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Register a new userThe Spanning Tree Model for the Assembly Kinetics of RNA Viruses
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We present a simple kinetic model for the assembly of small single-stranded RNA viruses that can be used to carry out analytical packaging contests between different types of RNA molecules. The RNA selection mechanism is purely kinetic and based on small differences between the assembly energy profiles. RNA molecules that win these packaging contests are characterized by having a minimum Maximum Ladder Distance and a maximum Wrapping Number.The former is a topological invariant that measures the branchiness of the genome molecule while the latter measures the ability of the genome molecule to maximally associate with the capsid proteins. The model can also be used study the applicability of the theory of nucleation and growth to viral assembly, which breaks down with increasing strength of the RNA-protein interaction.
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Single-stranded (ss) RNA viruses self-assemble spontaneously in solutions that contain the viral RNA genome molecules and the viral capsid proteins. The self-assembly of empty capsids can be understood on the basis of free energy minimization of rather simple models. However, during the self-assembly of complete viral particles in the cytoplasm of an infected cell, the viral genome molecules must be selected from a large pool of very similar host messenger RNA molecules. It is known that the assembly process takes the form of preferential heterogeneous nucleation of capsid proteins on viral RNA molecules (selective nucleation). Recently, a simple mathematical model was proposed for the selective nucleation of small ssRNA viruses. In this paper we present a statistical physics analysis of the thermal equilibrium and kinetic properties of that model and show that it can account, at least qualitatively, for numerous observations of the self-assembly of small ssRNA viruses.
Under many in vitro conditions, some small viruses spontaneously encapsidate a single stranded (ss) RNA into a protein shell called the capsid. While viral RNAs are found to be compact and highly branched because of long distance base-pairing between nucleotides, recent experiments reveal that in a head-to-head competition between a ssRNA with no secondary or higher order structure and a viral RNA, the capsid proteins preferentially encapsulate the linear polymer! In this paper, we study the impact of genome stiffness on the encapsidation free energy of the complex of RNA and capsid proteins. We show that an increase in effective chain stiffness because of base-pairing could be the reason why under certain conditions linear chains have an advantage over branched chains when it comes to encapsidation efficiency. While branching makes the genome more compact, RNA base-pairing increases the effective Kuhn length of the RNA molecule, which could result in an increase of the free energy of RNA confinement, that is, the work required to encapsidate RNA, and thus less efficient packaging.
By exerting mechanical force it is possible to unfold/refold RNA molecules one at a time. In a small range of forces, an RNA molecule can hop between the folded and the unfolded state with force-dependent kinetic rates. Here, we introduce a mesoscopic model to analyze the hopping kinetics of RNA hairpins in an optical tweezers setup. The model includes different elements of the experimental setup (beads, handles and RNA sequence) and limitations of the instrument (time lag of the force-feedback mechanism and finite bandwidth of data acquisition). We investigated the influence of the instrument on the measured hopping rates. Results from the model are in good agreement with the experiments reported in the companion article (1). The comparison between theory and experiments allowed us to infer the values of the intrinsic molecular rates of the RNA hairpin alone and to search for the optimal experimental conditions to do the measurements. We conclude that long handles and soft laser traps represent the best conditions to extract rate estimates that are closest to the intrinsic molecular rates. The methodology and rationale presented here can be applied to other experimental setups and other molecules.
We propose a description for the quasi-equilibrium self-assembly of small, single-stranded (ss) RNA viruses whose capsid proteins (CPs) have flexible, positively charged, disordered tails that associate with the negatively charged RNA genome molecules. We describe the assembly of such viruses as the interplay between two coupled phase-transition like events: the formation of the protein shell (the capsid) by CPs and the condensation of a large ss viral RNA molecule. Electrostatic repulsion between the CPs competes with attractive hydrophobic interactions and attractive interaction between neutralized RNA segments mediated by the tail-groups. An assembly diagram is derived in terms of the strength of attractive interactions between CPs and between CPs and the RNA molecules. It is compared with the results of recent studies of viral assembly. We demonstrate that the conventional theory of self-assembly, which does describe the assembly of textit{empty} capsids, is in general not applicable to the self-assembly of RNA-encapsidating virions.
We present a generalized Landau-Brazovskii free energy for the solidification of chiral molecules on a spherical surface in the context of the assembly of viral shells. We encounter two types of icosahedral solidification transitions. The first type is a conventional first-order phase transition from the uniform to the icosahedral state. It can be described by a single icosahedral spherical harmonic of even $l$. The chiral pseudo-scalar term in the free energy creates secondary terms with chiral character but it does not affect the thermodynamics of the transition. The second type, associated with icosahedral spherical harmonics with odd $l$, is anomalous. Pure odd $l$ icosahedral states are unstable but stability is recovered if admixture with the neighboring $l+1$ icosahedral spherical harmonic is included, generated by the non-linear terms. This is in conflict with the principle of Landau theory that symmetry-breaking transitions are characterized by only a textit{single} irreducible representation of the symmetry group of the uniform phase and we argue that this principle should be removed from Landau theory. The chiral term now directly affects the transition because it lifts the degeneracy between two isomeric mixed-$l$ icosahedral states. A direct transition is possible only over a limited range of parameters. Outside this range, non-icosahedral states intervene. For the important case of capsid assembly dominated by $l=15$, the intervening states are found to be based on octahedral symmetry.
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