Biological meaning,statistical significance,and classification of local spatial similarities in nonhomologous proteins

We have completed an exhaustive search for the common spatial arrangements of backbone fragments (SARFs) in nonhomologous proteins. This type of local structural similarity, incorporating short fragments of backbone atoms, arranged not necessarily in the same order along the polypeptide chain, appears to be important for protein function and stability. To estimate the statistical significance of the similarities, we have introduced a similarity score. We present several locally similar structures, with a large similarity score, which have not yet been reported. On the basis of the results of pairwise comparison, we have performed hierarchical cluster analysis of protein structures. Our analysis is not limited by comparison of single chains but also includes complex molecules consisting of several subunits. The SARFs with backbone fragments from different polypeptide chains provide a stable interaction between subunits in protein molecules. In many cases the active site of enzymes is located at the same position relative to the common SARFs, implying a function of the certain SARFs as a universal interface of the protein-substrate interaction.     

Sterics and solvation winnow accessible conformational space for unfolded proteins

The magnitude of protein conformational space is over-estimated by the traditional random-coil model, in which local steric restrictions arise exclusively from interactions between adjacent chain neighbors. Using a five-state model, we assessed the extent to which steric hindrance and hydrogen bond satisfaction, energetically significant factors, impose additional conformational restrictions on polypeptide chains, beyond adjacent residues. Steric hindrance is repulsive: the distance of closest approach between any two atoms cannot be less than the sum of their van der Waals radii. Hydrogen bond satisfaction is attractive: polar backbone atoms must form hydrogen bonds, either intramolecularly or to solvent water. To gauge the impact of these two factors on the magnitude of conformational space, we systematically enumerated and classified the disfavored conformations that restrict short polyalanyl backbone chains. Applying such restrictions to longer chains, we derived a scaling law to estimate conformational restriction as a function of chain length. Disfavored conformations predicted by the model were tested against experimentally determined structures in the coil library, a non-helix, non-strand subset of the PDB. These disfavored conformations are usually absent from the coil library, and exceptions can be uniformly rationalized.     

Computational simulation of the statistical properties of unfolded proteins

A simple Monte Carlo method was used to generate ensembles of simulated polypeptide conformations that are restricted only by steric repulsion. The models used for these simulations were based on the sequences of four real proteins, ranging in size from 26 to 268 amino acid residues, and included all non-hydrogen atoms. Two sets of calculations were performed, one that included only intra-residue steric repulsion terms and those between adjacent residues, and one that included repulsion terms between all possible atom pairs, so as to explicitly account for the excluded volume effect. Excluded volume was found to increase the average radius of gyration of the chains by 20-40%, with the expansion factor increasing with chain length. Contrary to recent suggestions, however, the excluded volume effect did not greatly restrict the distribution of dihedral angles or favor native-like topologies. The average dimensions of the ensembles calculated with excluded volume were consistent with those measured experimentally for unfolded proteins of similar sizes under denaturing conditions, without introducing any adjustable scaling factor. The simulations also reproduced experimentally determined effective concentrations for the formation of disulfide bonds in reduced and unfolded proteins. The statistically generated ensembles included significant numbers of conformations that were nearly as compact as the corresponding native proteins, as well as many that were as accessible to solvent as a fully extended chain. On the other hand, conformations with as much buried surface area as the native proteins were very rare, as were highly extended conformations. These results suggest that the overall properties of unfolded proteins can be usefully described by a random coil model and that an unfolded polypeptide can undergo significant collapse while losing only a relatively small fraction of its conformational entropy.     

The role of protein homochirality in shaping the energy landscape of folding

The homochirality, or isotacticity, of the natural amino acids facilitates the formation of regular secondary structures such as alpha-helices and beta-sheets. However, many examples exist in nature where novel polypeptide topologies use both l- and d-amino acids. In this study, we explore how stereochemistry of the polypeptide backbone influences basic properties such as compactness and the size of fold space by simulating both lattice and all-atom polypeptide chains. We formulate a rectangular lattice chain model in both two and three dimensions, where monomers are chiral, having the effect of restricting local conformation. Syndiotactic chains with alternating chirality of adjacent monomers have a very large ensemble of accessible conformations characterized predominantly by extended structures. Isotactic chains on the other hand, have far fewer possible conformations and a significant fraction of these are compact. Syndiotactic chains are often unable to access maximally compact states available to their isotactic counterparts of the same length. Similar features are observed in all-atom models of isotactic versus syndiotactic polyalanine. Our results suggest that protein isotacticity has evolved to increase the enthalpy of chain collapse by facilitating compact helical states and to reduce the entropic cost of folding by restricting the size of the unfolded ensemble of competing states.     

A novel exhaustive search algorithm for predicting the conformation of polypeptide segments in proteins

We present a fast ab initio method for the prediction of local conformations in proteins. The program, PETRA, selects polypeptide fragments from a computer-generated database (APD) encoding all possible peptide fragments up to twelve amino acids long. Each fragment is defined by a representative set of eight straight phi/psi pairs, obtained iteratively from a trial set by calculating how fragments generated from them represent the protein databank (PDB). Ninety-six percent (96%) of length five fragments in crystal structures, with a resolution better than 1.5 A and less than 25% identity, have a conformer in the database with less than 1 A root-mean-square deviation (rmsd). In order to select segments from APD, PETRA uses a set of simple rule-based filters, thus reducing the number of potential conformations to a manageable total. This reduced set is scored and sorted using rmsd fit to the anchor regions and a knowledge-based energy function dependent on the sequence to be modelled. The best scoring fragments can then be optimized by minimization of contact potentials and rmsd fit to the core model. The quality of the prediction made by PETRA is evaluated by calculating both the differences in rmsd and backbone torsion angles between the final model and the native fragment. The average rmsd ranges from 1.4 A for three residue loops to 3.9 A for eight residue loops.     

Observation of residual dipolar couplings in short peptides

Residual dipolar couplings provide information on the orientation of individual bond vectors with respect to a unique set of molecular axes. We report that short peptides from 2 to 15 amino acids in length of arbitrary sequence exhibit a modest range of residual dipolar couplings when aligned in either strained polyacrylamide gels or alkyl-PEG bicelles. The absence of significant line broadening in gels suggests peptides align predominantly through steric interactions with the polyacrylamide matrix. However, broadening of NMR lines for a subset of residues aligned in bicelles indicates some peptides bind weakly to these lipid disks, yet a weak negative correlation between the couplings measured in gels and bicelles is consistent with steric hindrance playing a role in both media. The observation of dipolar couplings for peptides of length 10-15 suggests the statistical segment lengths of polypeptide chains must often be >10-15 residues, with data from denatured proteins indicating even larger values. Presumably, local side-chain backbone interactions severely restrict chain flexibility, with the cumulative effect of many such restrictions giving rise to biases in chain direction that may persist for the entire length of a protein chain. Comparison of experimental dipolar couplings for peptides with couplings calculated for ensembles of conformations generated by molecular dynamics should permit evaluation of the accuracy of molecular mechanics potentials in reproducing sequence-specific preferences for phi and psi angles.     

Local structure of cytochrome c from horse heart in solution. Conformational analysis using data of two-dimensional nuclear Overhauser effect spectroscopy]

Using the earlier suggested method the calculation of the backbone conformations of horse heart cytochrome c in oxidized (ferricytochrome c) and reduced (ferrocytochrome c) states has been performed by the two-dimensional nuclear Overhauser effect spectroscopy data. For both protein forms the secondary structure elements have been revealed and the conformations of the irregular polypeptide chain segments have been analysed. The similarity of the secondary structures of ferri- and ferrocytochrome c in solution was established from the comparison of their conformations. Small differences between the conformations of two molecule forms are shown to be localized within the polypeptide chain fragments situated in the spatial structure near the heme crevice. The comparison of the dihedral phi and psi angles in the calculated conformations of horse cytochrome C with the corresponding characteristics of X-ray structures of tuna ferri- and ferrocytochrome c made for the oxidized and reduced protein forms using the quantitative criteria testifies the similarity of their conformations in solution and crystal. In is shown that the conformational changes of the separate amino acid residues which take place as the result of the "solution-to-crystal" transition occur on the surface fragments of protein globule and do not lead to essential alterations of the secondary molecule structure.     

Stabilization of local structures by pi-CH and aromatic-backbone amide interactions involving prolyl and aromatic residues

Weakly polar interactions between the side-chain aromatic rings and hydrogens of backbone amides (Ar-HN) and CHn of aliphatic groups (pi-CH) are known to form local structures and to stabilize secondary structure in peptides and proteins. To investigate the existence of these interactions and to explore their possible role in constraining the structures of Pro-Xaa and Xaa-Pro fragments in proteins, a database search was performed in a non-redundant set of proteins from the Brookheaven Protein Data Bank for pi-CH and Ar-HN interactions in Pro-Xaa and Xaa-Pro fragments (where Xaa is either Phe, Tyr or Trp). In Xaa-Pro fragments, the percentage of pi-CH interactions and Ar-HN interactions, respectively, was 20.6 and 3.2%, in Pro-Xaa fragments 26.8, 8.6 and 4.0% of the Pro-Xaa fragments contained both interactions, while no Xaa-Pro fragments had both. The protein fragments containing Ar-HN and/or pi-CH interactions were clustered on the basis of similarity of selected torsion angles. The clustering resulted in well defined clusters. Thus, pi-CH and Ar(i)-HN(i) interactions were able to constrain individual conformations of the Pro-Xaa and Xaa-Pro fragments. These local structures were found to be independent of the secondary structure of the polypeptide chains in which the fragments were found.     

Reduced representation model of protein structure prediction: statistical potential and genetic algorithms.

A reduced representation model, which has been described in previous reports, was used to predict the folded structures of proteins from their primary sequences and random starting conformations. The molecular structure of each protein has been reduced to its backbone atoms (with ideal fixed bond lengths and valence angles) and each side chain approximated by a single virtual united-atom. The coordinate variables were the backbone dihedral angles phi and psi. A statistical potential function, which included local and nonlocal interactions and was computed from known protein structures, was used in the structure minimization. A novel approach, employing the concepts of genetic algorithms, has been developed to simultaneously optimize a population of conformations. With the information of primary sequence and the radius of gyration of the crystal structure only, and starting from randomly generated initial conformations, I have been able to fold melittin, a protein of 26 residues, with high computational convergence. The computed structures have a root mean square error of 1.66 A (distance matrix error = 0.99 A) on average to the crystal structure. Similar results for avian pancreatic polypeptide inhibitor, a protein of 36 residues, are obtained. Application of the method to apamin, an 18-residue polypeptide with two disulfide bonds, shows that it folds apamin to native-like conformations with the correct disulfide bonds formed.     

Reconstruction of protein backbones from the BriX collection of canonical protein fragments

As modeling of changes in backbone conformation still lacks a computationally efficient solution, we developed a discretisation of the conformational states accessible to the protein backbone similar to the successful rotamer approach in side chains. The BriX fragment database, consisting of fragments from 4 to 14 residues long, was realized through identification of recurrent backbone fragments from a non-redundant set of high-resolution protein structures. BriX contains an alphabet of more than 1,000 frequently observed conformations per peptide length for 6 different variation levels. Analysis of the performance of BriX revealed an average structural coverage of protein structures of more than 99% within a root mean square distance (RMSD) of 1 Angstrom. Globally, we are able to reconstruct protein structures with an average accuracy of 0.48 Angstrom RMSD. As expected, regular structures are well covered, but, interestingly, many loop regions that appear irregular at first glance are also found to form a recurrent structural motif, albeit with lower frequency of occurrence than regular secondary structures. Larger loop regions could be completely reconstructed from smaller recurrent elements, between 4 and 8 residues long. Finally, we observed that a significant amount of short sequences tend to display strong structural ambiguity between alpha helix and extended conformations. When the sequence length increases, this so-called sequence plasticity is no longer observed, illustrating the context dependency of polypeptide structures.     

Using quantum mechanics to improve estimates of amino acid side chain rotamer energies

Amino acid side chains adopt a discrete set of favorable conformations typically referred to as rotamers. The relative energies of rotamers partially determine which side chain conformations are more often observed in protein structures and accurate estimates of these energies are important for predicting protein structure and designing new proteins. Protein modelers typically calculate side chain rotamer energies by using molecular mechanics (MM) potentials or by converting rotamer probabilities from the protein database (PDB) into relative free energies. One limitation of the knowledge‐based energies is that rotamer preferences observed in the PDB can reflect internal side chain energies as well as longer‐range interactions with the rest of the protein. Here, we test an alternative approach for calculating rotamer energies. We use three different quantum mechanics (QM) methods (second order Møller‐Plesset (MP2), density functional theory (DFT) energy calculation using the B3LYP functional, and Hartree‐Fock) to calculate the energy of amino acid rotamers in a dipeptide model system, and then use these pre‐calculated values in side chain placement simulations. Energies were calculated for over 36,000 different conformations of leucine, isoleucine, and valine dipeptides with backbone torsion angles from the helical and strand regions of the Ramachandran plot. In a subset of cases these energies differ significantly from those calculated with standard molecular mechanics potentials or those derived from PDB statistics. We find that in these cases the energies from the QM methods result in more accurate placement of amino acid side chains in structure prediction tests. Proteins 2008. © 2007 Wiley‐Liss, Inc.     

Simple and versatile restraints for the accurate modeling of alpha-helical coiled-coil structures of multiple strandedness, orientation and composition

We present a minimalist approach for the modeling of the three-dimensional structure of multistranded alpha-helical coiled coils. The approach is based on empirical principles introduced by F. H. C. Crick (F. H. C. Crick, Acta Crystallogr, 1953, Vol. 6, pp. 689-697). Crick hypothesized that keeping the distance between the residues at the interacting interface of alpha-helices constant would lead to supercoiling or the formation of a coiled coil through the knobs-into-holes mode of packing. We have implemented the latter hypothesis in a simulating annealing protocol in the simple form of interhelical distance restraints (two per heptad) between Calpha at the interfacial positions and. To demonstrate the authenticity of Crick's hypothesis and the precision and accuracy of our approach, we have modeled the crystal structures of six synthetic coiled coils in dimeric, trimeric, and tetrameric states. The mean root mean square deviations (RMSDs) between the backbone atoms of the ensemble of structures calculated and those of the corresponding geometric averages is always below 0.76 A, indicating that our protocol has an excellent degree of convergence and precision. The RMSDs between the backbone atoms of each of the six geometric average structures and the backbone of the corresponding crystal structures all range between 0.43 and 0.95 A, indicative of excellent accuracy and proving the authenticity of Crick's hypothesis. Moreover, without specifying any dihedral angles, we found that in 81% of the occurrences, the most populated conformer of the side chains at positions and in the ensembles calculated were identical to those observed in the crystal structures. This shows that our simple approach, which is the simplest reported so far, can generate accurate results for the backbone and side chains. Finally, as a test case for a wider application of our approach in the field of structural proteomics, we describe the successful modeling of the overall structure of SNARE and the organization of its interfacial ionic layer known to play an important functional role.     

Criteria that discriminate between native proteins and incorrectly folded models

Various theoretical concepts, such as free energy potentials, electrostatic interaction potentials, atomic packing, solvent-exposed surface, and surface charge distribution, were tested for their ability to discriminate between native proteins and misfolded protein models. Misfolded models were constructed by introducing incorrect side chains onto polypeptide backbones: side chains of the alpha-helical hemerythrin were modeled on the beta-sheeted backbone of immunoglobulin VL domain, whereas those of the VL domain were similarly modeled on the hemerythrin backbone. CONGEN, a conformational space sampling program, was used to construct the side chains, in contrast to the previous work, where incorrect side chains were modeled in all trans conformations. Capability of the conformational search procedure to reproduce native conformations was gauged first by rebuilding (the correct) side chains in hemerythrin and the VL domain: constructs with r.m.s. differences from the x-ray side chains 2.2-2.4 A were produced, and many calculated conformations matched the native ones quite well. Incorrectly folded models were then constructed by the same conformational protocol applied to incorrect amino acid sequences. All CONGEN constructs, both correctly and incorrectly folded, were characterized by exceptionally small molecular surfaces and low potential energies. Surface charge density, atomic packing, and Coulomb formula-based electrostatic interactions of the misfolded structures and the correctly folded proteins were similar, and therefore of little interest for diagnosing incorrect folds. The following criteria clearly favored the native structures over the misfolded ones: 1) solvent-exposed side-chain nonpolar surface, 2) number of buried ionizable groups, and 3) empirical free energy functions that incorporate solvent effects.     

Folding of polypeptide chains induced by the amino acid side-chains

Conformational calculations with the use of semi-empirical potential functions have been applied to the analysis of the folding of peptide chains. In particular, the part played by the amino acid side-chains in the adoption of folded conformations has been investigated.The results show that the preferred conformations of short peptides are mostly extended ones. However, from a given peptide chain-length, the side-chain to backbone and side-chain to side-chain interactions become strong enough so that definite sequences of amino acids can induce a transition from extended to folded conformations. We propose to call these folded structures “conformational nuclei”. The type of “nucleus” formed is dependent on both the amino acid composition and the sequence.Our results strongly support the hypothesis that folding of polypeptide chains can occur through a nucleation process that could be induced by the side-chains.     

IRECS: a new algorithm for the selection of most probable ensembles of side-chain conformations in protein models

We introduce a new algorithm, IRECS (Iterative REduction of Conformational Space), for identifying ensembles of most probable side-chain conformations for homology modeling. On the basis of a given rotamer library, IRECS ranks all side-chain rotamers of a protein according to the probability with which each side chain adopts the respective rotamer conformation. This ranking enables the user to select small rotamer sets that are most likely to contain a near-native rotamer for each side chain. IRECS can therefore act as a fast heuristic alternative to the Dead-End-Elimination algorithm (DEE). In contrast to DEE, IRECS allows for the selection of rotamer subsets of arbitrary size, thus being able to define structure ensembles for a protein. We show that the selection of more than one rotamer per side chain is generally meaningful, since the selected rotamers represent the conformational space of flexible side chains. A knowledge-based statistical potential ROTA was constructed for the IRECS algorithm. The potential was optimized to discriminate between side-chain conformations of native and rotameric decoys of protein structures. By restricting the number of rotamers per side chain to one, IRECS can optimize side chains for a single conformation model. The average accuracy of IRECS for the chi1 and chi1+2 dihedral angles amounts to 84.7% and 71.6%, respectively, using a 40 degrees cutoff. When we compared IRECS with SCWRL and SCAP, the performance of IRECS was comparable to that of both methods. IRECS and the ROTA potential are available for download from the URL http://irecs.bioinf.mpi-inf.mpg.de.     

Dihedral angle preferences of amino acid residues forming various non-local interactions in proteins

In theory, a polypeptide chain can adopt a vast number of conformations, each corresponding to a set of backbone rotation angles. Many of these conformations are excluded due to steric overlaps. Ramachandran and coworkers were the first to look into this problem by plotting backbone dihedral angles in a two-dimensional plot. The conformational space in the Ramachandran map is further refined by considering the energetic contributions of various non-bonded interactions. Alternatively, the conformation adopted by a polypeptide chain may also be examined by investigating interactions between the residues. Since the Ramachandran map essentially focuses on local interactions (residues closer in sequence), out of interest, we have analyzed the dihedral angle preferences of residues that make non-local interactions (residues far away in sequence and closer in space) in the folded structures of proteins. The non-local interactions have been grouped into different types such as hydrogen bond, van der Waals interactions between hydrophobic groups, ion pairs (salt bridges), and ππ-stacking interactions. The results show the propensity of amino acid residues in proteins forming local and non-local interactions. Our results point to the vital role of different types of non-local interactions and their effect on dihedral angles in forming secondary and tertiary structural elements to adopt their native fold.     

Folding of peptide fragments comprising the complete sequence of proteins. Models for initiation of protein folding. I. Myohemerythrin.

In an attempt to delineate potential folding initiation sites for different protein structural motifs, we have synthesized series of peptides that span the entire length of the polypeptide chain of two proteins, and examined their conformational preferences in aqueous solution using proton nuclear magnetic resonance and circular dichroism spectroscopy. We describe here the behavior of peptides derived from a simple four-helix bundle protein, myohemerythrin. The peptides correspond to the sequences of the four long helices (the A, B, C and D helices), the N- and C-terminal loops and the connecting sequences between the helices. The peptides corresponding to the helices of the folded protein all exhibit preferences for helix-like conformations in solution. The conformational ensembles of the A- and D-helix peptides contain ordered helical forms, as shown by extensive series of medium-range nuclear Overhauser effect connectivities, while the B- and C-helix peptides exhibit conformational preferences for nascent helix. All four peptides adopt ordered helical conformations in mixtures of trifluoroethanol and water. The terminal and interconnecting loop peptides also appear to contain appreciable populations of conformers with backbone phi and psi angles in the alpha-region and include highly populated hydrophobic cluster and/or turn conformations in some cases. Trifluoroethanol is unable to drive these peptides towards helical conformations. Overall, the peptide fragments of myohemerythrin have a marked preference towards secondary structure formation in aqueous solution. In contrast, peptide fragments derived from the beta-sandwich protein plastocyanin are relatively devoid of secondary structure in aqueous solution (see accompanying paper). These results suggest that the two different protein structural motifs may require different propensities for formation of local elements of secondary structure to initiate folding, and that there is a prepartitioning of conformational space determined by the local amino acid sequence that is different for the helical and beta-sandwich structural motifs.     

Boltzmann-type distribution of side-chain conformation in proteins

We analyze packing imperfections in globular proteins as reflected in deviations of torsion angles from the equilibrium values for the isolated side chains. The distribution of conformations of methionine and lysine residues in a database of high-resolution structures is compared with energies of model compounds calculated with high-level quantum-mechanics. The distribution of the C-C and C-S torsion angles (chi(3)) correlates well with the Boltzmann factor of the torsion energy, exp(-betaE) of the model compounds C(2)H(5)-C(2)H(5) and C(2)H(5)-S-CH(3). An exponential relation was again found between the relative occurrence of g+, g- and t conformations for C(alpha)-C(beta) bonds in long side chains and the energy differences of rotamers of alpha-amino n-butyric acid, when dependence on backbone conformation was taken into account. The distribution of all 27 rotamers of methionine was correlated with the energy differences between the model's rotamers, corrected for clashes with nearby residues, the correlation being good for a set with backbone in the beta-conformation, but less clear for backbone alpha-conformation. In all correlations, the value of the coefficient beta corresponds to a temperature of circa 300 K. These results can be interpreted with a model that considers the structure of a folded protein as resulting from packing imperfectly complementary parts, with a requirement of an overall low energy. Compromises are required to optimize the fit of nonbonded contacts with surrounding groups, and side chains assume conformations away from the energy minimum. An exponential distribution is a most probable distribution, and this can be established easily under conditions other than thermal equilibrium.     

Lipid-binding proteins: structure of the phospholipid ligands

Dihedral angles are evaluated for the phospholipid ligands of the lipid-binding proteins found in the Protein Data Base (PDB). Phospholipid structures occur with a trans C1-C2 configuration of the glycerol backbone and oppositely extended chains, in addition to the gauche C1-C2 rotamers found in membranes. Headgroup conformations are not restricted to the single bent-down configuration and gauche-gauche configuration of the phosphodiester that is found in phospholipid crystals. Additionally, fully extended headgroups and orientations directed away from the lipid chains are found for phospholipids in the protein binding pockets. On average, the hydrocarbon chains of the protein-bound lipids are conformationally more disordered than in fluid bilayer membranes. However, much of this configurational disorder arises from energetically disallowed skew conformations. This suggests a configurational heterogeneity in the lipids at a single binding site: Eclipsed conformations occur also in some lipid headgroups and glycerol backbones. Stereochemical violations appear for some of the ester carboxyl groups of the protein-bound phospholipids in the PDB, and two glycerol backbones have the incorrect enantiomeric configuration.