Self consistent field theory of virus assembly

Sequence disorder-induced first order phase transition in confined polyelectrolytes

We consider a statistical mechanical model of a generic flexible polyelectrolyte, comprised of identically charged monomers with long-range electrostatic interactions and short-range interactions quantified by a disorder field along the polymer contour sequence, which is randomly quenched. The free energy and the monomer density profile of the system for no electrolyte screening are calculated in the case of a system composed of two infinite planar bounding surfaces with an intervening oppositely charged polyelectrolyte chain. We show that the effect of the contour sequence disorder, mediated by short-range interactions, leads to an enhanced localization of the polyelectrolyte chain and a first order phase transition at a critical value of the inter-surface spacing. This phase transition results in an abrupt change of the pressure from negative to positive values, effectively eliminating polyelectrolyte mediated bridging attraction.

Analyzing the Geometry and Dynamics of Viral Structures: A Review of Computational Approaches Based on Alpha Shape Theory, Normal Mode Analysis, and Poisson-Boltzmann Theories

The current SARS-CoV-2 pandemic highlights our fragility when we are exposed to emergent viruses either directly or through zoonotic diseases. Fortunately, our knowledge of the biology of those viruses is improving. In particular, we have more and more structural information on virions, i.e., the infective form of a virus that includes its genomic material and surrounding protective capsid, and on their gene products. It is important to have methods that enable the analyses of structural information on such large macromolecular systems. We review some of those methods in this paper. We focus on understanding the geometry of virions and viral structural proteins, their dynamics, and their energetics, with the ambition that this understanding can help design antiviral agents. We discuss those methods in light of the specificities of those structures, mainly that they are huge. We focus on three of our own methods based on the alpha shape theory for computing geometry, normal mode analyses to study dynamics, and modified Poisson-Boltzmann theories to study the organization of ions and co-solvent and solvent molecules around biomacromolecules. The corresponding software has computing times that are compatible with the use of regular desktop computers. We show examples of their applications on some outer shells and structural proteins of the West Nile Virus.

Multiscale Modeling of Hepatitis B Virus Capsid Assembly and Its Dimorphism

Hepatitis B virus (HBV) is an endemic, chronic virus that leads to 800000 deaths per year. Central to the HBV lifecycle, the viral core has a protein capsid assembled from many copies of a single protein. The capsid protein adopts different (quasi-equivalent) conformations to form icosahedral capsids containing 180 or 240 proteins: T = 3 or T = 4, respectively, in Caspar-Klug nomenclature. HBV capsid assembly has become an important target for recently developed antivirals; nonetheless, the assembly pathways and mechanisms that control HBV dimorphism remain unclear. We describe computer simulations of the HBV assembly, using a coarse-grained model that has parameters learned from all-atom molecular dynamics simulations of a complete HBV capsid and yet is computationally tractable. Dynamical simulations with the resulting model reproduce experimental observations of HBV assembly pathways and products. By constructing Markov state models and employing transition path theory, we identify pathways leading to T = 3, T = 4, and other experimentally observed capsid morphologies. The analysis shows that capsid polymorphism is promoted by the low HBV capsid bending modulus, where the key factors controlling polymorphism are the conformational energy landscape and protein-protein binding affinities.

Relationships between RNA topology and nucleocapsid structure in a model icosahedral virus

The process of genome packaging in most of viruses is poorly understood, notably the role of the genome itself in the nucleocapsid structure. For simple icosahedral single-stranded RNA viruses, the branched topology due to the RNA secondary structure is thought to lower the free energy required to complete a virion. We investigate the structure of nucleocapsids packaging RNA segments with various degrees of compactness by small-angle x-ray scattering and cryotransmission electron microscopy. The structural differences are mild even though compact RNA segments lead on average to better-ordered and more uniform particles across the sample. Numerical calculations confirm that the free energy is lowered for the RNA segments displaying the larger number of branch points. The effect is, however, opposite with synthetic polyelectrolytes, in which a star topology gives rise to more disorder in the capsids than a linear topology. If RNA compactness and size account in part for the proper assembly of the nucleocapsid and the genome selectivity, other factors most likely related to the host cell environment during viral assembly must come into play as well.

Machine-learning a virus assembly fitness landscape

Realistic evolutionary fitness landscapes are notoriously difficult to construct. A recent cutting-edge model of virus assembly consists of a dodecahedral capsid with 12 corresponding packaging signals in three affinity bands. This whole genome/phenotype space consisting of 312 genomes has been explored via computationally expensive stochastic assembly models, giving a fitness landscape in terms of the assembly efficiency. Using latest machine-learning techniques by establishing a neural network, we show that the intensive computation can be short-circuited in a matter of minutes to astounding accuracy.

Effect of the charge distribution of virus coat proteins on the length of packaged RNAs

Single-stranded RNA viruses efficiently encapsulate their genome into a protein shell called the capsid. Electrostatic interactions between the positive charges in the capsid protein's N-terminal tail and the negatively charged genome have been postulated as the main driving force for virus assembly. Recent experimental results indicate that the N-terminal tail with the same number of charges and same lengths packages different amounts of RNA, which reveals that electrostatics alone cannot explain all the observed outcomes of the RNA self-assembly experiments. Using a mean-field theory, we show that the combined effect of genome configurational entropy and electrostatics can explain to some extent the amount of packaged RNA with mutant proteins where the location and number of charges on the tails are altered. Understanding the factors contributing to the virus assembly could promote the attempt to block viral infections or to build capsids for gene therapy applications.

Real-Time Assembly of Viruslike Nucleocapsids Elucidated at the Single-Particle Level

While the structure of a multitude of viral particles has been resolved to atomistic detail, their assembly pathways remain largely elusive. Key unresolved issues are particle nucleation, particle growth, and the mode of genome compaction. These issues are difficult to address in bulk approaches and are effectively only accessible by the real-time tracking of assembly dynamics of individual particles. This we do here by studying the assembly into rod-shaped viruslike particles (VLPs) of artificial capsid polypeptides. Using fluorescence optical tweezers, we establish that small oligomers perform one-dimensional diffusion along the DNA. Larger oligomers are immobile and nucleate VLP growth. A multiplexed acoustic force spectroscopy approach reveals that DNA is compacted in regular steps, suggesting packaging via helical wrapping into a nucleocapsid. By reporting how real-time assembly tracking elucidates viral nucleation and growth principles, our work opens the door to a fundamental understanding of the complex assembly pathways of both VLPs and naturally evolved viruses.

Confining annealed branched polymers inside spherical capsids

The Lifshitz equation for the confinement of a linear polymer in a spherical cavity of radius R has the form of the Schrödinger equation for a quantum particle trapped in a potential well with flat bottom and infinite walls at radius R. We show that the Lifshitz equation of a confined annealed branched polymer has the form of the Schrödinger equation for a quantum harmonic oscillator. The resulting confinement energy has a 1/R4 dependence on the confinement radius R, in contrast to the case of confined linear polymers, which have a 1/R2 dependence. We discuss the application of this result to the problem of the confinement of single-stranded RNA molecules inside spherical capsids.

The different faces of mass action in virus assembly

The spontaneous encapsulation of genomic and non-genomic polyanions by coat proteins of simple icosahedral viruses is driven, in the first instance, by electrostatic interactions with polycationic RNA binding domains on these proteins. The efficiency with which the polyanions can be encapsulated in vitro, and presumably also in vivo, must in addition be governed by the loss of translational and mixing entropy associated with co-assembly, at least if this co-assembly constitutes a reversible process. These forms of entropy counteract the impact of attractive interactions between the constituents and hence they counteract complexation. By invoking mass action-type arguments and a simple model describing electrostatic interactions, we show how these forms of entropy might settle the competition between negatively charged polymers of different molecular weights for co-assembly with the coat proteins. In direct competition, mass action turns out to strongly work against the encapsulation of RNAs that are significantly shorter, which is typically the case for non-viral (host) RNAs. We also find that coat proteins favor forming virus particles over nonspecific binding to other proteins in the cytosol even if these are present in vast excess. Our results rationalize a number of recent in vitro co-assembly experiments showing that short polyanions are less effective at attracting virus coat proteins to form virus-like particles than long ones do, even if both are present at equal weight concentrations in the assembly mixture.