Secondary structure determines protein topology

Using a test set of 13 small, compact proteins, we demonstrate that a remarkably simple protocol can capture native topology from secondary structure information alone, in the absence of long-range interactions. It has been a long-standing open question whether such information is sufficient to determine a protein's fold. Indeed, even the far simpler problem of reconstructing the three-dimensional structure of a protein from its exact backbone torsion angles has remained a difficult challenge owing to the small, but cumulative, deviations from ideality in backbone planarity, which, if ignored, cause large errors in structure. As a familiar example, a small change in an elbow angle causes a large displacement at the end of your arm; the longer the arm, the larger the displacement. Here, correct secondary structure assignments (alpha-helix, beta-strand, beta-turn, polyproline II, coil) were used to constrain polypeptide backbone chains devoid of side chains, and the most stable folded conformations were determined, using Monte Carlo simulation. Just three terms were used to assess stability: molecular compaction, steric exclusion, and hydrogen bonding. For nine of the 13 proteins, this protocol restricts the main chain to a surprisingly small number of energetically favorable topologies, with the native one prominent among them.     

Modeling structurally variable regions in homologous proteins with rosetta

A major limitation of current comparative modeling methods is the accuracy with which regions that are structurally divergent from homologues of known structure can be modeled. Because structural differences between homologous proteins are responsible for variations in protein function and specificity, the ability to model these differences has important functional consequences. Although existing methods can provide reasonably accurate models of short loop regions, modeling longer structurally divergent regions is an unsolved problem. Here we describe a method based on the de novo structure prediction algorithm, Rosetta, for predicting conformations of structurally divergent regions in comparative models. Initial conformations for short segments are selected from the protein structure database, whereas longer segments are built up by using three- and nine-residue fragments drawn from the database and combined by using the Rosetta algorithm. A gap closure term in the potential in combination with modified Newton's method for gradient descent minimization is used to ensure continuity of the peptide backbone. Conformations of variable regions are refined in the context of a fixed template structure using Monte Carlo minimization together with rapid repacking of side-chains to iteratively optimize backbone torsion angles and side-chain rotamers. For short loops, mean accuracies of 0.69, 1.45, and 3.62 A are obtained for 4, 8, and 12 residue loops, respectively. In addition, the method can provide reasonable models of conformations of longer protein segments: predicted conformations of 3A root-mean-square deviation or better were obtained for 5 of 10 examples of segments ranging from 13 to 34 residues. In combination with a sequence alignment algorithm, this method generates complete, ungapped models of protein structures, including regions both similar to and divergent from a homologous structure. This combined method was used to make predictions for 28 protein domains in the Critical Assessment of Protein Structure 4 (CASP 4) and 59 domains in CASP 5, where the method ranked highly among comparative modeling and fold recognition methods. Model accuracy in these blind predictions is dominated by alignment quality, but in the context of accurate alignments, long protein segments can be accurately modeled. Notably, the method correctly predicted the local structure of a 39-residue insertion into a TIM barrel in CASP 5 target T0186.     

Hydrogen-bonded turns in proteins: the case for a recount

Beta-turns are sites at which proteins change their overall chain direction, and they occur with high frequency in globular proteins. The Protein Data Bank has many instances of conformations that resemble beta-turns but lack the characteristic N-H(i) --> O=C(i - 3) hydrogen bond of an authentic beta-turn. Here, we identify potential hydrogen-bonded beta-turns in the coil library, a Web-accessible database utility comprised of all residues not in repetitive secondary structure, neither alpha-helix nor beta-sheet (http://www.roselab.jhu.edu/coil). In particular, candidate turns were identified as four-residue segments satisfying highly relaxed geometric criteria but lacking a strictly defined hydrogen bond. Such candidates were then subjected to a minimization protocol to determine whether slight changes in torsion angles are sufficient to shift the conformation into reference-quality geometry without deviating significantly from the original structure. This approach of applying constrained minimization to known structures reveals a substantial population of previously unidentified, stringently defined, hydrogen-bonded beta-turns. In particular, 33% of coil library residues were classified as beta-turns prior to minimization. After minimization, 45% of such residues could be classified as beta-turns, with another 8% in 3(10) helixes (which closely resemble type III beta-turns). Of the remaining coil library residues, 37% have backbone dihedral angles in left-handed polyproline II structure.     

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.     

Assembly and activation of a kinase ribozyme

RNA activities can be regulated by modulating the relative energies of all conformations in a folding landscape; however, it is often unknown precisely how peripheral elements perturb the overall landscape in the absence of discrete alternative folds (inactive ensemble). This work explores the effects of sequence and secondary structure in governing kinase ribozyme activity. Kin.46 catalyzes thiophosphoryl transfer from ATPγS onto the 5′ hydroxyl of polynucleotide substrates, and is regulated 10,000-fold by annealing an effector oligonucleotide to form activator helix P4. Transfer kinetics for an extensive series of ribozyme variants identified several dispensable internal single-stranded segments, in addition to a potential pseudoknot at the active site between segments J1/4 and J3/2 that is partially supported by compensatory rescue. Standard allosteric mechanisms were ruled out, such as formation of discrete repressive structures or docking P4 into the rest of the ribozyme via backbone 2′ hydroxyls. Instead, P4 serves both to complete an important structural element (100-fold contribution to the reaction relative to a P4-deleted variant) and to mitigate nonspecific, inhibitory effects of the single-stranded tail (an additional 100-fold contribution to the apparent rate constant, k_obs). Thermodynamic activation parameters ΔH^‡ and ΔS^‡, calculated from the temperature dependence of k_obs, varied with tail length and sequence. Inhibitory effects of the unpaired tail are largely enthalpic for short tails and are both enthalpic and entropic for longer tails. These results refine the structural view of this kinase ribozyme and highlight the importance of nonspecific ensemble effects in conformational regulation by peripheral elements.     

Physical�Cchemical determinants of coil conformations in globular proteins

We present a method with the potential to generate a library of coil segments from first principles. Proteins are built from α‐helices and/or β‐strands interconnected by these coil segments. Here, we investigate the conformational determinants of short coil segments, with particular emphasis on chain turns. Toward this goal, we extracted a comprehensive set of two‐, three‐, and four‐residue turns from X‐ray–elucidated proteins and classified them by conformation. A remarkably small number of unique conformers account for most of this experimentally determined set, whereas remaining members span a large number of rare conformers, many occurring only once in the entire protein database. Factors determining conformation were identified via Metropolis Monte Carlo simulations devised to test the effectiveness of various energy terms. Simulated structures were validated by comparison to experimental counterparts. After filtering rare conformers, we found that 98% of the remaining experimentally determined turn population could be reproduced by applying a hydrogen bond energy term to an exhaustively generated ensemble of clash‐free conformers in which no backbone polar group lacks a hydrogen‐bond partner. Further, at least 90% of longer coil segments, ranging from 5‐ to 20 residues, were found to be structural composites of these shorter primitives. These results are pertinent to protein structure prediction, where approaches can be divided into either empirical or ab initio methods. Empirical methods use database‐derived information; ab initio methods rely on physical–chemical principles exclusively. Replacing the database‐derived coil library with one generated from first principles would transform any empirically based method into its corresponding ab initio homologue.     

Detection of initiation sites in protein folding of the four helix bundle ACBP by chemical shift analysis

A simple alternative method for obtaining "random coil" chemical shifts by intrinsic referencing using the protein's own peptide sequence is presented. These intrinsic random coil backbone shifts were then used to calculate secondary chemical shifts, that provide important information on the residual secondary structure elements in the acid-denatured state of an acyl-coenzyme A binding protein. This method reveals a clear correlation between the carbon secondary chemical shifts and the amide secondary chemical shifts 3-5 residues away in the primary sequence. These findings strongly suggest transient formation of short helix-like segments, and identify unique sequence segments important for protein folding.     

Accurate computer-based design of a new backbone conformation in the second turn of protein L.

The rational design of loops and turns is a key step towards creating proteins with new functions. We used a computational design procedure to create new backbone conformations in the second turn of protein L. The Protein Data Bank was searched for alternative turn conformations, and sequences optimal for these turns in the context of protein L were identified using a Monte Carlo search procedure and an energy function that favors close packing. Two variants containing 12 and 14 mutations were found to be as stable as wild-type protein L. The crystal structure of one of the variants has been solved at a resolution of 1.9 A, and the backbone conformation in the second turn is remarkably close to that of the in silico model (1.1 A RMSD) while it differs significantly from that of wild-type protein L (the turn residues are displaced by an average of 7.2 A). The folding rates of the redesigned proteins are greater than that of the wild-type protein and in contrast to wild-type protein L the second beta-turn appears to be formed at the rate limiting step in folding.     

Folding of peptide fragments comprising the complete sequence of proteins. Models for initiation of protein folding. II. Plastocyanin.

In an attempt to understand the earliest events in the protein folding pathway, the complete sequence of French bean plastocyanin has been synthesized as a series of short peptide fragments, and the conformational preferences of each peptide examined in aqueous solution using proton n.m.r. methods. Plastocyanin consists largely of beta-sheet, with reverse turns and loops between the strands of the sheet, and one short helix. The n.m.r. experiments indicate that most of the peptides derived from the plastocyanin sequence have remarkably little propensity to adopt folded conformations in aqueous solution, in marked contrast to the peptides derived from the helical protein, myohemerythrin (accompanying paper). For most plastocyanin peptides, the backbone dihedral angles are predominantly in the beta-region of conformational space. Some of the peptides show weak NOE connectivities between adjacent amide protons, indicative of small local populations of backbone conformations in the a region of (phi,psi) space. A conformational preference for a reverse turn is seen in the sequence Ala65-Pro-Gly-Glu68, where a turn structure is found in the folded protein. Significantly, the peptide sequences that populate the alpha-region of (phi,psi) space are mostly derived from turn and loop regions in the protein. The addition of trifluoroethanol does not drive the peptides into helical conformations. In one region of the sequence, the n.m.r. spectra provide evidence of the formation of a hydrophobic cluster involving aromatic and aliphatic side-chains. These results have significance for understanding the initiation of protein folding. From these studies of the fragments of plastocyanin (this paper) and myohemerythrin (accompanying paper), it appears that there is a pre-partitioning of the conformational space sampled by the polypeptide backbone that is related to the secondary structure in the final folded state.     

Distance geometry generates native-like folds for small helical proteins using the consensus distances of predicted protein structures.

For successful ab initio protein structure prediction, a method is needed to identify native-like structures from a set containing both native and non-native protein-like conformations. In this regard, the use of distance geometry has shown promise when accurate inter-residue distances are available. We describe a method by which distance geometry restraints are culled from sets of 500 protein-like conformations for four small helical proteins generated by the method of Simons et al. (1997). A consensus-based approach was applied in which every inter-Calpha distance was measured, and the most frequently occurring distances were used as input restraints for distance geometry. For each protein, a structure with lower coordinate root-mean-square (RMS) error than the mean of the original set was constructed; in three cases the topology of the fold resembled that of the native protein. When the fold sets were filtered for the best scoring conformations with respect to an all-atom knowledge-based scoring function, the remaining subset of 50 structures yielded restraints of higher accuracy. A second round of distance geometry using these restraints resulted in an average coordinate RMS error of 4.38 A.     

Temporary secondary structures in tau,an intrinsically disordered protein

The tau protein belongs to the category of intrinsically disordered proteins, which in their native state do not have an average stable structure and fluctuate between many conformations. In its physiological state, tau helps nucleating and stabilising the microtubules in the axons of the neurons. On the other hand, the same tau is involved in the development of Alzheimer disease, when it aggregates in paired helical filaments forming fibrils, which form insoluble tangles. The beginning of the pathological aggregation of tau has been attributed to a local transition of protein portions from random coil to a β-sheet. These structures would very likely be transient; therefore, we performed a molecular dynamics simulation of tau to gather information on the existence of segments of tau endowed with a secondary structure. We combined the results of our simulation with small-angle X-ray scattering experimental data to extract from the dynamics a set of most probable conformations of tau. The analysis of these conformations highlights the presence of transient secondary structures such as turns, β-bridges, β-sheets and α-helices. It also shows that a large segment of the N-terminal region is found near the repeats domain in a globular-like shape.     

Dead‐end elimination with perturbations (DEEPer): A provable protein design algorithm with continuous sidechain and backbone flexibility

Computational protein and drug design generally require accurate modeling of protein conformations. This modeling typically starts with an experimentally determined protein structure and considers possible conformational changes due to mutations or new ligands. The DEE/A* algorithm provably finds the global minimum‐energy conformation (GMEC) of a protein assuming that the backbone does not move and the sidechains take on conformations from a set of discrete, experimentally observed conformations called rotamers. DEE/A* can efficiently find the overall GMEC for exponentially many mutant sequences. Previous improvements to DEE/A* include modeling ensembles of sidechain conformations and either continuous sidechain or backbone flexibility. We present a new algorithm, DEEPer (D ead‐E nd E limination with Per turbations), that combines these advantages and can also handle much more extensive backbone flexibility and backbone ensembles. DEEPer provably finds the GMEC or, if desired by the user, all conformations and sequences within a specified energy window of the GMEC. It includes the new abilities to handle arbitrarily large backbone perturbations and to generate ensembles of backbone conformations. It also incorporates the shear, an experimentally observed local backbone motion never before used in design. Additionally, we derive a new method to accelerate DEE/A*‐based calculations, indirect pruning, that is particularly useful for DEEPer. In 67 benchmark tests on 64 proteins, DEEPer consistently identified lower‐energy conformations than previous methods did, indicating more accurate modeling. Additional tests demonstrated its ability to incorporate larger, experimentally observed backbone conformational changes and to model realistic conformational ensembles. These capabilities provide significant advantages for modeling protein mutations and protein–ligand interactions. Proteins 2013. © 2012 Wiley Periodicals, Inc.     

Quantitative Analysis of the Conservation of the Tertiary Structure of Protein Segments

The publication of the crystallographic structure of calmodulin protein has offered an example leading us to believe that it is possible for many protein sequence segments to exhibit multiple 3D structures referred to as multi-structural segments. To this end, this paper presents statistical analysis of uniqueness of the 3D-structure of all possible protein sequence segments stored in the Protein Data Bank (PDB, Jan. of 2003, release 103) that occur at least twice and whose lengths are greater than 10 amino acids (AAs). We refined the set of segments by choosing only those that are not parts of longer segments, which resulted in 9297 segments called a sponge set. By adding 8197 signature segments, which occur uniquely in the PDB, into the sponge set we have generated a benchmark set. Statistical analysis of the sponge set demonstrates that rotating, missing and disarranging operations described in the text, result in the segments becoming multi-structural. It turns out that missing segments do not exhibit a change of shape in the 3D-structure of a multi-structural segment. We use the root mean square distance for unit vector sequence (URMSD) as an improved measure to describe the characteristics of hinge rotations, missing, and disarranging segments. We estimated the rate of occurrence for rotating and disarranging segments in the sponge set and divided it by the number of sequences in the benchmark set which is found to be less than 0.85%. Since two of the structure changing operations concern negligible number of segment and the third one is found not to have impact on the structure, we conclude that the 3D-structure of proteins is conserved statistically for more than 98% of the segments. At the same time, the remaining 2% of the sequences may pose problems for the sequence alignment based structure prediction methods.*Jishou Ruan research was supported by Liuhui Center for Applied Mathematics, China-Canada exchange program administered by MITACS and NSFC (10271061). ^#Ke Chen and Lukasz A. Kurgan research was partially supported by NSERC Canada. ^†Jack A. Tuszynkski research has been supported by MITACS, NSERC Canada and the Allard Foundation.     

Predicting the helix packing of globular proteins by self-correcting distance geometry.

A new self-correcting distance geometry method for predicting the three-dimensional structure of small globular proteins was assessed with a test set of 8 helical proteins. With the knowledge of the amino acid sequence and the helical segments, our completely automated method calculated the correct backbone topology of six proteins. The accuracy of the predicted structures ranged from 2.3 A to 3.1 A for the helical segments compared to the experimentally determined structures. For two proteins, the predicted constraints were not restrictive enough to yield a conclusive prediction. The method can be applied to all small globular proteins, provided the secondary structure is known from NMR analysis or can be predicted with high reliability.     

Protein fragment clustering and canonical local shapes

A novel clustering method is used to cluster protein fragments by shape. The centroids (mean fragments from each cluster) form a basis set of structural motifs. A database of 156,643 seven-residue fragments is used, and eight different basis sets with varying levels of resolution are generated. Coarse basis sets contain tens of centroids and provide meaningful local shapes, which are more detailed than the traditional secondary structure categories. High-resolution basis sets contain thousands of centroids and can be used to model tertiary structure of longer segments. The basis sets generated fit nontraining set proteins with the expected accuracy.     

Prediction of the membrane-spanning beta-strands of the major outer membrane protein of Chlamydia

There is preliminary experimental evidence indicating that the major outer-membrane protein (MOMP) of Chlamydia is a porin. We tested this hypothesis for the MOMP of the mouse pneumonitis serovar of Chlamydia trachomatis using two secondary structure prediction methods. First, an algorithm that calculates the mean hydrophobicity of one side of putative beta-strands predicted the positions of 16 transmembrane segments, a structure common to known porins. Second, outer loops typical of porins were assigned using an artificial neural network trained to predict the topology of bacterial outer-membrane proteins with a predominance of beta-strands. A topology model based on these results locates the four variable domains (VDs) of the MOMP on the outer loops and the five constant domains on beta-strands and the periplasmic turns. This model is consistent with genetic analysis and immunological and biochemical data that indicate the VDs are surface exposed. Furthermore, it shows significant homology with the consensus porin model of the program FORESST, which contrasts a proposed secondary structure against a data set of 349 proteins of known structure. Analysis of the MOMP of other chlamydial species corroborated our predicted model.     

Ab initio folding of terminal segments with secondary structures reveals the fine difference between two closely related all-atom statistical energy functions

One of the common methods for assessing energy functions of proteins is selection of native or near-native structures from decoys. This is an efficient but indirect test of the energy functions because decoy structures are typically generated either by sampling procedures or by a separate energy function. As a result, these decoys may not contain the global minimum structure that reflects the true folding accuracy of the energy functions. This paper proposes to assess energy functions by ab initio refolding of fully unfolded terminal segments with secondary structures while keeping the rest of the proteins fixed in their native conformations. Global energy minimization of these short unfolded segments, a challenging yet tractable problem, is a direct test of the energy functions. As an illustrative example, refolding terminal segments is employed to assess two closely related all-atom statistical energy functions, DFIRE (distance-scaled, finite, ideal-gas reference state) and DOPE (discrete optimized protein energy). We found that a simple sequence-position dependence contained in the DOPE energy function leads to an intrinsic bias toward the formation of helical structures. Meanwhile, a finer statistical treatment of short-range interactions yields a significant improvement in the accuracy of segment refolding by DFIRE. The updated DFIRE energy function yields success rates of 100% and 67%, respectively, for its ability to sample and fold fully unfolded terminal segments of 15 proteins to within 3.5 A global root-mean-squared distance from the corresponding native structures. The updated DFIRE energy function is available as DFIRE 2.0 upon request.     

Exhaustive enumeration of protein conformations using experimental restraints.

We present an efficient new algorithm that enumerates all possible conformations of a protein that satisfy a given set of distance restraints. Rapid growth of all possible self-avoiding conformations on the diamond lattice provides construction of alpha-carbon representations of a protein fold. We investigated the dependence of the number of conformations on pairwise distance restraints for the proteins crambin, pancreatic trypsin inhibitor, and ubiquitin. Knowledge of between one and two contacts per monomer is shown to be sufficient to restrict the number of candidate structures to approximately 1,000 conformations. Pairwise RMS deviations of atomic position comparisons between pairs of these 1,000 structures revealed that these conformations can be grouped into about 25 families of structures. These results suggest a new approach to assessing alternative protein folds given a very limited number of distance restraints. Such restraints are available from several experimental techniques such as NMR, NOESY, energy transfer fluorescence spectroscopy, and crosslinking experiments. This work focuses on exhaustive enumeration of protein structures with emphasis on the possible use of NOESY-determined distance restraints.