Electrostatics and the assembly of an RNA virus

Paul van der Schoot and Robijn Bruinsma

Phys. Rev. E 71, 061928 – Published 30 June 2005

Abstract

Electrostatic interactions play a central role in the assembly of single-stranded RNA viruses. Under physiological conditions of salinity and acidity, virus capsid assembly requires the presence of genomic material that is oppositely charged to the core proteins. In this paper we apply basic polymer physics and statistical mechanics methods to the self-assembly of a synthetic virus encapsidating generic polyelectrolyte molecules. We find that (i) the mean concentration of the encapsidated polyelectrolyte material depends on the surface charge density, the radius of the capsid, and the linear charge density of the polymer but neither on the salt concentration nor the Kuhn length, and (ii) the total charge of the capsid interior is equal but opposite to that of the empty capsid, a form of charge reversal. Unlike natural viruses, synthetic viruses are predicted not to be under an osmotic swelling pressure. The design condition that self-assembly only produces filled capsids is shown to coincide with the condition that the capsid surface charge exceeds the desorption threshold of polymer surface adsorption. We compare our results with studies on the self-assembly of both synthetic and natural viruses.

Received 25 October 2004

DOI:https://doi.org/10.1103/PhysRevE.71.061928

Authors & Affiliations

Paul van der Schoot^* and Robijn Bruinsma

Department of Physics and Astronomy, UCLA, Box 951547, Los Angeles, California 90095-1547, USA

^*On leave from the Faculteit Technische Natuurkunde, Technische Universiteit Eindhoven, The Netherlands.

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Vol. 71, Iss. 6 — June 2005

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Images

Figure 1
(a) Schematic model of capsid self-assembly: protein monomers (left) are in equilibrium with fully formed virus capsids of fixed radius $R$ (right). Upon assembly, hydrophobic patches of total area $a_{H}$ per monomer are shielded from contact with water. The assembly process brings together the charged surfaces of the proteins, with a total area of $a_{C}$ per protein. (b) In swollen capsids, or in capsids with holes, polymer molecules may freely enter and leave a formed capsid (left). The polymers inside the capsids are then in full equilibrium with the bulk polymer solution. In restricted equilibrium this is not the case and a fixed amount of polymer is trapped inside a capsid (right).Reuse & Permissions
Figure 2
Polymer monomer concentration profiles $ϕ (r)$ inside the capsid cavity as a function of the radial distance $r$ . Curve (a) shows the exponential regime where the correlation length $ξ$ is less than the capsid radius $R$ and curve (b) shows the power-law regime where the correlation length exceeds $R$ . In both regimes, most monomers are confined to a surface region with a thickness of order the extrapolation length $d$ and a concentration of order $ϕ_{S}$ .Reuse & Permissions
Figure 3
Coassembly free energy $Δ G_{p}$ of a capsid as a function of the mean polyelectrolyte monomer concentration $⟨ ϕ ⟩$ inside the capsid. Capsid-polyelectrolyte coassembly requires $Δ G_{p}$ to be negative. At the free energy minimum $Δ G_{p}^{*}$ , where filling concentration equals ${⟨ ϕ ⟩}^{*}$ , the correlation length $ξ$ is comparable to the capsid radius $R$ .Reuse & Permissions
Figure 4
Self-assembly diagram of capsid proteins in the presence and absence of oppositely charged polyelectrolyte as a function of the salt concentration $[c_{s}]$ . The full curves mark the critical subunit concentrations (CSC) beyond which capsid assembly takes place. In region A, empty capsids form in the absence of polyelectrolyte material. In region C, capsid-polyelectrolyte co-assembly takes place, while in region B neither empty nor filled capsids form. When we vary the salt concentration for fixed protein concentration—as indicated by the horizontal line—we encounter re-entrant phase behavior: capsids assemble for high, respectively, low salt concentrations producing empty, respectively, filled capsids, but over an intermediate interval of salt concentrations capsids are not stable. The intermediate interval terminates at the maximum of the CSC for filled capsids marking the desorption transition (vertical dashed line) beyond which polyelectrolyte molecules effectively lose their affinity for the capsid proteins.Reuse & Permissions

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