Fuzzy-oil-drop hydrophobic force field--a model to represent late-stage folding (in silico) of lysozyme

A model of hydrophobic collapse (in silico), which is generally considered to be the driving force for protein folding, is presented in this work. The model introduces the external field in the form of a fuzzy-oil-drop assumed to represent the environment. The drop is expressed in the form of a three-dimensional Gauss function. The usual probability value is assumed to represent the hydrophobicity distribution in the three-dimensional space of the virtual environment. The differences between this idealized hydrophobicity distribution and the one represented by the folded polypeptide chain is the parameter to be minimized in the structure optimization procedure. The size of fuzzy-oil-drop is critical for the folding process. A strong correlation between protein length and the dimension of the native and early-stage molecular form was found on the basis of single-domain proteins analysis. A previously presented early-stage folding (in silico) model was used to create the starting structure for the procedure of late-stage folding of lysozyme. The results of simulation were found to be promising, although additional improvements for the formation of beta-structure and disulfide bonds as well as the participation of natural ligand in folding process seem to be necessary.     

Fuzzy-Oil-Drop Hydrophobic Force Field—A Model to Represent Late-stage Folding (In Silico) of Lysozyme

Abstract

A model of hydrophobic collapse (in silico), which is generally considered to be the driving force for protein folding, is presented in this work. The model introduces the external field in the form of a fuzzy-oil-drop assumed to represent the environment. The drop is expressed in the form of a three-dimensional Gauss function. The usual probability value is assumed to represent the hydrophobicity distribution in the three-dimensional space of the virtual environment. The differences between this idealized hydrophobicity distribution and the one represented by the folded polypeptide chain is the parameter to be minimized in the structure optimization procedure. The size of fuzzy-oil-drop is critical for the folding process. A strong correlation between protein length and the dimension of the native and early-stage molecular form was found on the basis of single-domain proteins analysis. A previously presented early-stage folding (in silico) model was used to create the starting structure for the procedure of late-stage folding of lysozyme. The results of simulation were found to be promising, although additional improvements for the formation of β-structure and disulfide bonds as well as the participation of natural ligand in folding process seem to be necessary.     

Localization of ligand binding site in proteins identified in silico

Knowledge-based models for protein folding assume that the early-stage structural form of a polypeptide is determined by the backbone conformation, followed by hydrophobic collapse. Side chain–side chain interactions, mostly of hydrophobic character, lead to the formation of the hydrophobic core, which seems to stabilize the structure of the protein in its natural environment. The fuzzy-oil-drop model is employed to represent the idealized hydrophobicity distribution in the protein molecule. Comparing it with the one empirically observed in the protein molecule reveals that they are not in agreement. It is shown in this study that the irregularity of hydrophobic distributions is aim-oriented. The character and strength of these irregularities in the organization of the hydrophobic core point to the specificity of a particular protein’s structure/function. When the location of these irregularities is determined versus the idealized fuzzy-oil-drop, function-related areas in the protein molecule can be identified. The presented model can also be used to identify ways in which protein–protein complexes can possibly be created. Active sites can be predicted for any protein structure according to the presented model with the free prediction server at . The implication based on the model presented in this work suggests the necessity of active presence of ligand during the protein folding process simulation. Figure Fuzzy-oil-drop model applied to identify the ligation site in lysozyme complexed with N-acetylglucosamine (PDB ID:1LMQ) in form of hydrophobicity deficiency (ΔH) profile and three-dimensional distribution of on protein surface     

"Fuzzy oil drop" model verified positively

The "fuzzy oil drop" model assuming the structure of the hydrophobic core of the form of 3-D Gauss function appeared to be verified positively. The protein 1NMF belonging to downhill proteins was found to represent the hydrophobic density distribution accordant with the assumed model. The accordance of the protein structure with the assumed model was measured using elements of theory information. This observation opens the possibility to simulate the folding process as influenced by external force field of hydrophobic character.     

Two-intermediate model to characterize the structure of fast-folding proteins

This paper introduces a new model that enables researchers to conduct protein folding simulations. A two-step in silico process is used in the course of structural analysis of a set of fast-folding proteins. The model assumes an early stage (ES) that depends solely on the backbone conformation, as described by its geometrical properties—specifically, by the V-angle between two sequential peptide bond planes (which determines the radius of curvature, also called R-radius, according to a second-degree polynomial form). The agreement between the structure under consideration and the assumed model is measured in terms of the magnitude of dispersion of both parameters with respect to idealized values. The second step, called late-stage folding (LS), is based on the “fuzzy oil drop” model, which involves an external hydrophobic force field described by a three-dimensional Gauss function. The degree of conformance between the structure under consideration and its idealized model is expressed quantitatively by means of the Kullback-Leibler entropy, which is a measure of disparity between the observed and expected hydrophobicity distributions. A set of proteins, representative of the fast-folding group - specifically, cold shock proteins - is shown to agree with the proposed model.     

Computational and comparative investigation of hydrophobic profile of spike protein of SARS-CoV-2 and SARS-CoV

The hydrophobic force is one of the most dominant factors in protein folding. A protein becomes functional only when it achieves its three-dimensional structure and stability upon folding. For a better understanding of the hydrophobic effects and their function in protein folding, quantitative measurement of the hydrophobicity of amino acid side chains is crucial. Spike protein is the primary structural protein in SARS-CoV-2 and SARS-CoV. This study explores how protein sequences in SARS-CoV-2 and SARS-CoV spike proteins encode hydrophobic interactions. Computational tools/techniques have been utilized to investigate the protein sequences of the spike proteins of SARS-CoV-2 and SARS-CoV. Investigations provided an estimate of hydrophobic distribution and its relative strength, indicating a hydrophobic pattern. Analysis of the spike protein''s hydrophobic profile may help identify and treat the virus-caused disease; additionally, it can give an insight into the transmissibility and pathogenicity of the virus.Supplementary InformationThe online version contains supplementary material available at 10.1007/s10867-022-09615-x.     

Recognition of protein complexation based on hydrophobicity distribution

The identification of the surface area able to generate the protein-protein complexation ligand and ion ligation is critical for the recognition of the biological function of particular proteins. The technique based on the analysis of the irregularity of hydrophobicity distribution is used as the criterion for the recognition of the interaction regions. Particularly, the exposure of hydrophobic residues on the surface of protein as well as the localization of the hydrophilic residues in the hydrophobic core is treated as potential area ready to interact with external molecules. The model based on the “fuzzy oil drop” approach treating the protein molecule as the drop of hydrophobicity concentrated in the central part of structure with the hydrophobicity close to zero on the surface according to 3-dimensional Gauss function. The comparison with the observed hydrophobicy in particular protein reveals some irregularities. These irregularities seem to represent the aim-oriented localization.     

“Fuzzy oil drop” model applied to individual small proteins built of 70 amino acids

The proteins composed of short polypeptides (about 70 amino acid residues) representing the following functional groups (according to PDB notation): growth hormones, serine protease inhibitors, antifreeze proteins, chaperones and proteins of unknown function, were selected for structural and functional analysis. Classification based on the distribution of hydrophobicity in terms of deficiency/excess as the measure of structural and functional specificity is presented. The experimentally observed distribution of hydrophobicity in the protein body is compared to the idealized one expressed by a three-dimensional Gauss function. The differences between these two distributions reveal the specificity of structural/functional characteristics of the protein. The residues of hydrophobicity deficiency versus the idealized distribution are assumed to indicate cavities with the potential to bind ligands, while the residues of hydrophobicity excess are interpreted as potentially participating in protein-protein complexation. The distribution of hydrophobicity irregularity seems to be specific for particular structures and functions of proteins. A comparative analysis of such profiles is carried out to identify the potential biological activity of proteins of unknown function.     

Protein sequence and structure relationship ARMA spectral analysis: application to membrane proteins.

If it is assumed that the primary sequence determines the three-dimensional folded structure of a protein, then the regular folding patterns, such as alpha-helix, beta-sheet, and other ordered patterns in the three-dimensional structure must correspond to the periodic distribution of the physical properties of the amino acids along the primary sequence. An AutoRegressive Moving Average (ARMA) model method of spectral analysis is applied to analyze protein sequences represented by the hydrophobicity of their amino acids. The results for several membrane proteins of known structures indicate that the periodic distribution of hydrophobicity of the primary sequence is closely related to the regular folding patterns in a protein's three-dimensional structure. We also applied the method to the transmembrane regions of acetylcholine receptor alpha subunit and Shaker potassium channel for which no atomic resolution structure is available. This work is an extension of our analysis of globular proteins by a similar method.     

Sequence-structure-function relation characterized in silico

Methods for biological function recognition in silico appeared to be useful also for identifying characteristics of structure-to-function relations. The introduction of a three-dimensional Gauss function was assumed to represent the hydrophobic core in a protein molecule. The discrepancy between idealized "fuzzy oil-drop" and the observed one in real proteins appeared to be localized in the ligation site or in the area of biological function related part of protein molecule. The examples of proteins presented in this paper reveal that the structure-function relation can be evaluated and characterized also using the profile of the difference in value between idealized and real hydrophobicity distribution along the polypeptide chain. The specificity of particular polypeptide chain fragments in respect to their biological function and their specific participation in active site creation is discussed in this paper. The scale allowing comparison of different proteins in respect to their ligand-binding sites characteristics is introduced.     

Ligation site in proteins recognized in silico

Recognition of a ligation site in a protein molecule is important for identifying its biological activity. The model for in silico recognition of ligation sites in proteins is presented. The idealized hydrophobic core stabilizing protein structure is represented by a three-dimensional Gaussian function. The experimentally observed distribution of hydrophobicity compared with the theoretical distribution reveals differences. The area of high differences indicates the ligation site. AVAILABILITY: http://bioinformatics.cm-uj.krakow.pl/activesite.     

Structural transitions of confined model proteins: molecular dynamics simulation and experimental validation

Proteins fold in a confined space not only in vivo, i.e., folding assisted by molecular chaperons and chaperonins in a crowded cellular medium, but also in vitro as in production of recombinant proteins. Despite extensive work on protein folding in bulk, little is known about how and to what extent the thermodynamics and kinetics of protein folding are altered by confinement. In this work, we use a Gō-like off-lattice model to investigate the folding and stability of an all beta-sheet protein in spherical cages of different sizes and surface hydrophobicity. We find whereas extreme confinement inhibits correct folding, a hydrophilic cage stabilizes the protein due to restriction of the unfolded configurations. In a hydrophobic cage, however, strong attraction from the cage surface destabilizes the confined protein because of competition between self-aggregation and adsorption of hydrophobic residues. We show that the kinetics of protein collapse and folding is strongly correlated with both the cage size and the surface hydrophobicity. It is demonstrated that a cage of moderate size and hydrophobicity optimizes both the folding yield and kinetics of structural transitions. To support the simulation results, we have also investigated the refolding of hen-egg lysozyme in the presence of cetyltrimethylammoniumbromide (CTAB) surfactants that provide an effective confinement of the proteins by micellization. The influence of the surfactant hydrophobicity on the structural and biological activity of the protein is determined with circular dichroism spectrum, fluorescence emission spectrum, and biological activity assay. It is shown that, as predicted by coarse-grained simulations, CTAB micelles facilitate the collapse of denatured lysozyme, whereas the addition of beta-cyclodextrin-grafted-PNIPAAm, a weakly hydrophobic stripper, dissociates CTAB micelles and promotes the conformational rearrangement and thereby gives an improved recovery of lysozyme activity.     

Side chain burial and hydrophobic core packing in protein folding transition states

A critical step in the folding pathway of globular proteins is the formation of a tightly packed hydrophobic core. Several mutational studies have addressed the question of whether tight packing interactions are present during the rate-limiting step of folding. In some of these investigations, substituted side chains have been assumed to form native-like interactions in the transition state when the folding rates of mutant proteins correlate with their native-state stabilities. Alternatively, it has been argued that side chains participate in nonspecific hydrophobic collapse when the folding rates of mutant proteins correlate with side-chain hydrophobicity. In a reanalysis of published data, we have found that folding rates often correlate similarly well, or poorly, with both native-state stability and side-chain hydrophobicity, and it is therefore not possible to select an appropriate transition state model based on these one-parameter correlations. We show that this ambiguity can be resolved using a two-parameter model in which side chain burial and the formation of all other native-like interactions can occur asynchronously. Notably, the model agrees well with experimental data, even for positions where the one-parameter correlations are poor. We find that many side chains experience a previously unrecognized type of transition state environment in which specific, native-like interactions are formed, but hydrophobic burial dominates. Implications of these results to the design and analysis of protein folding studies are discussed.     

Protein folding stabilizing time measurement: a direct folding process and three-dimensional random walk simulation

Protein particles undergo Brownian motion and collisions in solution. The diffusive collisions may lead to aggregation. For proteins to fold successfully the process has to occur quickly and before significant collision takes place. The speed of protein folding was deduced by studying the correlation time of a lysozyme refolding process from autocorrelation function analysis of the mean collision time and aggregation/soluble ratio of protein. It is a measure of time before which an aggregate can be formed and also is the time measure for a protein to fold into a stable state. We report on the protein folding stabilizing time of a lysozyme system to be 25.5-27.5 micros (<+/-4%) between 295 and 279K via direct folding experimental studies, supported by a three-dimensional random walk simulation of diffusion-limited aggregation model. Aggregation is suppressed when the protein is folded to a stable form. Spontaneous folding and diffusion-limited aggregation are antagonistic in nature. Meanwhile, the resultant aggresome, suggested by Raman and mass spectroscopy, may be formed by cross-linkages of disulfide bonds and hydrophobic interactions.     

Statistical distribution of hydrophobic residues along the length of protein chains. Implications for protein folding and evolution.

We consider in this paper the statistical distribution of hydrophobic residues along the length of protein chains. For this purpose we used a binary hydrophobicity scale which assigns hydrophobic residues a value of one and non-hydrophobes a value of zero. The resulting binary sequences are tested for randomness using the standard run test. For the majority of the 5,247 proteins examined, the distribution of hydrophobic residues along a sequence cannot be distinguished from that expected for a random distribution. This suggests that (a) functional proteins may have originated from random sequences, (b) the folding of proteins into compact structures may be much more permissive with less sequence specificity than previously thought, and (c) the clusters of hydrophobic residues along chains which are revealed by hydrophobicity plots are a natural consequence of a random distribution and can be conveniently described by binomial statistics.     

Analysis on folding of misgurin using two-dimensional HP model

Misgurin is an antimicrobial peptide from the loach, while the hydrophobic-polar (HP) model is a way to study the folding conformations and native states in peptide and protein although several amino acids cannot be classified either hydrophobic or polar. Practically, the HP model requires extremely intensive computations, thus it has yet to be used widely. In this study, we use the two-dimensional HP model to analyze all possible folding conformations and native states of misgurin with conversion of natural amino acids according to the normalized amino acid hydrophobicity index as well as the shortest benchmark HP sequence. The results show that the conversion of misgurin into HP sequence with glycine as hydrophobic amino acid at pH 2 has 1212 folding conformations with the same native state of minimal energy -6; the conversion of glycine as polar amino acid at pH 2 has 13,386 folding conformations with three native states of minimal energy -5; the conversion of glycine as hydrophobic amino acid at pH 7 has 2538 folding conformations with three native states of minimal energy -5; and the conversion of glycine as polar amino acid at pH 7 has 12,852 folding conformations with three native states of minimal energy -4. Those native states can be ranked according to the normalized amino acid hydrophobicity index. The detailed discussions suggest two ways to modify misgurin.     

Role of hydrophobic interactions and salt-bridges in β-hairpin folding

β-Hairpins are the simplest form of β-sheets which, due to the presence of long-range interactions, can be considered as tertiary structures. Molecular dynamics simulation is a powerful tool that can unravel whole pathways of protein folding/unfolding at atomic resolution. We have performed several molecular dynamics simulations, to a total of over 250 ns, of a β-hairpin peptide in water using GROMACS. We show that hydrophobic interactions are necessary for initiating the folding of the peptide. Once formed, the peptide is stabilized by hydrogen bonds and disruption of hydrophobic interactions in the folded peptide does not denature the structure. In the absence of hydrophobic interactions, the peptide fails to fold. However, the introduction of a salt-bridge compensates for the loss of hydrophobic interactions to a certain extent. Figure Model of b-hairpin folding: Folding is initiated by hydrophobic interactions (Brown circles). The folded structure, once formed, is stabilized by hydrogen bonds (red lines) and is unaffected by loss of hydrophobic contacts     

Total chemical synthesis and oxidative folding of delta-conotoxin PVIA containing an N-terminal propeptide

Small disulfide-rich peptides are translated as larger precursors typically containing an N-terminal prepro sequence. In this study, we investigated the role of a propeptide in the oxidative folding of an extremely hydrophobic delta-conotoxin, PVIA. delta-Conotoxin PVIA (delta-PVIA) is a 29-amino acid neurotoxin stabilized by three disulfide bridges. Previous folding studies on delta-conotoxins revealed that their poor folding properties resulted from their hydrophobicity. However, low folding yields of delta-PVIA could be improved by the presence of a nonionic detergent, which acted as a chemical chaperone. delta-PVIA provided an attractive model to investigate whether the hydrophilic propeptide region could function as an intramolecular chaperone. A 58-amino acid precursor for delta-PVIA (pro-PVIA), containing the N-terminal propeptide covalently attached to the mature conotoxin, was synthesized using native chemical ligation. Oxidative folding of pro-PVIA resulted in a very low accumulation of the correctly folded form, comparable to that for the mature conotoxin delta-PVIA. Our results are in accord with the relevant data previously observed for alpha- and omega-conotoxins, indicating that conotoxin prepro sequences are so-called class II propeptides, which are not directly involved in the oxidative folding. We hypothesize that these propeptide regions may be important for interactions with protein folding catalysts and sorting receptors during the secretory process.     

Effects of Turn Stability and Side-Chain Hydrophobicity on the Folding of β-Structures

Key elements of β-structure folding include hydrophobic core collapse, turn formation, and assembly of backbone hydrogen bonds. In the present folding simulations of several β-hairpins and β-sheets (peptide 1, protein G B1 domain peptide, TRPZIP2, TRPZIP4, 20mer, and 20mer^DP6D), the folding free-energy landscape as a function of several reaction coordinates corresponding to the three key elements indicates apparent dependence on turn stability and side-chain hydrophobicity, which demonstrates different folding mechanisms of similar β-structures of varied sequences. Turn stability is found to be the key factor in determining the formation order of the three structural elements in the folding of β-structures. Moreover, turn stability and side-chain hydrophobicity both affect the stability of backbone hydrogen bonds. The three-stranded β-sheets fold through a three-state transition in which the formation of one hairpin always takes precedence over the other. The different stabilities of two anti-parallel hairpins in each three-stranded β-sheet are shown to correlate well with the different levels of their hydrophobic interactions.     

Calculation of the three-dimensional structure of Saccharomyces cerevisiae cytochrome b inserted in a lipid matrix

Cytochrome b is an integral membrane protein, which forms the core of the ubiquinol-cytochrome c oxidoreductase (cytochrome bc1) complex. A computer-aided three-dimensional modeling procedure was carried out in four steps. First, the candidate hydrophobic helices were searched for throughout the protein primary sequence by a computer procedure based upon the method of Eisenberg; second, a secondary helical structure was imposed to the transmembrane peptides; third, the helical segments at a lipid-water interface were oriented, and finally the possible interactions between helices with similar properties were investigated. This procedure enabled the identification of nine hydrophobic segments, of which eight are membrane-spanning helices while one has amphipathic properties. Three hydrophilic receptor-binding domains were also identified. Based upon their hydrophobicity profiles, the transmembrane helices could be associated in pairs inside the lipid bilayer. In our folding model proposed for cytochrome b, all mutation sites are not only located on the same side of the membrane but are also in close proximity in the three-dimensional structure. Inhibitor resistance mutational sites which were recently characterized (di Rago, J.-P., and Colson, A.-M. (1988) J. Biol. Chem. 263, 12564-12570) have been located on this model. Moreover, the receptor-binding domains and the mutation sites are close neighbors in the three-dimensional spatial representation.