Loopholes and missing links in protein modeling

This paper provides an unbiased comparison of four commercially available programs for loop sampling, Prime, Modeler, ICM, and Sybyl, each of which uses a different modeling protocol. The study assesses the quality of results and examines the relative strengths and weaknesses of each method. The set of loops to be modeled varied in length from 4-12 amino acids. The approaches used for loop modeling can be classified into two methodologies: ab initio loop generation (Modeler and Prime) and database searches (Sybyl and ICM). Comparison of the modeled loops to the native structures was used to determine the accuracy of each method. All of the protocols returned similar results for short loop lengths (four to six residues), but as loop length increased, the quality of the results varied among the programs. Prime generated loops with RMSDs <2.5 A for loops up to 10 residues, while the other three methods met the 2.5 A criteria at seven-residue loops. Additionally, the ability of the software to utilize disulfide bonds and X-ray crystal packing influenced the quality of the results. In the final analysis, the top-ranking loop from each program was rarely the loop with the lowest RMSD with respect to the native template, revealing a weakness in all programs to correctly rank the modeled loops.     

Conformational analysis and clustering of short and medium size loops connecting regular secondary structures: a database for modeling and prediction.

Loops are regions of nonrepetitive conformation connecting regular secondary structures. We identified 2,024 loops of one to eight residues in length, with acceptable main-chain bond lengths and peptide bond angles, from a database of 223 protein and protein-domain structures. Each loop is characterized by its sequence, main-chain conformation, and relative disposition of its bounding secondary structures as described by the separation between the tips of their axes and the angle between them. Loops, grouped according to their length and type of their bounding secondary structures, were superposed and clustered into 161 conformational classes, corresponding to 63% of all loops. Of these, 109 (51% of the loops) were populated by at least four nonhomologous loops or four loops sharing a low sequence identity. Another 52 classes, including 12% of the loops, were populated by at least three loops of low sequence similarity from three or fewer nonhomologous groups. Loop class suprafamilies resulting from variations in the termini of secondary structures are discussed in this article. Most previously described loop conformations were found among the classes. New classes included a 2:4 type IV hairpin, a helix-capping loop, and a loop that mediates dinucleotide-binding. The relative disposition of bounding secondary structures varies among loop classes, with some classes such as beta-hairpins being very restrictive. For each class, sequence preferences as key residues were identified; those most frequently at these conserved positions than in proteins were Gly, Asp, Pro, Phe, and Cys. Most of these residues are involved in stabilizing loop conformation, often through a positive phi conformation or secondary structure capping. Identification of helix-capping residues and beta-breakers among the highly conserved positions supported our decision to group loops according to their bounding secondary structures. Several of the identified loop classes were associated with specific functions, and all of the member loops had the same function; key residues were conserved for this purpose, as is the case for the parvalbumin-like calcium-binding loops. A significant number, but not all, of the member loops of other loop classes had the same function, as is the case for the helix-turn-helix DNA-binding loops. This article provides a systematic and coherent conformational classification of loops, covering a broad range of lengths and all four combinations of bounding secondary structure types, and supplies a useful basis for modelling of loop conformations where the bounding secondary structures are known or reliably predicted.     

Self-organization of domain structures by DNA-loop-extruding enzymes

The long chromosomal DNAs of cells are organized into loop domains much larger in size than individual DNA-binding enzymes, presenting the question of how formation of such structures is controlled. We present a model for generation of defined chromosomal loops, based on molecular machines consisting of two coupled and oppositely directed motile elements which extrude loops from the double helix along which they translocate, while excluding one another sterically. If these machines do not dissociate from DNA (infinite processivity), a disordered, exponential steady-state distribution of small loops is obtained. However, if dissociation and rebinding of the machines occurs at a finite rate (finite processivity), the steady state qualitatively changes to a highly ordered ‘stacked’ configuration with suppressed fluctuations, organizing a single large, stable loop domain anchored by several machines. The size of the resulting domain can be simply regulated by boundary elements, which halt the progress of the extrusion machines. Possible realizations of these types of molecular machines are discussed, with a major focus on structural maintenance of chromosome complexes and also with discussion of type I restriction enzymes. This mechanism could explain the geometrically uniform folding of eukaryote mitotic chromosomes, through extrusion of pre-programmed loops and concomitant chromosome compaction.     

A Full-automatic Sequence Design Algorithm for Branched DNA Structures

Abstract

Production of various structures by self-assembling single stranded DNA molecules is a widely used technology in the filed of DNA nanotechnology. Base sequences of single strands do predict the shape of the resulting nanostructure. Therefore, sequence design is crucial for the successful structure fabrication. This paper presents a sequence design algorithm based on mismatch minimization that can be applied to every desired DNA structure. With this algorithm, junctions, loops, single as well as double stranded regions, and very large structures up to several thousand base pairs can be handled. Thereby, the algorithm is fast for the most structures. Algorithm is Java-implemented. Its implementation is called Seed and is available publicly. As an example for a successful sequence generation, this paper presents the fabrication of DNA chain molecules consisting of double-crossover (DX) tiles as well.     

A full-automatic sequence design algorithm for branched DNA structures

Production of various structures by self-assembling single stranded DNA molecules is a widely used technology in the filed of DNA nanotechnology. Base sequences of single strands do predict the shape of the resulting nanostructure. Therefore, sequence design is crucial for the successful structure fabrication. This paper presents a sequence design algorithm based on mismatch minimization that can be applied to every desired DNA structure. With this algorithm, junctions, loops, single as well as double stranded regions, and very large structures up to several thousand base pairs can be handled. Thereby, the algorithm is fast for the most structures. Algorithm is Java-implemented. Its implementation is called Seed and is available publicly. As an example for a successful sequence generation, this paper presents the fabrication of DNA chain molecules consisting of double-crossover (DX) tiles as well.     

Structure refinement of the OpcA adhesin using molecular dynamics

OpcA from Neisseria meningitidis, the causative agent of meningococcal meningitis and septicemia, is an integral outer membrane protein that facilitates meningococcal adhesion through binding the proteoglycan receptors of susceptible cells. Two structures of OpcA have been determined by x-ray diffraction to 2 A resolution, revealing dramatically different conformations in the extracellular loops--the protein domain implicated in proteoglycan binding. In the first structure, a positively charged crevice formed by loops 1 and 2 was identified as the site for binding proteoglycans, whereas in the second structure the crevice was not evident as loops 1 and 2 adopted different conformations. To reconcile these results, molecular-dynamics simulations were carried out on both structures embedded in a solvated lipid bilayer membrane. Free of crystal contacts and crystallization agents, the loops were observed to undergo large structural transformations, suggesting that the conformation of the loops in either x-ray structure is affected by crystallization. Subsequent simulations of both structures in their crystal lattices confirmed this conclusion. Based on our molecular-dynamics trajectories, we propose a model for OpcA that combines stable structural features of the available x-ray structures. In this model, all five extracellular loops of OpcA have stable secondary structures. The loops form a funnel that leads to the base of the beta-barrel and that includes Tyr-169 on its exposed surface, which has been implicated in proteoglycan binding.     

Simultaneous modeling of multiple loops in proteins.

The most reliable methods for predicting protein structure are by way of homologous extension, using structural information from a closely related protein, or by "threading" through a set of predefined protein folds ("inverse folding"). Both sets of methods provide a model for the core of the protein--the structurally conserved secondary structures. Due to the large variability both in sequence and size of the loops that connect these secondary structures, they generally cannot be modeled using these techniques. Loop-closure algorithms are aimed at predicting loop structures, given their end-to-end distance. Various such algorithms have been described, and all have been tested by predicting the structure of a single loop in a known protein. In this paper we propose a method, which is based on the bond-scaling-relaxation loop-closure algorithm, for simultaneously predicting the structures of multiple loops, and demonstrate that, for two spatially close loops, simultaneous closure invariably leads to more accurate predictions than sequential closure. The accuracy of the predictions obtained for pairs of loops in the size range of 5-7 residues each is comparable to that obtained by other methods, when predicting the structures of single loops: the RMS deviations from the native conformations of various test cases modeled are approximately 0.6-1.7 A for backbone atoms and 1.1-3.3 A for all-atoms.     

Structures of the intradiskal loops and amino terminus of the G-protein receptor, rhodopsin.

The intradiskal surface of the transmembrane protein, rhodopsin, consists of the amino terminal domain and three loops connecting six of the seven transmembrane helices. This surface corresponds to the extracellular surface of other G-protein receptors. Peptides that represent each of the extramembraneous domains on this surface (three loops and the amino terminus) were synthesized. These peptides also included residues which, based on a hydrophobic plot, could be expected to be part of the transmembrane helix. The structure of each of these peptides in solution was then determined using two-dimensional 1H nuclear magnetic resonance. All peptide domains showed ordered structures in solution. The structures of each of the peptides from intradiskal loops of rhodopsin exhibited a turn in the central region of the peptide. The ends of the peptides show an unwinding of the transmembrane helices to form this turn. The amino terminal domain peptide exhibited alpha-helical regions with breaks and bends at proline residues. This region forms a compact domain. Together, the structures for the loop and amino terminus domains indicate that the intradiskal surface of rhodopsin is ordered. These data further suggest a structural motif for short loops in transmembrane proteins. The ordered structures of these loops, in the absence of the transmembrane helices, indicate that the primary sequences of these loops are sufficient to code for the turn.     

A hierarchical approach to all-atom protein loop prediction

The application of all-atom force fields (and explicit or implicit solvent models) to protein homology-modeling tasks such as side-chain and loop prediction remains challenging both because of the expense of the individual energy calculations and because of the difficulty of sampling the rugged all-atom energy surface. Here we address this challenge for the problem of loop prediction through the development of numerous new algorithms, with an emphasis on multiscale and hierarchical techniques. As a first step in evaluating the performance of our loop prediction algorithm, we have applied it to the problem of reconstructing loops in native structures; we also explicitly include crystal packing to provide a fair comparison with crystal structures. In brief, large numbers of loops are generated by using a dihedral angle-based buildup procedure followed by iterative cycles of clustering, side-chain optimization, and complete energy minimization of selected loop structures. We evaluate this method by using the largest test set yet used for validation of a loop prediction method, with a total of 833 loops ranging from 4 to 12 residues in length. Average/median backbone root-mean-square deviations (RMSDs) to the native structures (superimposing the body of the protein, not the loop itself) are 0.42/0.24 A for 5 residue loops, 1.00/0.44 A for 8 residue loops, and 2.47/1.83 A for 11 residue loops. Median RMSDs are substantially lower than the averages because of a small number of outliers; the causes of these failures are examined in some detail, and many can be attributed to errors in assignment of protonation states of titratable residues, omission of ligands from the simulation, and, in a few cases, probable errors in the experimentally determined structures. When these obvious problems in the data sets are filtered out, average RMSDs to the native structures improve to 0.43 A for 5 residue loops, 0.84 A for 8 residue loops, and 1.63 A for 11 residue loops. In the vast majority of cases, the method locates energy minima that are lower than or equal to that of the minimized native loop, thus indicating that sampling rarely limits prediction accuracy. The overall results are, to our knowledge, the best reported to date, and we attribute this success to the combination of an accurate all-atom energy function, efficient methods for loop buildup and side-chain optimization, and, especially for the longer loops, the hierarchical refinement protocol.     

Exploring the conformational diversity of loops on conserved frameworks

Loops are structurally variable regions, but the secondary structural elements bracing loops are often conserved. Motifs with similar secondary structures exist in the same and different protein families. In this study, we made an all-PDB-based analysis and produced 495 motif families accessible from the Internet. Every motif family contains some variable loops spanning a common framework (a pair of secondary structures). The diversity of loops and the convergence of frameworks were examined. In addition, we also identified 119 loops with conformational changes in different PDB files. These materials can give some directions for functional loop design and flexible docking.     

Prediction of protein loop geometries in solution

The ability to determine the structure of a protein in solution is a critical tool for structural biology, as proteins in their native state are found in aqueous environments. Using a physical chemistry based prediction protocol, we demonstrate the ability to reproduce protein loop geometries in experimentally derived solution structures. Predictions were run on loops drawn from (1)NMR entries in the Protein Databank (PDB), and from (2) the RECOORD database in which NMR entries from the PDB have been standardized and re-refined in explicit solvent. The predicted structures are validated by comparison with experimental distance restraints, a test of structural quality as defined by the WHAT IF structure validation program, root mean square deviation (RMSD) of the predicted loops to the original structural models, and comparison of precision of the original and predicted ensembles. Results show that for the RECOORD ensembles, the predicted loops are consistent with an average of 95%, 91%, and 87% of experimental restraints for the short, medium and long loops respectively. Prediction accuracy is strongly affected by the quality of the original models, with increases in the percentage of experimental restraints violated of 2% for the short loops, and 9% for both the medium and long loops in the PDB derived ensembles. We anticipate the application of our protocol to theoretical modeling of protein structures, such as fold recognition methods; as well as to experimental determination of protein structures, or segments, for which only sparse NMR restraint data is available.     

Canonical antigen-binding loop structures in immunoglobulins: more structures, more canonical classes?

Grafting the antigen-binding loops onto a human antibody scaffold is a widely used technique to humanise murine antibodies. The success of this approach depends largely on the observation that the antigen-binding loops adopt only a limited number of canonical structures. Identification of the correct canonical structure is therefore essential. Algorithms that predict the main-chain conformation of the hypervariable loops using only the amino acid sequence often provide this information. Here, we describe new canonical loop conformations for the hypervariable regions H1 and H2 as found in single-domain antibody fragments of dromedaries or llama. Although the occurrence of these new loop conformations was not predicted by the algorithms used, it seems that they could occur in human or mouse antigen-binding loops. Their discovery indicates that the currently used set of canonical structures is incomplete and that the prediction algorithms should be extended to include these new structures.     

Electron microscopy of membrane-associated folded chromosomes of Escherichia coli

Membrane-associated folded chromosomes were purified from log-phase cultures of Escherichia coli 15 TAU-bar and prepared for electron microscopy by aqueous spreading techniques. A spectrum of structures was observed, ranging from condensed structures with no DNA fibers visible, to extended structures with DNA fibers. In the extended structures, loops of DNA radiated from residual envelope, the loops sometimes appeared super-coiled, and both their number and apparent contour length approximated previous estimates from physical and biochemical data. It is proposed that the structures with free DNA arose from the condensed structures.     

mRNA环结构对蛋白质折叠速率的影响

前期的相关研究发现mRNA二级结构中存在对蛋白质折叠速率的重要影响因素.而mRNA二级结构中普遍存在着各种复杂的环结构,这些环结构是否对蛋白质折叠速率也有重要的影响呢?不同的环结构对蛋白质折叠速率的影响是否相同呢?基于此想法,建立了一个包含mRNA内部环、发夹环、膨胀环和多分支环等环结构信息和相应蛋白质折叠速率的数据库.对于数据库中的每一个蛋白质,计算了mRNA二级结构中各种环结构碱基含量、配对碱基含量及单链碱基含量等参量,分析了各参量与相应蛋白质折叠速率的相关性.结果显示,各种环结构碱基含量与蛋白质折叠速率均呈极显著或显著正相关.说明mRNA环结构对蛋白质折叠速率有重要的影响.进一步,把蛋白质按照不同折叠类型或不同二级结构类型分组后,对每一组蛋白质重复上述的分析工作.结果表明,对不同类蛋白质,mRNA的各种环结构对其相应蛋白质折叠速率的影响存在着显著差异.上述研究将为进一步开展有关mRNA和蛋白质折叠速率的研究奠定理论基础.     

The nature of the turn in omega loops of proteins

An analysis of Omega loops in a nonredundant set of protein structures from the Protein Data Bank has been carried out to determine the nature of the "turn elements" present. Because Omega loops essentially reverse their direction in three-dimensional space, this analysis was made with respect to four turn elements identified as (1) Gly; (2) Pro; (3) a residue with alpha-helical phi,psi angles, termed a helical residue; and (4) a cis peptide. A set of 1079 Omega loops from a set of 680 proteins were used for the analysis. Apart from other criteria that define Omega loops, the selection of an Omega loop from a cluster of loops is based on an exposure index. In this study, analyses have been made with two sets of data: (1) Omega loops arising from a minimum exposure index indicative of a less exposed loop (xmin set) and (2) Omega loops with a maximum exposure index indicative of a relatively exposed loop (xmax set). Overall residue preferences and positional preferences have been examined. Positions of the turn elements for Omega loops of varying length have also been studied. Specific positional preferences are observed for particular turn elements with regard to the length of Omega loops. Analysis in terms of the turn elements can provide guidelines for modeling of loops in proteins. Apart from Pro, which has the natural tendency to form cis peptide bonds, a higher occurrence of non-Pro cis peptide bonds is observed. Torsion angles in Omega loops also indicate the occurrence of a large number of residues with helical phi,psi angles, necessary for the turn in the loop structures.     

Modeling flexible loops in the dark-adapted and activated states of rhodopsin, a prototypical G-protein-coupled receptor

Conformational possibilities of flexible loops in rhodopsin, a prototypical G-protein-coupled receptor, were studied by modeling both in the dark-adapted (R) and activated (R*) states. Loop structures were built onto templates representing the R and R* states of the TM region of rhodopsin developed previously (G. V. Nikiforovich and G. R. Marshall. 2003. Biochemistry. 42:9110). Geometrical sampling and energy calculations were performed for each individual loop, as well as for the interacting intracellular loops IC1, IC2, and IC3 and the extracellular loops EC1, EC2, and EC3 mounted on the R and R* templates. Calculations revealed that the intra- and extracellular loops of rhodopsin possess low-energy structures corresponding to large conformational movements both in the R and R* states. Results of these calculations are in good agreement with the x-ray data available for the dark-adapted rhodopsin as well as with the available experimental biophysical data on the disulfide-linked mutants of rhodopsin. The calculated results are used to exemplify how the combined application of the results of independent calculations with emerging experimental data can be used to select plausible three-dimensional structures of the loops in rhodopsin.     

New efficient statistical sequence-dependent structure prediction of short to medium-sized protein loops based on an exhaustive loop classification.

A bank of 13,563 loops from three to eight amino acid residues long, representing motifs between two consecutive regular secondary structures, has been derived from protein structures presenting less than 95 % sequence identity. Statistical analyses of occurrences of conformations and residues revealed length-dependent over-representations of particular amino acids (glycine, proline, asparagine, serine, and aspartate) and conformations (alphaL, epsilon, betaPregions of the Ramachandran plot). A position-dependent distribution of these occurrences was observed for N and C-terminal residues, which are correlated to the nature of the flanking regions. Loops of the same length were clustered into statistically meaningful families on the basis of their backbone structures when placed in a common reference frame, independent of the flanks. These clusters present significantly different distributions of sequence, conformations, and endpoint residue Calphadistances. On the basis of the sequence-structure correlation of this clustering, an automatic loop modeling algorithm was developed. Based on the knowledge of its sequence and of its flank backbone structures each query loop is assigned to a family and target loop supports are selected in this family. The support backbones of these target loops are then adjusted on flanking structures by partial exploration of the conformational space. Loop closure is performed by energy minimization for each support and the final model is chosen among connected supports based upon energy criteria. The quality of the prediction is evaluated by the root-mean-square deviation (rmsd) between the final model and the native loops when the whole bank is re-attributed on itself with a Jackknife test. This average rmsd ranges from 1.1 A for three-residue loops to 3.8 A for eight-residue loops. A few poorly predicted loops are inescapable, considering the high level of diversity in loops and the lack of environment data. To overcome such modeling problems, a statistical reliability score was assigned for each prediction. This score is correlated to the quality of the prediction, in terms of rmsd, and thus improves the selection accuracy of the model. The algorithm efficiency was compared to CASP3 target loop predictions. Moreover, when tested on a test loop bank, this algorithm was shown to be robust when the loops are not precisely delimited, therefore proving to be a useful tool in practice for protein modeling.     

Conformational polymorphism in telomeric structures: Loop orientation and interloop pairing in d(G4TnG4)

Sequence repeats constituting the telomeric regions of chromosomes are known to adopt a variety of unusual structures, consisting of a G tetraplex stem and short stretches of thymines or thymines and adenines forming loops over the stem. Detailed model building and molecular mechanics studies have been carried out for these telomeric sequences to elucidate different types of loop orientations and possible conformations of thymines in the loop. The model building studies indicate that a minimum of two thymines have to be interspersed between guanine stretches to form folded-back structures with loops across adjacent strands in a G tetraplex (both over the small as well as large groove), while the minimum number of thymines required to build a loop across the diagonal strands in a G tetraplex is three. For two repeat sequences, these hairpins, resulting from different types of folding, can dimerize in three distinct ways—i.e., with loops across adjacent strands and on same side, with loops across adjacent strands and on opposite sides, and with loops across diagonal strands and on opposite sides—to form hairpin dimer structures. Energy minimization studies indicate that all possible hairpin dimers have very similar total energy values, though different structures are stabilized by different types of interactions. When the two loops are on the same side, in the hairpin dimer structures of d(G₄T_nG₄), the thymines form favorably stacked tetrads in the loop region and there is interloop hydrogen bonding involving two hydrogen bonds for each thymine–thymine pair. Our molecular mechanics calculations on various folded-back as well as parallel tetraplex structures of these telomeric sequences provide a theoretical rationale for the experimentally observed feature that the presence of intervening thymine stretches stabilizes folded-back structures, while isolated stretches of guanines adopt a parallel tetraplex structure. © 1994 John Wiley & Sons, Inc.     

Tumor suppressor INK4: determination of the solution structure of p18INK4C and demonstration of the functional significance of loops in p18INK4C and p16INK4A

Since the structures of several ankyrin-repeat proteins including the INK4 (inhibitor of cyclin-dependent kinase 4) family have been reported recently, the detailed structures and the functional roles of the loops have drawn considerable interest. This paper addresses the potential importance of the loops of ankyrin-repeat proteins in three aspects. First, the solution structure of p18INK4C was determined by NMR, and the loop structures were analyzed in detail. The loops adapt nascent antiparallel beta-sheet structures, but the positions are slightly different from those in the crystal structure. A detailed comparison between the solution structures of p16 and p18 has also been presented. The determination of the p18 solution structure made such detailed comparisons possible for the first time. Second, the [1H,15N]HSQC NMR experiment was used to probe the interactions between p18INK4C and other proteins. The results suggest that p18INK4C interacts very weakly with dna K and glutathione S-transferase via the loops. The third aspect employed site-specific mutagenesis and functional assays. Three mutants of p18 and 11 mutants of p16 were constructed to test functional importance of loops and helices. The results suggest that loop 2 is likely to be part of the recognition surface of p18INK4C or p16INK4A for CDK4, and they provide quantitative functional contributions of specific residues. Overall, our results enhance understanding of the structural and functional roles of the loops in INK4 tumor suppressors in particular and in ankyrin-repeat proteins in general.