Hydrophobic basis of packing in globular proteins

Controlling the Trimerization of the Collagen Triple-Helix by Solvent Switching

Collagen hybridizing peptides (CHPs) are a powerful tool for targeting collagen damage in pathological tissues due to their ability to specifically form a hybrid collagen triple-helix with the denatured collagen chains. However, CHPs have a strong tendency to self-trimerize, requiring preheating or complicated chemical modifications to dissociate their homotrimers into monomers, which hinders their applications. To control the self-assembly of CHP monomers, we evaluated the effects of 22 cosolvents on the triple-helix structure: unlike typical globular proteins, the CHP homotrimers (as well as the hybrid CHP-collagen triple helix) cannot be destabilized by the hydrophobic alcohols and detergents (e.g., SDS) but can be effectively dissociated by the cosolvents that dominate hydrogen bonds (e.g., urea, guanidinium salts, and hexafluoroisopropanol). Our study provided a reference for the solvent effects on natural collagen and a simple effective solvent-switch method, enabling CHP utilization in automated histopathology staining and in vivo imaging and targeting of collagen damage.

Capturing a Crucial ‘Disorder-to-Order Transition’ at the Heart of the Coronavirus Molecular Pathology—Triggered by Highly Persistent, Interchangeable Salt-Bridges

The COVID-19 origin debate has greatly been influenced by genome comparison studies of late, revealing the emergence of the Furin-like cleavage site at the S1/S2 junction of the SARS-CoV-2 Spike (FLCSSpike) containing its 681PRRAR685 motif, absent in other related respiratory viruses. Being the rate-limiting (i.e., the slowest) step, the host Furin cleavage is instrumental in the abrupt increase in transmissibility in COVID-19, compared to earlier onsets of respiratory viral diseases. In such a context, the current paper entraps a ‘disorder-to-order transition’ of the FLCSSpike (concomitant to an entropy arrest) upon binding to Furin. The interaction clearly seems to be optimized for a more efficient proteolytic cleavage in SARS-CoV-2. The study further shows the formation of dynamically interchangeable and persistent networks of salt-bridges at the Spike–Furin interface in SARS-CoV-2 involving the three arginines (R682, R683, R685) of the FLCSSpike with several anionic residues (E230, E236, D259, D264, D306) coming from Furin, strategically distributed around its catalytic triad. Multiplicity and structural degeneracy of plausible salt-bridge network archetypes seem to be the other key characteristic features of the Spike–Furin binding in SARS-CoV-2, allowing the system to breathe—a trademark of protein disorder transitions. Interestingly, with respect to the homologous interaction in SARS-CoV (2002/2003) taken as a baseline, the Spike–Furin binding events, generally, in the coronavirus lineage, seems to have preference for ionic bond formation, even with a lesser number of cationic residues at their potentially polybasic FLCSSpike patches. The interaction energies are suggestive of characteristic metastabilities attributed to Spike–Furin interactions, generally to the coronavirus lineage, which appears to be favorable for proteolytic cleavages targeted at flexible protein loops. The current findings not only offer novel mechanistic insights into the coronavirus molecular pathology and evolution, but also add substantially to the existing theories of proteolytic cleavages.

Estimating the Influence of Physicochemical and Biochemical Property Indexes on Selection for Amino Acids Usage in Eukaryotic Cells

Proteins can evolve by accumulating changes on amino acid sequences. These changes are mainly caused by missense mutations on its DNA coding sequences. Mutations with neutral or positive effects on fitness can be maintained while deleterious mutations tend to be eliminated by natural selection. Amino acid changes are influenced by the biophysical, chemical, and biological properties of amino acids. There is a multiplicity of amino acid properties that can influence the function and expression of proteins. Amino acid properties can be expressed into numerical indexes, which can help to predict functional and structural aspects of proteins and allow statistical inferences of selection pressure on amino acid usage. The accuracy of these analyses may be compromised by the existence of several numerical indexes that measure the same amino acid property, and the lack of objective parameters to determine the most accurate and biologically relevant index. In the present study, the gradient consistency test was used in order to estimate the magnitude of directional selection imparted by amino acid biochemical and biophysical properties on protein evolution.

Expanding MPEx Hydropathy Analysis to Account for Electrostatic Contributions to Protein Interactions with Anionic Membranes

Hydropathy plots are a crucial tool to guide experimental design, as they generate predictions of protein-membrane interactions and their bilayer topology. The predictions are based on experimentally determined hydrophobicity scales, which provide an estimate for the propensity and stability of these interactions. A significant improvement to the accuracy of hydropathy analyses was provided by the development of the popular Wimley-White interfacial and octanol hydrophobicity scales. These scales have been previously incorporated into the freely available MPEx (Membrane Protein Explorer) online application. Here, we introduce a substantial update to MPEx that allows for the consideration of electrostatic contributions to the bilayer partitioning free energy. This component originates from the Coulombic attraction or repulsion of charges between proteins and membranes. Its inclusion in hydropathy calculations increases the accuracy of hydropathy plot predictions and extends their use to more complex systems (i.e., anionic membranes). We illustrate the application of this analysis to studies on the membrane selectivity of antimicrobial peptides, the membrane partitioning of ion-channel gating modifiers, and the amyloid proteins α-synuclein and Tau, as well as pH-dependent bilayer interactions of diphtheria toxin and apoptotic inhibitor Bcl-xL.

Complex Gene Loss and Duplication Events Have Facilitated the Evolution of Multiple Loricrin Genes in Diverse Bird Species

The evolution of a mechanically resilient epidermis was a key adaptation in the transition of amniotes to a fully terrestrial lifestyle. Skin appendages usually form via a specialized type of programmed cell death known as cornification which is characterized by the formation of an insoluble cornified envelope (CE). Many of the substrates of cornification are encoded by linked genes located at a conserved genetic locus known as the epidermal differentiation complex (EDC). Loricrin is the main protein component of the mammalian CE and is encoded for by a gene located within the EDC. Recently, genes resembling mammalian loricrin, along with several other proteins most likely involved in CE formation, have been identified within the EDC of birds and several reptiles. To better understand the evolution and function of loricrin in birds, we screened the genomes of 50 avian species and 3 crocodilians to characterize their EDC regions. We found that loricrin is present within the EDC of all species investigated, and that three loricrin genes were present in birds. Phylogenetic and molecular evolution analyses found evidence that gene deletions and duplications as well as concerted evolution has shaped the evolution of avian loricrins. Our results suggest a complex evolutionary history of avian loricrins which has accompanied the evolution of bird species with diverse morphologies and lifestyles.

Quantitative Assessment of Thermodynamic Theory in Elucidating the Behavior of Water under Hydrophobic Confinement

A macroscopic thermodynamics-based theory that can quantitatively describe the behavior of water confined between hydrophobic solutes has so far remained elusive. In this work, we progress toward this goal by comparing the predictions of macroscopic theory with the results from computer simulations. We have determined free energy profiles of water confined between two nanometer-sized surfaces of varying hydrophobicity using molecular simulations and have estimated thermodynamic properties such as contact angle, line tension, and size of the critical vapor tube from independent simulations. We show that the scaling of free energy barrier to evaporation is fairly well captured by the factor ( D/2 + λ/ϒ_LV)², where D is the confinement gap and λ/ ϒ_LV is the ratio of line-tension and liquid-vapor surface tension. The radius of the critical vapor tube necessary for nucleating evaporation scales by the factor ( D/2 + λ/ϒ_LV). Exclusion of the line-tension term from thermodynamic theory leads to a qualitative disagreement between theoretical predictions and results from molecular simulations. We also demonstrate that macroscopic theory that includes the line-tension term is able to quantitatively match the entire free energy profile associated with the formation of a vapor-tube inside the confined region for conditions when the vapor state is the most stable state. The match is however only qualitatively correct for the conditions when the liquid state is more stable. Overall, the conclusion is that the inclusion of line-tension in macroscopic theory is necessary to describe the behavior of water under nanoscale confinement between two hydrophobic solutes.

The influence of polyanion molecular weight on polyelectrolyte multilayers at surfaces: protein adsorption and protein-polysaccharide complexation/stripping on natural polysaccharide films on solid supports

Two different fucoidan polymers (unfractionated Fucus vesiculosus fucoidan, and fractionated low molecular weight Fucus vesiculosus fucoidan) have been used to create substrates for protein adsorption studies. Polyelectrolyte multilayers were formed using the fucoidans (polyanions) with chitosan as the corresponding polycation. Multilayer formation was studied using zeta potential measurements, quartz crystal microbalance with dissipation monitoring (QCM-D) and attenuated total reflectance (ATR) FTIR spectroscopy. The formation studies reveal that the low molecular weight (LMW) fucoidan produces a less hydrated multilayer, with a significantly increased adsorbed mass, and with fucoidan as the diffusing species during formation. Protein adsorption studies using bovine serum albumin (BSA) were undertaken for solution conditions designed to mimic biological conditions, and to minimise the role of electrical double layer forces in influencing adsorption. Under these conditions, and as revealed by ATR FTIR spectroscopy, BSA is seen to adsorb less substantially to multilayers formed with the LMW fucoidan, and to cause extraction/stripping of the LMW fucoidan from the multilayer. FTIR spectra reveal that the protein adopts a different conformation when adsorbed to the LMW fucoidan multilayer, both relative to the protein in solution and when adsorbed at the surface of the multilayer formed from unfractionated fucoidan.

TSpred: a web server for the rational design of temperature-sensitive mutants

Temperature sensitive (Ts) mutants of proteins provide experimentalists with a powerful and reversible way of conditionally expressing genes. The technique has been widely used in determining the role of gene and gene products in several cellular processes. Traditionally, Ts mutants are generated by random mutagenesis and then selected though laborious large-scale screening. Our web server, TSpred (http://mspc.bii.a-star.edu.sg/TSpred/), now enables users to rationally design Ts mutants for their proteins of interest. TSpred uses hydrophobicity and hydrophobic moment, deduced from primary sequence and residue depth, inferred from 3D structures to predict/identify buried hydrophobic residues. Mutating these residues leads to the creation of Ts mutants. Our method has been experimentally validated in 36 positions in six different proteins. It is an attractive proposition for Ts mutant engineering as it proposes a small number of mutations and with high precision. The accompanying web server is simple and intuitive to use and can handle proteins and protein complexes of different sizes.

Quantitative theory of hydrophobic effect as a driving force of protein structure

Various studies suggest that the hydrophobic effect plays a major role in driving the folding of proteins. In the past, however, it has been challenging to translate this understanding into a predictive, quantitative theory of how the full pattern of sequence hydrophobicity in a protein shapes functionally important features of its tertiary structure. Here, we extend and apply such a phenomenological theory of the sequence-structure relationship in globular protein domains, which had previously been applied to the study of allosteric motion. In an effort to optimize parameters for the model, we first analyze the patterns of backbone burial found in single-domain crystal structures, and discover that classic hydrophobicity scales derived from bulk physicochemical properties of amino acids are already nearly optimal for prediction of burial using the model. Subsequently, we apply the model to studying structural fluctuations in proteins and establish a means of identifying ligand-binding and protein-protein interaction sites using this approach.

Structure-based Methods for Computational Protein Functional Site Prediction

Due to the advent of high throughput sequencing techniques and structural genomic projects, the number of gene and protein sequences has been ever increasing. Computational methods to annotate these genes and proteins are even more indispensable. Proteins are important macromolecules and study of the function of proteins is an important problem in structural bioinformatics. This paper discusses a number of methods to predict protein functional site especially focusing on protein ligand binding site prediction. Initially, a short overview is presented on recent advances in methods for selection of homologous sequences. Furthermore, a few recent structural based approaches and sequence-and-structure based approaches for protein functional sites are discussed in details.

Average conformations determined from PRE data provide high-resolution maps of transient tertiary interactions in disordered proteins

In the last decade it has become evident that disordered states of proteins play important physiological and pathological roles and that the transient tertiary interactions often present in these systems can play a role in their biological activity. The structural characterization of such states has so far largely relied on ensemble representations, which in principle account for both their local and global structural features. However, these approaches are inherently of low resolution due to the large number of degrees of freedom of conformational ensembles and to the sparse nature of the experimental data used to determine them. Here, we overcome these limitations by showing that tertiary interactions in disordered states can be mapped at high resolution by fitting paramagnetic relaxation enhancement data to a small number of conformations, which can be as low as one. This result opens up the possibility of determining the topology of cooperatively collapsed and hidden folded states when these are present in the vast conformational landscape accessible to disordered states of proteins. As a first application, we study the long-range tertiary interactions of acid-unfolded apomyoglobin from experimentally measured paramagnetic relaxation enhancement data.

SEARCH FOR FOLDING INITIATION SITES FROM AMINO ACID SEQUENCE

A crucial event in protein folding is the formation of a folding nucleus, which is a structured part of the protein chain in the transition state. We demonstrate a correlation between locations of residues involved in the folding nuclei and locations of predicted amyloidogenic regions. The average Φ-values are significantly greater inside amyloidogenic regions than outside them. We have found that fibril formation and normal folding involve many of the same key residues, giving an opportunity to outline the folding initiation site in protein chains. The search for folding initiation sites for apomyoglobin and ribonuclease. A coincides with the predictions made by other approaches.

A WAVELET APPROACH FOR THE ANALYSIS OF FOLDING TRAJECTORY OF PROTEIN TRP-CAGE

Understanding how protein folds into a functional native structure is arguably one of the most challenging problems remaining in computational biology. Currently, the protein folding mechanism is often characterized by calculating the free energy landscape in terms of various reaction coordinates such as the fraction of native contacts, the radius of gyration, the RMS deviation from the native and so on. In this paper, we present a wavelet approach towards understanding the global state changes during protein folding. The approach is based on the wavelet analysis on the trajectories of various reaction coordinates to identify the significant intermediate states or structural motifs in the folding process. We demonstrate through an example protein Trp-cage that this approach extracts crucial information about protein folding intermediate states as well as the time correlation among these states. Furthermore, the current approach reveals a meaningful structural pattern that had been overlooked in previous works, which provides a better understanding of the folding mechanism as well as the limitation of the current force fields.

Non-native hydrophobic interactions detected in unfolded apoflavodoxin by paramagnetic relaxation enhancement

Transient structures in unfolded proteins are important in elucidating the molecular details of initiation of protein folding. Recently, native and non-native secondary structure have been discovered in unfolded A. vinelandii flavodoxin. These structured elements transiently interact and subsequently form the ordered core of an off-pathway folding intermediate, which is extensively formed during folding of this α–β parallel protein. Here, site-directed spin-labelling and paramagnetic relaxation enhancement are used to investigate long-range interactions in unfolded apoflavodoxin. For this purpose, glutamine-48, which resides in a non-native α-helix of unfolded apoflavodoxin, is replaced by cysteine. This replacement enables covalent attachment of nitroxide spin-labels MTSL and CMTSL. Substitution of Gln-48 by Cys-48 destabilises native apoflavodoxin and reduces flexibility of the ordered regions in unfolded apoflavodoxin in 3.4 M GuHCl, because of increased hydrophobic interactions in the unfolded protein. Here, we report that in the study of the conformational and dynamic properties of unfolded proteins interpretation of spin-label data can be complicated. The covalently attached spin-label to Cys-48 (or Cys-69 of wild-type apoflavodoxin) perturbs the unfolded protein, because hydrophobic interactions occur between the label and hydrophobic patches of unfolded apoflavodoxin. Concomitant hydrophobic free energy changes of the unfolded protein (and possibly of the off-pathway intermediate) reduce the stability of native spin-labelled protein against unfolding. In addition, attachment of MTSL or CMTSL to Cys-48 induces the presence of distinct states in unfolded apoflavodoxin. Despite these difficulties, the spin-label data obtained here show that non-native contacts exist between transiently ordered structured elements in unfolded apoflavodoxin.

A unified hydrophobicity scale for multispan membrane proteins

The concept of hydrophobicity is critical to our understanding of the principles of membrane protein (MP) folding, structure, and function. In the last decades, several groups have derived hydrophobicity scales using both experimental and statistical methods that are optimized to mimic certain natural phenomena as closely as possible. The present work adds to this toolset the first knowledge-based scale that unifies the characteristics of both alpha-helical and beta-barrel multispan MPs. This unified hydrophobicity scale (UHS) distinguishes between amino acid preference for solution, transition, and trans-membrane states. The scale represents average hydrophobicity values of amino acids in folded proteins, irrespective of their secondary structure type. We furthermore present the first knowledge-based hydrophobicity scale for mammalian alpha-helical MPs (mammalian hydrophobicity scale--MHS). Both scales are particularly useful for computational protein structure elucidation, for example as input for machine learning techniques, such as secondary structure or trans-membrane span prediction, or as reference energies for protein structure prediction or protein design. The knowledge-based UHS shows a striking similarity to a recent experimental hydrophobicity scale introduced by Hessa and coworkers (Hessa T et al., Nature 2007;450:U1026-U1032). Convergence of two very different approaches onto similar hydrophobicity values consolidates the major differences between experimental and knowledge-based scales observed in earlier studies. Moreover, the UHS scale represents an accurate absolute free energy measure for folded, multispan MPs--a feature that is absent from many existing scales. The utility of the UHS was demonstrated by analyzing a series of diverse MPs. It is further shown that the UHS outperforms nine established hydrophobicity scales in predicting trans-membrane spans along the protein sequence. The accuracy of the present hydrophobicity scale profits from the doubling of the number of integral MPs in the PDB over the past four years. The UHS paves the way for an increased accuracy in the prediction of trans-membrane spans.

Folding by numbers: primary sequence statistics and their use in studying protein folding

The exponential growth over the past several decades in the quantity of both primary sequence data available and the number of protein structures determined has provided a wealth of information describing the relationship between protein primary sequence and tertiary structure. This growing repository of data has served as a prime source for statistical analysis, where underlying relationships between patterns of amino acids and protein structure can be uncovered. Here, we survey the main statistical approaches that have been used for identifying patterns within protein sequences, and discuss sequence pattern research as it relates to both secondary and tertiary protein structure. Limitations to statistical analyses are discussed, and a context for their role within the field of protein folding is given. We conclude by describing a novel statistical study of residue patterning in β-strands, which finds that hydrophobic (i,i+2) pairing in β-strands occurs more often than expected at locations near strand termini. Interpretations involving β-sheet nucleation and growth are discussed.

Extensive formation of off-pathway species during folding of an alpha-beta parallel protein is due to docking of (non)native structure elements in unfolded molecules

Detailed information about unfolded states is required to understand how proteins fold. Knowledge about folding intermediates formed subsequently is essential to get a grip on pathological aggregation phenomena. During folding of apoflavodoxin, which adopts the widely prevalent alpha-beta parallel topology, most molecules fold via an off-pathway folding intermediate with helical properties. To better understand why this species is formed, guanidine hydrochloride-unfolded apoflavodoxin is characterized at the residue level using heteronuclear NMR spectroscopy. In 6.0 M denaturant, the protein behaves as a random coil. In contrast, at 3.4 M denaturant, secondary shifts and (1)H-(15)N relaxation rates report four transiently ordered regions in unfolded apoflavodoxin. These regions have restricted flexibility on the (sub)nanosecond time scale. Secondary shifts show that three of these regions form alpha-helices, which are populated about 10% of the time, as confirmed by far-UV CD data. One region of unfolded apoflavodoxin adopts non-native structure. Of the alpha-helices observed, two are present in native apoflavodoxin as well. A substantial part of the third helix becomes beta-strand while forming native protein. Chemical shift changes due to amino acid residue replacement show that the latter alpha-helix has hydrophobic interactions with all other ordered regions in unfolded apoflavodoxin. Remarkably, these ordered segments dock non-natively, which causes strong competition with on-pathway folding. Thus, rather than directing productive folding, conformational preorganization in the unfolded state of an alpha-beta parallel-type protein promotes off-pathway species formation.

PAK: an essential motif for forming β-turn structures and exhibiting the thrombolytic effect of P6A and its analogs

Ala-Arg-Pro-Ala-Lys (ARPAK; also known as P6A) and 19 of its analogs were synthesized, and their thrombolytic activities were assessed in vitro and in vivo. The solution structures of 12 of the P6A analogs were determined using nuclear magnetic resonance (NMR) spectroscopy. The thrombolytic activity and conformational structure relationship was analyzed. We found that the Pro-Ala-Lys (PAK) sequence was essential for thrombolytic activity and was also responsible for the β-turn structure found in the P6A analogs studied. The well defined β turn may act as a binding head with the protruding lysine side-chain (positively charged) found at the target site for target recognition. Additionally, the N-terminal residue may be critical for thrombolytic activity, which for PAK-containing peptides, is likely achieved via a plasminogen-dependent pathway.

Prediction of functional sites based on the fuzzy oil drop model

A description of many biological processes requires knowledge of the 3-D structure of proteins and, in particular, the defined active site responsible for biological function. Many proteins, the genes of which have been identified as the result of human genome sequencing, and which were synthesized experimentally, await identification of their biological activity. Currently used methods do not always yield satisfactory results, and new algorithms need to be developed to recognize the localization of active sites in proteins. This paper describes a computational model that can be used to identify potential areas that are able to interact with other molecules (ligands, substrates, inhibitors, etc.). The model for active site recognition is based on the analysis of hydrophobicity distribution in protein molecules. It is shown, based on the analyses of proteins with known biological activity and of proteins of unknown function, that the region of significantly irregular hydrophobicity distribution in proteins appears to be function related.

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 http://www.bioinformatics.cm-uj.krakow.pl/activesite. The implication based on the model presented in this work suggests the necessity of active presence of ligand during the protein folding process simulation.

The role of hydrophobic interactions in initiation and propagation of protein folding

Globular proteins fold by minimizing the nonpolar surface that is exposed to water, while simultaneously providing hydrogen-bonding interactions for buried backbone groups, usually in the form of secondary structures such as alpha-helices, beta-sheets, and tight turns. A primary thermodynamic driving force for the formation of globular structure is thus the sequestration of nonpolar groups, but the correlation between the parts of proteins that are observed to fold first (termed folding initiation sites) and the "hydrophobicity" (as customarily defined) of the amino acids in these regions has been quite weak. It has previously been noted that many amino acid side chains contain considerable nonpolar sections, even if they also contain polar or charged groups. For example, a lysine side chain contains four methylenes, which may undergo hydrophobic interactions if the charged epsilon-NH(3)(+) group is salt-bridged or hydrogen-bonded. Folding initiation sites might therefore contain not only accepted "hydrophobic" amino acids, but also larger charged side chains. Recent experiments on the folding of mutant apomyoglobins provides corroboration for models based on the hypothesis that folding initiation sites arise from hydrophobic interactions. A near-perfect correlation was observed between the areas of the molecule that are present in the burst-phase kinetic intermediate and both the free energy of formation of hydrophobic initiation sites and the parameter "average area buried upon folding," which pinpoints large side chains, even those containing charged or polar portions. These results provide a putative mechanism for the control of protein-folding initiation and growth by polar/nonpolar sequence propensity alone.

Hydrophobic collapse in (in silico) protein folding

A model of hydrophobic collapse, which is treated as the driving force for protein folding, is presented. This model is the superposition of three models commonly used in protein structure prediction: (1) 'oil-drop' model introduced by Kauzmann, (2) a lattice model introduced to decrease the number of degrees of freedom for structural changes and (3) a model of the formation of hydrophobic core as a key feature in driving the folding of proteins. These three models together helped to develop the idea of a fuzzy-oil-drop as a model for an external force field of hydrophobic character mimicking the hydrophobicity-differentiated environment for hydrophobic collapse. All amino acids in the polypeptide interact pair-wise during the folding process (energy minimization procedure) and interact with the external hydrophobic force field defined by a three-dimensional Gaussian function. The value of the Gaussian function usually interpreted as a probability distribution is treated as a normalized hydrophobicity distribution, with its maximum in the center of the ellipsoid and decreasing proportionally with the distance versus the center. The fuzzy-oil-drop is elastic and changes its shape and size during the simulated folding procedure.

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.

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.

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Hydrophobic collapse in late-stage folding (in silico) of bovine pancreatic trypsin inhibitor

Hydrophobic collapse is commonly considered as a process of significance for protein folding. Many models have been applied for description of this event. A model introducing an external force field mimicking the hydrophobic environment and simultaneously the driving force for the folding process is presented in this paper. Bovine pancreatic trypsin inhibitor (BPTI) was taken as a test protein. An early-stage folding (in silico) model presented elsewhere was used to create the starting structure for hydrophobic collapse. The resulting structure was energy-refined using molecular dynamics simulation in an explicit solvent. The similarity versus the crystal structure of BPTI is estimated using visual analysis, residue-residue contacts, phi, psi angle distributions, RMSD, accessible solvent area, radii of gyration and hydrodynamic radii. A program allowing creation of early-stage folding structural forms to be created for any protein is available from http://bioinformatics.cm-uj.krakow.pl/earlystage. The program for late-stage folding simulation is available on request.

The hydrophobicity of the H3 histone fold differs from the hydrophobicity of the other three folds

The eukaryotic histone dimers, H3-H4 and H2A-H2B, are formed in the cytosol prior to being transported into the nucleus and assembled into the nucleosome. Residue side-chain distances from the interior of the histone dimers are obtained with an ellipsoidal spatial metric and structural information provided by X-ray analyses at atomic resolution of the nucleosome core particles. While the spatial hydrophobic moment profiles of the dimers are comparable with profiles obtained previously that characterize the hydrophobic core of single-chain, single-domain globular soluble proteins, correlation coefficients between the side-chain hydrophobicities and distances from the interior of the H3-H4 dimer and H2A-H2B dimer differ significantly. This difference is traced to the H3 histone fold, which segregates fewer hydrophobic residues within the protein interior than the three other folds. Examination of the correlation coefficient between residue hydrophobicity and side-chain distance from the dimer interior over local regions of the fold sequence shows that the region of reduced correlation is associated mainly with the residues at the carboxyl end of the H3 histone fold, the helical region of the fold involved in the H3-H3' binding of the (H3-H4)(2) tetramer of the nucleosome. Hydrophobic interactions apparently contribute to the binding of this fourfold helical bundle and this evolutionary requirement may trade off against the requirement for H3-H4 dimer stability. The present results provide a different view than previously proposed, albeit of similar origin, to account for the reduced stability of the H3-H4 dimer compared with the H2A-H2B dimer.

Underlying Hydrophobic Sequence Periodicity of Protein Tertiary Structure

Hydropathy plots or window averages over local stretches of the sequence of residue hydrophobicity have revealed patterns related to various protein tertiary structural features. This has enabled identification of regions of the sequence that are at the surface or within the interior of globular soluble proteins, regions located within the lipid bilayer of transmembrane proteins, portions of the sequence that characterize repeating motifs, as well as motifs that usefully characterize different protein structural families. This, therefore, provides one example of the generally expressed maxim that "sequence determines structure". On the other hand, a number of previous investigations have shown the rapidly varying values of residue hydrophobicity along the sequence to be distributed approximately randomly. So one might question just how much of the sequence actually determines structure. It is, therefore, of interest to extract that part of this rapidly varying distribution of residue hydrophobicity that is responsible for the longer wavelength variations that correlate with protein tertiary structural features and to determine their prevalence within the entire distribution. This is accomplished by a finite Fourier analysis of the sequence of residue hydrophobicity and of a new measure of residue distance from the protein interior. Calculations are performed on a number of globins, immunoglobulins, cuprodoxins, and papain-like structures. The spectral power of the Fourier amplitudes of the frequencies extracted, whose inverse transforms underlie the windowed values of residue hydrophobicity is shown to be a small fraction of the total power of the hydrophobicity distribution and thereby consistent with a distribution that might appear to be predominantly random. The wide range of sequence identity between proteins having the same fold, all exhibiting similar small fractions of power amplitude that correlate with the longer wavelength inside-to-outside excursions of the amino acid residues, supports the general contention that close sequence identity is an expression of a close evolutionary relationship rather than an expression of structural similarity. Practical implications of the present analysis for protein structure prediction and engineering are also described.

Hydropathy analysis to correlate structure and function of proteins

In post-genomic era, a plethora of protein structures have been solved but the functions of some of them are unknown. In this context, the role of hydropathy index of amino acids in predicting the function of a structurally known and functionally unknown protein was explored. Initially serine protease class was taken for analysis. Various methodologies like calculation of average hydropathy index for a five-residue window of a given sequence, hydropathy cluster analyses, etc., were done. Among these, the distribution of hydropathy clusters seems to suggest that the location of these clusters is conserved for a given class of proteins. Hence, this methodology was extended to different classes of proteins and to a protein with unknown function.

The Optimal Fraction of Hydrophobic Residues Required to Ensure Protein Collapse

The hydrophobic interaction is the main driving force for protein folding. Here, we address the question of what is the optimal fraction, f of hydrophobic (H) residues required to ensure protein collapse. For very small f (say f<0.1), the protein chain is expected to behave as a random coil, where the H residues are "wrapped" locally by polar (P) residues. However, for large enough f this local coverage cannot be achieved and the thermodynamic alternative to avoid contact with water is burying the H residues in the interior of a compact chain structure. The interior also contains P residues that are known to be clustered to optimize their electrostatic interactions. This means that the H residues are clustered as well, i.e. they effectively attract each other like the H-monomers in Dill's HP lattice model. Previously, we asked the question: assuming that the H monomers in the HP model are distributed randomly along the chain, what fraction of them is required to ensure a compact ground state? We claimed there that f approximately p(c), where p(c) is the site percolation threshold of the lattice (in a percolation experiment, each site of an initially empty lattice is visited and a particle is placed there with a probability p. The interest is in the critical (minimal) value, p(c), for which percolation occurs, i.e. a cluster connecting the opposite sides of the lattice is created). Due to the above correspondence between the HP model and real proteins (and assuming that the H residues are distributed at random) we suggest that the experimental f should lead to percolating clusters of H residues over the highly dense protein core, i.e. clusters of the core size. To check this theory, we treat a simplified model consisting of H and P residues represented by their alpha-carbon atoms only. The structure is defined by the C(alpha)-C(alpha) virtual bond lengths, angles and dihedral angles, and the X-ray structure is best-fitted onto a face-centered cubic lattice. Percolation experiments are carried out for 103 single-chain proteins using six different hydrophobic sets of residues. Indeed, on average, percolating clusters are generated, which supports our theory; however, some sets lead to a better core coverage than others. We also calculate the largest actual hydrophobic cluster of each protein and show that, on average, these clusters span the core, again in accord with our theory. We discuss the effect of protein size, deviations from the average picture, and implications of this study for defining reliable simplified models of proteins.

Study of the early steps of the Hepatitis B Virus life cycle

Hepatitis B virus (HBV) is a human pathogen, causing the serious liver disease. Despite considerable advances in the understanding of the natural history of HBV disease, most of the early steps in the virus life cycle remain unclear. Virus attachment to permissive cells, fusion and penetration through cell membranes and subsequent genome release, are largely a mystery. Current knowledge on the early steps of HBV life cycle has mostly come from molecular cloning, expression of individual genes and studies of the infection of duck hepatitis B virus (DHBV) with duck primary duck hepatocytes. However, considering of the difference of the surface protein of HBV and DHBV both in the composition and sequence, the degree to which information from DHBV applies to human HBV attachment and entry may be limited. A major obstacle to the study HBV infection is the lack of a reliable and sensitive in vitro infection system. We have found that the digestion of HBV and woodchuck hepatitis virus (WHBV) by protease V8 led to the infection of HepG2 cell, a cell line generally is refractory for their infection [Lu et al. J Virol. 1996. 70. 2277-2285 . Lu et al. Virus Research. 2001. 73(1): 27-4].. Further studies showed that a serine protease inhibitor Kazal (SPIK) was over expressed in the HepG2 cells. Therefore, it is possible that to silence the over expressed SPIK and thus to reinstate the activity of indispensable cellular proteases can result in the restoration of the susceptibility of HepG2 cells for HBV infection. The establishing a stable cell line for study of the early steps of HBV life cycle by silencing of SPIK is discussed.

Designing human m1 muscarinic receptor-targeted hydrophobic eigenmode matched peptides as functional modulators

A new proprietary de novo peptide design technique generated ten 15-residue peptides targeting and containing the leading nontransmembrane hydrophobic autocorrelation wavelengths, "modes", of the human m(1) muscarinic cholinergic receptor, m(1)AChR. These modes were also shared by the m(4)AChR subtype (but not the m(2), m(3), or m(5) subtypes) and the three-finger snake toxins that pseudoirreversibly bind m(1)AChR. The linear decomposition of the hydrophobically transformed m(1)AChR amino acid sequence yielded ordered eigenvectors of orthogonal hydrophobic variational patterns. The weighted sum of two eigenvectors formed the peptide design template. Amino acids were iteratively assigned to template positions randomly, within hydrophobic groups. One peptide demonstrated significant functional indirect agonist activity, and five produced significant positive allosteric modulation of atropine-reversible, direct-agonist-induced cellular activation in stably m(1)AChR-transfected Chinese hamster ovary cells, reflected in integrated extracellular acidification responses. The peptide positive allosteric ligands produced left-shifts and peptide concentration-response augmentation in integrated extracellular acidification response asymptotic sigmoidal functions and concentration-response behavior in Hill number indices of positive cooperativity. Peptide mode specificity was suggested by negative crossover experiments with human m(2)ACh and D(2) dopamine receptors. Morlet wavelet transformation of the leading eigenvector-derived, m(1)AChR eigenfunctions locates seven hydrophobic transmembrane segments and suggests possible extracellular loop locations for the peptide-receptor mode-matched, modulatory hydrophobic aggregation sites.

Proteins with H-bond packing defects are highly interactive with lipid bilayers: Implications for amyloidogenesis

We noticed that disease-related amyloidogenic proteins and especially cellular prion proteins have the highest proportion of incompletely desolvated backbone H bonds among soluble proteins. Such bonds are vulnerable to water attack and thus represent structural weaknesses. We have measured the adsorption of proteins onto phospholipid bilayers and found a strong correlation between the extent of underwrapping of backbone H bonds in the native structure of a protein and its extent of deposition on the bilayer: the less the H bond wrapping, the higher the propensity for protein-bilayer binding. These observations support the proposition that soluble proteins with amyloidogenic propensity and membrane proteins share a pervasive building motif: the underwrapped H bonds. Whereas in membrane proteins, this motif does not signal a structural vulnerability, in soluble proteins, it is responsible for their reactivity.

Hydrophobicity of transmembrane proteins: spatially profiling the distribution

A hallmark of soluble globular protein tertiary structure is a hydrophobic core and a protein exterior populated predominantly by hydrophilic residues. Recent hydrophobic moment profiling of the spatial distribution of 30 globular proteins of diverse size and structure had revealed features of this distribution that were comparable. Analogous profiling of the hydrophobicity distribution of the alpha-helical buried bundles of several transmembrane proteins, as the lipid/protein interface is approached from within the bilayer, reveals spatial hydrophobicity profiles that contrast with those obtained for the soluble proteins. The calculations, which enable relative changes of hydrophobicity to be simply identified over the entire spatial extent of the multimer within the lipid bilayer, show the accumulated zero-order moments of the bundles to be mainly inverted with respect to that found for the soluble proteins. This indicates a statistical increase in the average residue hydrophobic content as the lipid bilayer is approached. This result differs from that of a relatively recent calculation and qualitatively agrees with earlier calculations involving lipid exposed and buried residues of the alpha-helices of transmembrane proteins. Spatial profiling, over the entire spatial extent of the multimer with scaled values of residue hydrophobicity, provides information that is not available from calculations using lipid exposure alone.

Phospholipid membrane interactions of saposin C: in situ atomic force microscopic study

Saposin C (Sap C) is a small glycoprotein required for hydrolysis of glucosylceramidase in lysosomes. The full activity of glucosylceramidase requires the presence of both Sap C and acidic phospholipids. Interaction between Sap C and acidic phospholipid-containing membranes, a crucial step for enzyme activation, is not fully understood. In this study, the dynamic process of Sap C interaction with acidic phospholipid-containing membranes was investigated in aqueous buffer using atomic force microscopy. Sap C induced two types of membrane restructuring: formation of patch-like structural domains and the occurrence of membrane destabilization. The former caused thickness increase whereas the latter caused thickness reduction in the gel-phase membrane bilayer, possibly as a result of lipid loss or an interdigitating process. Patch-like domain formation was independent of acidic phospholipids, whereas membrane destabilization is dependent on the presence and concentration of acidic phospholipids. Sap C effects on membrane restructuring were further studied using synthetic peptides. Synthetic peptides corresponding to the amphipathic alpha-helical domains 1 (designated "H1 peptide") and 2 (H2 peptide) of Sap C were used. Our results indicated that H2 contributed to domain formation but not to membrane destabilization, whereas H1 induced neither type of membrane restructuring. However, H1 was able to mimic Sap C's destabilization effect in conjunction with H2, but only when H1 was present first and H2 was added afterwards. This study provides an approach to investigate the structure-function aspects of Sap C interaction with phospholipid membranes, with insights into the mechanism(s) of Sap C-membrane interaction.

A two-component nucleation model of protein hydrophobicity

A fundamental characteristic of soluble globular protein structure is a hydrophobic core and protein exterior comprised predominantly of hydrophilic residues. This distribution of amino acid residue hydrophobicity, from protein interior to exterior, has recently been profiled with the use of hydrophobic moments. The calculations enable comparison of the radial hydrophobicity distribution of different proteins and had revealed two features common to 30 proteins of diverse size and structure. One, a global feature, is the overall shape of the second-order ellipsoidal hydrophobic moment. The second, a specific feature, is a quasi-invariant hydrophobic-ratio of distances. Both features are dependent upon the rates of increase, from protein interior to exterior, of the accumulated numbers of hydrophobic and hydrophilic amino acid residues. These rates can be simulated simply with a two-component nucleation model of protein hydrophobicity. The model provides insight into the origin of the shape of the observed hydrophobic moment profiles and of the observed range of hydrophobic ratios. Consistent with observation, it is shown that a relatively wide range of hydrophobic and hydrophilic rates of increase yield a relatively narrow range of hydrophobic ratios. Furthermore, the model identifies one factor, the decrease in residue density with increasing distance from the protein interior, that is critical in providing the range of values that is comparable with the observed range.

Cracking the folding code. Why do some proteins adopt partially folded conformations, whereas other don't?

Many, but not all, globular proteins have been shown to have compact intermediate state(s) under equilibrium conditions in vitro, giving rise to the question: why do some proteins adopt partially folded conformations, whereas other do not? Here we show that charge to hydrophobicity ratio of a polypeptide chain may represent a key determinant in this respect, as proteins known to form equilibrium partially folded intermediates are specifically localized within a unique region of charge-hydrophobicity space. Thus, the competence of a protein to form equilibrium intermediate(s) may be determined by the bulk content of hydrophobic and charged amino acid residues rather than by the positioning of amino acids within the sequence.

Frequencies of amino acid strings in globular protein sequences indicate suppression of blocks of consecutive hydrophobic residues

Patterns of hydrophobic and hydrophilic residues play a major role in protein folding and function. Long, predominantly hydrophobic strings of 20-22 amino acids each are associated with transmembrane helices and have been used to identify such sequences. Much less attention has been paid to hydrophobic sequences within globular proteins. In prior work on computer simulations of the competition between on-pathway folding and off-pathway aggregate formation, we found that long sequences of consecutive hydrophobic residues promoted aggregation within the model, even controlling for overall hydrophobic content. We report here on an analysis of the frequencies of different lengths of contiguous blocks of hydrophobic residues in a database of amino acid sequences of proteins of known structure. Sequences of three or more consecutive hydrophobic residues are found to be significantly less common in actual globular proteins than would be predicted if residues were selected independently. The result may reflect selection against long blocks of hydrophobic residues within globular proteins relative to what would be expected if residue hydrophobicities were independent of those of nearby residues in the sequence.

Quantitative comparison of the ability of hydropathy scales to recognize surface beta-strands in proteins

Methods based on the use of hydropathy scales have been used widely to ascertain the secondary structures of proteins. However, over 100 such scales have been reported in the literature, and which of these is the most successful in terms of the prediction rate of the correct structure is not clear. This article, therefore, reports a comprehensive analysis of the relative success of hydropathy scales to locate beta-strands on the surfaces of proteins. The technique we used is based on the technique proposed by Fraser and Parry, but it includes a modification that allows a higher rate of successful prediction and a lower rate of overprediction. We used as a basis for assessing the predictions a database of sequence-unique structures that we previously established. Proteins 2001;42:243-255.

Chirality organization of ferrocenes bearing podand dipeptide chains: synthesis and structural characterization

A variety of ferrocenes bearing podand dipeptide chains have been synthesized to form an ordered structure in both solid and solution states and have been investigated by 1H NMR, FT-IR, CD, and X-ray crystallographic analyses. Conformational enantiomerization through chirality organization was achieved by the intramolecular hydrogen bondings between the podand dipeptide chains. The single-crystal X-ray structure determination of the ferrocene 2 bearing the podand dipeptide chains (-D-Ala-D-Pro-OEt) revealed two C2-symmetric intramolecular hydrogen bondings between CO (Ala) and NH (another Ala) of each podand dipeptide chain to induce the chirality-organized structure. The molecular structures of the ferrocene 1 composed of the podand L-dipeptide chains (-L-Ala-L-Pro-OEt) and 2 are in a good mirror image relationship, indicating that they are conformational enantiomers. An opposite helically ordered molecular arrangement was formed in the crystal packing of 2 as compared with 1. The ferrocene 2 exhibited induced circular dichroism (CD), which appeared at the absorbance of the ferrocene moiety. The mirror image of the CD signals between 1 and 2 was observed, suggesting that the chirality-organized structure via intramolecular hydrogen bondings is present even in solution. The ferrocene 4 bearing the podand dipeptide chains (-Gly-L-Leu-OEt) also showed an ordered structure in the crystal based on two intramolecular hydrogen bondings between CO (Gly) and NH (another Gly) of each podand dipeptide chain, together with intermolecular hydrogen bondings between CO adjacent to the ferrocene unit and NH (neighboring Leu) to create the highly organized self-assembly. A different self-assembly was observed in the crystal of the ferrocene 5 composed of the podand dipeptide chains (-Gly-L-Phe-OEt), wherein each molecule is bonded to two neighboring molecules through two pairs of symmetrical intermolecular hydrogen bonds to form a 14-membered intermolecularly hydrogen-bonded ring. These ordered structures based on the intramolecular hydrogen bondings in the solution state are also confirmed by 1H NMR and FT-IR.

Dynamics of compact denatured states of glutaminyl-tRNA synthetase probed by bis-ANS binding kinetics

Bis-ANS binds to native glutaminyl-tRNA synthetase (GlnRS) with a fast and a slow phase. The rate constant of the slow phase is independent of bis-ANS concentration suggesting a slow conformational change in the pathway of bis-ANS binding. Aging of GlnRS causes a large decrease of the slow phase amplitude with concomitant increase of the fast phase amplitude. Several other large, multi-domain proteins show similar patterns upon aging. The near UV-CD spectra of the native and the aged GlnRS remain similar. Significant changes in far UV-CD, acrylamide quenching and sulfhydryl reactivity, are seen upon aging, suggesting disruptions in native interactions. Refolding of GlnRS from the urea-denatured state rapidly produces a state that is very similar to the equilibrium molten globule state. Bis-ANS binds to the molten globule state with kinetics similar to that of the aged state and unlike that of the native state. This suggests that the slow binding phase of bis-ANS, seen in native proteins, originate from relatively high energy barriers between the native and the more open states. Thus bis-ANS can be used as a powerful probe for large amplitude, low-frequency motions of proteins.

Characterization of epitope regions of thyrotropin beta-subunit recognized by the monoclonal antibodies mAb279 and mAb299: a chimeric peptide approach

This investigation describes the design, synthesis and evaluation of chimeric peptides related to the bovine thyrotropin beta-subunit, bTSHbeta. The structures of these chimeric peptides were derived from investigations with linear peptides and sequence alignment studies, in association with a homology model of TSHbeta developed from the hCG X-ray crystallographic structure. The structures of these chimeric peptides comprised beta-turn regions of loop L1 [bTSHbeta(14-20)] and loop L3 [bTSHbeta(65-72)] held in close proximity by a bis-beta-alanine linker and the disulfide bond bTSHbeta[Cys16-Cys67]. Linear and cyclic chimeric peptides were evaluated in immunochemical assays for their ability to inhibit the binding of radio-iodinated bTSHbeta [125I-bTSHbeta] to the monoclonal antibodies, mAb279 and mAb299. Previously, mAb279 and mAb299 have been shown to recognize epitopes accessible on the surface of TSHbeta that lie in close proximity to the TSH receptor-binding site. The results indicate that these chimeric peptides can specifically inhibit in a dose-dependent manner the binding of 125I-bTSHbeta to mAb299, while having a lesser effect on the binding with mAb279. Based on these results, it can be concluded that the bTSHbeta-epitope recognized by mAb299 involves contributions from amino residues from the beta-turn regions of the L1 and L3 loops of TSHbeta, and that these loop regions flank part of the receptor binding site of the bTSH beta-subunit.

Experimental verification of the 'stability profile of mutant protein' (SPMP) data using mutant human lysozymes

The stability profile of mutant protein (SPMP) (Ota,M., Kanaya,S. and Nishikawa,K., 1995, J. Mol. Biol., 248, 733-738) estimates the changes in conformational stability due to single amino acid substitutions using a pseudo-energy potential developed for evaluating structure-sequence compatibility in the structure prediction method, the 3D-1D compatibility evaluation. Nine mutant human lysozymes expected to significantly increase in stability from SPMP were constructed, in order to experimentally verify the reliability of SPMP. The thermodynamic parameters for denaturation and crystal structures of these mutant proteins were determined. One mutant protein was stabilized as expected, compared with the wild-type protein. However, the others were not stabilized even though the structural changes were subtle, indicating that SPMP overestimates the increase in stability or underestimates negative effects due to substitution. The stability changes in the other mutant human lysozymes previously reported were also analyzed by SPMP. The correlation of the stability changes between the experiment and prediction depended on the types of substitution: there were some correlations for proline mutants and cavity-creating mutants, but no correlation for mutants related to side-chain hydrogen bonds. The present results may indicate some additional factors that should be considered in the calculation of SPMP, suggesting that SPMP can be refined further.

A procedure for the prediction of temperature-sensitive mutants of a globular protein based solely on the amino acid sequence

Temperature-sensitive (Ts) mutants of a protein are an extremely powerful tool for studying protein function in vivo and in cell culture. We have devised a method to predict those residues in a protein sequence that, when appropriately mutated, are most likely to give rise to a Ts phenotype. Since substitutions of buried hydrophobic residues often result in significant destabilization of the protein, our method predicts those residues in the sequence that are likely to be buried in the protein structure. We also indicate a set of amino acid substitutions, which should be made to generate a Ts mutant of the protein. This method requires only the protein sequence. No structural information or homologous sequence information is required. This method was applied to a test data set of 30 nonhomologous protein structures from the Protein Data Bank. All of the residues predicted by the method to be > or = 95% buried were, in fact, buried in the protein crystal structure. In contrast, only 50% of all hydrophobic residues in this data set were > or = 95% buried. This method successfully predicts several known Ts and partially active mutants of T4 lysozyme, lambda repressor, gene V protein, and staphylococcal nuclease. This method also correctly predicts residues that form part of the hydrophobic cores of lambda repressor, myoglobin, and cytochrome b562.