Ajaykumar Gopal

Predicting the sizes of large RNA molecules

We present a theory of the dependence on sequence of the three-dimensional size of large single-stranded (ss) RNA molecules. The work is motivated by the fact that the genomes of many viruses are large ssRNA molecules—often several thousand nucleotides long—and that these RNAs are spontaneously packaged into small rigid protein shells. We argue that there has been evolutionary pressure for the genome to have overall spatial properties—including an appropriate radius of gyration, Rg—that facilitate this assembly process. For an arbitrary RNA sequence, we introduce the (thermal) average maximum ladder distance (〈MLD〉) and use it as a measure of the “extendedness” of the RNA secondary structure. The 〈MLD〉 values of viral ssRNAs that package into capsids of fixed size are shown to be consistently smaller than those for randomly permuted sequences of the same length and base composition, and also smaller than those of natural ssRNAs that are not under evolutionary pressure to have a compact native form. By mapping these secondary structures onto a linear polymer model and by using 〈MLD〉 as a measure of effective contour length, we predict the Rg values of viral ssRNAs are smaller than those of nonviral sequences. More generally, we predict the average 〈MLD〉 values of large nonviral ssRNAs scale as N0.67±0.01, where N is the number of nucleotides, and that their Rg values vary as 〈MLD〉0.5 in an ideal solvent, and hence as N0.34. An alternative analysis, which explicitly includes all branches, is introduced and shown to yield consistent results.

Visualizing large RNA molecules in solution.

Single-stranded RNAs (ssRNAs) longer than a few hundred nucleotides do not have a unique structure in solution. Their equilibrium properties therefore reflect the average of an ensemble of structures. We use cryo-electron microscopy to image projections of individual long ssRNA molecules and characterize the anisotropy of their ensembles in solution. A flattened prolate volume is found to best represent the shapes of these ensembles. The measured sizes and anisotropies are in good agreement with complementary determinations using small-angle X-ray scattering and coarse-grained molecular dynamics simulations. A long viral ssRNA is compared with shorter noncoding transcripts to demonstrate that prolate geometry and flatness are generic properties independent of sequence length and origin. The anisotropy persists under physiological as well as low-ionic-strength conditions, revealing a direct correlation between secondary structure asymmetry and 3D shape and size. We discuss the physical origin of the generic anisotropy and its biological implications.

The Assembly Pathway of an Icosahedral Single-Stranded RNA Virus Depends on the Strength of Inter-Subunit Attractions

The strength of attraction between capsid proteins (CPs) of cowpea chlorotic mottle virus (CCMV) is controlled by the solution pH. Additionally, the strength of attraction between CP and the single-stranded RNA viral genome is controlled by ionic strength. By exploiting these properties, we are able to control and monitor the in vitro co-assembly of CCMV CP and single-stranded RNA as a function of the strength of CP-CP and CP-RNA attractions. Using the techniques of velocity sedimentation and electron microscopy, we find that the successful assembly of nuclease-resistant virus-like particles (VLPs) depends delicately on the strength of CP-CP attraction relative to CP-RNA attraction. If the attractions are too weak, the capsid cannot form; if they are too strong, the assembly suffers from kinetic traps. Separating the process into two steps-by first turning on CP-RNA attraction and then turning on CP-CP attraction-allows for the assembly of well-formed VLPs under a wide range of attraction strengths. These observations establish a protocol for the efficient in vitro assembly of CCMV VLPs and suggest potential strategies that the virus may employ in vivo.

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.