Standard atomic volumes in double-stranded DNA and packing in protein--DNA interfaces

Standard volumes for atoms in double-stranded B-DNA are derived using high resolution crystal structures from the Nucleic Acid Database (NDB) and compared with corresponding values derived from crystal structures of small organic compounds in the Cambridge Structural Database (CSD). Two different methods are used to compute these volumes: the classical Voronoi method, which does not depend on the size of atoms, and the related Radical Planes method which does. Results show that atomic groups buried in the interior of double-stranded DNA are, on average, more tightly packed than in related small molecules in the CSD. The packing efficiency of DNA atoms at the interfaces of 25 high resolution protein-DNA complexes is determined by computing the ratios between the volumes of interfacial DNA atoms and the corresponding standard volumes. These ratios are found to be close to unity, indicating that the DNA atoms at protein-DNA interfaces are as closely packed as in crystals of B-DNA. Analogous volume ratios, computed for buried protein atoms, are also near unity, confirming our earlier conclusions that the packing efficiency of these atoms is similar to that in the protein interior. In addition, we examine the number, volume and solvent occupation of cavities located at the protein-DNA interfaces and compared them with those in the protein interior. Cavities are found to be ubiquitous in the interfaces as well as inside the protein moieties. The frequency of solvent occupation of cavities is however higher in the interfaces, indicating that those are more hydrated than protein interiors. Lastly, we compare our results with those obtained using two different measures of shape complementarity of the analysed interfaces, and find that the correlation between our volume ratios and these measures, as well as between the measures themselves, is weak. Our results indicate that a tightly packed environment made up of DNA, protein and solvent atoms plays a significant role in protein-DNA recognition.     

Crystal packing effects on protein loops

The effects of crystal packing on protein loop structures are examined by (1) a comparison of loops in proteins that have been crystallized in alternate packing arrangements, and (2) theoretical prediction of loops both with and without the inclusion of the crystal environment. Results show that in a minority of cases, loop geometries are dependent on crystal packing effects. Explicit representation of the crystal environment in a loop prediction algorithm can be used to model these effects and to reconstruct the structures, and relative energies, of a loop in alternative packing environments. By comparing prediction results with and without the inclusion of the crystal environment, the loop prediction algorithm can further be used to identify cases in which a crystal structure does not represent the most stable state of a loop in solution. We anticipate that this capability has implications for structural biology.     

Structural determinants of the conformations of medium-sized loops in proteins

Loops are integral components of protein structures, providing links between elements of secondary structure, and in many cases contributing to catalytic and binding sites. The conformations of short loops are now understood to depend primarily on their amino acid sequences. In contrast, the structural determinants of longer loops involve hydrogen-bonding and packing interactions within the loop and with other parts of the protein. By searching solved protein structures for regions similar in main chain conformation to the antigen-binding loops in immunoglobulins, we identified medium-sized loops of similar structure in unrelated proteins, and compared the determinants of their conformations. For loops that form compact substructures the major determinant of the conformation is the formation of hydrogen bonds to inward-pointing main chain atoms. For loops that have more extended conformations, the major determinant of their structure is the packing of a particular residue or residues against the rest of the protein. The following picture emerges: Medium-sized loops of similar conformation are stabilized by similar interactions. The groups that interact with the loop have very similar spatial dispositions with respect to the loop. However, the residues that provide these interactions may arise from dissimilar parts of the protein: The conformation of the loop requires certain interactions that the protein may provide in a variety of ways.     

Inhomogeneous molecular density: reference packing densities and distribution of cavities within proteins

MOTIVATION: There is no consensus in the literature about how the deepest portions of protein structures are packed. Using an improved Voronoi procedure, we calculate reference packing densities for different regions in the protein interior. Furthermore, we want to clarify where cavities are located. RESULTS: Sets of reference packing densities are provided for regions in proteins that differ in their distance to the surface and to internal cavities, supplementing previous data. Packing in the protein interior is tight but generally inhomogeneous. There are about 4.4 cavities per 100 amino acids in protein structures, they occur in all regions, most frequently in a depth of 2.5-3.6 A underneath the Connolly surface. However, the deepest protein regions have a lower mean packing density than circumjacent regions, because more contacts to cavities occur in the core. AVAILABILITY/SUPPLEMENTARY INFORMATION: Calculation software and detailed packing data are available on request.     

A crumpled surface having transverse attractive interactions as a simplified model with biological significance

Using extensive analogical simulations with square sheets of paper we investigate the influence of short-range transverse attractive interactions on the packing properties of a crumpled surface. These interactions are due to transverse connections or local bridges associated with a given number of binding sites localized on the two-dimensional surface and distributed in several patterns in the three-dimensional physical space. Geometrical relations and critical exponents describing the statistical properties of the crumpled surface are obtained as a function of the strength of the attractive interactions. Our model suggests how the presence of short-range interactions as, e.g. van der Waals forces can be important for the geometric plasticity of biological molecules, which in turn is important for biological function. The relevance of our results to the study of molecular conformation of proteins and membranes is discussed, and a comparison is also made between the behavior of the crumpled surface studied here and other important non-equilibrium fractal structures.     

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.     

Does conformational free energy distinguish loop conformations in proteins?

Limitations in protein homology modeling often arise from the inability to adequately model loops. In this paper we focus on the selection of loop conformations. We present a complete computational treatment that allows the screening of loop conformations to identify those that best fit a molecular model. The stability of a loop in a protein is evaluated via computations of conformational free energies in solution, i.e., the free energy difference between the reference structure and the modeled one. A thermodynamic cycle is used for calculation of the conformational free energy, in which the total free energy of the reference state (i.e., gas phase) is the CHARMm potential energy. The electrostatic contribution of the solvation free energy is obtained from solving the finite-difference Poisson-Boltzmann equation. The nonpolar contribution is based on a surface area-based expression. We applied this computational scheme to a simple but well-characterized system, the antibody hypervariable loop (complementarity-determining region, CDR). Instead of creating loop conformations, we generated a database of loops extracted from high-resolution crystal structures of proteins, which display geometrical similarities with antibody CDRs. We inserted loops from our database into a framework of an antibody; then we calculated the conformational free energies of each loop. Results show that we successfully identified loops with a "reference-like" CDR geometry, with the lowest conformational free energy in gas phase only. Surprisingly, the solvation energy term plays a confusing role, sometimes discriminating "reference-like" CDR geometry and many times allowing "non-reference-like" conformations to have the lowest conformational free energies (for short loops). Most "reference-like" loop conformations are separated from others by a gap in the gas phase conformational free energy scale. Naturally, loops from antibody molecules are found to be the best models for long CDRs (> or = 6 residues), mainly because of a better packing of backbone atoms into the framework of the antibody model.     

Flexibility and structural conservation in a c-KIT G-quadruplex

A quadruplex sequence from the promoter region of the c-KIT gene forms a stable quadruplex, as characterized by crystallographic and NMR methods. Two new crystal structures are reported here, together with molecular dynamics simulation studies on these quadruplex crystal structures and an NMR structure. The new crystal structures, each in a distinct space group and lattice packing arrangement, together with the existing structures, demonstrate that the c-KIT quadruplex fold does not change with differing environments, suggesting that quadruplex topological dynamism is not a general phenomenon. The single and dinucleotide loops in these structures show a high degree of conformational flexibility within the three crystal forms and the NMR ensemble, with no evidence of clustering to particular conformers. This is in accord with the findings of high loop flexibility from the molecular dynamics studies. It is suggested that intramolecular quadruplexes can be grouped into two broad classes (i) those with at least one single-nucleotide loop, often showing singular topologies even though loops are highly flexible, and (ii) with all loops comprising at least two nucleotides, leading to topological dynamism. The loops can have more stable and less dynamic base-stacked secondary structures.     

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.     

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 novel scoring function for predicting the conformations of tightly packed pairs of transmembrane alpha-helices

Pairs of helices in transmembrane (TM) proteins are often tightly packed. We present a scoring function and a computational methodology for predicting the tertiary fold of a pair of alpha-helices such that its chances of being tightly packed are maximized. Since the number of TM protein structures solved to date is small, it seems unlikely that a reliable scoring function derived statistically from the known set of TM protein structures will be available in the near future. We therefore constructed a scoring function based on the qualitative insights gained in the past two decades from the solved structures of TM and soluble proteins. In brief, we reward the formation of contacts between small amino acid residues such as Gly, Cys, and Ser, that are known to promote dimerization of helices, and penalize the burial of large amino acid residues such as Arg and Trp. As a case study, we show that our method predicts the native structure of the TM homodimer glycophorin A (GpA) to be, in essence, at the global score optimum. In addition, by correlating our results with empirical point mutations on this homodimer, we demonstrate that our method can be a helpful adjunct to mutation analysis. We present a data set of canonical alpha-helices from the solved structures of TM proteins and provide a set of programs for analyzing it (http://ashtoret.tau.ac.il/~sarel). From this data set we derived 11 helix pairs, and conducted searches around their native states as a further test of our method. Approximately 73% of our predictions showed a reasonable fit (RMS deviation <2A) with the native structures compared to the success rate of 8% expected by chance. The search method we employ is less effective for helix pairs that are connected via short loops (<20 amino acid residues), indicating that short loops may play an important role in determining the conformation of alpha-helices in TM proteins.     

Recurring loop motif in proteins that occurs in right-handed and left-handed forms. Its relationship with alpha-helices and beta-bulge loops

A common feature of alpha-helices in proteins is a loop at the C-terminal end, with a characteristic hydrogen bond pattern. It is noted that several loops with the same structural features occur independently of alpha-helices; two are even situated at the loop ends of beta-hairpins. The name paperclip is suggested for loops possessing the appropriate hydrogen bonds. A number of features of paperclips are described: they exist in two classes, depending on the number of residues at the loop end; one class is very much commoner than the other. Two paperclips are found that belong to the common class, except that the main-chain conformation of each is the mirror image of that normally found. The majority of paperclips are shown to have tightly clustered sets of main-chain dihedral angles. These are somewhat similar to, but distinct from, a subgroup of another common family of loops that have been called beta-bulge loops; in the latter, the dihedral angles are also tightly clustered. The high degree of clustering in both cases is likely to be a result of steric constraints associated with hydrogen bond patterns at the ends of loops.     

Salt dependence of nucleic acid hairpin stability

Single-stranded junctions/loops are frequently occurring structural motifs in nucleic acid structures. Due to the polyanionic nature of the nucleic acid backbone, metal ions play a crucial role in the loop stability. Here we use the tightly bound ion theory, which can account for the possible ion correlation and ensemble (fluctuation) effects, to predict the ion-dependence of loop and stem-loop (hairpin) free energies. The predicted loop free energy is a function of the loop length, the loop end-to-end distance, and the ion (Na⁺ and Mg²⁺ in this study) concentrations. Based on the statistical mechanical calculations, we derive a set of empirical formulas for the loop thermodynamic parameters as functions of Na⁺ and Mg²⁺ concentrations. For three specific types of loops, namely, hairpin, bulge, and internal loops, the predicted free energies agree with the experimental data. Further applications of these empirical formulas to RNA and DNA hairpin stability lead to good agreements with the available experimental data. Our results indicate that the ion-dependent loop stability makes significant contribution to the overall ion-dependence of the hairpin stability.     

Modeling a self-avoiding chromatin loop: relation to the packing problem, action-at-a-distance, and nuclear context

There is now convincing evidence that genomes are organized into loops, and that looping brings distant genes together so that they can bind to local concentrations of polymerases in "factories" or "hubs." As there remains no systematic analysis of how looping affects the probability that a gene can access binding sites in such factories/hubs, we used an algorithm that we devised and Monte Carlo methods to model a DNA or chromatin loop as a semiflexible (self-avoiding) tube attached to a sphere; we examine how loop thickness, rigidity, and contour length affect where particular segments of the loop lie relative to binding sites on the sphere. Results are compared with those obtained with the traditional model of an (infinitely thin) freely jointed chain. They provide insights into the packing problem (how long genomes are packed into small nuclei), and action-at-a-distance (how firing of one origin or gene can prevent firing of an adjacent one).     

The solution structure and internal motions of a fragment of the cytidine-rich strand of the human telomere

We present the solution structure of d(CCCTA2CCCTA2CCCTA2CCCT), a fragment of the vertebrate telomere which folds intramolecularly. The four cytidine stretches form an i-motif which includes six intercalated C.C+ pairs and terminates with the cytidines at the 5' extremity of each stretch. Above, the second TA2 linker loops across one of the narrow grooves, while at the bottom, the first and third linkers loop across the wide grooves. At 30 degrees C, the spectra of the first and third linkers are quasi-degenerate. Severe broadening at lower temperature indicates that this results from motional averaging between at least two structures of each bottom loop, and makes it impossible to solve the configuration of the bottom loops directly, in contrast to the rest of the structure. We therefore turned to the modified sequence d(CCCTA(2)5MCCCTA2CCCUA2CCCT) in which the two base substitutions (underlined) break the quasi-symmetry between linkers 1 and 3. The three loops follow approximately the hairpin "second pattern" of Hilbers. In the first loop, T4 is in the syn orientation, whereas its analog in the third loop, U16, oriented anti, is in a central location, where it interacts with bases of both loops, thus contributing to their tight association. The only motion is a syn/anti flip of A18 in the third loop. Returning to the telomere fragment, we show that each of the bottom loops switches between the structures identified in the first and third loops of the modified structure. The motions are concerted, and the resulting configurations of the bottom loop cluster present a bulge to either right (T4 syn) or left (T16 syn).     

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.     

Two-dimensional combinatorial screening identifies specific 6'-acylated kanamycin A- and 6'-acylated neamine-RNA hairpin interactions

Herein, we report the RNA hairpin loops from a six-nucleotide hairpin library that bind 6'-acylated kanamycin A (1) and 6'-acylated neamine (2) identified by two-dimensional combinatorial screening (2DCS). Hairpins selected to bind 1 have K(d)'s ranging from 235 to 1035 nM, with an average K(d) of 618 nM. For 2, the selected hairpins bind with K(d)'s ranging from 135 to 2300 nM, with an average K(d) of 1010 nM. The selected RNA hairpin-ligand interactions are also specific for the ligand that they were selected to bind compared with the other arrayed ligand. For example, the mixture of hairpins selected for 1 on average bind 33-fold more tightly to 1 than to 2, while the mixtures of hairpins selected for 2 on average bind 11-fold more tightly to 2 than to 1. Secondary structure prediction of the selected sequences was completed to determine the motifs that each ligand binds, and the hairpin loop preferences for 1 and 2 were computed. For 1, the preferred hairpin loops contain an adenine separated by at least two nucleotides from a cytosine, for example, ANNCNN (two-tailed p-value = 0.0010) and ANNNCN (two-tailed p-value <0.0001). For 2, the preferred hairpin loops contain both 5'GC and 5'CG steps (two-tailed p-value <0.0001). These results expand the information available on the RNA hairpin loops that bind small molecules and could prove useful for targeting RNA.