Beta-strand interfaces of non-dimeric protein oligomers are characterized by scattered charged residue patterns

Protein oligomers are formed either permanently, transiently or even by default. The protein chains are associated through intermolecular interactions constituting the protein interface. The protein interfaces of 40 soluble protein oligomers of stœchiometries above two are investigated using a quantitative and qualitative methodology, which analyzes the x-ray structures of the protein oligomers and considers their interfaces as interaction networks. The protein oligomers of the dataset share the same geometry of interface, made by the association of two individual β-strands (β-interfaces), but are otherwise unrelated. The results show that the β-interfaces are made of two interdigitated interaction networks. One of them involves interactions between main chain atoms (backbone network) while the other involves interactions between side chain and backbone atoms or between only side chain atoms (side chain network). Each one has its own characteristics which can be associated to a distinct role. The secondary structure of the β-interfaces is implemented through the backbone networks which are enriched with the hydrophobic amino acids favored in intramolecular β-sheets (MCWIV). The intermolecular specificity is provided by the side chain networks via positioning different types of charged residues at the extremities (arginine) and in the middle (glutamic acid and histidine) of the interface. Such charge distribution helps discriminating between sequences of intermolecular β-strands, of intramolecular β-strands and of β-strands forming β-amyloid fibers. This might open new venues for drug designs and predictive tool developments. Moreover, the β-strands of the cholera toxin B subunit interface, when produced individually as synthetic peptides, are capable of inhibiting the assembly of the toxin into pentamers. Thus, their sequences contain the features necessary for a β-interface formation. Such β-strands could be considered as ‘assemblons’, independent associating units, by homology to the foldons (independent folding unit). Such property would be extremely valuable in term of assembly inhibitory drug development.     

Discrete restraint-based protein modeling and the Calpha-trace problem

We present a novel de novo method to generate protein models from sparse, discretized restraints on the conformation of the main chain and side chain atoms. We focus on Calpha-trace generation, the problem of constructing an accurate and complete model from approximate knowledge of the positions of the Calpha atoms and, in some cases, the side chain centroids. Spatial restraints on the Calpha atoms and side chain centroids are supplemented by constraints on main chain geometry, phi/xi angles, rotameric side chain conformations, and inter-atomic separations derived from analyses of known protein structures. A novel conformational search algorithm, combining features of tree-search and genetic algorithms, generates models consistent with these restraints by propensity-weighted dihedral angle sampling. Models with ideal geometry, good phi/xi angles, and no inter-atomic overlaps are produced with 0.8 A main chain and, with side chain centroid restraints, 1.0 A all-atom root-mean-square deviation (RMSD) from the crystal structure over a diverse set of target proteins. The mean model derived from 50 independently generated models is closer to the crystal structure than any individual model, with 0.5 A main chain RMSD under only Calpha restraints and 0.7 A all-atom RMSD under both Calpha and centroid restraints. The method is insensitive to randomly distributed errors of up to 4 A in the Calpha restraints. The conformational search algorithm is efficient, with computational cost increasing linearly with protein size. Issues relating to decoy set generation, experimental structure determination, efficiency of conformational sampling, and homology modeling are discussed.     

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.     

Heterogeneity of packing: structural approach.

Analysis of the heterogeneity of packing in proteins showed that different groups of the protein preferentially contribute to low- or high-density regions. Statistical distribution reveals the two preferable values for packing density in the form of two peaks. One peak occurs in the range of densities 0.55-0.65, the other occurs in the range 0.75-0.8. The high-density peak is originated primarily by high packing inside the hydrogen bonded backbone and to some extent by side chains. Polar/charged and apolar side chains both contribute to the low-density peak. The average packing density values of individual atomic groups significantly vary for backbone atoms as well as for side chain atoms. The carbonyl oxygen atoms of protein backbone and the end groups of side chains show lower packing density than the rest of the protein. The side-chain atomic groups of a secondary structure element when packed against the neighboring secondary structure element form stronger contacts with the side chains of this element than with its backbone. Analysis of the low-density regions around each buried peptide group was done for the set of proteins with different types of packing, including alpha-alpha, alpha-beta, and beta-beta packing. It was shown that cavities are regularly situated in the groove of secondary structure element packed against neighboring elements for all types of packing. Low density in the regions surrounding the peptide groups and the end groups of side chains can be explained by their positioning next to a cavity formed upon the association of secondary structure elements. The model proposed can be applied to the analysis of protein internal motions, mechanisms of cellular signal transduction, diffusion through protein matrix, and other events.     

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.     

Environment and exposure to solvent of protein atoms. Lysozyme and insulin

A computer program is described for calculating the environment and the exposure to solvent of atoms of a protein. The computation is based on the atomic co-ordinates of the protein and on assumptions like those of Lee &; Richards (1971). Results for lysozyme and insulin are presented. Changes in exposure to solvent and in the nature of contacts that develop through folding, association reactions and crystallization are described numerically. The computations suggest several generalizations. (a) Lattice contacts within the protein crystal are characterized by a significantly smaller involvement of non-polar side chains and a proportionately greater involvement of ionizable side chains than is found for protein folding or for protein association reactions important for biological function, (b) In helical regions the carbonyl oxygen of the first residue in the helix has high probability of being shielded from solvent, (c) Glycine is among the residues having exposure least affected by folding; this accords with the expectation that it lies at bends of the peptide chain on the surface of the molecule.     

Minimal ensembles of side chain conformers for modeling protein–protein interactions

The goal of this article is to reduce the complexity of the side chain search within docking problems. We apply six methods of generating side chain conformers to unbound protein structures and determine their ability of obtaining the bound conformation in small ensembles of conformers. Methods are evaluated in terms of the positions of side chain end groups. Results for 68 protein complexes yield two important observations. First, the end‐group positions change less than 1 Å on association for over 60% of interface side chains. Thus, the unbound protein structure carries substantial information about the side chains in the bound state, and the inclusion of the unbound conformation into the ensemble of conformers is very beneficial. Second, considering each surface side chain separately in its protein environment, small ensembles of low‐energy states include the bound conformation for a large fraction of side chains. In particular, the ensemble consisting of the unbound conformation and the two highest probability predicted conformers includes the bound conformer with an accuracy of 1 Å for 78% of interface side chains. As more than 60% of the interface side chains have only one conformer and many others only a few, these ensembles of low‐energy states substantially reduce the complexity of side chain search in docking problems. This approach was already used for finding pockets in protein–protein interfaces that can bind small molecules to potentially disrupt protein–protein interactions. Side‐chain search with the reduced search space will also be incorporated into protein docking algorithms. Proteins 2012. © 2011 Wiley Periodicals, Inc.     

Intermolecular interactions between protein and other molecules including hydration effects

The structural aspects of protein functions, e.g., molecular recognition such as enzyme-substrate and antibody-antigen interactions, are elucidated in terms of dehydration and atomic interactions. When a protein interacts with some target molecule, water molecules at the interacting regions of both molecules are removed, with loss of the hydration free energy, but gaining atomic interactions between atoms of the contact sites in both molecules. The free energies of association originating from the dehydration and interactions between the atoms can be computed from changes in the accessible surface areas of the atoms involved. The free energy due to interactions between atomic groups at the contact sites is estimated as the sum of those estimated from the changes in the accessible surface area of 7 atomic groups, assuming that the interactions are proportional to the change of the area. The chain enthalpies and entropies evaluated from experimental thermodynamic properties and hydration quantities at the standard temperature for 10 proteins were available to determine the proportional constants for the atomic groups. This method was applied to the evaluation of association constants for the dimerization of proteins and the formation of proteolytic enzyme-inhibitor complexes, and the computed constants were in agreement with the experimental ones. However, the method is not accurate enough to account quantitatively for the change in the thermal stability of mutants of T4 lysozyme. Nevertheless, this method provides a way to elucidate the interactions between molecules in solution.     

A three dimensional visualisation approach to protein heavy-atom structure reconstruction

Background

A commonly recurring problem in structural protein studies, is the determination of all heavy atom positions from the knowledge of the central α-carbon coordinates.

Results

We employ advances in virtual reality to address the problem. The outcome is a 3D visualisation based technique where all the heavy backbone and side chain atoms are treated on equal footing, in terms of the C_α coordinates. Each heavy atom is visualised on the surfaces of a different two-sphere, that is centered at another heavy backbone and side chain atoms. In particular, the rotamers are visible as clusters, that display a clear and strong dependence on the underlying backbone secondary structure.

Conclusions

We demonstrate that there is a clear interdependence between rotameric states and secondary structure. Our method easily detects those atoms in a crystallographic protein structure which are either outliers or have been likely misplaced, possibly due to radiation damage. Our approach forms a basis for the development of a new generation, visualization based side chain construction, validation and refinement tools. The heavy atom positions are identified in a manner which accounts for the secondary structure environment, leading to improved accuracy.

     

Buried water in homologous serine proteases.

Buried water molecules in the structurally homologous family of eukaryotic serine proteases were examined to determine whether buried waters and their protein environments are conserved in these proteins. We found 16 equivalent water sites conserved in trypsin/ogen, chymotrypsin/ogen, elastase, kallikrein, thrombin, rat tonin and rat mast cell protease, and 5 additional water sites in enzymes which share the primary specificity of trypsin. Based on an alignment of 30 serine protease sequences, it appears that the protein environments of these 21 conserved buried waters are highly conserved. The protein environments of buried waters are comprised primarily of atoms from highly conserved residues or main chain atoms from nonconserved residues. In one instance, the protein environment of a water is conserved even in the presence of an unlikely Pro/Ala substitution. We also note 3 instances in which a histidine side chain substitutes for water, suggesting that the structural role of water at these sites is satisfied by the presence of an alternative hydrogen bonding partner. Buried waters appear to be integral structural components of these proteins and should be incorporated into protein structures predicted on the basis of sequence homology to this family, including the catalytic domains of coagulation proteases.     

A rewired green fluorescent protein: folding and function in a nonsequential, noncircular GFP permutant

The sequential order of secondary structural elements in proteins affects the folding and activity to an unknown extent. To test the dependence on sequential connectivity, we reconnected secondary structural elements by their solvent-exposed ends, permuting their sequential order, called "rewiring". This new protein design strategy changes the topology of the backbone without changing the core side chain packing arrangement. While circular and noncircular permutations have been observed in protein structures that are not related by sequence homology, to date no one has attempted to rationally design and construct a protein with a sequence that is noncircularly permuted while conserving three-dimensional structure. Herein, we show that green fluorescent protein can be rewired, still functionally fold, and exhibit wild-type fluorescence excitation and emission spectra.     

Mechanical property of a TIM-barrel protein

The mechanical response of a TIM-barrel protein to an applied pressure has been studied. We generated structures under an applied pressure by assuming the volume change to be a linear function of normal mode variables. By Delaunay tessellation, the space occupied by protein atoms is divided uniquely into tetrahedra, whose four vertices correspond to atomic positions. Based on the atoms that define them, the resulting Delaunay tetrahedra are classified as belonging to various secondary structures in the protein. The compressibility of various regions identified with respect to secondary structural elements in this protein is obtained from volume changes of respective regions in two structures with and without an applied pressure. We found that the β barrel region located at the core of the protein is quite soft. The interior of the β barrel, occupied by side chains of β strands, is the softest. The helix, strand, and loop segments themselves are extremely rigid, while the regions existing between these secondary structural elements are soft. These results suggest that the regions between secondary structural elements play an important role in protein dynamics. Another aspect of tetrahedra, referred to as bond distance, is introduced to account for rigidities of the tetrahedra. Bond distance is a measure of separation of the atoms of a tetrahedron in terms of number of bonds along the polypeptide chain or side chains. Tetrahedra with longer bond distances are found to be softer on average. From this behavior, we derive a simple empirical equation, which well describes the compressibilities of various regions. © 1997 Wiley-Liss Inc.     

Hydrophobic‐hydrophilic forces in protein folding

The process of protein folding is obviously driven by forces exerted on the atoms of the amino‐acid chain. These forces arise from interactions with other parts of the protein itself (direct forces), as well as from interactions with the solvent (solvent‐induced forces). We present a statistical–mechanical formalism that describes both these direct and indirect, solvent‐induced thermodynamic forces on groups of the protein. We focus on 2 kinds of protein groups, commonly referred to as hydrophobic and hydrophilic. Analysis of this result leads to the conclusion that the forces on hydrophilic groups are in general stronger than on hydrophobic groups. This is then tested and verified by a series of molecular dynamics simulations, examining both hydrophobic alkanes of different sizes and hydrophilic moieties represented by polar‐neutral hydroxyl groups. The magnitude of the force on assemblies of hydrophilic groups is dependent on their relative orientation: with 2 to 4 times larger forces on groups that are able to form one or more direct hydrogen bonds.     

Building proteins from C alpha coordinates using the dihedral probability grid Monte Carlo method.

Dihedral probability grid Monte Carlo (DPG-MC) is a general-purpose method of conformational sampling that can be applied to many problems in peptide and protein modeling. Here we present the DPG-MC method and apply it to predicting complete protein structures from C alpha coordinates. This is useful in such endeavors as homology modeling, protein structure prediction from lattice simulations, or fitting protein structures to X-ray crystallographic data. It also serves as an example of how DPG-MC can be applied to systems with geometric constraints. The conformational propensities for individual residues are used to guide conformational searches as the protein is built from the amino-terminus to the carboxyl-terminus. Results for a number of proteins show that both the backbone and side chain can be accurately modeled using DPG-MC. Backbone atoms are generally predicted with RMS errors of about 0.5 A (compared to X-ray crystal structure coordinates) and all atoms are predicted to an RMS error of 1.7 A or better.     

Fitting protein chains to cubic lattice is NP-complete

It is known that folding a protein chain into a cubic lattice is an NP-complete problem. We consider a seemingly easier problem: given a three-dimensional (3D) fold of a protein chain (coordinates of its C(alpha) atoms), we want to find the closest lattice approximation of this fold. This problem has been studied under names such as "lattice approximation of a protein chain", "the protein chain fitting problem", and "building of protein lattice models". We show that this problem is NP-complete for the cubic lattice with side close to 3.8 A and coordinate root mean square deviation.     

Computer simulations of protein folding with a small number of distance restraints

A high coordination lattice model was used to represent the protein chain. Lattice points correspond to amino-acid side groups. A complicated force field was designed in order to reproduce a protein-like behavior of the chain. Long-distance tertiary restraints were also introduced into the model. The Replica Exchange Monte Carlo method was applied to find the lowest energy states of the folded chain and to solve the problem of multiple minima. In this method, a set of replicas of the model chain was simulated independently in different temperatures with the exchanges of replicas allowed. The model chains, which consisted of up to 100 residues, were folded to structures whose root-mean-square deviation (RMSD) from their native state was between 2.5 and 5 A. Introduction of restrain based on the positions of the backbone hydrogen atoms led to an improvement in the number of successful simulation runs. A small improvement (about 0.5 A) was also achieved in the RMSD of the folds. The proposed method can be used for the refinement of structures determined experimentally from NMR data.     

Effects of hydrated water on protein unfolding

The conformational stability of a protein in aqueous solution is described in terms of the thermodynamic properties such as unfolding Gibbs free energy, which is the difference in the free energy (Gibbs function) between the native and random conformations in solution. The properties are composed of two contributions, one from enthalpy due to intramolecular interactions among constituent atoms and chain entropy of the backbone and side chains, and the other from the hydrated water around a protein molecule. The hydration free energy and enthalpy at a given temperature for a protein of known three-dimensional structure can be calculated from the accessible surface areas of constituent atoms according to a method developed recently. Since the hydration free energy and enthalpy for random conformations are computed from those for an extended conformation, the thermodynamic properties of unfolding are evaluated quantitatively. The evaluated hydration properties for proteins of known transition temperature (Tm) and unfolding enthalpy (delta Hm) show an approximately linear dependence on the number of constituent heavy atoms. Since the unfolding free energy is zero at Tm, the enthalpy originating from interatomic interactions of a polypeptide chain and the chain entropy are evaluated from an experimental value of delta Hm and computed properties due to the hydrated water around the molecule at Tm. The chain enthalpy and entropy thus estimated are largely compensated by the hydration enthalpy and entropy, respectively, making the unfolding free energy and enthalpy relatively small. The computed temperature dependences of the unfolding free energy and enthalpy for RNase A, T4 lysozyme, and myoglobin showed a good agreement with the experimental ones.(ABSTRACT TRUNCATED AT 250 WORDS)     

A method to search for similar protein local structures at ligand-binding sites and its application to adenine recognition

We have developed a method of searching for similar spatial arrangements of atoms around a given chemical moiety in proteins that bind a common ligand. The first step in this method is to consider a set of atoms that closely surround a given chemical moiety. Then, to compare the spatial arrangements of such surrounding atoms in different proteins, they are translated and rotated so that the chemical moieties are superposed on each other. Spatial arrangements of surrounding atoms in a pair of proteins are judged to be similar, when there are many corresponding atoms occupying similar spatial positions. Because the method focuses on the arrangements of surrounding atoms, it can detect structural similarities of binding sites in proteins that are dissimilar in their amino acid sequences or in their chain folds. We have applied this method to identify modes of nucleotide base recognition by proteins. An all-against-all comparison of the arrangements of atoms surrounding adenine moieties revealed an unexpected structural similarity between protein kinases, cAMP-dependent protein kinase (cAPK), and casein kinase-1 (CK1), and D-Ala:D-Ala ligase (DD-ligase) at their adenine-binding sites, despite a lack of similarity in their chain folds. The similar local structure consists of a four-residue segment and three sequentially separated residues. In particular the four-residue segments of these enzymes were found to have nearly identical conformations in their backbone parts, which are involved in the recognition of adenine. This common local structure was also found in substrate-free three-dimensional structures of other proteins that are similar to DD-ligase in the chain fold and of other protein kinases. As the proteins with different folds were found to share a common local structure, these proteins seem to constitute a remarkable example of convergent evolution for the same recognition mechanism. Received: 9 December 1996 / Accepted: 7 February 1997     

Refinement of the structure of Escherichia coli-derived rat intestinal fatty acid binding protein with bound oleate to 1.75-A resolution. Correlation with the structures of the apoprotein and the protein with bound palmitate.

The structure of rat intestinal fatty acid binding protein (I-FABP) with bound oleate (C18:1) has been refined with x-ray diffraction data to a resolution of 1.75 A. The protein contains 10 anti-parallel beta strands composed of 99 residues and 2 short helices of 14 residues. Oleate is located in the interior of the protein in a bent conformation with C1-C12 more ordered than C13-C18. Two of the eight ordered waters in I-FABP:oleate are part of a hydrogen bond network that includes the carboxylate of oleate, the guanidinium group of Arg106, the nitrogen of the indole group of Trp82, and the side chain of Gln115. Most of the methylenes of bound oleate reside in a crevice formed by hydrophobic and aromatic side chains. Tyr70 and Tyr117 envelop the acyl chain from C3 to C8 forming contacts with both the convex and concave faces of its van der Waals surface. The hydroxyls of each phenolic side chain hydrogen bond to ordered water molecules. Two ordered waters make van der Waals contact with the concave face of the bound fatty acid. The omega-terminal methyl of oleate is oriented so that it points toward the center of the benzene of Phe55 allowing it to form van der Waals interactions with its component methylenes. Comparison of the structure of I-FABP:oleate with a recently refined 1.19-A model of apoI-FABP and an earlier 2.0-A model of I-FABP:palmitate revealed a remarkable degree of similarity in the positions of their main chain and side chain atoms and in the conformations of the bound oleate and palmitate. The principal differences were confined to a few discrete regions of the protein. The helical domain, the type I turn between beta strands C and D, and the ring of Phe55 together form a solvent-accessible portal to the interior of the protein. They are repositioned in I-FABP:oleate (and I-FABP:palmitate) so that the binding cavity is even more accessible to solvent and its volume is increased. The side chain of Phe55 which shows discrete disorder in the apoprotein functions as an omega-terminal "sensing device": moving progressively outward toward the surface as the chain length of the bound fatty acid increases by 2 methylenes. Tyr70 and Tyr117 which also show discrete disorder in the apoprotein structure due to rotation around their C alpha-C beta bonds, are stabilized in a single, well ordered position in the holoproteins.(ABSTRACT TRUNCATED AT 400 WORDS)