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.     

Protein synthesis rhythm.

The three-dimensional structure of a protein molecule appears to depend on the amino acid sequence of the protein in an as yet incompletely described manner. If the amino acid sequence is replaced by a numerical sequence of values representing a physical or chemical property of amino acids, the resulting numerical sequence is amenable to autocorrelation analysis. Further, if certain geometrical parameters are calculated from the three-dimensional structure of a protein to form a configurational series, pairs of property series and configurational series can be analyzed by cross-correlation techniques. The data base for the analysis was the three-dimensional structures of ten proteins as determined by X-ray crystallography. Such analysis yields the result that the hydrophobicity of an amino acid residue in a protein influences the orientation angle of the amino acid side chain. This result is consistent with the widely current “oil-drop” model of protein structure. Hydrophobicity also appears to influence the backbone dihedral angle φ, but not ψ Such a directional effect cannot be explained by a current model of information transfer in protein helices. The magnitude of the cross correlations does not appear to be satisfactory for construction of a transfer function model for the prediction of general features of protein structure from amino acid sequences.     

Reading the three-dimensional structure of lattice model-designed proteins from their amino acid sequence.

While all the information required for the folding of a protein is contained in its amino acid sequence, one has not yet learned how to extract this information to predict the detailed, biological active, three-dimensional structure of a protein whose sequence is known. Using insight obtained from lattice model simulations of the folding of small proteins (fewer than 100 residues), in particular of the fact that this phenomenon is essentially controlled by conserved contacts (Mirny et al., Proc Natl Acad Sci USA 1995;92:1282) among (few) strongly interacting ("hot") amino acids (Tiana et al., J Chem Phys 1998;108:757-761), which also stabilize local elementary structures formed early in the folding process and leading to the (postcritical) folding core when they assemble together (Broglia et al., Proc Natl Acad Sci USA 1998;95:12930, Broglia & Tiana, J Chem Phys 2001;114:7267), we have worked out a successful strategy for reading the three-dimensional structure of lattice model-designed proteins from the knowledge of only their amino acid sequence and of the contact energies among the amino acids.     

Fuzzy cluster analysis of simple physicochemical properties of amino acids for recognizing secondary structure in proteins.

Fuzzy cluster analysis has been applied to the 20 amino acids by using 65 physicochemical properties as a basis for classification. The clustering products, the fuzzy sets (i.e., classical sets with associated membership functions), have provided a new measure of amino acid similarities for use in protein folding studies. This work demonstrates that fuzzy sets of simple molecular attributes, when assigned to amino acid residues in a protein''s sequence, can predict the secondary structure of the sequence with reasonable accuracy. An approach is presented for discriminating standard folding states, using near-optimum information splitting in half-overlapping segments of the sequence of assigned membership functions. The method is applied to a nonredundant set of 252 proteins and yields approximately 73% matching for correctly predicted and correctly rejected residues with approximately 60% overall success rate for the correctly recognized ones in three folding states: alpha-helix, beta-strand, and coil. The most useful attributes for discriminating these states appear to be related to size, polarity, and thermodynamic factors. Van der Waals volume, apparent average thickness of surrounding molecular free volume, and a measure of dimensionless surface electron density can explain approximately 95% of prediction results. hydrogen bonding and hydrophobicity induces do not yet enable clear clustering and prediction.     

Relationships between sequence and structure for the four-alpha-helix bundle tertiary motif in proteins.

The sequences of four-alpha-helical bundle proteins are characterized by a pattern of hydrophilic and hydrophobic amino acids which is repeated every seven residues. At each position of the heptad repeat there are specific constraints on the amino acid properties which result from the topology of the tertiary motif. These constraints give rise to patterns of amino acid distribution which are distinct from those of other proteins. The distributions in each of the heptad positions have been determined by a statistical analysis of structural and sequence data derived from seven families of aligned protein sequences. The constitution of each position is dominated by a very small number of different amino acids, with the core positions consisting overwhelmingly of Leu and Ala. The positional preferences of the individual amino acids can be generally interpreted in terms of residue properties and topological constraints. The potential for four-alpha-helix bundle folding is reflected primarily in the pattern of residue occurrence in the heptad and not in the overall amino acid composition of the protein. Possible applications of this analysis in structure predictions, sequence alignments and in the rational design and engineering of four-alpha-helical bundle proteins are discussed.     

Computational methods for predicting structure of membrane proteins using amino acid sequences

The structure of membrane proteins specifies their functional properties, which are important for medicine and pharmacology and, therefore, is of significant interest. The repetition of transmembrane regions that consist of hydrophobic amino acids is a characteristic and organic feature of polytopic membrane proteins. The ordered repetition (periodicity) can be detected by the Fourier method applied to a digital image of the symbolic amino acid sequence of a protein. In the present work, this investigation was carried out for 24 transmembrane proteins (successfully for 14 of them). If the repetition of transmembrane regions is aperiodic, it can be revealed by another method, that is, the method of the reiterated (four to five times) averaging of the protein hydrophobicity function in a window within the limits of 9–11 amino acids that moves along the sequence. This novel method was applied to the 24 transmembrane proteins (successfully for 19 of them) and demonstrated higher suitability than the Fourier method for predicting the secondary structure of these proteins and the corresponding functional properties.     

Are the same or different amino acid residues responsible for correct and incorrect protein folding?

It has been shown for 20 proteins that amino acid residues included into the protein folding nucleus, determined experimentally, are often involved in the theoretically determined amyloidogenic fragments. For 18 proteins, Φ-values indicative of the extent of residue involvement into the folding nucleus are on average higher for amino acid residues within amyloidogenic regions. Amyloidogenic fragments were predicted for 20 proteins by two methods chosen from four on the basis of comparison of prediction of amyloidogenic regions known from experimental data. Since theoretical folding nuclei are detected by the protein three-dimensional structure and amyloidogenic regions by the protein chain primary structure, the detected regularity makes possible predictions of folding nucleation sites on the basis of amino acid sequence.     

The protein side of the central dogma: permanence and change

There are two facets to the central dogma proposed by Francis Crick in 1957. One concerns the relation between the sequence of nucleotides and the sequence of amino acids, the second is devoted to the relation between the sequence of amino acids and the native three-dimensional structure of proteins. 'Folding is simply a function of the order of the amino acids,' i.e. no information is required for the proper folding of a protein other than the information contained in its sequence. This protein side of the central dogma was elaborated in a scientific context in which the characteristics and functions of proteins, and the mechanisms of protein folding, were seen very differently. This context, which made the folding problem a simple one, supported the bold proposition of Francis Crick. The protein side of the central dogma was not challenged by the discovery of prions if one adopts the definition of information given by Francis Crick. It might have been challenged by the discovery that regulatory enzymes exist in different conformations, and the evidence for the existence of chaperones assisting protein folding. But it was not, and folding remains what it was for Francis Crick, 'simply a function of the order of amino acids'. But the meaning of 'function' has dramatically changed. It is no longer the result of simple physicochemical laws, but that of a long evolutionary process which has optimized protein folding. Molecular mechanistic explanations have to be allied with evolutionary explanations, in a way characteristic of present biology.     

Gauss-function-Based model of hydrophobicity density in proteins

The model adopting the three-dimensional Gauss function to express the hydrophobicity distribution in proteins is presented in this paper. The tendency to create the hydrophobic center during protein folding is expressed in form of an external force field of the form of three-dimensional Gauss function which directs the folding polypeptide to locate the hydrophobic residues in a central part of the molecule and hydrophilic ones exposed toward the molecular surface. The decrease of the differences between hydrophobicity distribution as it appears at each step of the folding simulation and the expected hydrophobicity distribution (three-dimensional Gauss function) is the convergence criterion together with traditional non-bonding interaction optimization. The model was applied to fold the hypothetical membrane protein (target protein in CASP6) TA0354_69_121 from Thermoplasma acidophilum.     

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.     

Single amino acid substitutions globally suppress the folding defects of temperature-sensitive folding mutants of phage P22 coat protein.

The amino acid sequence of a polypeptide defines both the folding pathway and the final three-dimensional structure of a protein. Eighteen amino acid substitutions have been identified in bacteriophage P22 coat protein that are defective in folding and cause their folding intermediates to be substrates for GroEL and GroES. These temperature-sensitive folding (tsf) substitutions identify amino acids that are critical for directing the folding of coat protein. Additional amino acid residues that are critical to the folding process of P22 coat protein were identified by isolating second site suppressors of the tsf coat proteins. Suppressor substitutions isolated from the phage carrying the tsf coat protein substitutions included global suppressors, which are substitutions capable of alleviating the folding defects of numerous tsf coat protein mutants. In addition, potential global and site-specific suppressors were isolated, as well as a group of same site amino acid substitutions that had a less severe phenotype than the tsf parent. The global suppressors were located at positions 163, 166, and 170 in the coat protein sequence and were 8-190 amino acid residues away from the tsf parent. Although the folding of coat proteins with tsf amino acid substitutions was improved by the global suppressor substitutions, GroEL remained necessary for folding. Therefore, we believe that the global suppressor sites identify a region that is critical to the folding of coat protein.     

Amino acid sequence predicts folding rate for middle-size two-state proteins

The significant correlation between protein folding rates and the sequence-predicted secondary structure suggests that folding rates are largely determined by the amino acid sequence. Here, we present a method for predicting the folding rates of proteins from sequences using the intrinsic properties of amino acids, which does not require any information on secondary structure prediction and structural topology. The contribution of residue to the folding rate is expressed by the residue's Omega value. For a given residue, its Omega depends on the amino acid properties (amino acid rigidity and dislike of amino acid for secondary structures). Our investigation achieves 82% correlation with folding rates determined experimentally for simple, two-state proteins studied until the present, suggesting that the amino acid sequence of a protein is an important determinant of the protein-folding rate and mechanism.     

Alignment of protein sequences using secondary structure: a modified dynamic programming method

A method for comparison of protein sequences based on their primary and secondary structure is described. Protein sequences are annotated with predicted secondary structures (using a modified Chou and Fasman method). Two lettered code sequences are generated (Xx, where X is the amino acid and x is its annotated secondary structure). Sequences are compared with a dynamic programming method (STRALIGN) that includes a similarity matrix for both the amino acids and secondary structures. The similarity value for each paired two-lettered code is a linear combination of similarity values for the paired amino acids and their annotated secondary structures. The method has been applied to eight globin proteins (28 pairs) for which the X-ray structure is known. For protein pairs with high primary sequence similarity (greater than 45%), STRALIGN alignment is identical to that obtained by a dynamic programming method using only primary sequence information. However, alignment of protein pairs with lower primary sequence similarity improves significantly with the addition of secondary structure annotation. Alignment of the pair with the least primary sequence similarity of 16% was improved from 0 to 37% 'correct' alignment using this method. In addition, STRALIGN was successfully applied to seven pairs of distantly related cytochrome c proteins, and three pairs of distantly related picornavirus proteins.     

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.     

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.     

Prediction of the three-dimensional structure of proteins using the electrostatic screening model and hierarchic condensation

We describe a method for predicting the three-dimensional (3-D) structure of proteins from their sequence alone. The method is based on the electrostatic screening model for the stability of the protein main-chain conformation. The free energy of a protein as a function of its conformation is obtained from the potentials of mean force analysis of high-resolution x-ray protein structures. The free energy function is simple and contains only 44 fitted coefficients. The minimization of the free energy is performed by the torsion space Monte Carlo procedure using the concept of hierarchic condensation. The Monte Carlo minimization procedure is applied to predict the secondary, super-secondary, and native 3-D structures of 12 proteins with 28–110 amino acids. The 3-D structures of the majority of local secondary and super-secondary structures are predicted accurately. This result suggests that control in forming the native-like local structure is distributed along the entire protein sequence. The native 3-D structure is predicted correctly for 3 of 12 proteins composed mainly from the α-helices. The method fails to predict the native 3-D structure of proteins with a predominantly β secondary structure. We suggest that the hierarchic condensation is not an appropriate procedure for simulating the folding of proteins made up primarily from β-strands. The method has been proved accurate in predicting the local secondary and super-secondary structures in the blind ab initio 3-D prediction experiment. Proteins 31:74–96, 1998. © 1998 Wiley-Liss, Inc.     

Conformational preference functions for predicting helices in membrane proteins

A suite of FORTRAN programs, PREF, is described for calculating preference functions from the data base of known protein structures and for comparing smoothed profiles of sequence-dependent preferences in proteins of unknown structure. Amino acid preferences for a secondary structure are considered as functions of a sequence environment. Sequence environment of amino acid residue in a protein is defined as an average over some physical, chemical, or statistical property of its primary structure neighbors. The frequency distribution of sequence environments in the data base of soluble protein structures is approximately normal for each amino acid type of known secondary conformation. An analytical expression for the dependence of preferences on sequence environment is obtained after each frequency distribution is replaced by corresponding Gaussian function. The preference for the α-helical conformation increases for each amino acid type with the increase of sequence environment of buried solvent-accessible surface areas. We show that a set of preference functions based on buried surface area is useful for predicting folding motifs in α-class proteins and in integral membrane proteins. The prediction accuracy for helical residues is 79% for 5 integral membrane proteins and 74% for 11 α-class soluble proteins. Most residues found in transmembrane segments of membrane proteins with known α-helical structure are predicted to be indeed in the helical conformation because of very high middle helix preferences. Both extramembrane and transmembrane helices in the photosynthetic reaction center M and L subunits are correctly predicted. We point out in the discussion that our method of conformational preference functions can identify what physical properties of the amino acids are important in the formation of particular secondary structure elements. © 1993 John Wiley & Sons, Inc.     

Underlying Hydrophobic Sequence Periodicity of Protein Tertiary Structure

Abstract

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.     

A protein sequence that can encode native structure by disfavoring alternate conformations

The linear sequence of amino acids contains all the necessary information for a protein to fold into its unique three-dimensional structure. Native protein sequences are known to accomplish this by promoting the formation of stable, kinetically accessible structures. Here we describe a Pro residue in the center of the third transmembrane helix of the cystic fibrosis transmembrane conductance regulator that promotes folding by a distinct mechanism: disfavoring the formation of a misfolded structure. The generality of this mechanism is supported by genome-wide transmembrane sequence analyses. Furthermore, the results provide an explanation for the increased frequency of Pro residues in transmembrane alpha-helices. Incorporation by nature of such 'negative folding determinants', aimed at preventing the formation of off-pathway structures, represents an additional mechanism by which folding information is encoded within the evolved sequences of proteins.