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.     

Analysis of accessible surface of residues in proteins

We analyzed the total, hydrophobic, and hydrophilic accessible surfaces (ASAs) of residues from a nonredundant bank of 587 3D structure proteins. In an extended fold, residues are classified into three families with respect to their hydrophobicity balance. As expected, residues lose part of their solvent-accessible surface with folding but the three groups remain. The decrease of accessibility is more pronounced for hydrophobic than hydrophilic residues. Amazingly, Lysine is the residue with the largest hydrophobic accessible surface in folded structures. Our analysis points out a clear difference between the mean (other studies) and median (this study) ASA values of hydrophobic residues, which should be taken into consideration for future investigations on a protein-accessible surface, in order to improve predictions requiring ASA values. The different secondary structures correspond to different accessibility of residues. Random coils, turns, and beta-structures (outside beta-sheets) are the most accessible folds, with an average of 30% accessibility. The helical residues are about 20% accessible, and the difference between the hydrophobic and the hydrophilic residues illustrates the amphipathy of many helices. Residues from beta-sheets are the most inaccessible to solvent (10% accessible). Hence, beta-sheets are the most appropriate structures to shield the hydrophobic parts of residues from water. We also show that there is an equal balance between the hydrophobic and the hydrophilic accessible surfaces of the 3D protein surfaces irrespective of the protein size. This results in a patchwork surface of hydrophobic and hydrophilic areas, which could be important for protein interactions and/or activity.     

Hydrophobic moments of tertiary protein structures

The helical hydrophobic moment is a measure of the amphiphilicity of a segment of protein secondary structure. Such measure yields information of potential relevance for issues relating to cell surface binding and secondary structure function. The present article describes a global analog of the helical hydrophobic moment. The global moment provides a concise measure of the degree and direction of the amphiphilicity or hydrophobic imbalance across the entire protein tertiary structure. Therefore, this measure is a succinct representation of the spatial organization of residue hydrophobicity for each protein. With this measure, a simple comparison of the hydrophobic imbalance or segregation of different protein structures can be made. For example, two structures having the same fold and close in root-mean-square deviation may exhibit very different overall hydrophobic organization. Such difference is classified simply by the global moment. Furthermore, the direction of the global moment may point to regions of functional interest. Certain formal issues in the development of such moment are described, and a number of applications to particular protein structures are discussed.     

Molecular dynamics simulations of individual alpha-helices of bacteriorhodopsin in dimyristoylphosphatidylcholine. II. Interaction energy analysis.

The concepts of hydrophobicity and hydrophobic moments have been applied in attempts to predict membrane protein secondary and tertiary structure. The current paper uses molecular dynamics computer calculations of individual bacteriorhodopsin helices in explicit dimyristoylphosphatidylcholine bilayers to examine the atomic basis of these approaches. The results suggest that the types of interactions between a particular amino acid and the surrounding bilayer depend on the position and type of the amino acid. In particular, aromatic residues are seen to interact favorably at the interface region. Analysis of the trajectories in terms of hydrophobic moments suggests the presence of a particular face that prefers lipid. The results of these simulations may be used to improve secondary structure prediction methods and to provide further insights into the two-stage model of protein folding.     

Accounting for protein-solvent contacts facilitates design of nonaggregating lattice proteins

The folding specificity of proteins can be simulated using simplified structural models and knowledge-based pair-potentials. However, when the same models are used to simulate systems that contain many proteins, large aggregates tend to form. In other words, these models cannot account for the fact that folded, globular proteins are soluble. Here we show that knowledge-based pair-potentials, which include explicitly calculated energy terms between the solvent and each amino acid, enable the simulation of proteins that are much less aggregation-prone in the folded state. Our analysis clarifies why including a solvent term improves the foldability. The aggregation for potentials without water is due to the unrealistically attractive interactions between polar residues, causing artificial clustering. When a water-based potential is used instead, polar residues prefer to interact with water; this leads to designed protein surfaces rich in polar residues and well-defined hydrophobic cores, as observed in real protein structures. We developed a simple knowledge-based method to calculate interactions between the solvent and amino acids. The method provides a starting point for modeling the folding and aggregation of soluble proteins. Analysis of our simple model suggests that inclusion of these solvent terms may also improve off-lattice potentials for protein simulation, design, and structure prediction.     

Simulating the folding of small proteins by use of the local minimum energy and the free solvation energy yields native-like structures

Assuming that the protein primary sequence contains all information required to fold a protein into its native tertiary structure, we propose a new computational approach to protein folding by distributing the total energy of the macromolecular system along the torsional axes.We further derive a new semiempirical equation to calculate the total energy of a macromolecular system including its free energy of solvation. The energy of solvation makes an important contribution to the stability of biological structures. The segregation of hydrophilic and hydrophobic domains is essential for the formation of micelles, lipid bilayers, and biological membranes, and it is also important for protein folding. The free energy of solvation consists of two components: one derived from interactions between the atoms of the protein, and the second resulting from interactions between the protein and the solvent. The latter component is expressed as a function of the fractional area of protein atoms accessible to the solvent.The protein-folding procedure described in this article consists of two successive steps: a theoretical transition from an ideal α helix to an ideal β sheet is first imposed on the protein conformation, in order to calculate an initial secondary structure. The most stable secondary structure is built from a combination of the lowest energy structures calculated for each amino acid during this transition. An angular molecular dynamics step is then applied to this secondary structure. In this computational step, the total energy of the system consisting of the sum of the torsional energy, the van der Waals energy, the electrostatic energy, and the solvation energy is minimized. This process yields 3-D structures of minimal total energy that are considered to be the most probable native-like structures for the protein.This method therefore requires no prior hypothesis about either the secondary or the tertiary structure of the protein and restricts the input of data to its sequence. The validity of the results is tested by comparing the crystalline and computed structures of four proteins, i.e., the avian and bovine pancreatic polypeptide (36 residues each), uteroglobin (70 residues), and the calcium-binding protein (75 residues); the C_α-C_α maps show significant homologies and the position of secondary structure domains; that of the α helices is particularly close.     

Nonatomic solvent-driven Voronoi tessellation of proteins: an open tool to analyze protein folds

A three-dimensional Voronoi tessellation of folded proteins is used to analyze geometrical and topological properties of a set of proteins. To each amino acid is associated a central point surrounded by a Voronoi cell. Voronoi cells describe the packing of the amino acids. Special attention is given to reproduction of the protein surface. Once the Voronoi cells are built, a lot of tools from geometrical analysis can be applied to investigate the protein structure; volume of cells, number of faces per cell, and number of sides per face are the usual signatures of the protein structure. A distinct difference between faces related to primary, secondary, and tertiary structures has been observed. Faces threaded by the main-chain have on average more than six edges, whereas those related to helical packing of the amino acid chain have less than five edges. The faces on the protein surface have on average five edges within 1% error. The average number of faces on the protein surface for a given type of amino acid brings a new point of view in the characterization of the exposition to the solvent and the classification of amino acid as hydrophilic or hydrophobic. It may be a convenient tool for model validation.     

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.     

Infrared reflection absorption spectroscopy of amphipathic model peptides at the air/water interface

The linear sequence KLAL (KLALKLALKALKAALKLA-NH(2)) and its corresponding d,l-isomers k(9)a(10)-KLAL (KLALKLALkaLKAALKLA-NH(2)) and l(11)k(12)-KLAL (KLALKLALKAlkAALKLA-NH(2)) are model compounds for potentially amphipathic alpha-helical peptides which are able to bind to membranes and to increase the membrane permeability in a structure- and target-dependent manner (Dathe and Wieprecht, 1999) We first studied the secondary structure of KLAL and its analogs bound to the air/water using infrared reflection absorption spectroscopy. For the peptide films the shape and position of the amide I and amide II bands indicate that the KLAL adopts at large areas per molecule an alpha-helical secondary structure, whereas at higher surface pressures or smaller areas it converts into a beta-sheet structure. This transition could be observed in the compression isotherm as well as during the adsorption at the air/water interface from the subphase as a function of time. The secondary structures are essentially orientated parallel to the air/water interface. The analogs with d-amino acids in two different positions of the sequence, k(9)a(10)-KLAL and l(11)k(12)-KLAL, form only beta-sheet structures at all surface pressures. The observed results are interpreted using a comparison of hydrophobic moments calculated for alpha-helices and beta-sheets. The differences between the hydrophobic moments calculated using the consensus scale are not large. Using the optimal matching hydrophobicity scale or the whole-residue hydrophobicity scale the beta-sheet even has the larger hydrophobic moment.     

The folding of an enzyme. VI. The folding pathway of barnase: comparison with theoretical models.

The sequence of events in the refolding pathway of barnase has been analysed to search for general principles in protein folding. There appears to be a correlation between burying hydrophobic surface area and early folding events. All the regions that fold early interact extensively with the beta-sheet. These interactions involve predominantly hydrophobic interactions and the burial of very extensive hydrophobic areas in which multiple, close, hydrophobic-hydrophobic contacts are established around a central group of aliphatic residues. There is no burial of hydrophilic residues in these regions; those that are partly screened from the solvent make hydrogen bonds. All the regions or interactions that are made late in the folding pathway do not make extensive contacts with the beta-sheet. Their buried hydrophobic regions lack a central hydrophobic residue or residues around which other hydrophobic residues pack. Further, in some of these regions there is an extensive burial of hydrophilic residues. The results are consistent with one of the earlier events in protein folding being the local formation of native-like secondary structure elements driven by local hydrophobic surface burial. A possible candidate for an initiation site is a beta-hairpin between beta-strands 3 and 4 that is conserved in the microbial ribonuclease family. A comparison of structures in this family shows that those regions that can be superimposed, or have sequence homology, correspond to elements of structure that are formed and interact with each other early in the folding pathway, suggesting that some of these residues could be involved in directing the folding process. The data on barnase combined with results from other laboratories suggest the following tentative conclusions for the refolding of small monomeric proteins. (1) The refolding pathway is, at least in part, sequential and of compulsory order. (2) Secondary structure formation is driven by local hydrophobic surface burial and precedes the formation of most tertiary interactions. These elements are then stabilized and sometimes elongated by tertiary interactions. It is plausible that there are stop signals encoded in the linear sequence that prevent the elongation of isolated secondary structure elements in solution to a larger extent than is found in the folded protein. (3) Many tertiary interactions are not very constrained in the intermediate but become more and more defined as the hydrophobic cores consolidate, loop structures form and the configuration of surface residues takes place. The interactions between different elements of secondary structure are the last ones to be consolidated while the interactions within the secondary structure elements are consolidated earlier.(ABSTRACT TRUNCATED AT 400 WORDS)     

Alternatively folded states of an immunoglobulin

Well-defined, non-native protein structures of low stability have been increasingly observed as intermediates in protein folding or as equilibrium structures populated under specific solvent conditions. These intermediate structures, frequently referred to as molten globule states, are characterized by the presence of secondary structure, a lack of significant tertiary contacts, increased hydrophobicity and partial specific volume as compared to native structures, and low cooperativity in thermal unfolding. The present study demonstrates that under acidic conditions (pH less than 3) the antibody MAK33 can assume a folded stable conformation. This A-state is characterized by a high degree of secondary structure, increased hydrophobicity, a native-like maximum wavelength of fluorescence emission, and a tendency toward slow aggregation. A prominent feature of this low-pH conformation is the stability against denaturant and thermal unfolding that is manifested in highly cooperative reversible phase transitions indicative of the existence of well-defined tertiary contacts. These thermodynamic results are corroborated by the kinetics of folding from the completely unfolded chain to the alternatively folded state at pH 2. The given data suggest that MAK33 at pH 2 adopts a cooperative structure that differs from the native immunoglobulin fold at pH 7. This alternatively folded state exhibits certain characteristics of the molten globule but differs distinctly from it by its extraordinary structural stability that is characteristic for native protein structures.     

Free energy determinants of tertiary structure and the evaluation of protein models

We develop a protocol for estimating the free energy difference between different conformations of the same polypeptide chain. The conformational free energy evaluation combines the CHARMM force field with a continuum treatment of the solvent. In almost all cases studied, experimentally determined structures are predicted to be more stable than misfolded "decoys." This is due in part to the fact that the Coulomb energy of the native protein is consistently lower than that of the decoys. The solvation free energy generally favors the decoys, although the total electrostatic free energy (sum of Coulomb and solvation terms) favors the native structure. The behavior of the solvation free energy is somewhat counterintuitive and, surprisingly, is not correlated with differences in the burial of polar area between native structures and decoys. Rather. the effect is due to a more favorable charge distribution in the native protein, which, as is discussed, will tend to decrease its interaction with the solvent. Our results thus suggest, in keeping with a number of recent studies, that electrostatic interactions may play an important role in determining the native topology of a folded protein. On this basis, a simplified scoring function is derived that combines a Coulomb term with a hydrophobic contact term. This function performs as well as the more complete free energy evaluation in distinguishing the native structure from misfolded decoys. Its computational efficiency suggests that it can be used in protein structure prediction applications, and that it provides a physically well-defined alternative to statistically derived scoring functions.     

Differentiation of lipid-associating helices by use of three-dimensional molecular hydrophobicity potential calculations.

Several types of lipid-associating helices exist: transmembrane helices such as in receptor proteins, pore-forming helices in ion channel proteins, fusion-inducing peptides in viral proteins, and amphipathic helices such as in plasma apolipoproteins. In order to propose a classification of these helices according to their molecular properties, we introduce the concept of molecular hydrophobicity potential for such helical segments. The calculation of this parameter for alpha-helices enables the visualization of the hydrophobic and hydrophilic envelopes around the peptide and their three-dimensional representation by molecular graphics. We have used this parameter to differentiate between pore-forming helices with a hydrophobic envelope larger than the hydrophilic component, membrane-spanning helices surrounded almost entirely by an hydrophobic envelope, fusiogenic peptides with an hydrophobicity gradient both around the helix and along the axis, and finally, amphipathic helices with a predominantly hydrophilic envelope. The structure of the lipid-protein complexes is determined by a number of different interactions: the hydrophobic interaction of the apolar faces of the helices with lipids, the polar interaction of the hydrophilic sides of different helices with each other, and the interaction of hydrophilic residues with the aqueous solvent. The relative magnitude of the hydrophobic and hydrophilic envelopes accounts for the differences in the structure of the lipid-protein complexes. Purely hydrophobic interactions stabilize transmembrane helical segments, while hydrophobic interactions with the lipid phase and with each other are involved in the stabilization of the pore-forming helices. In contrast, both hydrophobic interactions with the lipids and hydrophilic interactions with the aqueous phase contribute to the arrangement of amphipathic helices around the edges of the discoidal lipid-apoprotein complexes.     

Conservation of inter-residue interactions and prediction of folding rates of domain repeats

Domains are the main structural and functional units of larger proteins. They tend to be contiguous in primary structure and can fold and function independently. It has been observed that 10–20% of all encoded proteins contain duplicated domains and the average pairwise sequence identity between them is usually low. In the present study, we have analyzed the structural similarity between domain repeats of proteins with known structures available in the Protein Data Bank using structure-based inter-residue interaction measures such as the number of long-range contacts, surrounding hydrophobicity, and pairwise interaction energy. We used RADAR program for detecting the repeats in a protein sequence which were further validated using Pfam domain assignments. The sequence identity between the repeats in domains ranges from 20 to 40% and their secondary structural elements are well conserved. The number of long-range contacts, surrounding hydrophobicity calculations and pairwise interaction energy of the domain repeats clearly reveal the conservation of 3-D structure environment in the repeats of domains. The proportions of mainchain–mainchain hydrogen bonds and hydrophobic interactions are also highly conserved between the repeats. The present study has suggested that the computation of these structure-based parameters will give better clues about the tertiary environment of the repeats in domains. The folding rates of individual domains in the repeats predicted using the long-range order parameter indicate that the predicted folding rates correlate well with most of the experimentally observed folding rates for the analyzed independently folded domains.     

Physicochemical evaluation of protein folds predicted by threading

Protein structure prediction remains an unsolved problem. Since prediction of the native structure seems very difficult, one usually tries to predict the correct fold of a protein. Here the "fold" is defined by the approximate backbone structure of the protein. However, physicochemical factors that determine the correct fold are not well understood. It has recently been reported that molecular mechanics energy functions combined with effective solvent terms can discriminate the native structures from misfolded ones. Using such a physicochemical energy function, we studied the factors necessary for discrimination of correct and incorrect folds. We first selected correct and incorrect folds by a conventional threading method. Then, all-atom models of those folds were constructed by simply minimizing the atomic overlaps. The constructed correct model representing the native fold has almost the same backbone structure as the native structure but differs in side-chain packing. Finally, the energy values of the constructed models were compared with that of the experimentally determined native structure. The correct model as well as the native structure showed lower energy than misfolded models. However, a large energy gap was found between the native structure and the correct model. By decomposing the energy values into their components, it was found that solvent effects such as the hydrophobic interaction or solvent shielding and the Born energy stabilized the correct model rather than the native structure. The large energetic stabilization of the native structure was attained by specific side-chain packing. The stabilization by solvent effects is small compared to that by side-chain packing. Therefore, it is suggested that in order to confidently predict the correct fold of a protein, it is also necessary to predict correct side-chain packing.     

An analysis of incorrectly folded protein models. Implications for structure predictions

Proteins with homologous amino acid sequences have similar folds and it has been assumed that an unknown three-dimensional structure can be obtained from a known homologous structure by substituting new side-chains into the polypeptide chain backbone, followed by relatively small adjustment of the model. To examine this approach of structure prediction and, more generally, to isolate the characteristics of native proteins, we constructed two incorrectly folded protein models. Sea-worm hemerythrin and the variable domain of mouse immunoglobulin K-chain, two proteins with no sequence homology, were chosen for study; the former is composed of a bundle of four alpha-helices and the latter consists of two 4-stranded beta-sheets. Using an automatic computer procedure, hemerythrin side-chains were substituted into the immunoglobulin domain and vice versa. The structures were energy-minimized with the program CHARMM and the resulting structures compared with the correctly folded forms. It was found that the incorrect side-chains can be incorporated readily into both types of structures (alpha-helices, beta-sheets) with only small structural adjustments. After constrained energy-minimization, which led to an average atomic co-ordinate shift of no more than 0.7 to 0.9 A, the incorrectly folded models arrived at potential energy values comparable to those of the correct structures. Detailed analysis of the energy results shows that the incorrect structures have less stabilizing electrostatic, van der Waals' and hydrogen-bonding interactions. The difference is particularly pronounced when the electrostatic and van der Waals' energy terms are calculated by modified equations that include an approximate representation of solvent effects. The incorrectly folded structures also have a significantly larger solvent-accessible surface and a greater fraction of non-polar side-chain atoms exposed to solvent. Examination of their interior shows that the packing of side-chains at the secondary structure interfaces, although corresponding to sterically allowed conformations, deviates from the characteristics found in normal proteins. The analysis of incorrectly folded structures has made it clear that the absence of bad non-bonded contacts, though necessary, is not sufficient to demonstrate the validity of model-built structures and that modeling of homologous structures has to be accompanied by a thorough quantitative evaluation of the results. Further, certain features that characterize native proteins are made evident by their absence in misfolded models.     

Repacking of hydrophobic residues in a stable mutant of apocytochrome b562 selected by phage-display and proteolysis

To test a hydrophobic core-directed protein design approach, we previously have used phage-display and proteolysis to select stably folded proteins from a library of mutants of apocytochrome b562. The consensus sequence of the selected mutants has hydrophilic residues at two of the three positions that are designed to form a hydrophobic core. To understand this unexpected result, we determined the high-resolution structure of one of the selected mutants using multi-dimensional nuclear magnetic resonance (NMR). The structure shows that the two hydrophilic residues in the consensus sequence were on the surface of the structure. Instead, two of their neighboring hydrophobic residues reorganized their side-chain conformations and formed the hydrophobic core. This result suggests that the hydrophobic core-directed protein design by phage-display and proteolysis is a valid method in general but alternative hydrophobic packing needs to be considered in the initial design. The unexpected repacking of the hydrophobic residues also highlights the plastic nature of protein structures.     

The investigation of the secondary structure propensities and free-energy landscapes of peptide ligands by replica exchange molecular dynamics simulations

The conformational states of two peptide sequences that bind to staphylococcal enterotoxin B are sampled by replica exchange molecular dynamic (REMD) simulations in explicit water. REMD simulations were treated with 52 replicas in the range of 280–501 K for both peptides. The conformational ensembles of both peptides are dominated by random coil, bend and turn structures with a small amount of helical structures for each temperature. In addition, while an insignificant presence of β-bridge structures were observed for both peptides, the β-sheet structure was observed only for peptide 3. The results obtained from simulations at 300 K are consistent with the experimental results obtained from circular dichroism spectroscopy. From the analysis of REMD results, we also calculated hydrophobic and hydrophilic solvent accessible surface areas for both peptides, and it was observed that the hydrophobic segments of the peptides tend to form bend or turn structures. Moreover, the free-energy landscapes of both peptides were obtained by principal component analysis to understand how the secondary structural properties change according to their complex space. From the free-energy analysis, we have found several minima for both peptides at decreased temperature. For these obvious minima of both peptides, it was observed that the random coil, bend and turn structures are still dominant and the helix, β-bridge or β-sheet structures can appear or disappear with respect to minima. On the other hand, when we compare the results of REMD with conventional MD simulations for these peptides, the configurations of peptide 3 might be trapped in energy minima during the conventional MD simulations. Hence, it can be said that the REMD simulations have provided a sufficiently high sampling efficiency.     

Correlation between sequence hydrophobicity and surface-exposure pattern of database proteins

Hydrophobicity is thought to be one of the primary forces driving the folding of proteins. On average, hydrophobic residues occur preferentially in the core, whereas polar residues tend to occur at the surface of a folded protein. By analyzing the known protein structures, we quantify the degree to which the hydrophobicity sequence of a protein correlates with its pattern of surface exposure. We have assessed the statistical significance of this correlation for several hydrophobicity scales in the literature, and find that the computed correlations are significant but far from optimal. We show that this less than optimal correlation arises primarily from the large degree of mutations that naturally occurring proteins can tolerate. Lesser effects are due in part to forces other than hydrophobicity, and we quantify this by analyzing the surface-exposure distributions of all amino acids. Lastly, we show that our database findings are consistent with those found from an off-lattice hydrophobic-polar model of protein folding.