A curved RNA helix incorporating an internal loop with G·A and A·A non-Watson–Crick base pairing

The crystal structure of the RNA dodecamer 5′-GGCC(GAAA)GGCC-3′ has been determined from x-ray diffraction data to 2.3-Å resolution. In the crystal, these oligomers form double helices around twofold symmetry axes. Four consecutive non-Watson–Crick base pairs make up an internal loop in the middle of the duplex, including sheared G·A pairs and novel asymmetric A·A pairs. This internal loop sequence produces a significant curvature and narrowing of the double helix. The helix is curved by 34° from end to end and the diameter is narrowed by 24% in the internal loop. A Mn2+ ion is bound directly to the N7 of the first guanine in the Watson–Crick region following the internal loop and the phosphate of the preceding residue. This Mn2+ location corresponds to a metal binding site observed in the hammerhead catalytic RNA.

Broken symmetry and strangeness of the semiconductor impurity band metal-insulator transition

The filamentary model of the metal-insulator transition in randomly doped semiconductor impurity bands is geometrically equivalent to similar models for continuous transitions in dilute antiferromagnets and even to the λ transition in liquid He, but the critical behaviors are different. The origin of these differences lies in two factors: quantum statistics and the presence of long range Coulomb forces on both sides of the transition in the electrical case. In the latter case, in addition to the main transition, there are two satellite transitions associated with disappearance of the filamentary structure in both insulating and metallic phases. These two satellite transitions were first identified by Fritzsche in 1958, and their physical origin is explained here in geometrical and topological terms that facilitate calculation of critical exponents.

Heteroduplex joint formation in Escherichia coli recombination is initiated by pairing of a 3′-ending strand

The formation of heteroduplex joints in Escherichia coli recombination is initiated by invasion of double-stranded DNA by a single-stranded homologue. To determine the polarity of the invasive strand, linear molecules with direct terminal repeats were released by in vivo restriction of infecting chimeric phage DNA and heteroduplex products of intramolecular recombination were analyzed. With this substrate, the invasive strand is expected to be incorporated into the circular crossover product and the complementary strand is expected to be incorporated into the reciprocal linear product. Strands of both polarities were incorporated into heteroduplex structures, but only strands ending 3′ at the break were incorporated into circular products. This result indicates that invasion of the 3′-ending strand initiates the heteroduplex joint formation and that the complementary 5′-ending strand is incorporated into heteroduplex structures in the process of reciprocal strand exchange. The polarity of the invasive strand was not affected by recD, recJ, or xonA mutations. However, xonA and recJ mutations increased the proportion of heteroduplexes containing 5′-ending strands. This observation suggests that RecJ exonuclease and exonuclease I may enhance recombination by degrading the displaced strands during branch migration and thereby causing strand exchange to be unidirectional.

Content mixing and membrane integrity during membrane fusion driven by pairing of isolated v-SNAREs and t-SNAREs

Membrane bilayer fusion has been shown to be mediated by v- and t-SNAREs initially present in separate populations of liposomes and to occur with high efficiency at a physiologically meaningful rate. Lipid mixing was demonstrated to involve both the inner and the outer leaflets of the membrane bilayer. Here, we use a fusion assay that relies on duplex formation of oligonucleotides introduced in separate liposome populations and report that SNARE proteins suffice to mediate complete membrane fusion accompanied by mixing of luminal content. We also find that SNARE-mediated membrane fusion does not compromise the integrity of liposomes.

A thymidine triphosphate shape analog lacking Watson–Crick pairing ability is replicated with high sequence selectivity

Compound 1 (F), a nonpolar nucleoside analog that is isosteric with thymidine, has been proposed as a probe for the importance of hydrogen bonds in biological systems. Consistent with its lack of strong H-bond donors or acceptors, F is shown here by thermal denaturation studies to pair very poorly and with no significant selectivity among natural bases in DNA oligonucleotides. We report the synthesis of the 5′-triphosphate derivative of 1 and the study of its ability to be inserted into replicating DNA strands by the Klenow fragment (KF, exo− mutant) of Escherichia coli DNA polymerase I. We find that this nucleotide derivative (dFTP) is a surprisingly good substrate for KF; steady-state measurements indicate it is inserted into a template opposite adenine with efficiency (Vmax/Km) only 40-fold lower than dTTP. Moreover, it is inserted opposite A (relative to C, G, or T) with selectivity nearly as high as that observed for dTTP. Elongation of the strand past F in an F–A pair is associated with a brief pause, whereas that beyond A in the inverted A–F pair is not. Combined with data from studies with F in the template strand, the results show that KF can efficiently replicate a base pair (A–F/F–A) that is inherently very unstable, and the replication occurs with very high fidelity despite a lack of inherent base-pairing selectivity. The results suggest that hydrogen bonds may be less important in the fidelity of replication than commonly believed and that nucleotide/template shape complementarity may play a more important role than previously believed.

Broken symmetry and critical transport properties of random metals

Recent experimental data on the conductivity σ+(T), T → 0, on the metallic side of the metal–insulator transition in ideally random (neutron transmutation-doped) 70Ge:Ga have shown that σ+(0) ∝ (N − Nc)μ with μ = ½, confirming earlier ultra-low-temperature results for Si:P. This value is inconsistent with theoretical predictions based on diffusive classical scaling models, but it can be understood by a quantum-directed percolative filamentary amplitude model in which electronic basis states exist which have a well-defined momentum parallel but not normal to the applied electric field. The model, which is based on a new kind of broken symmetry, also explains the anomalous sign reversal of the derivative of the temperature dependence in the critical regime.

RecA tests homology at both pairing and strand exchange

RecA is a 38-kDa protein from Escherichia coli that polymerizes on single-stranded DNA, forming a nucleoprotein filament that pairs with homologous duplex DNA and carries out strand exchange in vitro. To observe the effects of mismatches on the kinetics of the RecA-catalyzed recombination reaction, we used assays based upon fluorescence energy transfer that can differentiate between the pairing and strand displacement phases. Oligonucleotide sequences that produced 2–14% mismatches in the heteroduplex product of strand exchange were tested, as well as completely homologous and heterologous sequences. The equilibrium constant for pairing decreased as the number of mismatches increased, which appeared to result from both a decrease in the rate of formation and an increase in the rate of dissociation of the intermediates. In addition, the rate of strand displacement decreased with increasing numbers of mismatches, roughly in proportion to the number of mismatches. The equilibrium constant for pairing and the rate constant for strand displacement both decreased 6-fold as the heterology increased to 14%. These results suggest that discrimination of homology from heterology occurs during both pairing and strand exchange.

The crystal structure of the Rev binding element of HIV-1 reveals novel base pairing and conformational variability

The crystal and molecular structure of an RNA duplex corresponding to the high affinity Rev protein binding element (RBE) has been determined at 2.1-Å resolution. Four unique duplexes are present in the crystal, comprising two structural variants. In each duplex, the RNA double helix consists of an annealed 12-mer and 14-mer that form an asymmetric internal loop consisting of G-G and G-A noncanonical base pairs and a flipped-out uridine. The 12-mer strand has an A-form conformation, whereas the 14-mer strand is distorted to accommodate the bulges and noncanonical base pairing. In contrast to the NMR model of the unbound RBE, an asymmetric G-G pair with N2-N7 and N1-O6 hydrogen bonding, is formed in each helix. The G-A base pairing agrees with the NMR structure in one structural variant, but forms a novel water-mediated pair in the other. A backbone flip and reorientation of the G-G base pair is required to assume the RBE conformation present in the NMR model of the complex between the RBE and the Rev peptide.

Twist fields, the elliptic genus, and hidden symmetry

We combine infinite dimensional analysis (in particular a priori estimates and twist positivity) with classical geometric structures, supersymmetry, and noncommutative geometry. We establish the existence of a family of examples of two-dimensional, twist quantum fields. We evaluate the elliptic genus in these examples. We demonstrate a hidden SL(2,ℤ) symmetry of the elliptic genus, as suggested by Witten.

Homologous pairing in stretched supercoiled DNA

By using elastic measurements on single DNA molecules, we show that stretching a negatively supercoiled DNA activates homologous pairing in physiological conditions. These experiments indicate that a stretched unwound DNA locally denatures to alleviate the force-driven increase in torsional stress. This is detected by hybridization with 1 kb of homologous single-stranded DNA probes. The stretching force involved (≈2 pN) is small compared with those typically developed by molecular motors, suggesting that this process may be relevant to DNA processing in vivo. We used this technique to monitor the progressive denaturation of DNA as it is unwound and found that distinct, stable denaturation bubbles formed, beginning in A+T-rich regions.

Nanohedra: Using symmetry to design self assembling protein cages, layers, crystals, and filaments

A general strategy is described for designing proteins that self assemble into large symmetrical nanomaterials, including molecular cages, filaments, layers, and porous materials. In this strategy, one molecule of protein A, which naturally forms a self-assembling oligomer, An, is fused rigidly to one molecule of protein B, which forms another self-assembling oligomer, Bm. The result is a fusion protein, A-B, which self assembles with other identical copies of itself into a designed nanohedral particle or material, (A-B)p. The strategy is demonstrated through the design, production, and characterization of two fusion proteins: a 49-kDa protein designed to assemble into a cage approximately 15 nm across, and a 44-kDa protein designed to assemble into long filaments approximately 4 nm wide. The strategy opens a way to create a wide variety of potentially useful protein-based materials, some of which share similar features with natural biological assemblies.

Homologous-pairing activity of the human DNA-repair proteins Xrcc3⋅Rad51C

The human Xrcc3 protein is involved in the repair of damaged DNA through homologous recombination, in which homologous pairing is a key step. The Rad51 protein is believed to be the only protein factor that promotes homologous pairing in recombinational DNA repair in mitotic cells. In the brain, however, Rad51 expression is extremely low, whereas XRCC3, a human homologue of Saccharomyces cerevisiae RAD57 that activates the Rad51-dependent homologous pairing with the yeast Rad55 protein, is expressed. In this study, a two-hybrid analysis conducted with the use of a human brain cDNA library revealed that the major Xrcc3-interacting protein is a Rad51 paralog, Rad51C/Rad51L2. The purified Xrcc3⋅Rad51C complex, which shows apparent 1:1 stoichiometry, was found to catalyze the homologous pairing. Although the activity is reduced, the Rad51C protein alone also catalyzed homologous pairing, suggesting that Rad51C is a catalytic subunit for homologous pairing. The DNA-binding activity of Xrcc3⋅Rad51C was drastically decreased in the absence of Xrcc3, indicating that Xrcc3 is important for the DNA binding of Xrcc3⋅Rad51C. Electron microscopic observations revealed that Xrcc3⋅Rad51C and Rad51C formed similar filamentous structures with circular single-stranded DNA.

A brief survey of symmetry in mathematics

This paper presents a brief survey of the idea of symmetry in mathematics, as exemplified by some particular developments in algebra, differential equations, topology, and number theory.

Symmetry, stability, and dynamics of multidomain and multicomponent protein systems

Symmetry is commonly observed in many biological systems. Here we discuss representative examples of the role of symmetry in structural molecular biology. Point group symmetries are observed in many protein oligomers whose three-dimensional atomic structures have been elucidated by x-ray crystallography. Approximate symmetry also occurs in multidomain proteins. Symmetry often confers stability on the molecular system and results in economical usage of basic components to build the macromolecular structure. Symmetry is also associated with cooperativity. Mild perturbation from perfect symmetry may be essential in some systems for dynamic functions.

Symmetry and the energy landscapes of biomolecules

The role of symmetry in the folding of proteins is discussed using energy landscape theory. An analytical argument shows it is much easier to find sequences with funneled energy landscape capable of fast folding if the structure is symmetric. The analogy with phase transitions of small clusters with magic numbers is discussed.