Predicting the sizes of large RNA molecules

Abstract

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, R g-that facilitate this assembly process. For an arbitrary RNA sequence, we introduce the (thermal) average maximum ladder distance (͗MLD͘) and use it as a measure of the ''extendedness'' of the RNA secondary structure. The ͗MLD͘ 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 ͗MLD͘ as a measure of effective contour length, we predict the R g values of viral ssRNAs are smaller than those of nonviral sequences. More generally, we predict the average ͗MLD͘ values of large nonviral ssRNAs scale as N 0.67؎0.01 , where N is the number of nucleotides, and that their R g values vary as ͗MLD͘ 0.5 in an ideal solvent, and hence as N 0.34 . An alternative analysis, which explicitly includes all branches, is introduced and shown to yield consistent results.branched polymer ͉ ladder distance ͉ radius of gyration ͉ secondary structure ͉ viral RNA

RNA topology remolds electrostatic stabilization of viruses

“…The figure also illustrates that the encapsulation free energy becomes more negative with increasing propensity of RNA to form branch points for a given number of monomers. This stabilization behavior suggests that branching is not only conducive to more efficient packing of the genome material into the virus shell, but also allows viral RNAs that have more branch points than other types of cellular RNAs [12] to out-compete the latter during replication in infected, susceptible host cells.…”

“…While the theoretical studies of linear polymers shed some light on the overcharging phenomenon, recent experiments reveal the importance of RNA structure that goes beyond its polyelectrolyte nature as a linear charged chain [11,12,25,26]. Intrachain base paring, promoted by hydrogen bonding between mutually complementary nucleotides along the backbone, leads to a highly branched structure of the RNA molecule that furthermore promotes its compaction in free solution.…”

“…For example, when viral RNA1 of BMV (brome mosaic virus) and CCMV (cowpea chlorotic mottle virus) are mixed in solution with the capsid proteins from CCMV, the BMV RNA is packaged three times more efficiently [11]. As the two RNAs differ in the amount of branching and their tertiary structure, both a straightforward consequence of their primary sequence, there must be a tight connection between capsid packing preferences and the structure of RNA [12,13].…”

Thermodynamic basis for the genome to capsid charge relationship in viral encapsidation

“…If the RNA are sufficiently large, and on account of their electrostatic repulsion with each other, the likelihood of multiple RNA nucleating one capsid is low and, for the optimal length question, we may confine ourselves to the population of single RNA-encapsidated viral particles. Also, following previous theoretical works (3,(5)(6)(7)(10)(11)(12)(13)(14)(15), we treat the RNA as a linear polyelectrolyte, and ignore the secondary structures (16). This approximation is in part a computational necessity and in part guided by the motivation to elucidate the generic features of electrostatically driven viral assembly by using simple models.…”

Electrostatics of capsid-induced viral RNA organization

“…[11][12][13][14][15][16][17][18] A molecular understanding of the dominant forces behind the organization of the genome inside virus capsids would enable development of strategies to package desired new RNA/DNA sequences with the use of required proteins or their equivalents. A fundamental understanding of how evolution has sculpted the viral assembly via interdependence between proteins and nucleic acids would thus enable biomimicry in aqueous assembly of natural and synthetic polymers with potential technological implications in applications such as safe gene delivery platforms.…”