Viral RNAs are unusually compact.

A majority of viruses are composed of long single-stranded genomic RNA molecules encapsulated by protein shells with diameters of just a few tens of nanometers. We examine the extent to which these viral RNAs have evolved to be physically compact molecules to facilitate encapsulation. Measurements of equal-length viral, non-viral, coding and non-coding RNAs show viral RNAs to have among the smallest sizes in solution, i.e., the highest gel-electrophoretic mobilities and the smallest hydrodynamic radii. Using graph-theoretical analyses we demonstrate that their sizes correlate with the compactness of branching patterns in predicted secondary structure ensembles. The density of branching is determined by the number and relative positions of 3-helix junctions, and is highly sensitive to the presence of rare higher-order junctions with 4 or more helices. Compact branching arises from a preponderance of base pairing between nucleotides close to each other in the primary sequence. The density of branching represents a degree of freedom optimized by viral RNA genomes in response to the evolutionary pressure to be packaged reliably. Several families of viruses are analyzed to delineate the effects of capsid geometry, size and charge stabilization on the selective pressure for RNA compactness. Compact branching has important implications for RNA folding and viral assembly

The ends of a large RNA molecule are necessarily close

We show on general theoretical grounds that the two ends of single-stranded (ss) RNA molecules (consisting of roughly equal proportions of A, C, G and U) are necessarily close together, largely independent of their length and sequence. This is demonstrated to be a direct consequence of two generic properties of the equilibrium secondary structures, namely that the average proportion of bases in pairs is ∼60% and that the average duplex length is ∼4. Based on mfold and Vienna computations on large numbers of ssRNAs of various lengths (1000–10 000 nt) and sequences (both random and biological), we find that the 5′–3′ distance—defined as the sum of H-bond and covalent (ss) links separating the ends of the RNA chain—is small, averaging 15–20 for each set of viral sequences tested. For random sequences this distance is ∼12, consistent with the theory. We discuss the relevance of these results to evolved sequence complementarity and specific protein binding effects that are known to be important for keeping the two ends of viral and messenger RNAs in close proximity. Finally we speculate on how our conclusions imply indistinguishability in size and shape of equilibrated forms of linear and covalently circularized ssRNA molecules

Higher-order branching in random and viral RNAs.

<p> is shown versus in both plots. Inset B shows 4000-nt random-sequence data (gray squares) with (red squares) and (blue squares) plotted against (see Eqs. 4 & 5). Values of / (gray squares) are consistent with , indicating that most higher-order junctions in random RNAs have . Plot A compares the random sequences with eleven distinct families of viral RNA. Families with more than half their members having are shown with circular symbols.</p

Gel electrophoretic mobilities of 2117-nt RNAs.

<p>Lanes 1–4 show a viral RNA (B3) and sequences engineered from it, while lanes 5 & 7–10 show yeast-based transcripts. Each lane contains ≈ 1 <i>μ</i>g of RNA, i.e., an ensemble of molecules. B3 & Y2 were mixed prior to running in lane 6. Mobility is measured as the distance from the DNA marker (see Methods), and reported relative to B3.</p

Effects of Salt Concentrations and Bending Energy on the Extent of Ejection of Phage Genomes☆

Recent work has shown that pressures inside dsDNA phage capsids can be as high as many tens of atmospheres; it is this pressure that is responsible for initiation of the delivery of phage genomes to host cells. The forces driving ejection of the genome have been shown to decrease monotonically as ejection proceeds, and hence to be strongly dependent on the genome length. Here we investigate the effects of ambient salts on the pressures inside phage-λ, for the cases of mono-, di-, and tetravalent cations, and measure how the extent of ejection against a fixed osmotic pressure (mimicking the bacterial cytoplasm) varies with cation concentration. We find, for example, that the ejection fraction is halved in 30 mM Mg2+ and is decreased by a factor of 10 upon addition of 1 mM spermine. These effects are calculated from a simple model of genome packaging, using DNA-DNA repulsion energies as determined independently from x-ray diffraction measurements on bulk DNA solutions. By comparing the measured ejection fractions with values implied from the bulk DNA solution data, we predict that the bending energy makes the d-spacings inside the capsid larger than those for bulk DNA at the same osmotic pressure

Viral RNAs Are Unusually Compact

A majority of viruses are composed of long single-stranded genomic RNA molecules encapsulated by protein shells with diameters of just a few tens of nanometers. We examine the extent to which these viral RNAs have evolved to be physically compact molecules to facilitate encapsulation. Measurements of equal-length viral, non-viral, coding and non-coding RNAs show viral RNAs to have among the smallest sizes in solution, i.e., the highest gel-electrophoretic mobilities and the smallest hydrodynamic radii. Using graph-theoretical analyses we demonstrate that their sizes correlate with the compactness of branching patterns in predicted secondary structure ensembles. The density of branching is determined by the number and relative positions of 3-helix junctions, and is highly sensitive to the presence of rare higher-order junctions with 4 or more helices. Compact branching arises from a preponderance of base pairing between nucleotides close to each other in the primary sequence. The density of branching represents a degree of freedom optimized by viral RNA genomes in response to the evolutionary pressure to be packaged reliably. Several families of viruses are analyzed to delineate the effects of capsid geometry, size and charge stabilization on the selective pressure for RNA compactness. Compact branching has important implications for RNA folding and viral assembly