Discrete state model and accurate estimation of loop entropy of RNA secondary structures

Conformational entropy makes important contribution to the stability and folding of RNA molecule, but it is challenging to either measure or compute conformational entropy associated with long loops. We develop optimized discrete k-state models of RNA backbone based on known RNA structures for computing entropy of loops, which are modeled as self-avoiding walks. To estimate entropy of hairpin, bulge, internal loop, and multibranch loop of long length (up to 50), we develop an efficient sampling method based on the sequential Monte Carlo principle. Our method considers excluded volume effect. It is general and can be applied to calculating entropy of loops with longer length and arbitrary complexity. For loops of short length, our results are in good agreement with a recent theoretical model and experimental measurement. For long loops, our estimated entropy of hairpin loops is in excellent agreement with the Jacobson-Stockmayer extrapolation model. However, for bulge loops and more complex secondary structures such as internal and multibranch loops, we find that the Jacobson-Stockmayer extrapolation model has large errors. Based on estimated entropy, we have developed empirical formulae for accurate calculation of entropy of long loops in different secondary structures. Our study on the effect of asymmetric size of loops suggest that loop entropy of internal loops is largely determined by the total loop length, and is only marginally affected by the asymmetric size of the two loops. Our finding suggests that the significant asymmetric effects of loop length in internal loops measured by experiments are likely to be partially enthalpic. Our method can be applied to develop improved energy parameters important for studying RNA stability and folding, and for predicting RNA secondary and tertiary structures. The discrete model and the program used to calculate loop entropy can be downloaded at http://gila.bioengr.uic.edu/resources/RNA.html.     

Topology variation and loop structural homology in crystal and simulated structures of a bimolecular DNA quadruplex

The topology of DNA quadruplexes depends on the nature and number of the nucleotides linking G-quartet motifs. To assess the effects of a three-nucleotide TTT linker, the crystal structure of the DNA sequence d(G(4)T(3)G(4)) has been determined at 1.5 A resolution, together with that of the brominated analogue d(G(4)(Br)UTTG(4)) at 2.4 A resolution. Both sequences form bimolecular intermolecular G-quadruplexes with lateral loops. d(G(4)(Br)UTTG(4)) crystallized in the monoclinic space group P2(1) with three quadruplex molecules in the asymmetric unit, two associating together as a head-to-head stacked dimer, and the third as a single head-to-tail dimer. The head-to-head dimers have two lateral loops on the same G-quadruplex face and form an eight-G-quartet stack, with a linear array of seven K(+) ions between the quartets. d(G(4)T(3)G(4)) crystallized in the orthorhombic space group C222 and has a structure very similar to the head-to-tail dimer in the P2(1) unit cell. The sequence studied here is able to form several different folds; however, all four quadruplexes in the two structures have lateral loops, in contrast to the diagonal loops reported for the analogous quadruplex with T(4) loops. A total of seven independent T(3) loops were observed in the two structures. These can be classified into two discrete conformational classes, suggesting that these represent preferred loop conformations that are independent of crystal-packing forces.     

Loop-length-dependent folding of G-quadruplexes

Guanine-rich DNA sequences can form a large number of structurally diverse quadruplexes. These vary in terms of strand polarity, loop composition, and conformation. We have derived guidelines for understanding the influence of loop length on the structure adopted by intramolecular quadruplex-forming sequences, using a combination of experimental (using CD and UV melting data) and molecular modeling and simulation techniques. We find that a parallel-stranded intramolecular quadruplex structure is the only possible fold when three single residue loops are present. When single thymine loops are present in combination with longer length loops, or when all loops are longer than two residues, both parallel- and antiparallel-folded structures are able to form. Multiple conformations of each structure are likely to coexist in solution, as they were calculated to have very similar free energies.     

Key issues in the computational simulation of GPCR function: representation of loop domains

Some key concerns raised by molecular modeling and computational simulation of functional mechanisms for membrane proteins are discussed and illustrated for members of the family of G protein coupled receptors (GPCRs). Of particular importance are issues related to the modeling and computational treatment of loop regions. These are demonstrated here with results from different levels of computational simulations applied to the structures of rhodopsin and a model of the 5-HT2A serotonin receptor, 5-HT2AR. First, comparative Molecular Dynamics (MD) simulations are reported for rhodopsin in vacuum and embedded in an explicit representation of the membrane and water environment. It is shown that in spite of a partial accounting of solvent screening effects by neutralization of charged side chains, vacuum MD simulations can lead to severe distortions of the loop structures. The primary source of the distortion appears to be formation of artifactual H-bonds, as has been repeatedly observed in vacuum simulations. To address such shortcomings, a recently proposed approach that has been developed for calculating the structure of segments that connect elements of secondary structure with known coordinates, is applied to 5-HT2AR to obtain an initial representation of the loops connecting the transmembrane (TM) helices. The approach consists of a simulated annealing combined with biased scaled collective variables Monte Carlo technique, and is applied to loops connecting the TM segments on both the extra-cellular and the cytoplasmic sides of the receptor. Although this initial calculation treats the loops as independent structural entities, the final structure exhibits a number of interloop interactions that may have functional significance. Finally, it is shown here that in the case where a given loop from two different GPCRs (here rhodopsin and 5-HT2AR) has approximately the same length and some degree of sequence identity, the fold adopted by the loops can be similar. Thus, in such special cases homology modeling might be used to obtain initial structures of these loops. Notably, however, all other loops in these two receptors appear to be very different in sequence and structure, so that their conformations can be found reliably only by ab initio, energy based methods and not by homology modeling.     

Unique structural features of interconverting monomeric and dimeric G-quadruplexes adopted by a sequence from the intron of the N-myc gene

A multidimensional heteronuclear NMR study has demonstrated that a guanine-rich DNA oligonucleotide originating from the N-myc gene folds into G-quadruplex structures in the presence of K(+), NH(4)(+), and Na(+) ions. A monomeric G-quadruplex formed in K(+) ion containing solution exhibits three G-quartets and flexible propeller-type loops. The 3D structure with three single nucleotide loops represents a missing element in structures of parallel G-quadruplexes. The structural features together with the high temperature stability are suggestive of the specific biological role of G-quadruplex formation within the intron of the N-myc gene. An increase in K(+) ion and oligonucleotide concentrations resulted in transformation of the monomeric G-quadruplex into a dimeric form. The dimeric G-quadruplex exhibits six stacked G-quartets, parallel strand orientations, and propeller-type loops. A link between the third and the fourth G-quartets consists of two adenine residues that are flipped out to facilitate consecutive stacking of six G-quartets.     

Differentiate RNA Single‐Stranded Region of the Branched Structures and Hairpin Loops by an Octahedral Cobalt(II) Complex

Single‐stranded RNA molecules usually include secondary structural elements such as bulges, internal loops, and hairpin loops. These RNA secondary structural elements are often essential for the biological activity and functions of the RNA molecule. Chemical probe Co^II(HAPP)(TFA)₂ in the presence of H₂O₂ is found to differentiate single‐stranded RNA from branched structures and hairpin loops. This study uses Co^II(HAPP)(TFA)2 to analyze the structures of two RNA molecules: a fragment of HIV TAR RNA (TAR‐27) and the catalytic domain 5 of group II intron (D5‐29). The electrophoretic mobility of TAR‐27 does not shift in the presence of Co^II(HAPP)(TFA)₂, suggesting that the reagent does not change the conformation of RNA substrate. Cleavage of the RNA substrates by Co^II(HAPP)(TFA)₂ unambiguously differentiated RNA internal looped structures from hairpin loops. The results show that Co^II(HAPP)(TFA)2 is a sensitive, informative and convenient tool for analysis of RNA secondary structures.     

Energy minimization of rigid-geometry polypeptides with exactly closed disulfide loops

A method has been developed for minimizing the energy of a polypeptide with rigid geometry while keeping all disulfide loops closed exactly. Exact closure of disulfide loops implies that some dihedral angles become implicit functions of the remaining dihedral angles in the polypeptide; the efficacy of the method is related to the manner in which the implicitly defined dihedral angles are chosen. The method has been used to find minimum-energy conformations of bovine pancreatic trypsin inhibitor, ribonuclease A, crambin, the defensin HNP3 dimer, and ω-conotoxin. For the first two proteins, the starting conformations for energy minimization had been derived previously from crystal structures using pseudopotentials to keep the disulfide loops almost closed. Starting conformations for the remaining three proteins were derived from their crystal or NMR structures by similar procedures. In all cases, the energy-minimized structures had a significantly and, in some cases, substantially, lower energy than the starting structures. The RMS deviations between the exactly closed energy- minimized structures and the crystal or NMR structures from which they were derived ranged from 0.9 Å to 1.9 Å, suggesting that the computed structures can serve as “regularized” native structures for these proteins. The energy of a ribonuclease derivative lacking the 65–72 disulfide bridge was minimized using the procedure; the result showed that this derivative has a low-energy structure with a conformation very close to that of native ribonuclease, and is consistent with its postulated role in the folding of ribonuclease. These results offer strong support for the validity of the rigid-geometry model in the studies of the conformational energy of proteins. © 1997 by John Wiley & Sons, Inc.     

Two-dimensional combinatorial screening identifies specific aminoglycoside-RNA internal loop partners

Herein is described the identification of RNA internal loops that bind to derivatives of neomycin B, neamine, tobramycin, and kanamycin A. RNA loop-ligand partners were identified by a two-dimensional combinatorial screening (2DCS) platform that probes RNA and chemical spaces simultaneously. In 2DCS, an aminoglycoside library immobilized onto an agarose microarray was probed for binding to a 3 x 3 nucleotide RNA internal loop library (81,920 interactions probed in duplicate in a single experiment). RNAs that bound aminoglycosides were harvested from the array via gel excision. RNA internal loop preferences for three aminoglycosides were identified from statistical analysis of selected structures. This provides consensus RNA internal loops that bind these structures and include: loops with potential GA pairs for the neomycin derivative, loops with potential GG pairs for the tobramycin derivative, and pyrimidine-rich loops for the kanamycin A derivative. Results with the neamine derivative show that it binds a variety of loops, including loops that contain potential GA pairs that also recognize the neomycin B derivative. All studied selected internal loops are specific for the aminoglycoside that they were selected to bind. Specificity was quantified for 16 selected internal loops by studying their binding to each of the arrayed aminoglycosides. Specificities ranged from 2- to 80-fold with an average specificity of 20-fold. These studies show that 2DCS is a unique platform to probe RNA and chemical space simultaneously to identify specific RNA motif-ligand interactions.     

Lone-pair self-containment in tellurite tubes: hydrothermal syntheses and structures of BaTe(3)O(7) and BaTe(4)O(9)

The hydrothermal syntheses and single-crystal structures of BaTe3O7 and BaTe4O9 are reported. These closely related new phases, which can be regarded as the n = 3 and 4 members of the BaTenO2n+1 family, are built up from infinite, tubular, columns of Te/O polyhedra (6 ring loops for BaTe3O7 and 8 ring loops for BaTe4O9) with barium cations completing the structures. The tubes represent a novel way to accommodate the lone pair of electrons associated with each TeIV species and suggest the possibility of redox intercalation chemistry for these types of material.     

An evaluation of molecular models of the cytochrome P450 Streptomyces griseolus enzymes P450SU1 and P450SU2

Summary P450SU1 and P450SU2 are herbicide-inducible bacterial cytochrome P450 enzymes from Streptomyces griseolus. They have two of the highest sequence identities to camphor hydroxylase (P450cam from Pseudomonas putida), the cytochrome P450 with the first known crystal structure. We have built several models of these two proteins to investigate the variability in the structures that can occur from using different modeling protocols. We looked at variability due to alignment methods, backbone loop conformations and refinement methods. We have constructed two models for each protein using two alignment algorithms, and then an additional model using an identical alignment but different loop conformations for both buried and surface loops. The alignments used to build the models were created using the Needleman-Wunsch method, adapted for multiple sequences, and a manual method that utilized both a dotmatrix search matrix and the Needleman-Wunsch method. After constructing the initial models, several energy minimization methods were used to explore the variability in the final models caused by the choice of minimization techniques. Features of cytochrome P450cam and the cytochrome P450 superfamily, such as the ferredoxin binding site, the heme binding site and the substrate binding site were used to evaluate the validity of the models. Although the final structures were very similar between the models with different alignments, active-site residues were found to be dependent on the conformations of buried loops and early stages of energy minimization. We show which regions of the active site are the most dependent on the particular methods used, and which parts of the structures seem to be independent of the methods.     

Two-repeat human telomeric d(TAGGGTTAGGGT) sequence forms interconverting parallel and antiparallel G-quadruplexes in solution: distinct topologies, thermodynamic properties, and folding/unfolding kinetics

We demonstrate by NMR that the two-repeat human telomeric sequence d(TAGGGTTAGGGT) can form both parallel and antiparallel G-quadruplex structures in K(+)-containing solution. Both structures are dimeric G-quadruplexes involving three stacked G-tetrads. The sequence d(TAGGGUTAGGGT), containing a single thymine-to-uracil substitution at position 6, formed a predominantly parallel dimeric G-quadruplex with double-chain-reversal loops; the structure was symmetric, and all guanines were anti. Another modified sequence, d(UAGGGT(Br)UAGGGT), formed a predominantly antiparallel dimeric G-quadruplex with edgewise loops; the structure was asymmetric with six syn guanines and six anti guanines. The two structures can coexist and interconvert in solution. For the latter sequence, the antiparallel form is more favorable at low temperatures (<50 degrees C), while the parallel form is more favorable at higher temperatures; at temperatures lower than 40 degrees C, the antiparallel G-quadruplex folds faster but unfolds slower than the parallel G-quadruplex.     

Formation of a Ligand‐Assisted Complex of Two RNA Hairpin Loops

The hairpin structure is one of the most common secondary structures in RNA and holds a central position in the stream of RNA folding from a non‐structured RNA to structurally complex and functional ribonucleoproteins. Since the RNA secondary structure is strongly correlated to the function and can be modulated by the binding of small molecules, we have investigated the modulation of RNA folding by a ligand‐assisted formation of loop–loop complexes of two RNA hairpin loops. With a ligand (NCT6), designed based on the ligand binding to the G–G mismatches in double‐stranded DNA, we successfully demonstrated the formation of both inter‐ and intra‐molecular NCT6‐assisted complex of two RNA hairpin loops. NCT6 selectively bound to the two hairpin loops containing (CGG)₃ in the loop region. Native polyacrylamide gel electrophoresis analysis of two doubly‐labeled RNA hairpin loops clearly showed the formation of intermolecular NCT6‐assisted loop–loop complex. Förster resonance energy‐transfer studies of RNA constructs containing two hairpin loops, in which each hairpin was labeled with Alexa488 and Cy3 fluorophores, showed the conformational change of the RNA constructs upon binding of NCT6. These experimental data showed that NCT6 simultaneously bound to two hairpin RNAs at the loop region, and can induce the conformational change of the RNA molecule. These data strongly support that NCT6 functions as molecular glue for two hairpin RNAs.     

G-quadruplex DNA assemblies: loop length, cation identity, and multimer formation

G-rich DNA sequences are able to fold into structures called G-quadruplexes. To obtain general trends in the influence of loop length on the structure and stability of G-quadruplex structures, we studied oligodeoxynucleotides with random bases in the loops. Sequences studied are dGGGW(i)GGGW(j)GGGW(k)GGG, with W = thymine or adenine with equal probability, and i, j, and k comprised between 1 and 4. All were studied by circular dichroism, native gel electrophoresis, UV-monitored thermal denaturation, and electrospray mass spectrometry, in the presence of 150 mM potassium, sodium, or ammonium cations. Parallel conformations are favored by sequences with short loops, but we also found that sequences with short loops form very stable multimeric quadruplexes, even at low strand concentration. Mass spectrometry reveals the formation of dimers and trimers. When the loop length increases, preferred quadruplex conformations tend to be more intramolecular and antiparallel. The nature of the cation also has an influence on the adopted structures, with K(+) inducing more parallel multimers than NH4(+) and Na(+). Structural possibilities are discussed for the new quadruplex higher-order assemblies.     

Water-soluble para-Sulfonated 1,2;3,4-Calix[4]arene-biscrowns in the 1,2-Alternate Conformation

The preparation of a series of p-sulfonated 1,2;3,4-calix[4]arene-biscrowns in the 1,2-alternate conformation is reported. These compounds are of two types:symmetrical p-sulfonated 1,2;3,4-calix[4]arene-biscrowns in which the two crown loops are the same and unsymmetrical p-sulfonated1,2;3,4-calix[4]arene-biscrowns in which the two crown loops are different. The X-ray structures of two synthetic intermediates are given. Preliminary complexation studies showed the ligands to present pronounced Cs⁺/Na⁺ selectivities.     

Reconfigurable T-junction DNA Origami

DNA self-assembly allows the construction of nanometre-scale structures and devices. Structures with thousands of unique components are routinely assembled in good yield. Experimental progress has been rapid, based largely on empirical design rules. Herein, we demonstrate a DNA origami technique designed as a model system with which to explore the mechanism of assembly. The origami fold is controlled through single-stranded loops embedded in a double-stranded DNA template and is programmed by a set of double-stranded linkers that specify pairwise interactions between loop sequences. Assembly is via T-junctions formed by hybridization of single-stranded overhangs on the linkers with the loops. The sequence of loops on the template and the set of interaction rules embodied in the linkers can be reconfigured with ease. We show that a set of just two interaction rules can be used to assemble simple T-junction origami motifs and that assembly can be performed at room temperature.     

The stability of intramolecular DNA quadruplexes with extended loops forming inter- and intra-loop duplexes

We have examined the formation of intramolecular quadruplex DNA structures in which the loops have been extended so as to generate short DNA duplexes. Fluorescence melting and DNase I cleavage studies show that duplexes can be formed within each loop, but that duplexes between the loops are not stable.     

Analysis of stacking overlap in nucleic acid structures: algorithm and application

RNA contains different secondary structural motifs like pseudo-helices, hairpin loops, internal loops, etc. in addition to anti-parallel double helices and random coils. The secondary structures are mainly stabilized by base-pairing and stacking interactions between the planar aromatic bases. The hydrogen bonding strength and geometries of base pairs are characterized by six intra-base pair parameters. Similarly, stacking can be represented by six local doublet parameters. These dinucleotide step parameters can describe the quality of stacking between Watson–Crick base pairs very effectively. However, it is quite difficult to understand the stacking pattern for dinucleotides consisting of non canonical base pairs from these parameters. Stacking interaction is a manifestation of the interaction between two aromatic bases or base pairs and thus can be estimated best by the overlap area between the planar aromatic moieties. We have calculated base pair overlap between two consecutive base pairs as the buried van der Waals surface between them. In general, overlap values show normal distribution for the Watson–Crick base pairs in most double helices within a range from 45 to 50 Å² irrespective of base sequence. The dinucleotide steps with non-canonical base pairs also are seen to have high overlap value, although their twist and few other parameters are rather unusual. We have analyzed hairpin loops of different length, bulges within double helical structures and pseudo-continuous helices using our algorithm. The overlap area analyses indicate good stacking between few looped out bases especially in GNRA tetraloop, which was difficult to quantitatively characterise from analysis of the base pair or dinucleotide step parameters. This parameter is also seen to be capable to distinguish pseudo-continuous helices from kinked helix junctions.     

Theory and simulation of ovoidal disclination loops in nematic liquid crystals under conical confinement

We present analysis, scaling and modelling based on a previously presented nonlinear nonlocal nematic elastica equation of disclination loop growth in nematic liquid crystals con?ned to conical geometries with homeotropic anchoring conditions. The +1/2 disclination loops arise during the well-known planar radial to planar polar texture transformation and are attached to +1 singular core disclination at two branch points. The shape of the +1/2 loops is controlled by the axial speed of the branch points and the bending stiffness of the disclination both of which being affected by the confinement gradients (reduction in cross-sectional area) of a conical geometry. Motion towards the cone apex results in faster branch point motions and weaker curvature changes, but motion away from the apex results in slower branch point motion and stronger curvature changes. The simultaneous action of these effects results in novel ovoidal disclination loops. The numerical results are condensed into useful power laws and integrated into a shape/energy analysis that reveals the effects of confinement and its gradient on ovoidal disclination loops. These new findings are useful to characterise the Frank elasticity of new nematic mesophases and to predict novel defect structures under complex confinement.