A novel energy-based stochastic method for positioning polar protons in protein structures from X-rays

A novel automated method for the optimal placement of polar hydrogens in a protein structure is presented. The algorithm adds initially, to a protein data bank file of the protein, nonrotatable hydrogens such as peptide backbone hydrogens according to geometric considerations. Then, water protons and polar side chain protons of lysine, serine, threonine, tyrosine, aspartic acid, glutamic acid, and the C and N termini of a protein are added according to energy considerations. A unique stochastic approach has been developed to overcome a combinatorial explosion in the search for the lowest energy structure. First, the system is divided into ensembles. Each ensemble is treated separately: N conformations are sampled at random, their energies computed, whereas common components of high-energy combinations are gathered on one hand, and low-energy combinations on the other. Components that yield only high-energy conformations and do not contribute to any low energies are excluded. This is reiterated while the total amount of combinations is decreased along the iterative process. When the total number of combinations is lower than a user defined threshold, all remaining combinations are evaluated by exhaustive search. Energy evaluations use nonbonding energy expressions alone. The program was tested on five high-resolution crystal structures: bovine pancreatic trypsin inhibitor (Brookhaven Protein Data Bank file 5PTI), RNase-A (5RSA), trypsin (1NTP), and carbon monoxymyoglobin (2MB5), for which neutron diffraction structures are available, as well as phosphate binding protein (1IXH) for which very high resolution X-ray crystallography was used. The low RMS values prove the efficiency of this algorithm as a tool for positioning protons in proteins. It may be used for other biological structures.     

Patterns in ionizable side chain interactions in protein structures

In a selected set of 44 high-resolution, non-homologous protein structures, the intramolecular hydrogen bonds or salt bridges formed by ionizable amino acid side chains were identified and analyzed. The analysis was based on the investigation of several properties of the involved residues such as their solvent exposure, their belonging to a certain secondary structural element, and their position relative to the N- and C-termini of their respective structural element. It was observed that two-thirds of the interactions made by basic or acidic side chains are hydrogen bonds to polar uncharged groups. In particular, the majority (78%) of the hydrogen bonds between ionizable side chains and main chain polar groups (sch:mch bonds) involved at least one buried atom, and in 42% of the cases both interacting atoms were buried. In α-helices, the sch:mch bonds observed in the proximity of the C- and N-termini show a clear preference for acidic and basic side chains, respectively. This appears to be due to the partial charges of peptide group atoms at the termini of α-helices, which establish energetically favorable electrostatic interactions with side chain carrying opposite charge, at distances even greater than 4.5 Å. The sch:mch interactions involving ionizable side chains that belong either to β-strands or to the central part of α-helices are based almost exclusively on basic residues. This results from the presence of main chain carbonyl oxygen atoms in the protein core which have unsatisfied hydrogen bonding capabilities.     

Hydrogen bonding increases packing density in the protein interior

The contribution of hydrogen bonds and the burial of polar groups to protein stability is a controversial subject. Theoretical studies suggest that burying polar groups in the protein interior makes an unfavorable contribution to the stability, but experimental studies show that burying polar groups, especially those that are hydrogen bonded, contributes favorably to protein stability. Understanding the factors that are not properly accounted for by the theoretical models would improve the models so that they more accurately describe experimental results. It has been suggested that hydrogen bonds may contribute to protein stability, in part, by increasing packing density in the protein interior, and thereby increasing the contribution of van der Waals interactions to protein stability. To investigate the influence of hydrogen bonds on packing density, we analyzed 687 crystal structures and determined the volume of buried polar groups as a function of their extent of hydrogen bonding. Our findings show that peptide groups and polar side chains that form hydrogen bonds occupy a smaller volume than the same groups when they do not form hydrogen bonds. For example, peptide groups in which both polar groups are hydrogen bonded occupy a volume, on average, 5.2 A3 less than a peptide group that is not hydrogen bonded.     

Contribution of hydrogen bonds to protein stability

Our goal was to gain a better understanding of the contribution of the burial of polar groups and their hydrogen bonds to the conformational stability of proteins. We measured the change in stability, Δ(ΔG), for a series of hydrogen bonding mutants in four proteins: villin headpiece subdomain (VHP) containing 36 residues, a surface protein from Borrelia burgdorferi (VlsE) containing 341 residues, and two proteins previously studied in our laboratory, ribonucleases Sa (RNase Sa) and T1 (RNase T1). Crystal structures were determined for three of the hydrogen bonding mutants of RNase Sa: S24A, Y51F, and T95A. The structures are very similar to wild type RNase Sa and the hydrogen bonding partners form intermolecular hydrogen bonds to water in all three mutants. We compare our results with previous studies of similar mutants in other proteins and reach the following conclusions. (1) Hydrogen bonds contribute favorably to protein stability. (2) The contribution of hydrogen bonds to protein stability is strongly context dependent. (3) Hydrogen bonds by side chains and peptide groups make similar contributions to protein stability. (4) Polar group burial can make a favorable contribution to protein stability even if the polar groups are not hydrogen bonded. (5) The contribution of hydrogen bonds to protein stability is similar for VHP, a small protein, and VlsE, a large protein.     

Environment-specific amino acid substitution tables: tertiary templates and prediction of protein folds.

The local environment of an amino acid in a folded protein determines the acceptability of mutations at that position. In order to characterize and quantify these structural constraints, we have made a comparative analysis of families of homologous proteins. Residues in each structure are classified according to amino acid type, secondary structure, accessibility of the side chain, and existence of hydrogen bonds from the side chains. Analysis of the pattern of observed substitutions as a function of local environment shows that there are distinct patterns, especially for buried polar residues. The substitution data tables are available on diskette with Protein Science. Given the fold of a protein, one is able to predict sequences compatible with the fold (profiles or templates) and potentially to discriminate between a correctly folded and misfolded protein. Conversely, analysis of residue variation across a family of aligned sequences in terms of substitution profiles can allow prediction of secondary structure or tertiary environment.     

Some observations on conserved polar side chains in immunoglobulin V-domains

1. The roles of conserved polar residues have been studied in 12 V-domains for which atomic coordinates are available. 2. In most cases a particular residue had a similar side chain conformation in all V-domains examined and the polar group provided the same hydrogen bonds which helped to stabilize the conformations of the domains. 3. In the case of a conserved glutamine/glutamic acid residue the buried side chain could adopt a variety of conformations and the polar group could form different hydrogen bonds from one domain to another. However, they contributed similarly to domain stability. 4. In the case of a conserved threonine/serine residue its side chain showed relative rotations of up to 180 degrees from one domain to another. The hydroxyl group could be buried or exposed at the domain surface. In some domains it formed hydrogen bonds to two other protein atoms but in other domains there was a single hydrogen bond or none at all. The varied roles of this residue are discussed in the text.     

Incorporating protein conformational flexibility into the calculation of pH-dependent protein properties.

A method for combining calculations of residue pKa's with changes in the position of polar hydrogens has been developed. The Boltzmann distributions of proton positions in hydroxyls and neutral titratable residues are found in the same Monte Carlo sampling procedure that determines the amino acid ionization states at each pH. Electrostatic, Lennard-Jones potentials, and torsion angle energies are considered at each proton position. Many acidic and basic residues are found to have significant electrostatic interactions with either a water- or hydroxyl-containing side chain. Protonation state changes are coupled to reorientation of the neighboring hydroxyl dipoles, resulting in smaller free energy differences between neutral and ionized residues than when the protein is held rigid. Multiconformation pH titration gives better agreement with the experimental pKa's for triclinic hen egg lysozyme than conventional rigid protein calculations. The hydroxyl motion significantly increases the protein dielectric response, making it sensitive to the composition of the local protein structure. More than one conformer per residue is often found at a given pH, providing information about the distribution of low-energy lysozyme structures.     

The 2.8 A crystal structure of Gla-domainless activated protein C.

The structure of the Gla-domainless form of the human anticoagulant enzyme activated protein C has been solved at 2.8 A resolution. The light chain is composed of two domains: an epidermal growth factor (EGF)-like domain modified by a large insert containing an additional disulfide, followed by a typical EGF-like domain. The arrangement of the long axis of these domains describes an angle of approximately 80 degrees. Disulfide linked to the light chain is the catalytic domain, which is generally trypsin-like but contains a large insertion loop at the edge of the active site, a third helical segment, a prominent cationic patch analogous to the anion binding exosite I of thrombin and a trypsin-like Ca[II] binding site. The arrangement of loops around the active site partially restricts access to the cleft. The S2 and S4 subsites are much more polar than in factor Xa and thrombin, and the S2 site is unrestricted. While quite open and exposed, the active site contains a prominent groove, the surface of which is very polar with evidence for binding sites on the primed side, in addition to those typical of the trypsin class found on the non-primed side.     

Theory of protein molecule self-organization. I. Thermodynamic parameters of local secondary structures in the unfolded protein chain

This paper presents the results of a stereochemical analysis of local interactions in unfolded protein chains (sterical repulsions, hydrogen, and hydrophobic bonds, etc.) by means of space-filling modeles. On the basis of this analysis, an evaluation is made of thermodynamic parameters controlling the building-in of all the 20 natural amino acid residues in all the physically possible position of local secondary structures (α-helices, including α-helices with short fragments of helices 3₁₀ at the C-terminus; β-bends of different types, helices 3₁₀, and their combinations) as well as thermodynamic parameters of separate hydrogen bonds of polar side groups with the neighbor peptide groups (“local contacts”). The accuracy of the obtained results is discussed.     

Sequence determination of reduction potentials by cysteinyl hydrogen bonds and peptide pipoles in [4Fe-4S] ferredoxins.

A sequence determinant of reduction potentials is reported for bacterial [4Fe-4S]-type ferredoxins. The residue that is four residues C-terminal to the fourth ligand of either cluster is generally an alanine or a cysteine. In five experimental ferredoxin structures, the cysteine has the same structural orientation relative to the nearest cluster, which is stabilized by the SH...S bond. Although such bonds are generally considered weak, indications that Fe-S redox site sulfurs are better hydrogen-bond acceptors than most sulfurs include the numerous amide NH...S bonds noted by Adman and our quantum mechanical calculations. Furthermore, electrostatic potential calculations of 11 experimental ferredoxin structures indicate that the extra cysteine decreases the reduction potential relative to an alanine by approximately 60 mV, in agreement with experimental mutational studies. Moreover, the decrease in potential is due to a shift in the polar backbone stabilized by the SH...S bond rather than to the slightly polar cysteinyl side chain. Thus, these cysteines can "tune" the reduction potential, which could optimize electron flow in an electron transport chain. More generally, hydrogen bonds involving sulfur can be important in protein structure/function, and mutations causing polar backbone shifts can alter electrostatics and thus affect redox properties or even enzymatic activity of a protein.     

Contribution of polar groups in the interior of a protein to the conformational stability

It has been generally believed that polar residues are usually located on the surface of protein structures. However, there are many polar groups in the interior of the structures in reality. To evaluate the contribution of such buried polar groups to the conformational stability of a protein, nonpolar to polar mutations (L8T, A9S, A32S, I56T, I59T, I59S, A92S, V93T, A96S, V99T, and V100T) in the interior of a human lysozyme were examined. The thermodynamic parameters for denaturation were determined using a differential scanning calorimeter, and the crystal structures were analyzed by X-ray crystallography. If a polar group had a heavy energy cost to be buried, a mutant protein would be remarkably destabilized. However, the stability (Delta G) of the Ala to Ser and Val to Thr mutant human lysozymes was comparable to that of the wild-type protein, suggesting a low-energy penalty of buried polar groups. The structural analysis showed that all polar side chains introduced in the mutant proteins were able to find their hydrogen bond partners, which are ubiquitous in protein structures. The empirical structure-based calculation of stability change (Delta Delta G) [Takano et al. (1999) Biochemistry 38, 12698--12708] revealed that the mutant proteins decreased the hydrophobic effect contributing to the stability (Delta G(HP)), but this destabilization was recovered by the hydrogen bonds newly introduced. The present study shows the favorable contribution of polar groups with hydrogen bonds in the interior of protein molecules to the conformational stability.     

Assignment of polar states for protein amino acid residues using an interaction cluster decomposition algorithm and its application to high resolution protein structure modeling

We have developed a new method (Independent Cluster Decomposition Algorithm, ICDA) for creating all-atom models of proteins given the heavy-atom coordinates, provided by X-ray crystallography, and the pH. In our method the ionization states of titratable residues, the crystallographic mis-assignment of amide orientations in Asn/Gln, and the orientations of OH/SH groups are addressed under the unified framework of polar states assignment. To address the large number of combinatorial possibilities for the polar hydrogen states of the protein, we have devised a novel algorithm to decompose the system into independent interacting clusters, based on the observation of the crucial interdependence between the short range hydrogen bonding network and polar residue states, thus significantly reducing the computational complexity of the problem and making our algorithm tractable using relatively modest computational resources. We utilize an all atom protein force field (OPLS) and a Generalized Born continuum solvation model, in contrast to the various empirical force fields adopted in most previous studies. We have compared our prediction results with a few well-documented methods in the literature (WHATIF, REDUCE). In addition, as a preliminary attempt to couple our polar state assignment method with real structure predictions, we further validate our method using single side chain prediction, which has been demonstrated to be an effective way of validating structure prediction methods without incurring sampling problems. Comparisons of single side chain prediction results after the application of our polar state prediction method with previous results with default polar state assignments indicate a significant improvement in the single side chain predictions for polar residues.     

A view of the three dimensional structure of globular proteins

A view of the three dimensional structure of globular proteins based on continuous networks of hydrogen bonds is proposed. Active sites of enzymes and ion sites are prominent and, within the networks, there are islands of hydrophobic regions giving an overall piebald effect to the appearance of the molecule. This point of view was originally suggested by the results of quantum mechanical computations on the coupling between hydrogen bonds. A formalism for the total energy of a globular protein in water is also suggested.The study of five lines of experimental evidence supports this suggestion. The analysis of the experimental X-ray data for ten globular proteins, using the NETWORK program, revealed the existence of these hydrogen bond networks; X-ray data showed that water molecules tend to occupy fixed positions relative to the protein molecule; a survey has shown that water molecules tend to occupy specific positions relative to the hydrogen bonding side chains; experimental evidence on the bulk properties of lysozyme showed that there exist tightly bound water molecules; graphics studies of the ribonucleaseA molecule demonstrated the networks and the piebald effect. This point of view is pictorially simple and, to illustrate the use of such networks, we discuss the simple ion pairs which occur as substructures within the networks.     

Apolar and polar solvation thermodynamics related to the protein unfolding process.

Thermodynamics related to hydrated water upon protein unfolding is studied over a broad temperature range (5-125 degrees C). The hydration effect arising from the apolar interior is modeled as an increased number of hydrogen bonds between water molecules compared with bulk water. The corresponding contribution from the polar interior is modeled as a two-step process. First, the polar interior breaks hydrogen bonds in bulk water upon unfolding. Second, due to strong bonds between the polar surface and the nearest water molecules, we assume quantization using a simplified two-state picture. The heat capacity change upon hydration is compared with model compound data evaluated previously for 20 different proteins. We obtain good correspondence with the data for both the apolar and the polar interior. We note that the effective coupling constants for both models have small variations among the proteins we have investigated.     

Use of a potential of mean force to analyze free energy contributions in protein folding.

A method for calculation of the free energy of residues as a function of residue burial is proposed. The method is based on the potential of mean force, with a reaction coordinate expressed by residue burial. Residue burials are calculated from high-resolution protein structures. The largest individual contributions to the free energy of a residue are found to be due to the hydrophobic interactions of the nonpolar atoms, interactions of the main chain polar atoms, and interactions of the charged groups of residues Arg and Lys. The contribution to the free energy of folding due to the uncharged side chain polar atoms is small. The contribution to the free energy of folding due to the main chain polar atoms is favorable for partially buried residues and less favorable or unfavorable for fully buried residues. Comparison of the accessible surface areas of proteins and model spheres shows that proteins deviate considerably from a spherical shape and that the deviations increase with the size of a protein. The implications of these results for protein folding are also discussed.     

Long-range side-chain-main-chain interactions play crucial roles in stabilizing the (betaalpha)8 barrel motif of the alpha subunit of tryptophan synthase

The role of hither-to-fore unrecognized long-range hydrogen bonds between main-chain amide hydrogens and polar side chains on the stability of a well-studied (betaalpha)8, TIM barrel protein, the alpha subunit of tryptophan synthase (alphaTS), was probed by mutational analysis. The F19-D46 and I97-D124 hydrogen bonds link the N terminus of a beta-strand with the C terminus of the succeeding antiparallel alpha-helix, and the A103-D130 hydrogen bond links the N terminus of an alpha-helix with the C terminus of the succeeding antiparallel beta-strand, forming clamps for the respective betaalpha or alphabeta hairpins. The individual replacement of these aspartic acid side chains with alanine leads to what appear to be closely related partially folded structures with significantly reduced far-UV CD ellipticity and thermodynamic stability. Comparisons with the effects of eliminating another main-chain-side-chain hydrogen bond, G26-S33, and two electrostatic side-chain-side-chain hydrogen bonds, D38-H92 and D112-H146, all in the same N-terminal folding unit of alphaTS, demonstrated a unique role for the clamp interactions in stabilizing the native barrel conformation. Because neither the asparagine nor glutamic acid variant at position 46 can completely reproduce the spectroscopic, thermodynamic, or kinetic folding properties of aspartic acid, both size and charge are crucial to its unique role in the clamp hydrogen bond. Kinetic studies suggest that the three clamp hydrogen bonds act in concert to stabilize the transition state leading to the fully folded TIM barrel motif.     

The role of local hydrogen bonds in formation of irregular regions of globular protein polypeptide chains]

An assumption is made on the substantial role of local hydrogen bonds in formation of irregular regions of globular protein polypeptide chains. The statistics of the amino acid composition of irregular regions is examined from this point of view. A statistical analysis of side group-backbone hydrogen bonds is carried out for three proteins: alpha-chy-motrypsin, lysozyme and myoglobin. It is shown that short side groups participate in formation of local hydrogen bonds more often than long ones. Conformations of amino acid residues in the first and the last positions are studied in beta-bends of 9 proteins. It is shown that over 70% of these residues are in conformations corresponding to the formation of local hydrogen bonds of three types: backbone-backbone, side groupbackbone, backbone-water molecule-backbone. Thus, the participation of the cooperative hydrogen-bonding network in stabilization of beta-bends is demonstrated.     

Deterministic features of side-chain main-chain hydrogen bonds in globular protein structures

A total of 19 835 polar residues from a data set of 250 non-homologous and highly resolved protein crystal structures were used to identify side-chain main-chain (SC-MC) hydrogen bonds. The ratio of the number of SC-MC hydrogen bonds to the total number of polar residues is close to 1:2, indicating the ubiquitous nature of such hydrogen bonds. Close to 56% of the SC-MC hydrogen bonds are local involving side-chain acceptor/donor ('i') and a main-chain donor/acceptor within the window i-5 to i+5. These short-range hydrogen bonds form well defined conformational motifs characterized by specific combinations of backbone and side-chain torsion angles. (a) The Ser/Thr residues show the greatest preference in forming intra-helical hydrogen bonds between the atoms O(gamma)(i) and O(i-4). More than half the examples of such hydrogen bonds are found at the middle of alpha-helices rather than at their ends. The most favoured motif of these examples is alpha(R)alpha(R)alpha(R)alpha(R)(g(-)). (b) These residues also show great preference to form hydrogen bonds between O(gamma)(i) and O(i-3), which are closely related to the previous type and though intra-helical, these hydrogen bonds are more often found at the C-termini of helices than at the middle. The motif represented by alpha(R)alpha(R)alpha(R)alpha(R)(g(+)) is most preferred in these cases. (c) The Ser, Thr and Glu are the most frequently found residues participating in intra-residue hydrogen bonds (between the side-chain and main-chain of the same residue) which are characterized by specific motifs of the form beta(g(+)) for Ser/Thr residues and alpha(R)(g(-)g(+)t) for Glu/Gln. (d) The side-chain acceptor atoms of Asn/Asp and Ser/Thr residues show high preference to form hydrogen bonds with acceptors two residues ahead in the chain, which are characterized by the motifs beta (tt')alphaR and beta(t)alpha(R), respectively. These hydrogen bonded segments, referred to as Asx turns, are known to provide stability to type I and type I' beta-turns. (e) Ser/Thr residues often form a combination of SC-MC hydrogen bonds, with the side-chain donor hydrogen bonded to the carbonyl oxygen of its own peptide backbone and the side-chain acceptor hydrogen bonded to an amide hydrogen three residues ahead in the sequence. Such motifs are quite often seen at the beginning of alpha-helices, which are characterized by the beta(g(+))alpha(R)alpha(R) motif. A remarkable majority of all these hydrogen bonds are buried from the protein surface, away from the surrounding solvent. This strongly indicates the possibility of side-chains playing the role of the backbone, in the protein interiors, to satisfy the potential hydrogen bonding sites and maintaining the network of hydrogen bonds which is crucial to the structure of the protein.     

Secondary structures without backbone: an analysis of backbone mimicry by polar side chains in protein structures.

Backbone mimicry by the formation of closed-loop C7, C10 and C13 (mimics of gamma-, beta- and alpha-turns) conformations through side chain-main chain hydrogen bonds by polar groups is a frequent observation in protein structures. A data set of 250 non-homologous and high-resolution protein crystal structures was used to analyze these conformations for their characteristic features. Seven out of the nine polar residues (Ser, Thr, Asn, Asp, Gln, Glu and His) have hydrogen bonding groups in their side chains which can participate in such mimicry and as many as 15% of all these polar residues engage in such conformations. The distributions of dihedral angles of these mimics indicate that only certain combinations of the dihedral angles involved aid the formation of these mimics. The observed examples were categorized into various classes based on these combinations, resulting in well defined motifs. Asn and Asp residues show a very high capability to perform such backbone secondary structural mimicry. The most highly mimicked backbone structure is of the C10 conformation by the Asx residues. The mimics formed by His, Ser, Thr and Glx residues are also discussed. The role of such conformations in initiating the formation of regular secondary structures during the course of protein folding seems significant.     

Prudent modeling of core polar residues in computational protein design

Hydrogen bond interactions were surveyed in a set of protein structures. Compared to surface positions, polar side-chains at core positions form a greater number of intra-molecular hydrogen bonds. Furthermore, the majority of polar side-chains at core positions form at least one hydrogen bond to main-chain atoms that are not involved in hydrogen bonds to other main-chain atoms. Based on this structural survey, hydrogen bond rules were generated for each polar amino acid for use in protein core design. In the context of protein core design, these prudent polar rules were used to eliminate from consideration polar amino acid rotamers that do not form a minimum number of hydrogen bonds. As an initial test, the core of Escherichia coli thioredoxin was selected as a design target. For this target, the prudent polar strategy resulted in a minor increase in computational complexity compared to a strategy that did not allow polar residues. Dead-end elimination was used to identify global minimum energy conformations for the prudent polar and no polar strategies. The prudent polar strategy identified a protein sequence that was thermodynamically stabilized by 2.5 kcal/mol relative to wild-type thioredoxin and 2.2 kcal/mol relative to a thioredoxin variant whose core was designed without polar residues.