SummaryQuantitatively describing RNA structure and conformational elements remains a formidable problem. Seven standard torsion angles and the sugar pucker are necessary to completely characterize the conformation of an RNA nucleotide. Progress has been made toward understanding the discrete nature of RNA structure, but classifying simple and ubiquitous structural elements such as helices and motifs remains a difficult task. One approach for describing RNA structure in a simple, mathematically consistent, and computationally accessible manner involves the invocation of two pseudotorsions, η (C4' n-1 , P n , C4' n , P n+1 ) and θ (P n , C4' n , P n+1 , C4' n+1 ), which can be used to describe RNA conformation in much the same way that ϕ and ψ are used to describe backbone configuration of proteins. Here we conduct an exploration and statistical evaluation of pseudotorsional space and of the Ramachandran-like η−θ plot. We show that, through the rigorous quantitative analysis of the η−θ plot, the pseudotorsional descriptors η and θ, together with sugar pucker, are sufficient to describe RNA backbone conformation fully in most cases. These descriptors are also shown to contain considerable information about nucleotide base conformation, revealing a previously uncharacterized interplay between backbone and base orientation. A window function analysis is used to discern statistically relevant regions of density in the η−θ scatter plot and then nucleotides in colocalized clusters in the η−θ plane are shown to have similar three-dimensional structures through RMSD analysis of the RNA structural constituents. We find that major clusters in the η−θ plot are few in number, thereby underscoring the discrete nature of RNA backbone conformation. Like the Ramachandran plot, the η−θ plot is a valuable system for conceptualizing biomolecular conformation, it is a useful tool for analyzing RNA tertiary structures, and it is a vital component of new approaches for solving the three-dimensional structures of large RNA molecules and RNA assemblies.

Given the wealth of new RNA structures and the growing list of RNA functions in biology, it is of great interest to understand the repertoire of RNA folding motifs. The ability to identify new and known motifs within novel RNA structures, to compare tertiary structures with one another and to quantify the characteristics of a given RNA motif are major goals in the field of RNA research; however, there are few systematic ways to address these issues. Using a novel approach for visualizing and mathematically describing macromolecular structures, we have developed a means to quantitatively describe RNA molecules in order to rapidly analyze, compare and explore their features. This approach builds on the alternative eta,theta convention for describing RNA torsion angles and is executed using a new program called PRIMOS. Applying this methodology, we have successfully identified major regions of conformational change in the 50S and 30S ribosomal subunits, we have developed a means to search the database of RNA structures for the prevalence of known motifs and we have classified and identified new motifs. These applications illustrate the powerful capabilities of our new RNA structural convention, and they suggest future adaptations with important implications for bioinformatics and structural genomics.

Recurring RNA structural motifs are important sites of tertiary interaction and as such, are integral to RNA macromolecular structure. Although numerous RNA motifs have been classified and characterized, the identification of new motifs is of great interest. In this study, we discovered four new conformationally recurring motifs: the pi-turn, the Omega-turn, the alpha-loop and the C2'-endo mediated flipped adenosine motif. Not only do they have complex and interesting structures, but they participate in contacts of high biological significance. In a first for the RNA field, new motifs were discovered by a fully automated algorithm. This algorithm, COMPADRES, utilized a reduced representation of the RNA backbone and was highly successful at discerning unique structural relationships. This study also shows that recurring RNA substructures are not necessarily accompanied by consistent primary or secondary structure.

Gravitational waves provide a laboratory for general relativity and a window to energetic astrophysical phenomena invisible with electromagnetic radiation. Several terrestrial detectors are currently under construction, and a space-based interferometer is envisioned for launch early next century to detect test-mass motions induced by waves of relatively short wavelength. Very-long-wavelength gravitational waves can be detected using the plasma in the early Universe as test masses; the motion induced in the plasma by a wave is imprinted onto the cosmic microwave background ͑CMB͒. While the signature of gravitational waves on the CMB temperature fluctuations is not unique, the polarization pattern can be used to unambiguously detect gravitational radiation. Thus, forthcoming CMB polarization experiments, such as the Microwave Anisotropy Probe and Planck, will be the first space-based gravitational-wave detectors. ͓S0556-2821͑99͒01002-4͔ PACS number͑s͒: 95.55. Ym, 04.80.Nn, 98.70.Vc One of the most spectacular predictions of general relativity is the existence of gravitational waves. A gravitational wave conveys information about the motions of mass and ripples in curvature-the shape of spacetime. Detection of gravitational radiation would allow us to probe ''invisible'' astrophysical phenomena hidden from view by absorption of electromagnetic radiation. Observations of the binary pulsar PSR1913ϩ16, which confirm the orbital-inspiral rate due to the emission of gravitational waves ͓1͔, bring us tantalizingly close to this goal. However, we would still like to detect gravitational radiation directly. Thus, a variety of efforts are now under way to detect gravitational waves ͓2͔. Here, we show that forthcoming maps of the polarization of the cosmic microwave background ͑CMB͒ can be used to detect very-long-wavelength gravitational radiation.Gravitational waves are detected by observing the motion they induce in test masses ͓3,4͔. High-frequency (1 -10 4 Hz) gravitational waves, produced by the inspiral and catastrophic collision of astrophysical objects, may be detectable by terrestrial laser interferometers ͓e.g., the Laser Interferometric Gravitational Wave Observatory ͑LIGO͒ ͓5͔͔ or resonant-mass antennae currently under construction. Low-frequency (10 Ϫ4 Ϫ10 Ϫ1 Hz) gravitational waves, produced by the orbital motion of binaries, could be detected by the Laser Interferometer Space Antenna ͑LISA͒ ͓6͔, a spacebased interferometer targeted for launch circa 2015.How can one detect ultra-low-frequency (10 Ϫ15-10 Ϫ18 Hz) gravitational radiation, with wavelengths comparable to the size of the observable Universe? The photonbaryon fluid in the early Universe acts as a set of test masses for such waves. A gravitational wave in this frequency range alternately squeezes and stretches the primordial plasma. Just as a resonant-mass detector is equipped with electronics to monitor the oscillation modes of the test body, the CMB photons are the electromagnetic signal upon which these plasma motions are imprinted.One might des...

Given the availability of sequence information for many species, one can examine how the sequence of a gene varies among different organisms. This is accomplished by aligning the sequences and observing patterns of conservation, mutation and counter-mutation at different positions in the gene. Imbedded in these patterns is information on energetic coupling and macromolecular interactions, which can be deciphered by application of statistical algorithms. Here we report a robust approach for predicting interactions within (or between) any type of biopolymer, including proteins, RNAs and RNA-protein complexes. Rather than maximize the number of predictions, this approach is designed to detect a limited number of highly significant interactions, thereby providing accurate results from alignments that contain a modest number of sequences (20-60). The versatility and accuracy of the algorithm is demonstrated by the successful prediction of important intramolecular interactions within RNAs, modified RNAs, and proteins, as well as the prediction of RNA-protein and protein-protein interactions.