micelle-like structures (concentration of hydrophobic residues in the center of the molecule forming a hydrophobic core with the exposure of polar residues on the surface) also plays a role in the amyloid forms of α-synuclein. The polymorphic forms of α-synuclein reveal local structural differentiation with a common tendency to accept the micelle-like structuralization in certain common fragments of the polypeptide chain of this protein.

Symmetrization in the Calculation Pipeline of Gauss Function-Based Modeling of Hydrophobicity in Protein Structures

In this paper, we show, discuss, and compare the effects of symmetrization in two calculation subroutines of the Fuzzy Oil Drop model, a coarse-grained model of density of hydrophobicity in proteins. In the FOD model, an input structure is enclosed in an axis-aligned ellipsoid called a drop. Two profiles of hydrophobicity are then calculated for its residues: theoretical (based on the 3D Gauss function) and observed (based on pairwise hydrophobic interactions). Condition of the hydrophobic core is revealed by comparing those profiles through relative entropy, while analysis of their local differences allows, in particular, determination of the starting location for the search for protein–protein and protein–ligand interaction areas. Here, we improve the baseline workflow of the FOD model by introducing symmetry to the hydrophobicity profile comparison and ellipsoid bounding procedures. In the first modification (FOD–JS), Kullback–Leibler divergence is enhanced with its Jensen–Shannon variant. In the second modification (FOD-PCA), the molecule is optimally aligned with the axes of the coordinate system via principal component analysis, and the size of its drop is determined by the standard deviation of all its effective atoms, making it less susceptible to structural outliers. Tests on several molecules with various shapes and functions confirm that the proposed modifications improve the accuracy, robustness, speed, and usability of Gauss function-based modeling of the density of hydrophobicity in protein structures.

In Silico Modeling of COVID-19 Pandemic Course Differentiation Using the FOD Model

Background: The strange and still unclear scenarios of Covid-19 pandemic development have raised the question about the reason for the observed essential state and personal differences concerning the expansion and severity of the infection process. Some custom activities are taken into consideration in an attempt to explain the phenomenon. Alcohol in the diet is suggested in this paper as the possible factor which could explain the observed differentiation. It easily penetrates cells modifying their natural internal environment, and independently influences tissues as the toxic agent being the source of acetyl aldehyde. Objective: The process in which the cell seems to be the most sensitive to altered environmental conditions is the protein folding; in particular, its portion occurring in the endoplasmic reticulum where freshly synthesized polypeptides fold and then are introduced to the cell membrane influencing its property and in particular its fluidity, which is the critical parameter deciding the virus penetration into the cell. Methods: The application of a mathematical model, fuzzy oil drop model FOD, expressing the influence of the environment on the protein folding process shows the mechanism of this influence. Results: The differences between statistical assessment of epidemy in Europe and the Far East, which may be correlated with alcohol consumption, suggest the influence of diet on the status of epidemy in these regions. Conclusion: The protein folding seems to be the process most sensitive to environmental conditions in the cell. The different diet customs, including the use of alcohol, may disturb the folding process, lowering as the result the number of proteins needed for cell membrane stability, thus increasing its fluidity and the cell susceptibility to virus penetration. Observations presented in this paper are based on the initial period of pandemic development and have not been intentionally modified to prevent the influence of additional factors, like government activities or virus mutations.

Connexins and Pannexins-Similarities and Differences According to the FOD-M Model.

Connexins and pannexins are the transmembrane proteins of highly distinguished biological activity in the form of transport of molecules and electrical signals. Their common role is to connect the external environment with the cytoplasm of the cell, while connexin is also able to link two cells together allowing the transport from one to another. The analysis presented here aims to identify the similarities and differences between connexin and pannexin. As a comparative criterion, the hydrophobicity distribution in the structure of the discussed proteins was used. The comparative analysis is carried out with the use of a mathematical model, the FOD-M model (fuzzy oil drop model in its Modified version) expressing the specificity of the membrane’s external field, which in the case of the discussed proteins is significantly different from the external field for globular proteins in the polar environment of water. The characteristics of the external force field influence the structure of protein allowing the activity in a different environment.

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.

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.

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.

Contribution to the Understanding of Protein–Protein Interface and Ligand Binding Site Based on Hydrophobicity Distribution—Application to Ferredoxin I and II Cases

Ferredoxin I and II are proteins carrying a specific ligand—an iron-sulfur cluster—which allows transport of electrons. These two classes of ferredoxin in their monomeric and dimeric forms are the object of this work. Characteristic of hydrophobic core in both molecules is analyzed via fuzzy oil drop model (FOD) to show the specificity of their structure enabling the binding of a relatively large ligand and formation of the complex. Structures of FdI and FdII are a promising example for the discussion of influence of hydrophobicity on biological activity but also for an explanation how FOD model can be used as an initial stage adviser (or a scoring function) in the search for locations of ligand binding pockets and protein–protein interaction areas. It is shown that observation of peculiarities in the hydrophobicity distribution present in the molecule (in this case—of a ferredoxin) may provide a promising starting location for computer simulations aimed at the prediction of quaternary structure of proteins.

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.

Solubility and Aggregation of Selected Proteins Interpreted on the Basis of Hydrophobicity Distribution.

Protein solubility is based on the compatibility of the specific protein surface with the polar aquatic environment. The exposure of polar residues to the protein surface promotes the protein’s solubility in the polar environment. The aquatic environment also influences the folding process by favoring the centralization of hydrophobic residues with the simultaneous exposure to polar residues. The degree of compatibility of the residue distribution, with the model of the concentration of hydrophobic residues in the center of the molecule, with the simultaneous exposure of polar residues is determined by the sequence of amino acids in the chain. The fuzzy oil drop model enables the quantification of the degree of compatibility of the hydrophobicity distribution observed in the protein to a form fully consistent with the Gaussian 3D function, which expresses an idealized distribution that meets the preferences of the polar water environment. The varied degrees of compatibility of the distribution observed with the idealized one allow the prediction of preferences to interactions with molecules of different polarity, including water molecules in particular. This paper analyzes a set of proteins with different levels of hydrophobicity distribution in the context of the solubility of a given protein and the possibility of complex formation.