Kinetics of viral self-assembly: Role of the single-stranded RNA antenna

Many viruses self-assemble from a large number of identical capsid proteins with long flexible N-terminal tails and single-stranded (ss) RNA. We study the role of the strong Coulomb interaction of positive N-terminal tails with ssRNA in the kinetics of in vitro virus self-assembly. Capsid proteins stick to the unassembled chain of ssRNA (which we call an “antenna”) and slide on it toward the assembly site. We show that at excess of capsid proteins such one-dimensional diffusion accelerates self-assembly more than ten times. On the other hand at excess of ssRNA, the antenna slows self-assembly down. Several experiments are proposed to verify the role of the ssRNA antenna.

Figure 1

(Color online) (a) An enlarged view from the inside of the virus. The brush of positive N-terminal tails [red (dark gray) line] is rooted at the inner surface of the capsid [blue (light gray) block]. The ssRNA [green (gray) line] strongly interacts with the tails and glues all the CPs together. (b) Schematic model of the capsid self-assembly. The unassembled ssRNA makes an antenna of size $R$ for the one-dimensional pathway of the CPs toward the capsid assembly site at the capsid fragment (dashed circle with radius $r$ of the size of a CP.

Figure 2

Schematic plot of the diffusion-limited self-assembly rate $J$ as a function of the protein concentration $c$. The full line is for the sliding of capsid proteins on ssRNA. The rate for the slower three-dimensional diffusion is shown by the dashed line.

Figure 3

Self-assembly times plotted schematically as a function of $x=c∕M{c}_R$. ${\tau }_0=M∕\left(4\pi c{D}_{3}r\right)$ is the assembly time without the effect of ssRNA at $x>1$. The black and gray lines correspond to the intact ssRNA and short ssRNA pieces, respectively.